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A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
Accepted Manuscript Review A critical review of flow maps for gas-liquid flows in vertical pipes and annuli Benjamin Wu, Mahshid Firouzi, Travis Mitchell, Thomas E. Rufford, Christopher Leonardi, Brian Towler PII: DOI: Reference:
S1385-8947(17)30893-8 http://dx.doi.org/10.1016/j.cej.2017.05.135 CEJ 17034
To appear in:
Chemical Engineering Journal
Received Date: Revised Date: Accepted Date:
16 March 2017 20 May 2017 22 May 2017
Please cite this article as: B. Wu, M. Firouzi, T. Mitchell, T.E. Rufford, C. Leonardi, B. Towler, A critical review of flow maps for gas-liquid flows in vertical pipes and annuli, Chemical Engineering Journal (2017), doi: http:// dx.doi.org/10.1016/j.cej.2017.05.135
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A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
Benjamin Wu a,†, Mahshid Firouzia, †,*, Travis Mitchellb, Thomas E. Rufforda, Christopher Leonardib and Brian Towlera
a.
School of Chemical Engineering, The University of Queensland St. Lucia 4072 Australia b.
School of Mechanical and Mining Engineering, The University of Queensland St. Lucia
4072 Australia †
First authors
*
Email: [email protected]
Abstract The accurate prediction of two-phase gas and liquid flow regimes is important in the proper design, operation and scale-up of pressure management and fluid handling systems in a wide range of industrial processes. This paper provides a comprehensive review of 3947 published experimental data points for gas-liquid flow maps in vertical pipes and annuli, including a critical analysis of state-of-the-art measurement techniques used to identify bubble, slug, churn and annular flow regimes. We examine the critical factors of pipe geometry (diameters, deviation from vertical), fluid properties and flow conditions that affect the transition from one flow regime to another. The review surveys the theoretical models available to predict flow regime transitions, and we validate the accuracy of these models using the published experimental data. The most reliable flow regime transition models for upward co-current flows are analytically shown to be: (i) Barnea 1987 for dispersed bubble to -1-
bubble flow, (ii) Taitel, Bornea and Dukler 1980 for bubble to slug flow, (iii) Barnea 1987 for slug to churn flow, and (iv) Mishima and Ishii 1984 for churn to annular flow regime transition. Moreover, based on the review we provide an outlook on the research needs and important developments in prediction of two-phase flow in vertical pipes including the use of computational fluid dynamics (CFD) techniques to simulate gas-liquid flows in vertical geometries. Keywords: experimental, vertical, flow regime, flow map, regime transition, CFD
1
Introduction Gas and liquid are required to flow simultaneously inside vertical pipes and vertical
annuli in a wide range of industrial and engineering processes. Two-phase gas and liquid flows manifest in steam boilers, condensers, chemical reactors and associated process piping [1-4] in petrochemical plants, food-processing plants and in nuclear energy facilities [5, 6]. The proper design and operation of these two-phase fluid systems requires accurate prediction of pressure drops in the system, and that prediction relies on understanding the nature of the flow regimes that could manifest in a two-phase system. This review paper surveys the published experimental data and mathematical models that describe two-phase flows in (a) vertical pipes and (b) vertical annuli, which is a pipe geometry of significant interest in pumped coal seam gas (CSG, or coal bed methane CBM) wells [7]. When gas and liquid flow in a pipe or conduit several flow regimes can result depending on the pipe geometry, fluid properties, volume fractions and velocities of each phase [2]. In vertical pipes, the most commonly described flow regimes are bubble, slug, churn and annular flows as illustrated in Figure 1 [6, 8, 9]. When both gas and liquid flow velocities are -2-
low (for example superficial liquid and gas velocities less than approximately 0.1 and 1 m/s respectively for co-current upward flows of air-water), the dominant flow regime will be bubble flow with individual gas bubbles dispersed in a continuous liquid phase. A number of studies [8, 10] have also documented a dispersed bubble flow regime at high liquid velocities/flow rates, which can produce large turbulent forces and inhibit bubble coalescence. An alternate theory is that the existence of bubble flow regime at high void fractions is due to the inlet conditions that are determined by the sparging device [11]. For co-current upward air-water flows in a vertical pipe, Taitel, et al. [8] showed that the bubble flow regime exists up to void fractions of 0.25 whilst suggesting that the dispersed bubble flow regime is present up to void fractions of 0.52 at higher liquid flow rates. Increasing the gas velocity results in the slug flow regime where, bubbles coalesce to form large gas bubbles, called Taylor bubbles, which occupy the entire cross section of the pipe except for a thin liquid film on the wall. A further increase in gas velocity can collapse the slugs and lead to an unstable flow that is described as the churn regime due to the large degree of turbulence in the flow. The fourth main flow regime, annular flow, can develop once the gas velocity is sufficiently high to form a continuous gas column flowing in the centre of the pipe. This column pushes the liquid into a film at the pipe wall and entrained liquid droplets in the gas core. There also exists flooding at very high gas or liquid flow rates, that presents the limit of counter-current flow, beyond which the system will transition to co-current flow [12]. Alternatively the flow regimes have been described as homogenous (bubble flow regime) and heterogeneous (slug and churn flow regimes) mainly in bubble columns [13].
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Figure 1: Illustration of the four main flow regimes that can manifest when gas and liquid flow upward and co-currently in a vertical pipe, namely (a) bubble, (b) slug, (c) churn, and (d) annular. Direct observation and identification of flow regimes in pipes of industrial plants is difficult as almost all these industrial fluids flow in steel pipes and often at high pressures and or temperatures. Therefore, most experimental observations of gas-liquid flow regimes have been collected in controlled laboratory conditions with transparent pipes or pipes with inset observation windows, or in recent studies advanced phase detection approaches which are discussed in Section 2. To translate the results of laboratory experiments to industrial scale applications, various published flow maps attempt to predict flow regimes based on superficial gas and liquid velocities [12] and theoretical correlations have been described to model the transitions between flow regimes. Although plenty of transition criteria have been developed, an accurate universal map of gas-liquid flow patterns has yet to be achieved [14].
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Therefore, integration of the available experimental flow regime data to a generalised flow map is of great importance. There have been several reports of different approaches to develop flow maps based on dimensionless parameters other than just superficial velocities. These approaches attempt to account for the effect of factors such as fluid density, viscosity, surface tension, and pipe geometry within their proposed flow map systems [15-22]. However, there are two significant limitations to application of these currently available flow maps. First, most of the published flow maps are synthesised from datasets that included less than 20% of the relevant studies now available publicly. Second, the vast majority of experimental and modelling studies have focussed on flow in horizontal (or near horizontal) pipes, which behave differently from vertical flows due to the influence of gravity. This paper presents an update and validation of existing flow maps for gas and liquid flow in vertical pipes and annuli (co-current and counter-current flows), incorporating 3947 experimental data points from 35 studies. We begin in Section 2 with a survey of the experimental techniques used to identify flow regimes. In Sections 3 and 4, the available data sets for gas-liquid flow experiments in vertical pipes and annuli are summarised, respectively. A range of non-dimensional parameters is used in Section 5 to evaluate flow maps. Section 6 reviews the mathematical models available for the prediction of flow regime transitions and Section 7 introduces computational fluid dynamics as a potential means of improving these predictions. Finally, Section 8 summarises the work presented along with an outlook to future research. 2
Survey of experimental techniques used to identify flow regimes Experimental studies on two-phase flows in vertical pipes often utilise more than one
measurement technique. Reasons for this may include confirmation of results and reassurance, comparison of techniques, and the desire to examine multiple parameters or properties. Flow regimes can either be identified through direct observation or indirect -5-
determination [23]. Direct observation involves the researcher visually interpreting an image of the flow to categorise it into a flow regime. Indirect or analytical determination is a twopart process. The researcher must firstly utilise a reliable experimental methodology to accurately measure characteristic flow parameters. This flow characteristic must then be objectively analysed to determine the flow regime [24]. This review finds that the most common practices for flow regime identification have been visual observation and analysis of void fractions. A summary of the various methods that have been adopted in the collated published experimental works, documented in Sections 3 and 4, is presented in Table 1. Subjectivity is perhaps the greatest issue when identifying flow regimes. Flow regime discrimination through visual observation, even with the aid of high speed cameras, is at the discretion of the researcher or operator. Even more advanced techniques based on flow characteristics such as void fractions that are inserted into Probabilistic Density Functions (PDFs), which intend to reduce subjectivity, still require the researcher to define the conditions at which each flow regime exists. This results in a level of subjectivity being retained. Delineation of flow regimes is further complicated by the transitions as the progression from one flow regime to the next is not instantaneous, rather it develops through intermediate regimes that exhibit mixed characteristics [25]. The axial location at which measurements or observations are made is an important factor that has seemingly been ignored in many of the examined experimental works. Sufficient flow time, and hence distance, must be permitted in order for the desired two-phase flow phenomena to fully develop. Studies have confirmed that the axial location of conductance probes had a significant influence on the adjudication of flow regimes [26-30]. This error is not exclusive to probes and is also applicable to all other flow regime identification and observation equipment.
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Consideration must also be given to the physical impacts of the selected measurement technique. The physical presence of the tool may impede on and thus directly impact the experimental flow path. This is of particular concern with flow in annulus as the available flow path is already limited. Sensors and their physical influence can be described as invasive or intrusive with Figure 2 illustrating their differences. An invasive device requires direct contact with the experimental medium whilst an intrusive device must be located within the experimental medium, impeding the flow path. The use of invasive electrodes may also lead to issues with corrosion and polarising effects [31]. For experimental studies on two-phase flows, avoiding both of these characteristics is highly recommended. The inlet conditions for two-phase flow experiments are determined by the adopted sparger design. A sparger disperses the gas flow into the test section as bubbles, ideally allowing for the development of flow regimes. Exclusion of a sparger results in influxes of large air bubbles into the system. It has been found in bubble columns that the sparger design and sparger hole diameters directly impact upon the gas holdup curve of the system [32-34]. The gas holdup curve describes the relationship between the gas holdup and superficial velocity, and can influence the flow regime that ensues. Mudde, et al. [11] examined uniform flows in bubble columns and reported that only a limited number of publications reported well defined and controlled inlet conditions. A similar observation is made in this review with only a limited number of the examined studies detailing the experimental inlet conditions, and so no comparisons could be made regarding their impact on flow regimes. Perhaps the most prohibitive limitation of all is the cost of the equipment required to facilitate the desired experimental method for identifying flow regimes. The compromise between simplicity, accuracy and affordability must often be managed by a research team in order to meet their objectives.
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Figure 2: Intrusive and invasive sensors, modified after Abdul Wahab, et al. [31].
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Table 1: Classification of experimental techniques used to identify flow regimes in gas-liquid systems. Method
Instrument types
Flow regime identification process
Visual
- Researcher observation
The flow regime is visually determined at the behest of the researcher
Observation
- Still photography
using either the naked eye or aided by some form of imagery.
- High speed camera - X-ray tomography Gas Holdup or Global Void Fraction
Image analysis - X-ray tomography
Measurement
Flow regimes are analytically determined using a Probabilistic Density Function of the measured void fractions. In this process, X-ray tomography is used to capture void fractions via image analysis rather than providing
- Neutron radiography imagery directly for visual delineation of the flow regime. - Electrical impedance tomography - Double wire mesh sensors Volumetric measurement - Quick-closing ball valve technique
The quick-closing ball valve technique physically captures the volume of liquid inside the test section, allowing for a direct measurement of the void
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fraction.
Local Void Fraction Measurement
- Conductance probes - Wire mesh sensor
Local flow regimes are analytically determined using a Probabilistic Density Function of the measured local void fractions. The global flow regime is subsequently determined from a combination of the local flow regimes.
Differential Pressure Measurement
- Differential pressure sensors
Differential pressure measurements can be used to determine flow regimes due to the differing densities, and hence pressure, exerted by the gas and liquid phases. Alternatively, the differential pressure measurements can be used to find volume averaged void fractions to then be analysed using a Probabilistic Density Function to determine the flow regime.
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2.1
Visual observation Visual observation, a direct measurement technique, is the simplest and most commonly
used method of identifying flow regimes and is believed to have been first attempted around 1960 [35, 36]. This is perhaps the most subjective approach with results determined at the discretion of the researcher thus resulting in very low levels of repeatability and replicability by others. Hewitt and Roberts [9] saw X-rays as a natural extension of visible light photography but this technique was not widely adopted by future researchers. This is likely due to advances in technology and the relatively long exposure times, comparative to photography, as well as safety requirements. Previous works have attempted to mitigate the issue of subjective visual interpretation in flow regime identification by including photographs or illustrations of the observed flow regimes. This is not an effective approach as results from these studies cannot easily be compared against one another. Although visual inspection cannot provide an objective classification of flow regimes, it is still a useful complement to modern techniques as it is simple, cost effective, non-intrusive and noninvasive. Photographs and high speed cameras can also be used to aid and improve the visual inspection process. High speed cameras are those with a frame rate greater than 250 frames per second [37]. Software is also available to analyse the documented flow patterns and calculate physical parameters such as bubble size and velocity [38]. Around 1980 the use of statistical parameters, specifically void fractions, was introduced as a means of identifying flow regimes. Analysing these parameters with Probability Density Functions (PDFs) allowed for identification of flow regimes from experimental data. Figure 3 presents typical plots of slug, churn, and annular flow classified using the PDF of time varying flow fraction in accordance with the rules set by Costigan and Whalley [39]. However, the rules regarding identification of flow regimes using the statistical parameters are at the behest of the researcher, retaining the possibility of a subjective analysis as well as -11-
complications when comparing results between studies [27]. Comparison with high speed video has found the PDF approach performs poorly when delineating between slug and churn flows but this is effective at discriminating between churn and annular flow regimes [40].
Figure 3: Typical Probabilistic Density Function (PDF) plots, sourced from OmebereIyari and Azzopardi [40]. The introduction of Artificial Neural Networks around 1990 is seen as a significant advance in the objective identification of flow regimes [41-43]. A much more objective process was achieved by classifying the flow regime indicators, obtained using non-intrusive impedance probes, with the Kohonen Self Organising Neural Network (SONN) [24]. SONN classification was originally performed using the PDF of the void fraction, Į, signals as an indicator. However, this approach had a major drawback in that a long period of observation was required to obtain reliable statistical parameters of the void fraction signal. This was later improved when the Cumulative PDF (CPDF) of the impedance void meter signals was used by Lee, et al. [44]. The CPDF is more stable due to it being an integral parameter and is also faster than the PDF methodology as it requires less input data. 2.2
Gas Holdup or Global Void Fraction In gas-liquid two-phase flow, the gas or liquid hold-up is the fraction of the available flow
channel volume occupied by the respective phase. Gas holdup is synonymous with the global
-12-
void fraction [45]. Recorded void fractions enable the use of PDFs in delineating between flow regimes [46-48]. One of the first approaches to capture void fractions and interpret flow regimes was to use tomography. A linearised X-ray system was employed by Jones and Zuber [46] to inspect flow regimes using void fraction fluctuations. However, the safety requirements necessary for the safe and proper handling of radiation are a major hindrance in the application of such techniques. Mishima and Hibiki [49] later used neutron radiography and image processing to measure void fractions. The process involved using aluminium alloy tubes to allow for a neutron beam to perpendicularly penetrate the pipe. This neutron beam was proportionately attenuated by the encountered hydrogen within the water phase along its path and able to project an image of the residing two-phase flow that could then be converted to an optical image [50, 51]. Schmidt, et al. [52] employed a gamma ray system following the same basic principles. Yamaguchi and Yamazaki [5] and Caetano, et al. [53] elected to use the quick-closing (ball) valve technique, with Caetano, et al. [53] reporting excellent repeatability in the obtained liquid hold-up measurements. This technique involves incorporating two valves at either end of the test section. The valves are closed and flow is diverted to a by-pass pipe when the desired flow rates have been reached and steady-state conditions have been established. Measurement of the enclosed liquid volume yields the liquid holdup when compared to the total available channel volume. The addition of markings to the outside of the test section can allow for a simple means of attaining the liquid volume once it has settled. Alternatively, the liquid can be drained and measured. In a two-phase flow the remaining volume is occupied by gas and hence the gas holdup or global void fraction is also obtained. The use of ball valves in pipe test sections is recommended due to the circular geometrical configuration. Inaccuracies in this method arise from potential changes to the -13-
flow pattern during the closing of the valves. It is also necessary to stop and restart the test for each desired set of flow rates which can be very time consuming. The effect of pressure upon the compressible gas phase has not been acknowledged in these studies and may influence the void fraction measurements acquired using this technique. Schlegel, et al. [54] and Smith, et al. [55] determined void fractions using electrical impedance tomography through electrical impedance void meters, shown in Figure 4(a). This technique is dependent on the electrical impedance of the gas-liquid phases and requires simultaneous measurements at multiple locations along the test section to obtain a global void fraction. A voltage output is acquired at each measurement area and then related to a void fraction in a relatively complex manner which is dependent on the existing flow pattern. Since the flow pattern must already be known, pressure differential measurements are also required in order to initially identify the flow patterns. The electrical impedance void meters can then be cross-calibrated against the differential pressure void fractions. This process was developed by Mi, et al. [56]. Schlegel, et al. [54] reported overall relative errors in the resultant void fraction measurements of less than 10% for void fractions between 0.2-0.4 and less than 5% for void fractions greater than 0.4. The accuracy of this technique was also reported by Prasser, et al. [57] to be 5% void fraction. This approach has a greater level of complexity but is non-intrusive, and does not obstruct the flow channel which would risk affecting the flow pattern.
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Figure 4:Apparatus used in electrical impedance tomography, including (a) arch-type electrical impedance void meter [54] and (b) wire mesh sensor [58]. Wire mesh sensors are a form of electric resistivity tomography and another means of measuring void fractions that is also capable of reconstructing the three-dimensional structure of a two-phase flow. This is achieved with double wire mesh sensors that can also be used to calculate bubble velocity and total interfacial area concentrations from the measured bubble shapes. The sensor is able to operate using conductivity or permittivity based on the selected gas-liquid combination, typically air-water or air-oil respectively. Figure 4(b) displays the -15-
wire electrodes that are orthogonally positioned across two planes of the flow cross-section. The set of wires in one orientation act as electrical transmitters whilst the other set acts as electrical receivers. Conductivity or permittivity is measured within the gaps by alternately sending an excitation voltage to each of the sender electrodes [58]. The accuracy of this technique was reported to be 1-4% of the area-averaged void fraction [57]. Rapid calculations are possible with this tool, however, resolution is limited to approximately 3 mm [30]. Another significant concern regarding this measurement technique is the invasive and intrusive nature of the wire mesh sensors. Wire mesh sensors have been found to distort the shape of Taylor bubbles at low liquid flow rates and tend to underestimate the gas fraction in large bubbles. The two main intrusive effects are bubble break-up and bubble deceleration [59]. It must be noted that gas holdup can be influenced by the experimental setup used in the studies. The gas holdup curve, describing the relationship between the gas holdup and gas superficial velocity, is dependent upon the selected air sparger design and hole sizes [32-34]. 2.3
Local void fraction Juliá, et al. [24] conceptualised a means of identifying the Global Flow Regime (GFR)
using simultaneously obtained Local Flow Regime (LFR) data from three radially distributed local conductivity probes. A LFR identifies the flow regime present in a specific cross section of the flow path at a given moment in time where as a GFR describes the flow regime occurring throughout the system or pipe section. Combinations of the three local signals corresponded to different GFRs. The majority of two-phase flow experiments are conducted using air-water as the gas-liquid phases due to their convenience and safety. This allows for local void fraction measurements using the conductance technique. Conductance probes are invasive sensors that can provide estimates of local void fractions because tap water is electrically conductive whilst air is essentially resistant. Pure water is also essentially -16-
resistant and would not work in such experiments. Local void fractions are limited to one point in the test apparatus and so multiple probes or measurements are required. Once the relationship between electrical impedance and phase distribution has been established, the cross-sectional averaged void fraction can then be estimated [40]. Prasser, et al. [57] reported the accuracy of conductivity probes to be 5% void fraction. Optical fibre probes operate similarly to conductance probes but rely upon differences in refractive index rather than conductivity to measure local void fractions [60]. However, no studies have been seen to use optical fibre probes for the identification of flow regimes. Ghosh, et al. [61] compared the efficiency of parallel wire conductivity probes and ring conductivity probes in a vertical pipe, as shown in Figure 5. It was experimentally determined that the parallel wire probe is capable of identifying individual flow regimes whilst the ring probe is not. This was due to the geometric configuration of the ring probe wherein both of its electrodes are flush mounted on the walls of the pipe. Thus, throughout all of the different flow regimes, the ring probes were always partially or fully submerged in water and showed little variation in conductivity. So, in order for conductance probes to properly identify flow regimes they must be intrusive in addition to being invasive. Smith, et al. [55] stated that there are generally two main sources of uncertainty regarding the use of conductivity probes, namely the probe structure itself and the deformation of the interfaces of large bubbles on contact with the probe. Wire mesh tomography is a similar approach that utilises single layer wire mesh sensors to capture local void fractions. A study comparing the results of wire mesh tomography with an optical, or visual, method found theirs accuracies to be within 10% of one another [59]. This study was limited to the bubble flow regime and concluded that the accuracy of wire mesh tomography in counter-current flow is in the same order of magnitude as for stagnant and co-current bubble flow.
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Figure 5: (a) Parallel wire conductivity probe and (b) ring conductivity probe, sourced from Ghosh, et al. [61]
2.4
Differential pressure measurement The physical mechanisms controlling pressure drop are intrinsically linked to local flow
patterns [2]. This makes differential pressure measurements an alternative flow characteristic to void fractions for identifying flow regimes. It must be noted that in experimental works, pressure measurements may be complicated by the potential presence of trapped gas within the pressure lines [24]. This can directly affect the pressure readings and hence the flow regime delineation. Differential pressure measurements can be also used to determine void fractions. The differential pressure method for determining volume-averaged void fractions is well known for its low cost, simplicity and ruggedness and is a viable option for the cross-calibration of more advanced sensors [62].
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3 3.1
Summary of available data sets for two-phase flow in vertical pipes Co-current upward flow in vertical pipes A total of 22 publications that described flow regimes in upward, co-current, gas-liquid
flows in vertical pipes with diameters of 10 to 100 mm (see Table 2) and diameters larger than 100 mm (see Table 3) have been analysed. The delineation of these size categories is detailed in Section 3.3.1. Experiments in tube diameters less than 10 mm were not included in our analysis because in tubes narrower than 10 mm the capillary forces begin to dominate the gravitational force, producing a different set of unique flow regimes[63]. We did not include in this study the limited number of reports for downward concurrent gas-liquid flows in vertical pipes [64-66] because conditions that draw gas bubbles or slugs down with liquid flows are less common in industrial applications than upward flow conditions. Although most of the co-current upward flow studies used air with water, eight studies report co-current experiments in vertical pipes with hydrocarbon liquids or glycerol-water solutions [21, 52, 58, 67-71]. Three studies report experiments with nitrogen gas instead of air [52, 70, 71]. Figure 6 presents flow maps generated from flow regimes described in the air-water studies listed in Table 2 and Table 3. Figure 6a shows the approximate regions of gas and liquid superficial velocity that each flow regime exists within, for small-medium diameter pipe flows. Barnea, et al. [72] recorded slug flows within pipe diameters of 25 mm and 51 mm at comparatively high gas and liquid superficial velocities, where other experimental works recorded churn or even annular flows. This was likely due to the subjective identification of flow regimes and or a flaw in the adopted measurement technique. These experiments were reliant upon visual observation and basic conductance probes for flow regime identification, neither of which is capable of objective interpretations. Churn flow in particular can be difficult to distinguish through visual observation and could be misinterpreted as either slug or annular flow regimes. Identification of slug flows where an -19-
annular flow regime is expected by other researchers is inexplicable. Therefore, these recorded improbable slug flows have been excluded from further analysis in this review but have been highlighted in Figure 6a for clarity. Figure 6b shows the data for gas-liquid flows in large pipes (D>100 mm). Large diameter vertical pipes are incapable of sustaining the slug flow regime. However, observations of the slug flow regime are reported by Hills [73] who did not document their fluids’ physical properties. Oddie, et al. [70], Schlegel, et al. [54] and Smith, et al. [55] conducted studies using a similar pipe diameter, approximately 150 mm, and did not observe any slug flow regime. The remaining results shown in Figure 6b support the absence of the slug flow regime within large diameter pipes. Transition boundaries are poorly defined in Figure 6b, with significant overlap observed between all of the flow regime regions. In particular, the bubble to churn flow regime transition observed by Ohnuki and Akimoto [74] and Ohnuki and Akimoto [26] occurred at a significantly lower gas superficial velocity. This may be due to the axial location of the observation points in the experiments. The presented flow map data from Ohnuki and Akimoto [74] and Ohnuki and Akimoto [26] were recorded at length to diameter (L/D) ratios of 4.2 and 61.5 and temperatures of 35 and 30 degrees Celsius respectively. Previous studies have shown that flow regimes require a certain distance, measured as L/D ratios, to fully develop and this L/D ratio of 4.2 is unlikely to be sufficient [26-30]. Because the other researchers did not report their experimental L/D ratios or accurate pressures and temperatures, a consistent comparison cannot be made. Further to the aforementioned uncertainties, Ohnuki and Akimoto [26, 74] relied solely upon visual observation without the aid of a high speed camera, which may explain the observed discrepancy shown in Figure 6b. Omebere-Iyari, et al. [71] conducted experiments at very high pressures of 20 kPa and 90 kPa resulting in the annular flow regime developing at
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comparatively very low gas superficial velocities. Their results account for all of the observed annular flows that occur below a gas superficial velocity of 5 m/s shown in Figure 6b. Table 2: Survey of published experiments of co-current upward gas-liquid flow regimes in vertical pipes with diameters 10 < D < 100 mm. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification techniques
࢛ࡳࡿ (m/s) ࢛ࡸࡿ (m/s) Akhiyarov et al.
Air
Oil
52.5
16
[67]
Visual obs. (still)
0.50 – 4 .0 0.10 – 1.0
Alruhaimani
Air
[68]
ND50
50.8
Mineral Oil
183
Visual obs. (video 1000
0.01 – 5.0
frame/s)
0.05 – 2.6
Barnea et al.
Air
Water
12.3
[75]
164
Visual obs., conductance
0.04 – 63.5
probe
3.8e-3 – 4.1 Barnea et al.
Air
Water
25
[72]
103 (excluding
Visual obs., conductance
19 improbable
probe
slug flow data points) 0.04 – 25 3.8e-3 – 2.6
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Air
Water
51
63 (excluding
Visual obs., conductance
43 improbable
probe
slug flow data points) 0.16 – 25 2.6e-3 – 1.6 Furukawa and
Air
Water
19.2
Fukano [69]
73
Visual obs. (still
0.05 – 41
photography)
0.10 – 1.0 Air
Glycerol
19.2
53wt%
52
Visual obs. (still
0.03 – 5.6
photography)
0.10 – 1.0 Air
Glycerol
19.2
72wt%
72
Visual obs. (still
0.05 – 40
photography)
0.09 – 0.76 Govier and
Air
Water
16
11
Short [15]
Visual obs.
0.60 – 8.1 0.26 – 0.26 Air
Water
26
11
Visual obs.
0.84 – 4.1 0.27 – 0.27 Air
Water
38.1
13
Visual obs.
0.80 – 9.6 0.27 – 0.27 Air
Water
63.5
11
-22-
Visual obs.
0.52 – 4.6
0.26 – 0.26 Juliá et al. [24]
Air
Water
50.8
121
Visual obs., conductance
0.02 – 9.7
probe
0.03 – 2.5 Lucas et al. [29]
Air
Water
51.2
89
Wire mesh conductance
1.4e-3 – 0.52
sensor
0.02 – 6.3 Rosa et al. [76]
Air
Water
54.5
73
Visual obs., resistivity
0.12 – 29
probe
0.22 – 3.1 Schmidt et al.
Nitrogen
[52]
Luviskol in
54.5
Water
20
Visual obs.,
0.04 – 21
gamma ray,
4.6e-3 – 3.3
quickclosing valves
Spedding et al.
Air
Water
26
291
[25]
Visual obs., dP
0.35 – 37 7.7e-3 – 1.1
Szalinski et al.
Air
Water
67
[58]
Air
Silicone
67
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29
Visual obs., wire mesh
0.05 – 5.7
conductivity &
0.20 – 0.71
permittivity
28
Visual obs., wire mesh
0.06 – 5.6
conductivity &
0.20 – 0.72
permittivity
Taitel et al. [8]
Air
Water
25
108
Visual obs.
0.04 – 27 2.7e-3 – 2.8 Air
Water
51
79
Visual obs.
0.01 – 19 0.02 – 3.6
Table 3: Survey of published experiments of co-current upward gas-liquid flow regimes in vertical pipes with diameters D > 100 mm. Study
Gas
Liquid
Pipe dia.
Data points
Flow regime
(mm)
࢛ࡿࡳ (m/s)
identification techniques
࢛ࡿࡸ (m/s) Farman Ali and
Air
Water
254
124
Yeung [62]
Visual obs. (video), dP
0.06 – 2.3 0.19 – 1.08
Hills [77]
Air
Water
150
44
Visual obs., dP
0.07 – 3.6 0.00 – 2.6 Oddie et al. [70]
Ohnuki and
Nitrogen Naptha
Air
Water
150
480
Akimoto [74]
-24-
14
Visual obs., gamma ray,
0.04 – 0.98
conductance probe
0.03 – 1.5
(parallel wire)
89
Visual obs. (still & video
0.02 – 0.77
200 frame/s)
9.8e-3 – 0.21
Ohnuki and
Air
Water
200
Akimoto [26]
58
Visual obs. (still & video
0.03 – 4.7
200 frame/s)
0.02 – 0.70 Omebere-Iyari et
Nitrogen Naptha
189
121
al. [71]
Conductance probe (ring)
0.09 – 15 3.9e-3 – 3.9
Schlegel et al.
Air
Water
150
63
[54]
Impendence probe (arch)
0.07 – 11 0.01 – 2.03
Smith et al. [55]
Air
Water
102
83
Visual obs. (video 10,000
0.01 - 21
frame/s)
0.02 – 2.0 Air
Water
152
129
Visual obs. (video 10,000
0.02 – 10
frame/s)
0.02 – 0.99 Sun et al. [78]
Air
Water
101.6
10
Conductance probe (4
0.05 – 0.51
sensor)
0.06 – 1.0
-25-
Figure 6: Flow maps for upward co-current air-water flow in vertical pipes, including (a) small pipes with diameter 12.3 < D < 67 mm (with improbable slug flow regime data points -26-
recorded by Barnea, et al. [72] in pipe diameters of: 25mm, shown as +, and 51mm, shown as ×), and (b) larger pipes with diameters D > 100 mm. The data points are taken from the literature and listed in Tables 2 and 3. 3.2
Counter-current flow in vertical pipes Despite the existence of numerous experimental investigations on the flow regimes of co-
current two-phase flow, there are few studies available on the flow regimes of counter-current flows in pipes [5, 61, 79-82]and no experimental studies on flow regimes of counter-current flows in annuli. Besagni, et al. [83] experimentally investigated the influence of two inner pipes on counter-current flow in a bubble column, however this study is not directly relevant to the focus of this review paper due to the difference in geometry. The majority of the available experimental investigations of counter-current flows in vertical pipes focus on identifying the onset of flooding or counter-current flow limitation (CCFL). Table 4 summarises the available experimental studies on flow regimes of counter-current gas-liquid flows in vertical pipes. The flow regime data are shown in Figure 7. It must be noted that at low gas and liquid flow rates in a continuous gas medium an annular or falling liquid film flow would be expected, however all of the identified experiments have been conducted within a continuous liquid phase. Figure 7 shows extensive overlapping of the identified flow regimes. Kim, et al. [82] only investigated the slug to churn flow transition. Results from the experiments of Yamaguchi and Yamazaki [5] cannot be analysed nor comparatively examined, as a broad range of experimental conditions, pressure and temperature, was reported for the two investigated pipe diameters and so the exact fluid properties are unknown. The flow map data published by Ghiaasiaan, et al. [80] was solely dependent upon unaided visual observation whilst Ghiaasiaan, et al. [81] investigated two-phase flows with significantly different fluid -27-
properties. The results published by Ghosh et al. [61, 79] are likely to be the most reliable as they adopted multiple flow regime identification techniques. Overall, the poor performance of this collated flow map can be attributed to the limited number of available experimental results, and the results that are available being for significantly different experimental conditions and fluid properties. Table 4: Survey of published experiments of counter-current upward gas-liquid flow regimes within a continuous liquid phase in vertical pipes with diameters 10 < D < 100 mm. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification techniques
࢛ࡳࡿ (m/s) ࢛ࡸࡿ (m/s) Kim, et al. [82]
Air
Water
20
86
Visual obs. (video)
0.02 – 2.7 5.0e-3 – 0.15 Ghiaasiaan et al.
Air
Water
19
60
[80]
Visual obs.
0.10 – 1.7 7.5e-3 – 0.14
Ghiaasiaan et al.
Air
Mineral oil
19
94
[81]
Visual obs.
0.01 – 1.7 1.4e-3 – 0.22 Air
Paraffinic
19
66
oil
Visual obs.
0.01 – 2.2 1.4e-3 – 0.07
Ghosh et al. [61]
Air
Water
25.4
-28-
18
Visual obs. (still & video)
0.19 – 4.9
6.4e-3 – 0.06 Ghosh et al. [79]
Air
Water
25.4
159
Conductance probe (ring,
0.20 – 5.2
parallel wire)
7.0e-3 – 0.15 Yamaguchi and
Air
Water
40
141
Visual obs.
4.0e-3 – 1.6
Yamazaki [5]
3.8e-6 – 0.29 Air
Water
80
74 7.3e-3 – 1.4 1.0e-5 – 0.54
-29-
Visual obs.
Figure 7: Flow maps for counter-current flow within a continuous liquid phase in vertical pipes with diameters 19 < D < 80 mm. The negative sign on the liquid superficial velocity in the vertical axis indicates downward flow. The data points are taken from the literature and listed in Table 4. 3.3
Effect of Pipe Geometry The effect of pipe geometry on flow regimes has been studied extensively in co-current
upward flows in vertical pipes. This flow configuration is the most well studied and hence provided the greatest depth of information for an investigation into the influence of pipe geometry. ϯ͘ϯ͘ϭ ĨĨĞĐƚŽĨWŝƉĞŝĂŵĞƚĞƌ Mishima and Hibiki [49] considered upward co-current flows within very small pipe diameters ranging from 1 to 4 mm, described by the authors as capillary tubes. Two-phase
-30-
flows in such pipe sizes produce special flow regimes due to the capillary forces influencing the shape of the gas bubbles. Pipes of inner diameters smaller than 5 to 9 mm can be defined as capillary tubes in which capillary pressure replaces gravity as the dominant force [63]. This review paper will focus on pipes, with diameters greater than 10 mm. Taitel, et al. [8] experimentally investigated upward co-current flows in vertical pipes with internal diameters of 21 and 51 mm. The study found that the bubble flow regime did not exist for the smaller, 21 mm, pipe, which was explained by bridging of bubbles in the small pipe diameter and therefore, forming Taylor bubbles. Taitel, et al. [8] showed that at low liquid flow rates, when the rise velocity of gas bubbles, U 0 = 1.53 ª¬ g ( ρ L − ρ G ) σ / ρ L2 º¼
1/ 4
[84] is greater than the rise velocity of a Taylor
bubble, UG ≅ 0.35 gD [85], the bubble flow regime does not occur. This is because the rising bubbles approach, from behind, and coalesce with the larger bubble, increasing its size and resulting in a Taylor bubble and, therefore, the slug flow regime. Conversely, if the rise velocity of the Taylor bubble is greater than the velocity of the gas bubbles then coalescence does not occur as the forces at the nose of the Taylor bubble disperse the smaller bubbles [8]. Therefore, the critical pipe diameter, below which bubble flow regime does not exist can be determined by equating the rise velocity of the gas bubbles and Taylor bubbles [8],
D critical = 19.1
( ρ L − ρ G )σ
(1)
g ρ L2
For an air-water system close to the atmospheric pressure, Eq. (1) results in a critical internal pipe diameter of 50 mm. Pipes and annuli of hydraulic diameters between 10 to 100 mm will be defined in this paper as small to medium diameter pipes and annuli. Kataoka and Ishii [86] defined a critical diameter above which, Taylor bubbles and therefore the slug flow regime cannot exist due to interfacial instability. This critical diameter -31-
was defined as D = 40 σ / g ( ρ L − ρG ) ͕which results in a diameter of approximately 108 mm
for an air-water system at an atmospheric condition. Schlegel, et al. [54] experimentally demonstrated that Taylor bubbles in such configurations are unable to bridge the pipe and achieve stability. Smith, et al. [55] conducted studies on co-current upward flows in larger pipes with inner diameters of 102 and 152 mm. Slug flows were absent from both of the produced flow maps. Figure 6b supports this theoretical pipe size limitation of 108 mm for the existence of slug flow through the absence of any experimentally observed slug bubbles, with the exception of the results produced by Hills [73]. Slug flow was documented by Hills [77] in a pipe diameter of 150 mm, which is much larger than the limitation for slug flow that any other researchers have theoretically predicted or experimentally observed. For the purposes of this paper the maximum pipe size for the existence of the slug flow regime, acknowledged as the limit between medium and large sized pipes, will be taken as 100 mm. The effect of pipe diameter on vertical counter-current two-phase flows was analysed by Yamaguchi and Yamazaki [5] using pipes of 40 and 80 mm diameters. The bubble flow regime appeared to exist at similar air-water flow rates in both pipes. However, the annular flow regime could not be attained within the 80 mm pipe. This was attributed to the considerable volume of air escaping through the liquid exit of the apparatus. This is an experimental issue and no conclusions can be made. At higher volumetric flux densities, it was found that void fractions were significantly greater within the 40 mm pipe, compared to the 80 mm, for the same liquid and gas volumetric flux densities. This difference in void fractions was seen to decrease as the absolute volumetric flux density decreased. Literature on vertically downward two-phase flow is sparse in comparison to its upward counterpart, however, an investigation into the effects of pipe diameter was conducted by Barnea, et al. [64] in pipes of 25 and 51 mm diameters. The transition to bubble flow from slug flow regime at high liquid flow rates (dispersed bubble flow) within the 25 mm pipe was -32-
similar to that seen for the vertical upward flow case. However, the same transition within the 51 mm pipe occurred at relatively lower liquid flow rates, subsequently reducing the range of the slug flow regime. ϯ͘ϯ͘Ϯ ĨĨĞĐƚŽĨWŝƉĞĞǀŝĂƚŝŽŶ Although this review is focused on vertical two-phase flows, it is important to understand the effect on flow patterns caused by deviation from a vertical configuration. Barnea, et al. [72] investigated the effect of pipe inclination from 0 to 90° on co-current upward flow regimes and they reported that slight deviations from vertical had little effect on flow patterns while small inclination from horizontal can significantly influence the flow regime. The smallest deviation from vertical that was published in their study was 40°, and so the description of a slight deviation cannot be quantified. Spedding, et al. [87] were able to consider even smaller angles and found that pipe deviations of as small as 3.5° had a significant influence on co-current upward flow regimes at gas flow rates of smaller than 10 m/s. The inclination was found to generate a preferential build-up of liquid on the lower pipe wall, developing anisotropy and eventually blow through slug. This blow through slug is best described as a slug bubble that occurs due to a gradual ramp up of the void fraction behind the liquid build-up, eventually a slug bubble is formed that displaces the accumulated liquid. Oddie, et al. [70] investigated a minimum deviation of 5° for co-current upward flows and their results showed that the flow regimes were barely effected. Ghiaasiaan, et al. [80] investigated counter-current flows in deviations as low as 8° and found that this led to the development of stratified flow. This deviation also caused the slug flow regime to persist at a considerably higher gas flow rate when compared to the vertical case. The critical observation here is that when the pipe deviation significantly impacts the flow regimes, the influence is seen through a change in the regimes themselves. Stratified and anisotropic flow behaviour are non-existent in vertical two-phase flows. As such, imperfect -33-
experimental setups containing significantly deviated vertical test sections should be readily identified, and subsequently ignored, due to the existence of atypical flow behaviour. 3.4
Effect of fluid properties on flow regimes in vertical pipes
ϯ͘ϰ͘ϭ sŝƐĐŽƐŝƚLJ Investigations into the effect of fluid physical properties are complicated by the intrinsic difficulty of isolating and manipulating individual fluid properties. Most of the studies on the effect of fluid physical properties on flow regimes focus on the effect of liquid viscosity. A summary of the fluid properties utilised in the available investigations on the effect of liquid viscosity on the flow regime transition in pipes is presented in Table 5. Ghiaasiaan, et al. [81] investigated the effect of increased liquid viscosity on countercurrent flows in small diameter pipes with mineral oil and paraffinic oil, which increased the viscosity from that of water by a factor of 35 and 185, respectively. It was found that the increasing viscosity resulted in flow regime transitions occurring at significantly lower gas and liquid superficial velocities. Table 5: Summary of experimental studies on the effect of fluid properties on flow regimes of gas-liquid flows in pipes. Author
Experimental Parameters
Liquid Properties
Fluids
Pipe
ȡL
ȝL
ȝL/ ȡL
ıL
Diameter
(kg/m3)
(mPa.s)
(St)
(N/m)
(mm) Counter-current Flow in Pipes Ghiaasiaan, et al.
Air-Water
19
996
1
0.010
0.072
Air-Mineral Oil
19
843.1
35.2
0.418
0.014
[80] Ghiaasiaan, et al.
-34-
[81]
Air-Paraffinic Oil
19
871.4
185
2.124
0.013
Co-current Upward Flow in Pipes Furukawa and
Air-Water
19.2
1000
1
0.010
0.072
Fukano [69]
Air-Glycerol
19.2
1125
6.4
0.057
0.065
19.2
1172
17.2
0.147
0.062
Air-water
19
995
0.848
0.009
0.071
Air-Glycerol
19
1121
4.48
0.040
0.065
54.5
982-
900-
8.227-
0.072
1094
7000
71.283
53wt% Air-Glycerol 72wt% Da Hlaing et al.[21]
50wt% Schmidt et al.[52]
Air-Luviskol in Water
Szalinski et al.
Air-Water
67
1000
1
0.01
0.072
Air-Silicone
67
900
5.3
0.059
0.020
Gas-Oil
52.5
884
100-500
1.131
0.036
Air-Water
50.8
1000
1
0.01
0.072
Air-ND50 Mineral
50.8
884
127-586
1.437-
0.036
[58]
Akhiyarov, et al. [67] Alruhaimani [68]
Oil
6.629
Furukawa and Fukano [69] attempted to isolate the liquid dynamic viscosity in their work on co-current upward flows in small diameter pipes by adding glycerol to water. This procedure provided a six and seventeen-fold increase in liquid viscosity from water whilst retaining similar densities and surface tensions. Their results showed that the bubble to slug -35-
flow transition boundary shifts towards a lower superficial gas velocity with increasing liquid viscosity. The transition to the churn flow regime, denoted as froth and froth-annular, shifts towards a higher superficial gas velocity with increasing liquid viscosity. The occurrence of a falling film, annular flow regime, appeared to be independent of the liquid viscosity. Da Hlaing, et al. [88] also investigated the effect of liquid viscosity in co-current upwards flows within small diameter pipes, 19 mm. Water and a 50 vol. % glycerol solution were used as the working liquid with dynamic viscosities of 0.848 and 4.48 mPa s. They observed a pronounced shift in the bubble to slug transition to higher gas superficial velocities due to the formation of fewer bubbles in the higher viscous liquid. However, the slug to churn and churn to annular transitions remained largely unaffected by the increased fluid viscosity. This was assigned to the dominant effect of high turbulent flow at the high gas flow rates at which these transitions occur. Szalinski, et al. [58] conducted a comparative study of flow regimes in co-current upward flows within 67 mm diameter pipes using air-water and air-oil, with a liquid viscosity of approximately five times greater than that of water. This study also reported opposing results to those of Furukawa and Fukano [69] regarding the effect of viscosity on the bubble-slug and churn-annular transitions. Their experimental results indicated that the bubble to slug flow transition occurred at greater gas superficial velocities with increasing liquid viscosity and the churn to annular flow transition occurred at lower gas superficial velocities with increasing viscosity. It was reported that there was more coalescence, and hence larger gas bubbles in the air-water flows than the air-oil flows. In another study Schmidt et al.[52] investigated the effect of liquid viscosity on upward vertical gas-liquid flows in a tube with 54.5 mm inner diameter and mixtures of nitrogen and solutions of polyvinylpyrrolidone in water with dynamic viscosities in the range of 900!7000 mPa s. They observed a decrease in the gas holdup with increasing the liquid viscosity from -36-
1 to 480 mPa s. They also compared the flow map for liquid viscosity of 1600 mPa s with the air-water flow map of Taitel, et al. [8] and concluded that the transition to annular regime occurred at lower gas superficial velocities in the viscous liquid. Akhiyarov, et al. [67] conducted experiments on gas-oil flows in vertical pipes with internal diameter of 52.5 mm and oil viscosities of 100-500 mPa s to assess the performance of the available mechanistic models to predict the pressure gradient and liquid holdup. No comparison was reported on the effect of liquid viscosity on the liquid holdup and flow regimes. Alruhaimani [68] also performed a comparative study for co-current upward flows in medium diameter pipes. Air-water and various compositions of air-oil were used. They did not observe any viscosity effect on bubble-slug and slug-churn transitions. However, the transition to the annular flow regime occurred at a lower superficial gas velocity as the liquid viscosity increased. The lack of consensus regarding the effect of fluid viscosity ranges outside of experiments on liquid viscosity on flow regime transition in vertical two-phase pipe flow. Early work in bubble columns/pipes also observed contradictory results for varying fluid viscosities on gas holdup which is an indirect indication of flow regimes. For example Weiss, et al. [89] observed an increase in gas holdup with increasing liquid viscosity from 0.92 mPa s to 1670 mPa s in a 15.1 mm pipe. Eissa and Schügerl [90] observed a dual effect of liquid viscosity on gas holdup in a bubble column with 15.9 cm diameter. They found an initial increase in gas holdup for liquid viscosity below 3 mPa s, a decrease between 3 and 11 mPa s and an almost constant gas holdup at viscosities greater than 11 mPa s. This dual effect of liquid viscosity was also observed by Kuncová and Zahradník [91] who studied the effect of liquid viscosity on gas
-37-
holdup in a bubble column with 15.2 cm diameter by using saccharose solutions to achieve viscosities ranging from 1.4 mPa s to 110 mPa s. They observed an increase in gas holdup for liquid viscosities smaller than 3 mPa s and significant reduction in gas holdup in liquids with viscosities greater than 3 and smaller than 30 mPa s. Recent research by Besagni, et al. [33] into the effect of viscosity in bubble columns also reported similar findings. The reduced gas holdup in high viscous liquids, viscosity greater than 3 mPa s, is explained by the increase in bubble coalescence due to the effect of wake with stable vortex [92]. Therefore, in gas-liquid flows with high liquid viscosities gas holdup reduces due to the higher coalescence rate. This results in a shift in bubble-slug transition towards higher gas velocities whereas the transition to churn flow regime occurs in smaller gas velocities due to the formation of large bubbles. This is in agreement with the prediction of Mishima and Ishii [6] for the churn to annular regime transition. The experimental results of Da Hlaing et al.[21], Schmidt et al.[52], Szalinski et al. [58] for bubble-slug transition in viscous liquids is in agreement with the above explanation for the effect of liquid viscosities greater than 3 mPa s unlike the results of Furukawa and Fukano [69] and Alruhaimani [68] for bubble-slug and slug-churn regime transitions. The conflicting results for flow regime transition in the above studies may be attributed to varying surface tension and/or different pipe sizes. These inconsistent results highlight the need for a better experimental design to investigate the effect of fluid physical properties by controlling other effective parameters. ϯ͘ϰ͘Ϯ ^ĂůŝŶŝƚLJ Salts are known to inhibit bubble coalescence beyond a concentration called the critical salt concentration, which is unique for each salt [93-98]. To explore this further, we performed experiments that investigated the effect of sodium chloride at different
-38-
concentrations on bubble coalescence and size in a bubble column. Results were captured using a high-speed camera at a frequency of 5000 frames per second. The bubble size at different salt concentrations was determined through image analysis by utilising ImageJ software. The Sauter mean bubble diameter, D32, was calculated as [99],
¦ (4 A / π ) , ¦ (4 A / π ) 3/2
D 32 =
(2)
p
p
where Ap is the projected bubble area. Figure 8 shows the effect of salt concentration on bubble size. The results indicate that bubble size decreases with increasing salt concentration. This effect is more pronounced at a concentration of approximately 0.13 Molar, which is close to the critical salt concentration of sodium chloride. Gas holdup, which is an indirect method for measuring bubble size, was reported to increase with salt concentration owing to the inhibiting effect of salt on bubble coalescence [96, 100]. Different mechanisms including colloidal forces, Gibbs-Marangoni effect, and ion specific effect have been proposed to explain the inhibiting effect of salts on bubble coalescence which have been reviewed by Firouzi, et al. [101]. To our knowledge there is no direct data available on the effect of salinity on flow regimes of gas-liquid two-phase flows with the exception of the recent study by Besagni and Inzoli [102] in a large bubble column (240 cm inner diameter) where flow regimes are mainly defined as homogenous (characterised by small and uniformly distributed bubbles) and heterogeneous (characterised by bubbles from different sizes due to high interactions between bubbles). Besagni and Inzoli investigated the effect of sodium chloride on these flow regime of counter-current air-water flows. Their experimental results indicated the stabilising effect of electrolytes with concentration up to the critical/transition concentration on the homogenous regime due to the inhibiting effect of salts on bubble coalescence.
-39-
Based on the available data on the stabilising effect of inhibiting salts, we postulate that at concentrations above the critical salt concentration, the transition from bubble to slug and slug to churn/annular can be significantly delayed compared with that in fresh water. This is in agreement with the empirical expression for the critical void fraction at the bubble-slug transition, αc = 0.55− 2.37 Db D , proposed by Guet, et al. [103] based on an interpolation of
Song et al. [104] experiments in a 25 mm diameter pipe. Here, the critical void fraction for the bubble-slug transition, αc , increases with decreasing bubble size, Db. Therefore, the bubble-slug transition occurs at a higher gas velocity (flow rate).
-40-
Figure 8: The Sauter mean diameter, D32, of bubbles as a function of salt concentration at QG= 0.46 L/min. 4
Summary of experimental data for co-current flow in vertical annuli Available experimental studies on flow regimes in annuli indicate that despite the
existence of similar flow regimes as in pipes, there are small differences in distribution of gas and liquid phases, which characterise different flow regimes, in these two geometries. This difference is more pronounced in the slug flow regime. Table 6 and Figure 9 show the -41-
experimental conditions and data in annuli for upward co-current flows. Some studies reported an asymmetric structure of Taylor bubbles in annular geometries [53, 105, 106]. Hasan and Kabir [107] observed Taylor bubbles with a sharper nose which causes the bubbles to rise faster. Annular flow configurations are described by the inside diameter (ID) of the outside pipe or casing, DC, and the outside diameter (OD) of the inside pipe or tubing, DT. The effect of annular eccentricity was examined by Kelessidis and Dukler [105], who compared co-current upward flows between concentric annuli and annuli with 50% eccentricity using 76.2 mm ID casing and 50.8 mm outside diameter (OD) tubing. It was found that the eccentricity had minimal effect on the global flow regimes. However, local flow regimes were observed to develop more readily at lower gas flow rates in the larger rather than smaller annulus. This anisotropy was applicable to all of the flow regime transitions, with transitions always occurring first in the larger annulus then the smaller one, as the gas flow rate increased. In another experimental study by Caetano, et al. [53] using concentric and fully eccentric annuli with 76.2 mm ID casing and 42.2 mm OD tubing, no major difference was observed for the churn to annular flow regime transition in concentric and eccentric annuli. However, bubble-slug and bubble-dispersed bubble flow regimes were observed at respectively smaller and larger gas flow rate compared with that in a concentric annulus.
-42-
Table 6 Survey of published experiments of co-current upward gas-liquid flow regimes in vertical annuli with small hydraulic diameters DH < 50 mm where the hydraulic diameter DH=DC-DT. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification
࢛ࡿࡳ (m/s)
techniques
࢛ࡿࡸ (m/s) Kelessidis and Dukler
Air
Water
DH: 25.4
85
DC: 76.2
0.02 – 19
DT: 50.8
1.0e-3 – 1.8
DH: 34.0
100
DC: 76.2
0.01 – 23
DT: 42.2
2.1e-3 – 3.1
Kerose
DH: 34.0
170
ne
DC: 76.2
0.03 – 23
DT: 42.2
2.7e-3 – 2.4
DH: 25.4
Results from
Conductance probe
DC: 50.8
three annuli
(parallel plate)
DT: 25.4
published in
[105]
Caetano et al. [53]
Air
Air
Das et al. [106]
Air
Water
Water
Visual obs.
Visual obs.
Visual obs.
a single flow Air
Water
DH: 25.4 DC: 38.1 DT: 12.7
Air
Water
DH: 12.7
-43-
Conductance probe map with no (parallel plate) distinctions made. Conductance probe
DC: 25.4
307
DT: 12.7
0.04 – 8.7
(parallel plate)
0.10 – 2.6
Sun et al. [108]
Jeong et al. [109]
Ozar et al. [110]
Julia et al. [27]
Air
Air
Air
Air
Air-
DH: 19.0
132
Visual obs.,
Water
DC: 38.1
0.02 – 0.90
Impendence probe
DT: 19.1
0.37 – 2.7
Air-
DH: 19.0
19
Conductance probe (4
Water
DC: 38.1
0.04 – 3.9
sensor)
DT: 19.1
0.24 – 3.3
Air-
DH: 19.0
19
Water
DC: 38.1
0.05 – 5.5
DT: 19.1
0.25 – 3.4
Air-
DH: 19.0
72
Conductance probe (4
Water
DC: 38.1
0.02 – 20
sensor)
DT: 19.1
0.21 – 3.4
-44-
Visual obs.
Figure 9: Flow maps for co-current flow in vertical annuli with small hydraulic diameters 19 < DH < 34 mm. The data points are taken from the literature and listed in Table 6. 5
Evaluation of flow maps based on non-dimensional parameters Wallis [111] was the first to present flow regimes on a flow map co-ordinate system using
superficial velocities of gas and liquid as its axes. This flow map coordinate is still most commonly used due to its simplicity. However, its presented results are also limited by this simplicity as they may not be reliably related to two-phase flows under dissimilar conditions. In order for a widely applicable solution to be found, non-dimensional parameters should be used to include the effect of fluid physical properties, geometry, and the velocity or flow rate.
-45-
Troniewski and Ulbrich [112] identified three groups of parameters that could be used as co-ordinates for flow maps, namely phase velocities or fluxes (i.e. gas superficial velocity), quantities representing homogenous transformations of the phase velocities or fluxes (i.e. mixture superficial velocity), and parameters including physical properties of phases (i.e. Reynolds number). The authors highlighted the latter as being the most likely to provide a universal solution. Table 7 examines the fluid properties that may affect two-phase gas-liquid flow and summarises their inclusion within dimensionless parameters. In order to include all of the fluid properties a combination of dimensionless parameters may be required. Chen [38] suggested that the Weber number, describing the inertial force of a flow in relation to its surface tension, may be the best parameter to deduce general correlations. However, it must be highlighted that the study by Chen [38] was focussed on capillary tubes of D < 5 mm. Since flows in pipes of diameters greater than 9 mm are dominated by gravity rather than capillary pressure and hence surface tension, it is expected that the Reynolds and Froude numbers will be of greatest importance [63]. Reynolds number is similar to the Weber number but considers the inertial force of the flow in relation to the viscous force instead of the surface tension force. The Froude number describes the inertial force of the flow against the gravitational force. Abdelsalam, et al. [22] proposed a flow map coordinate based on a new dimensionless number called slippage number (SL) and the mixture Froude number (FrM). S L takes into account the slippage between phases and is defined as the ratio of the gravitational force difference between slip and no-slip (homogenous) conditions. The proposed flow map coordinates were tested against experimental data of different studies for air-water and air-oil systems for a range of liquid visocity of 0.001 to 0.589 Pa.s, pipe diameters of 25 to 152 mm and inclinations of 1 to 90°. It was shown that S L decreases exponentionally with FrM and the smallest and greatest S L represent bubble and annular flow regimes. The proposed -46-
coordinates do not include viscosity and surface tension of the fluids as well as flow inclination, however, the liquid holdup (HL), which is an indication for identifying flow regimes, includes the influence of these parameters. S L requires the value of the liquid holdup at each gas and liquid flowrates which, is not always provided in the experimental studies of flow regimes. Unfortunately, the majority of studies did not document liquid holdup data for each flow map data point and so this set of proposed flow map coordinates could not be tested. Table 7: Flow regime map co-ordinates in vertical pipes Flow map coordinates
Author(s)
uLS vs. uGS
Wallis [111]
D
uGS
uLS
3
3
3
3
3
3
3
ȡG
ȡL
3
3
3
3
3
3
3
3
3
3
3
3
3
ȝG
ȝL
ı
Govier and
uLS vs.
uGS uLS
Leigh Short [15] Griffith and
u FrM2 vs. GS uM
3
Wallis [16] Moissis [113] Hewitt and
2 2 ρLuLS vs. ρGuGS
Roberts [17]
1/4
1/4
uLS ( sLσ S ) vs. uGS ( sLσ S )
sG1/3 Aziz, et al.
3
[114]
FrM
vs.
µS 3
( S Lσ S )
1
4
WeLS vs. WeGS
uSG uSL
Oshinowo and 3
3
Charles [19] Rezkallah and Zhao [20]
-47-
3
3
3
Da Hlaing, et
ReLS vs. ReGS
3
3
3
3
3
3
3
3
3
3
3
3
al. [21]
( ρ M − ρ H ) gD vs. 2 ρ G u SG
ρL Fr Abdelsalam, et ρ L − ρG M al. [22]
uM = uGS + uLS ρM = ρ L H L + ρG (1 − H L ) & ρH = ρL
uLS u + ρG GS uM uM
FrM = uM / Dg
WeGS =
2 ρGuGS D ρ u2 D & WeLS = L LS σ σ
ReGS =
ρGuGS D ρu D & ReLS = L LS µG µL
sL , σS
and
µS
are the liquid specific density, surface tension and viscosity and
sG is the gas
superficial density
Previous attempts to create a universally applicable flow pattern map through the use of non-dimensional parameters have been limited and were only verified against limited experimental data sets [22, 88]. Here, the suggested non-dimensional numbers listed in Table 7 were examined against the compiled experimental flow regimes. Flow maps presented in non-dimensional space were visually inspected against the popular superficial velocity space to gauge the success of the dimensionless solution. Ideally the selected parameters would result in plots containing clearly defined flow regime transition boundaries that align themselves similarly, regardless of experimental conditions and fluid properties. This would allow for the production of a widely applicable flow pattern map.
-48-
The majority of published experimental work did not report the utilised fluid properties nor laboratory conditions, and as such it was necessary to make some assumptions to complete this analysis. Standard laboratory conditions (room temperature of 25°C and atmospheric pressure) were assumed where necessary to make this analysis possible. The range of observed experimental conditions and fluid properties that will be considered are presented in Table 8. Table 8: Range of experimental pipe sizes and fluid properties.
uGS
uLS
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(m/s)
(m/s)
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Having considered the available experimental data, it was decided that results from cocurrent upward flows in small-medium diameter vertical pipes were the most suitable for the development of a dimensionless solution. A summary of the studies that have been utilised is presented in Table 2. Due to the complex nature of two-phase flows, the calculation of dimensionless flow map coordinates has been based on superficial velocity as shown in Table 7. Theoretically, mass flow rates would provide a better interpretation of the flow phenomena, however, this would require detailed void fraction data corresponding to the superficial flow rates. This information has not been made available in the examined studies and in most cases, has not been recorded. Based on the parameters considered in Table 7 and a visual assessment of the produced flow maps, the Reynolds number solution, ReLS vs. ReGS, is recommended and presented in Figure 10. In addition to our visual assessment of flow maps, liquid viscosity which has a pronounced effect on flow regimes is taken into account in
-49-
our recommended flow map. Flow maps in different coordinates listed in Table 7 are shown in the appendix.
Figure 10: Recommended dimensionless solution, ReLS vs. ReGS, for co-current upward flow in small-medium diameter vertical pipes and annuli, 10 < D < 100mm.
6
Theoretical prediction of flow regime transitions This section reviews the empirical models, which are the most popular, and tested against
experimental data, for predicting the transition of flow regimes. Note that these transitions were developed for co-current, upward flow in vertical pipes, which is the most well-studied of the vertical two-phase flow configurations. -50-
6.1 Transition from bubble to slug flow regime The transition from bubble to slug flow regime occurs due to the agglomeration and coalescence of bubbles in the bubble flow regime at low liquid flow rates. Taitel, et al. [8] showed that this transition in a vertical co-current upward flow takes place when the gas void fraction, Į, is greater than 0.25. Substituting this value for the gas void fraction into the equation for rise velocity of bubbles relative to the average liquid velocity defines the bubble to slug transition as,
uLS = 3uGS −0.75u∞ ,
(3)
where ݑஶ describes the rise velocity of fairly large bubbles which is quite insensitive to bubble size [84], 1/4
ª g ( ρL − ρG ) σ º u∞ = 1.53 « » . ρL2 ¬ ¼
(4)
McQuillan and Whalley [115] followed the same approach for predicting the transition between bubble and slug flow regimes. Barnea [116] also followed the same approach and modified the bubble to slug transition model to include pipe inclination. Mishima and Ishii [6] considered α = 0.3 as the criterion for the transition from bubble to slug flow and proposed a model to predict this transition by employing the drift velocity for bubble flow, 1/4
§ 3.33 · 0.76 § σ g ( ρL − ρG ) · uLS = ¨ −1¸ uGS − ¨ ¸ , ρL2 C0 © © C0 ¹ ¹ in which C0 is the approximate ratio of the centreline velocity to the average velocity and is defined as C 0 = 1.2 − 0.2
ρg for round tubes. Hasan and Kabir [117] followed the same ρL
-51-
(5)
approach and proposed their own model to predict the bubble-slug transition by considering
α = 0.25 as the transition criterion. § 4 · u u LS = ¨ − 1 ¸ u GS − ∞ , C0 © C0 ¹
in which
(6)
C0 =1.2 .
At high liquid flow rates Taitel, et al. [8] suggested that the bubble coalescence and agglomeration will be overcome by the breakup of bubbles due to the turbulence of the high liquid flow rate. As a result, dispersed bubble flow occurs at high liquid flow rates wherein gas bubbles remain dispersed due to turbulence. These small bubbles can exist at void fractions up to 0.52 at higher water flow rates. Taitel, et al. [8] proposed the bubble-dispersed bubble transition by employing the theory of breakup of immiscible fluids by turbulence forces, given by Hinze [118] as, 0.54
0.43
uLS = 3.97 D
§σ · ¨ ¸ © ρL ¹
0.071
§ ρL · ¨ ¸ © µL ¹
0.45
§ g ( ρL − ρG ) · ¨ ¸ σ © ¹
− uGS .
(7)
It has been assumed that at high enough gas concentration, bubbles coalesce again to form slug or churn flow regimes. A gas void fraction of 0.52 was considered as the transition between dispersed bubble and slug/churn flow regime, which yields,
uLS = 0.92uGS
(8)
This model was later improved by [119] to consider the relatively small effect of the gas void fraction on the coalescence and breakup of bubbles [120]. 0.4σ § ρL · 2 ¨ ¸ g ( ρ L − ρG ) © σ ¹
0.6
− 0.2 § 2 § DρL · · ¨ 0.046 ¨ ¸ ¸ ¨ D © µL ¹ ¸ © ¹
0.4
-52-
u 1.12 = 0.725 + 4.15 α . M
(9)
where the average velocity,
u M , is defined as uM = uLS + uGS . Substituting a void fraction of
0.52 into Eq. (9) and solving this nonlinear algebraic equation for the liquid superficial velocity results in, 0.54
0.43
uLS = 6.14D
§σ · ¨ ¸ © ρL ¹
0.071
§ ρL · ¨ ¸ © µL ¹
0.45
§ g ( ρL − ρG ) · ¨ ¸ σ © ¹
− uGS .
(10)
Mishima and Ishii [6] made no distinction between bubble and dispersed flow regimes. McQuillan and Whalley [115] employed the empirically modified model proposed by Taitel and Dukler [121] for horizontal pipes, to predict the bubble to dispersed bubble transition in vertical pipes. It was postulated that at high liquid flow rates, the effect of slip between two phases is negligible and the turbulence is caused only by the bulk flow. Therefore, the modified expression for the horizontal pipes should be independent of the pipe inclination and can be used for vertical pipes as well. The correlation suggests that the transition is independent of the gas flow rate and dispersed flow regime exists if,
uLS =
6.8
0.11
ª gσ ( ρL − ρG ) º¼
ρL0.44 ¬
0.28
§ D· ¨ ¸ © µL ¹
.
(11)
McQuillan and Whalley [115] considered a gas void fraction of 0.74 as limit for stability of dispersed bubbles and transition to slug/churn flow regime which yields,
uLS = 0.35uGS .
(12)
6.2 Slug to churn flow transition Accurate prediction of the transition from slug to churn flow regime is difficult as there is no clear definition of the churn flow regime. Different mechanisms have been proposed for the transition from slug to churn flow regime. These include flooding, bubble coalescence, wake effect and entrance effect [8]. Taitel, et al. [8] proposed that the churn flow regime is -53-
an entrance related phenomenon. It was suggested that the entry length, lE, in which churn flow can form before a stable slug flow occurs, depends on the gas and liquid flow rates and pipe diameter. An expression was proposed to evaluate the required entrance length to form stable slugs,
§ u · lE = 40.6¨ M + 0.22¸ , ¨ gD ¸ D © ¹
(13)
Rearranging Eq. (13) results in an equation for the superficial liquid velocity at which the slug-churn transition occurs,
§l / D · uLS = gD ¨ E − 0.22 ¸ − uGS . © 40.6 ¹
(14)
Mishima and Ishii [6] suggested that just before the slug-churn transition, the nose of the following bubble touches the tail of the proceeding bubble and therefore, the liquid slug becomes too unstable to support the bridge between two consecutive Taylor bubbles due to the strong wake effect. This condition was mathematically described as when the mean void fraction, Įmean, within the entire flow reaches the void fraction within the slug-bubble section, Įbs, where, ª º gD ( ρ L − ρG ) « » ( C0 − 1) uM + 0.35 « » ρL » α bs = 1 − 0.813 « 1/18 » « 3 § · « u + 0.75 gD ( ρ L − ρ G ) ¨ ª« ρ L D ( ρ L − ρ G ) º» ¸ » M 2 ¨ ¸ « ρL µL ¼ ¹ »¼ ©¬ ¬
0.75
(15)
and,
αavg =
uGS C0uM + 0.35
gD ( ρL − ρG )
.
(16)
ρL
-54-
In the model proposed by Barnea [116] for the entire range of pipe inclination it was suggested that the slug to churn transition takes place due to the coalescence of bubbles within the liquid slug and, therefore, destruction of the liquid slug. Mathematically, it was described as when the average void fraction in the liquid slug reaches the maximum bubble volumetric packing, 0.52, and bubbles become close enough to each other to collide and coalesce. This model postulates that the gas bubbles in the liquid slugs behaves similar to bubbles in the dispersed flow regimes. Tengesdal, et al. [122] proposed a model based on the drift flux approach to predict the transition from slug to churn flow regimes,
α=
uGS 1.2uM + 0.35
gD ( ρL − ρG )
.
(17)
ρL
This work considered the void fraction of 0.78, which was experimentally observed by Owen [123], as the void fraction in which this transition occurs. By substituting α = 0.78 into Eq. (17) and rearranging, the resultant prediction of slug-churn transition is,
uLS = 0.0684uGS −
0.35 gD ( ρL − ρG ) . 1.2 ρL
(18)
McQuillan and Whalley [115] attributed the slug to churn transition to the flooding of the liquid film around a Taylor bubble in the slug flow regime. They employed the semiempirical correlation suggested by Wallis [124] to predict the gas and liquid flow rates at the flooding point in pipes, * 1/2 * 1/2 (uGS ) + m (uLS ) =C,
(19)
-55-
where the empirical constants m = 1 and 0.725 C 1 depend on the pipe entrance conditions. McQuillan and Whalley [115] considered C as 1. The dimensionless superficial *
*
velocities of the gas, uGS , and liquid, u LS , are defined as,
u *KS = u KS
ρK gD ( ρ L − ρ G )
K = G, L .
(20)
McQuillan and Whalley [115] proposed that the gas and liquid superficial velocities in the flooding model be replaced by the Taylor bubble superficial velocity, § 4δ ubS = ¨1 − D ©
gD ( ρ L − ρG ) · ·§ ¸, ¸ ¨¨1.2uM + 0.35 ¸ ρL ¹© ¹
and the liquid film superficial velocity,
(21)
uFS = ubS −uM . The film thickness, į, can be calculated
by Nusselt’s expression for a laminar falling film as, 1/3
§ 3uFS DµL · δ = ¨¨ ¸¸ . © 4 g ( ρ L − ρG ) ¹
(22)
Jayanti and Hewitt [125] identified the assumption of a laminar liquid film around the Taylor bubble as a shortcoming in the model by McQuillan and Whalley [115]. To address this concern, the superficial liquid film velocity,
uFS can be correlated to a constant film
thickness as a result of the balance between the effect of gravity on the liquid in the film and the wall shear forces for sufficiently long bubbles [126]. This can be expressed as [12, 120], 1/ CM
uFS
½ ° ° ° 4δ µL ° δ 1−CM = ® 1/3 ¾ D 4ρ L ° § · ° µL2 C ° K ¨ g ρ −ρ ¸ ° G)¹ ¯ © ( L ¿
,
(23)
-56-
where CM and CK were analytically determined to be 0.3333 and 0.9086 for laminar flow and recommended to be 0.6666 and 0.0682 for turbulent flow. As already mentioned, the value of C in the flooding model depends on the pipe entrance condition. Therefore, different C values were investigated to find the best model to predict the slug to churn transition. A value of C = 1 resulted in the best match compared with the experimental data points. Therefore, the following is proposed as the best model to predict the slug-churn transition, § ¨ ¨ µL ¨ ¨ ρ L gD 3/ 2 ∆ρ ¨ ¨ ©
1/ 2
δ 1/C
M
1/ C M
§ § µ 2 ·1/3 · ¨ CK ¨ L ¸ ¸ ¨ © g ∆ρ ¹ ¸ © ¹
§ ©
where ∆ρ = ( ρ L − ρG ) and αb = ¨1−
· ¸ ¸ ¸ ¸ ¸ ¸ ¹
1/2
§ ρG ρG · + ¨¨ 1.2u M α b + 0.35ε b ¸ gD∆ρ ρ L ¸¹ ©
= 1,
(24)
4δ · ¸ . The statistical analysis for this model as well as D¹
other models discussed in this section is summarised in Table 9.
6.3 Churn to annular flow transition: The transition to annular flow might be the most important transition to predict because this transition represents the transition from a liquid continuous phase to a gas continuous phase. Consequently, the pressure gradient undergoes a step change at this transition. Taitel, et al. [8] predicted the gas superficial velocity at which the churn to annular transition occurs as the minimum gas velocity required to prevent the entrained droplets from falling. Therefore, balancing the buoyancy and drag forces acting on a droplet results in, 1/4
§ σ g ( ρL − ρG ) · uGS = 3.1¨ ¸ . ρG2 © ¹
(25)
-57-
Mishima and Ishii [6] proposed the criteria for churn to annular transition based on two different mechanisms, namely flow reversal in the liquid film around large bubbles and destruction of the liquid slug or large wave that can be sustained as small droplets in a gas core. This mechanism is applicable to flows in large diameters pipes,
σ g ( ρ L − ρG ) Nµ−0.4
D>
L
( (1 − 0.11C0 ) C0 )
2
.
(26)
where, N µL =
µL
(
ρ Lσ σ g ( ρ L − ρG )
1/2
)
.
(27)
For small pipes, the following correlation was proposed to predict the transition from churn to annular flow regimes,
uGS =
gD ( ρL − ρG )
ρG
(α − 0.11) ,
(28)
where the void fraction needs to satisfy Eq. (15). For flows in large pipes where the second mechanism is applicable, the transition to the annular regime can be predicted by determining the onset of entrainment. Therefore, 1/4
−0.2
uGS > NµL
§ σ g ( ρL − ρG ) · ¨ ¸ . ρG2 © ¹
(29)
Lastly, McQuillan and Whalley [115] proposed an inequality to predict the existence of the annular flow regime by considering zero liquid superficial velocity in the flooding equation,
uGS
ρG gD ( ρ L − ρ G )
≥ 1.
(30)
-58-
6.4 Validation of the Existing Models In order to determine the most accurate theoretical model for each flow regime transition, the discussed models were assessed against the collated experimental results. Flow map data from co-current upward flows in pipes and annuli with diameters ranging from 12.3 to 67 mm were used for this assessment. To ensure consistency in the analysis, the physical fluid properties applied in each model are consistent with the experimental studies. Only through examination of the developed models against a large collated database is it possible to verify their effectiveness. This work has taken 20 experimental studies generating over 2500 data points in order to assess the transition models of Taitel, et al. [8], Barnea [116], McQuillan and Whalley [115], Mishima and Ishii [6], Tengesdal, et al. [122] and Eq.(24). The latter has been proposed in this work as an improvement for the slug to churn transition criterion proposed by McQuillan and Whalley [115]. To validate the models, the number of conforming and non-conforming points for each transition boundary was determined. In order to assess each experimental data point, a critical superficial liquid velocity was calculated for each given superficial gas velocity (or vice versa if a superficial gas velocity provided the transition criterion, for example in the churn-annular model by McQuillan and Whalley [115] given in Eq.(30). An example of the analysis can be seen in Figure 11, where all slug and churn data points in small pipes are shown first, along with the critical transition values using the model of Mishima and Ishii [6], before the filtering out of all conforming values as shown in Figure 11 (b). In this study, non-conforming points are those data points reported in the literature to be of one flow regime, but predicted to be another by a given transition model.
-59-
Figure 11: An example of the statistical analysis using the Mishima and Ishii [6] slugchurn transition model showing (a) the full experimental slug and churn regimes for pipe diameters smaller than 50 mm and (b) non-conforming points (i.e. slug flow observed in the region that predicted to be churn and vice versa).
-60-
Table 9 shows the results of this analysis, highlighting the best performing models for each flow regime. This statistical analysis shows that for the bubble-dispersed transition, Eq. (10) proposed by Barnea [116] produced the best results. For the bubble-slug transition, the same model used by both Taitel, et al. [8] and Barnea [116] given by Eqs. (3) and (4) outperformed the work of Mishima and Ishii [6]. The slug-churn transition presents a more challenging analysis with empirical constants often used for tuning purposes. Here, the model proposed by Taitel, et al. [8] is dependent on the L/D ratio. For the purposes of this analysis, a set ratio of 250 was assumed for all cases as this information was not often available in literature. This limits the validity of this particular transition criterion, and as such, the model proposed by Barnea [116] provides a more general solution. The modification proposed in this work for the model of McQuillan and Whalley [115] for the slug-churn transition improved the transition prediction from 69% to 76% of conforming data points. For the final transition from churn to annular flow, it was found that the model proposed by Mishima and Ishii [6] was able to best capture the experimental data. Figure 12 presents the best performing models overlain upon the collated experimental flow map data used for their assessment. Table 9: Analysis of conforming and non-conforming experimental data points for smallmedium and annuli pipes with respect to transition models discussed in Section 6. ŝƐƉĞƌƐĞĚ ďƵďďůĞƚŽ
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-62-
Figure 12: Comparison of the best flow regime transition models with the experimentally identified flow regimes. 7
Development of numerical methods for the prediction of flow regime transitions This review has demonstrated that multiphase flow in pipes and annuli is sensitive to a
number of material, geometrical, and operational parameters. This makes comprehensive experimental investigation of the relevant phenomena difficult. Further, many of the experimental studies that have been reviewed exhibit incongruent or contradictory findings. In spite of these challenges, a range of criteria has been developed for the description of the various multiphase flow regimes and their transitions, but these are constrained by their empirical basis.
-63-
Numerical methods represent one possibility for improving the description of the various regimes of multiphase flow in industrial-scale pipes and annuli. These techniques are typically founded in the discretisation of widely-accepted analytical systems of equations, which are then solved using computers. Prominent examples in engineering include the finite element method (FEM) for structural mechanics and computational fluid dynamics (CFD) for vehicle aerodynamics. Some of the major benefits of such numerical methods is that they are deterministic, readily able to explore a wide range of problem parameters, and relatively inexpensive to use once developed. As an extension to CFD, the use of computational multiphase fluid dynamics (CMFD) has become common practice in a number of industrial sectors such as nuclear, thermalhydraulics, and petrochemical [127]. This first started with the introduction and development of the two-fluid model (TFM) in the 1970 - 80s, which acted as a key driver in the removal of limitations associated with the use of empirically determined parameters for 1D modelling [128-130]. The use of high resolution 3D simulation has allowed for more accurate closure relations in 1D models and insights into transition mechanisms which had previously not been possible. Additionally, the development of interface tracking methods (ITM) provides researchers with the ability to further reduce modelling assumptions, particularly those associated with flow topology and momentum interactions between phases [131]. This section describes and presents examples of how numerous simulation methods have been applied to capture multiphase flow regimes and their development. A detailed description of the governing equations and their discretisation is not attempted here. For more information the interested reader is pointed towards texts such as those by Prosperetti [132] and Martin [133]. Instead, it is the intention that this section elucidates the potential for numerical methods to contribute to the state of knowledge in multiphase flows and highlights the aspects in need of further research. -64-
7.1 Numerical Methods The TFM has seen extensive use in commercial codes including OLGA [134] in the oil and gas industry or the more recent PeTra [135], as well as in general simulation software such as ANSYS Fluent and CFX. The method relies on phases being treated as interpenetrating continua [132], and in this sense, continuity equations for each phase are solved throughout a fixed, or Eulerian numerical domain. This can be expressed by weighted continuity equations [131],
∂t Įi ȡi +∇⋅ ( Įi ȡiui ) = 0 ,
(31)
∂t (αi ρi ui ) + ∇⋅ (αi ρi ui × ui ) = −αi∇p +∇⋅ (αiTi ) + αi ρi g + Fiinter
(32)
where, the subscript i indicates the phase (gas/liquid/oil) present in the system, ߙ is the void fraction of phase i with
¦α i
i
int er = 1 , and Fi represents the interfacial forces that are used to
couple interactions between phases. Additionally,
Ti represents the viscous stress tensor
while ࢛ ǡ ߩǡ and g represent the fluid velocity, density, pressure and gravitational acceleration, respectively. It is noted that closure relations need to be incorporated to account for the phase interactions including drag, lift, wall lubrication, virtual mass and turbulent dispersion forces within Fi
int er
. For a detailed description of the available correlations for
these forces, the reader is referred to [133, 136-138]. The ITMs discussed here are generally implemented on an Eulerian grid, however, these methods only solve one set of continuity equations. The ITMs can be divided further into volume-tracking or front-tracking methods. The volume-tracking methods were developed from the marker-and-cell approach proposed by Harlow [139]. In these methods, for example volume-of-fluid (VoF) [140], level-set (LS) [141] or Phase Field (PF) [142], an order parameter is advected through the flow field to track the location of each phase present in the -65-
system. Thus, the volume of each phase is effectively being tracked and the interface can be re-constructed from this information. These methods typically solve a single set of continuity equations weighted by the phase fraction or order parameter, which is tracked by a marker function of the form,
∂t Į + u ⋅∇Į = 0
(33)
The implementation of interfacial interactions, such as surface tension, on an Eulerian grid is performed via a volumetric force in the momentum equation to account for the likelihood of the interface location to be ‘off-grid.’ In this sense the force is applied to a regularised region about the interface, rather than as a force at the interface point only. There are two ways in which the surface tension force can be derived. Firstly, one can consider a geometric argument, in which the force acts to minimise the interfacial area. Alternatively, one can also look at the system from a chemical potential perspective in which the force acts to minimise the free energy functional of the system [142]. In addition to the previously mentioned TFM (also referred to as the Euler-Euler approach or multifluid model if more than two phases are present) and interface tracking techniques, another important class of two-phase solvers is the Euler-Lagrange method. Here, the dispersed phase is no longer captured on an Eulerian grid, but the position of each particle or bubble is tracked and propagated using Newton’s laws of motion. The behaviour of the individual bubbles is then coupled to the bulk media, which is solved through the Reynoldsaveraged Navier Stokes (RANS) equations. The bulk media can be resolved with varying techniques including the finite volume and lattice Boltzmann methods [143]. In multiphase pipe flows, various flow regimes are observed in which the gas-liquid interface acquires characteristic topologies that affect the phase interactions. As such, the traditional form of methods such as the one-, two- or three-dimensional TFM, which require -66-
correlations to describe the phase interactions, become dependent on the flow regime [144]. This means that a priori knowledge is required to describe how the flow will manifest before predictions and or simulations are conducted and, therefore, the importance of flow regime maps is realised. Contrary to this, recent works have developed hybrid models that effectively couple the TFM with either a population balance model (PBM) or an ITM in an attempt to eliminate the dependency on prior knowledge of the flow regime. The commercial CFD code, CFX for example has implemented an inhomogenous multiple size group (MUSIG) model [145-147] that has been reported to capture flow regimes consistent with the work of Taitel, et al. [8] on vertical co-current flow. One criticism of experimentally generated flow maps is the level of subjectivity that arises in determining the current flow regime. To cater for this, Krepper, et al. [147] looked to use more objective criteria when analysing co-current vertical flows by measuring the bubble size distributions and radial gas volume fraction profiles. This was performed in both their experimental setup and CFD simulations. They were able to show that their model could quite accurately capture bubble size distributions correlating to the transition from bubble to slug flow. Parvareh, et al. [148] used the VoF technique to capture the liquid-gas interface development in co-current flow for both horizontal and upwards vertical flow configurations. Experimental work was performed in small diameter pipes of 2 cm diameter and 4 m length. In the tested cases, the researchers were able to qualitatively match simulation and experimental results for slug, churn and annular flows, but only a limited discussion of the numerics was given. Dakshinamoorthy [149] followed the approach of coupling the TFM with the VoF technique to analyse flow in a large vertical pipe (ID of 189 mm) with a superficial liquid velocity of 0.05 m/s and varying superficial gas velocities from 0.1 to 1.0 m/s. In this study, -67-
the authors were able to qualitatively identify flow regimes consistent with experimental results and without the need for pre-identification. It is noted that slight trouble in identifying a pure bubble regime was observed, with small regions of high void fraction possibly indicating a move to intermittent slug flow, again highlighting the difficulty that can arise in determining specific transition points. Quantitatively the same study compared both pressure drop and void fraction profiles for the slug and annular flow cases that showed reasonable agreement with experimental measurements. The following sections discuss the aforementined simulation techniques for simulation of different flow regimes.
7.2 Bubbly Flow Modelling of dispersed bubbly flow in pipes is typically approached using either the TFM or an Euler-Lagrangian technique. In order to model this flow regime with an ITM alone, a high-resolution grid is required to fully resolve the bubble motion which leads to excessive computations for practically sized scenarios. However, this approach is often used for direct numerical simulation (DNS) of a finite number of bubbles in order to derive correlations also known as closure models, for the interfacial forcing terms, such as drag and lift. These forces need to be modelled as sub-grid-scale interactions in both the TFM and Euler-Lagrange methods [138, 150, 151]. The TFM was validated by Rzehak and Krepper [152] against experimental void fraction and mean fluid superficial velocities of the bubble flow regime in upward flows through ANSYS CFX. It is noted that extensive validation with experimental data is still required for closure models under a wide range of flow conditions (e.g. counter-current flows) and configurations (e.g. inclined or annular pipe geometry, different pipe sizes). This can
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potentially limit the TFM, but the possibility of formulating these correlations from CFD experiments is one option to streamline the process.
7.3 Slug Flow Capturing the bubble to slug regime transition can be quite complex using the TFM as the bubble size tends to be predefined in order to apply closure models. Therefore, MUSIG solvers along with PBMs have been developed to account for bubble coalescence and breakup. Such models were used by Lucas et al. [146] and further developed by Das et al. [153] to simulate the transition from bubbly to slug flow regimes in upwards vertical pipes and annular geometries, respectively. These studies highlighted the importance of capturing the radial position of different sized bubbles in predicting the transition point as a function of pipe length over diameter. The simulation results showed that small bubbles moved closer to the wall, but after coalescence they shifted towards the centre of the pipe. The application of ITMs such as the VoF, LS and PF techniques have been utilised in the literature to resolve the shape, velocity and liquid film parameters of Taylor bubbles to assist in the understanding of the slug flow regime. Additionally, these techniques have been used to analyse the wake region of the liquid slug in which smaller bubbles are typically found. Taha and Cui [154] used the VoF technique within the ANSYS CFX platform to analyse all of these parameters. They used a vertical pipe with a 19 mm diameter and concluded ranges of dimensionless numbers for which varying shape profiles, rise velocities and wake behaviour could be expected. In the study, the bubble rise velocity, in the form of the bubble Froude number, was shown to be a function of the surface tension. The results were consistent with experimental data from the literature with Eötvös numbers ranging from five to 500. Additionally, the inverse viscosity number (ܰ ) was found to be correlated to the length of the bubble wake, with numerical results presented for ܰ between 100 and -69-
750.These such relations can be essential to close the system of equations in 1D mechanistic models.
7.4 Churn/Annular Flow With a continued increase in gas velocity, Taylor bubbles become unstable and the flow within a pipe breaks down into the churn regime. Da Riva and Del Col [155] used the VoF technique and the ANSYS CFX simulation software in order to simulate the churn flow regime and its transition mechanisms in small diameter pipes (ID of 32 mm). Deforming bubbles in the churn flow regime introduce a great level of complexity in modelling via the TFM due to the lack of robust closure models for this regime. A DNS approach is also complicated due to the variation in bubble size and the requirement of a finely-resolved solution to capture the break-up of small bubbles. Montoya et al. [156] proposed that perhaps a hybrid model would be effective to capture the sub-grid-scale behaviour, however, this required the development of accurate break-up and coalescence models. Further increase in gas flow leads to the annular flow regime in which gas flows in the core of the pipe carrying entrained liquid droplets and surrounded by a thin liquid film. A simplified view of annular flow tends to be particularly well suited for interface tracking methods with a high level of separation. However, similar to the churn flow regime, there is a range of scales evident in the system and to accurately capture the behaviour of entrained droplets would require a high computational grid resolution using an ITM alone. Such a problem was addressed by Liu, et al. [157] where a two-phase, two-component numerical model was proposed to analyse vertical upwards annular flow in a small diameter pipe (ID of 31.8 mm). This study used a two-fluid-type mixture model in the gas core and a VoF method to differentiate the gas core from the liquid film. Good predictions were found for the pressure gradient, wall shear stress, film thickness and the film flow flux and the parameters
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associated with the wave-like behaviour in the liquid film. This presents an interesting technique for capturing the various scales present in two-phase flows, however, a complete understanding of deposition and entrainment of liquid droplets is required for varying flow configurations. Despite a large body of existing literature in the simulation of flow regimes, complete validation of these models across a large range of flow geometries has not yet been achieved. This indicates potential work in the future to develop either robust coupling methods to capture bubble size of varying scales or improved closure relations to model the complex phase interactions. 8
Conclusions and outlook
This critical review of the published experimental data for gas-liquid flow maps in vertical pipes and annuli has highlighted the complications behind the accurate prediction of two-phase flow regime. Examination of the experimental methods adopted for the identification of bubbles, slug, churn and annular flow regimes identified subjectivity as being the greatest hindrance to the acquisition of reliable results. Measurement tools may also impede upon the development of flow phenomenon, and so objective, non-intrusive and noninvasive measurement techniques are required. However, this may be unachievable and a more feasible approach is to adopt multiple measurement techniques for validation. Review of the critical factors of pipe geometry (diameters, deviation from vertical), fluid properties (density, viscosity, interfacial tension, salinity) and flow conditions found that the effect of liquid viscosity upon flow transitions is a polarising topic with plenty of room for clarification. Alternative flow map coordinates were tested in an attempt to create a universal map which can be applied to any industrial application regardless of fluid type and experimental conditions.
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Transition criteria were assessed against a large collated data set consisting of over 2500 flow map data points from 20 experimental studies of co-current upward flows in vertical pipes and annuli of diameters ranging from 12.3 to 67 mm. The statistical analysis identified the most reliable flow regime transition models as being: (i) Barnea [116] for dispersed bubble to bubble flow, (ii) Taitel, et al. [8] for bubble to slug flow, (iii) Barnea [116] for slug to churn flow, and (iv) Mishima and Ishii [6] for churn to annular flow regime. Although an abundance of experimental flow regime studies have been reviewed, it is observed that important information regarding the flow regimes is often ignored. In particular, the void fraction, or gas holdup, that is considered in developed transition criteria is rarely documented. Future experimental work should take into consideration the inputs required for computational modelling, thus improving comparability and the validation of results. Computational fluid dynamics techniques also need to be further developed in order to capture the complex behaviour of individual bubbles and thus better understand the interaction between the gas and liquid phases in different flow regimes.
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Nomenclature
Ap
Projected bubble area (m2)
* uKS
Dimensionless phase superficial velocity
C
Empirical constant
uLS
Liquid superficial velocity (m/s)
CK
Empirical constant
* u LS
Dimensionless liquid superficial velocity
CM
Empirical constant
uM
Mixture superficial velocity (m/s)
C0
Approximate ratio of centreline
u∞
Rise velocity of fairly large bubbles
velocity to average velocity
(m/s)
(dimensionless)
D
Pipe inner diameter (m)
Greek symbols
Db
Bubble diameter (m)
α
Void fraction (dimensionless)
DC
Casing inner diameter (m)
αavg
Average void fraction (dimensionless)
Dcritical
Critical pipe inner diameter (m)
αb
Bubble void fraction (dimensionless)
DH
Hydraulic diameter (m)
α bs
Bubble-slug void fraction (dimensionless)
DT
Tubing outer diameter (m)
αmean
Mean void fraction (dimensionless)
D32
Sauter mean bubble diameter (m)
δ
Liquid film thickness (m)
Fi inter
Interfacial forces (N/m2)
εc
Critical void fraction (dimensionless)
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HL
Liquid holdup (dimensionless)
µG
Gas viscosity (mPa.s)
lE
Entry length (m)
µL
Liquid viscosity (mPa.s)
m
Empirical constant
µS
Liquid specific viscosity (dimensionless)
N µl
Liquid viscosity number
ρG
Gas density (kg/m3)
sG
Gas specific density
ρH
Homogenous or no-slip density (kg/m3 )
ρL
Liquid density (kg/m3)
(dimensionless)
sL
Liquid specific density (dimensionless)
SL
Slippage number (dimensionless)
ρM
Mixture density (kg/m3)
Ti
Viscous stress tensor
σ
Surface tension (N/m)
σS
Liquid specific surface tension
(dimensionless)
U0
Bubble rise velocity (m/s)
(dimensionless)
UG
Taylor bubble rise velocity (m/s)
Non-dimensional parameters
ubS
Taylor bubble superficial velocity
FrM
= uM / Dg
ReGS
=
ρGuGS D µG
ReLS
=
ρLuLS D µL
(m/s)
uFS
Liquid film superficial velocity (m/s)
uGS
Gas superficial velocity (m/s)
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* uGS
Dimensionless gas superficial
WeGS
velocity
uKS
Phase superficial velocity (m/s)
WeLS
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=
2 ρGuGS D σ
2 D ρLuLS = σ
Acknowledgements
This project received industry funding through The University of Queensland’s Centre for Coal Seam Gas (www.ccsg.uq.edu.au). TM would like to acknowledge the support of the Australian Government Research Training Program Scholarship during the development of this work. References
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[148] A. Parvareh, M. Rahimi, A. Alizadehdakhel, A.A. Alsairafi, CFD and ERT investigations on two-phase flow regimes in vertical and horizontal tubes, International Communications in Heat and Mass Transfer 37 (2010) 304-311. [149] D. Dakshinamoorthy, Dai, Y., Agrawal, M., CFD Modeling of Bubbly, Slug and Annular Flow Regimes in Vertical Pipelines, Offshore Technology Conference, 6-9 MayHouston, Texas, USA, 2013, pp. OTC-24245-MS. [150] A. Tomiyama, Zun, I., Sou, A., Sakaguchi, T., Numerical Analysis of Bubble Motion with the VOF Method, Nuclear Engineering and Design (1993) 141(141-142), 169-182. [151] K. Sankaranarayanan, Shan, X., Kevrekidis, I.G., Sundaresan, S., Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method, Journal of Fluid Mechanics (2002) 452, 461-496. [152] R. Rzehak, Krepper, E., Closure models for turbulent bubbly flows: A CFD Study, Nuclear Engineering and Design (2013) 265, 701-711. [153] A.K. Das, Das, P.K., Modelling bubbly flow and its transitions in vertical annuli using population balance technique, International Journal of Heat and Fluid Flow (2009) 31, 101114. [154] T. Taha, Cui, Z.F., CFD modelling of slug flow in vertical tubes, Chemical Engineering Science (2006) 61(62), 676-687. [155] E. Da Riva, Del Col, D., Numerical simulation of churn flow in a vertical pipe, Chemical Engineering Science (2009) 64(17), 3753-3765. [156] G. Montoya, Lucas, D., Baglietto, E., Liao, Y., A review on mechanisms and models for the churn-turbulent flow regime, Chemical Engineering Science (2015) 141, 186-103. [157] Y. Liu, J. Cui, W.Z. Li A two-phase, two-component model for vertical upward gasliquid annular flow, International Journal of Heat and Fluid Flow (2011) 32(34), 796-804.
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Appendix
Flow maps of co-current upward vertical flows in pipe of diameters between 12.3 and 67 mm plotted with alternate coordinates as presented in Table 7.
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Highlights
• • •
Critical review and analysis of 3947 flow regime data points for vertical flows. Assessment of the available models for prediction of upward flow regime transition. Generation of a universal flow map for upward flows based on Reynolds numbers.
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S1385-8947(17)30893-8 http://dx.doi.org/10.1016/j.cej.2017.05.135 CEJ 17034
To appear in:
Chemical Engineering Journal
Received Date: Revised Date: Accepted Date:
16 March 2017 20 May 2017 22 May 2017
Please cite this article as: B. Wu, M. Firouzi, T. Mitchell, T.E. Rufford, C. Leonardi, B. Towler, A critical review of flow maps for gas-liquid flows in vertical pipes and annuli, Chemical Engineering Journal (2017), doi: http:// dx.doi.org/10.1016/j.cej.2017.05.135
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A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
Benjamin Wu a,†, Mahshid Firouzia, †,*, Travis Mitchellb, Thomas E. Rufforda, Christopher Leonardib and Brian Towlera
a.
School of Chemical Engineering, The University of Queensland St. Lucia 4072 Australia b.
School of Mechanical and Mining Engineering, The University of Queensland St. Lucia
4072 Australia †
First authors
*
Email: [email protected]
Abstract The accurate prediction of two-phase gas and liquid flow regimes is important in the proper design, operation and scale-up of pressure management and fluid handling systems in a wide range of industrial processes. This paper provides a comprehensive review of 3947 published experimental data points for gas-liquid flow maps in vertical pipes and annuli, including a critical analysis of state-of-the-art measurement techniques used to identify bubble, slug, churn and annular flow regimes. We examine the critical factors of pipe geometry (diameters, deviation from vertical), fluid properties and flow conditions that affect the transition from one flow regime to another. The review surveys the theoretical models available to predict flow regime transitions, and we validate the accuracy of these models using the published experimental data. The most reliable flow regime transition models for upward co-current flows are analytically shown to be: (i) Barnea 1987 for dispersed bubble to -1-
bubble flow, (ii) Taitel, Bornea and Dukler 1980 for bubble to slug flow, (iii) Barnea 1987 for slug to churn flow, and (iv) Mishima and Ishii 1984 for churn to annular flow regime transition. Moreover, based on the review we provide an outlook on the research needs and important developments in prediction of two-phase flow in vertical pipes including the use of computational fluid dynamics (CFD) techniques to simulate gas-liquid flows in vertical geometries. Keywords: experimental, vertical, flow regime, flow map, regime transition, CFD
1
Introduction Gas and liquid are required to flow simultaneously inside vertical pipes and vertical
annuli in a wide range of industrial and engineering processes. Two-phase gas and liquid flows manifest in steam boilers, condensers, chemical reactors and associated process piping [1-4] in petrochemical plants, food-processing plants and in nuclear energy facilities [5, 6]. The proper design and operation of these two-phase fluid systems requires accurate prediction of pressure drops in the system, and that prediction relies on understanding the nature of the flow regimes that could manifest in a two-phase system. This review paper surveys the published experimental data and mathematical models that describe two-phase flows in (a) vertical pipes and (b) vertical annuli, which is a pipe geometry of significant interest in pumped coal seam gas (CSG, or coal bed methane CBM) wells [7]. When gas and liquid flow in a pipe or conduit several flow regimes can result depending on the pipe geometry, fluid properties, volume fractions and velocities of each phase [2]. In vertical pipes, the most commonly described flow regimes are bubble, slug, churn and annular flows as illustrated in Figure 1 [6, 8, 9]. When both gas and liquid flow velocities are -2-
low (for example superficial liquid and gas velocities less than approximately 0.1 and 1 m/s respectively for co-current upward flows of air-water), the dominant flow regime will be bubble flow with individual gas bubbles dispersed in a continuous liquid phase. A number of studies [8, 10] have also documented a dispersed bubble flow regime at high liquid velocities/flow rates, which can produce large turbulent forces and inhibit bubble coalescence. An alternate theory is that the existence of bubble flow regime at high void fractions is due to the inlet conditions that are determined by the sparging device [11]. For co-current upward air-water flows in a vertical pipe, Taitel, et al. [8] showed that the bubble flow regime exists up to void fractions of 0.25 whilst suggesting that the dispersed bubble flow regime is present up to void fractions of 0.52 at higher liquid flow rates. Increasing the gas velocity results in the slug flow regime where, bubbles coalesce to form large gas bubbles, called Taylor bubbles, which occupy the entire cross section of the pipe except for a thin liquid film on the wall. A further increase in gas velocity can collapse the slugs and lead to an unstable flow that is described as the churn regime due to the large degree of turbulence in the flow. The fourth main flow regime, annular flow, can develop once the gas velocity is sufficiently high to form a continuous gas column flowing in the centre of the pipe. This column pushes the liquid into a film at the pipe wall and entrained liquid droplets in the gas core. There also exists flooding at very high gas or liquid flow rates, that presents the limit of counter-current flow, beyond which the system will transition to co-current flow [12]. Alternatively the flow regimes have been described as homogenous (bubble flow regime) and heterogeneous (slug and churn flow regimes) mainly in bubble columns [13].
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Figure 1: Illustration of the four main flow regimes that can manifest when gas and liquid flow upward and co-currently in a vertical pipe, namely (a) bubble, (b) slug, (c) churn, and (d) annular. Direct observation and identification of flow regimes in pipes of industrial plants is difficult as almost all these industrial fluids flow in steel pipes and often at high pressures and or temperatures. Therefore, most experimental observations of gas-liquid flow regimes have been collected in controlled laboratory conditions with transparent pipes or pipes with inset observation windows, or in recent studies advanced phase detection approaches which are discussed in Section 2. To translate the results of laboratory experiments to industrial scale applications, various published flow maps attempt to predict flow regimes based on superficial gas and liquid velocities [12] and theoretical correlations have been described to model the transitions between flow regimes. Although plenty of transition criteria have been developed, an accurate universal map of gas-liquid flow patterns has yet to be achieved [14].
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Therefore, integration of the available experimental flow regime data to a generalised flow map is of great importance. There have been several reports of different approaches to develop flow maps based on dimensionless parameters other than just superficial velocities. These approaches attempt to account for the effect of factors such as fluid density, viscosity, surface tension, and pipe geometry within their proposed flow map systems [15-22]. However, there are two significant limitations to application of these currently available flow maps. First, most of the published flow maps are synthesised from datasets that included less than 20% of the relevant studies now available publicly. Second, the vast majority of experimental and modelling studies have focussed on flow in horizontal (or near horizontal) pipes, which behave differently from vertical flows due to the influence of gravity. This paper presents an update and validation of existing flow maps for gas and liquid flow in vertical pipes and annuli (co-current and counter-current flows), incorporating 3947 experimental data points from 35 studies. We begin in Section 2 with a survey of the experimental techniques used to identify flow regimes. In Sections 3 and 4, the available data sets for gas-liquid flow experiments in vertical pipes and annuli are summarised, respectively. A range of non-dimensional parameters is used in Section 5 to evaluate flow maps. Section 6 reviews the mathematical models available for the prediction of flow regime transitions and Section 7 introduces computational fluid dynamics as a potential means of improving these predictions. Finally, Section 8 summarises the work presented along with an outlook to future research. 2
Survey of experimental techniques used to identify flow regimes Experimental studies on two-phase flows in vertical pipes often utilise more than one
measurement technique. Reasons for this may include confirmation of results and reassurance, comparison of techniques, and the desire to examine multiple parameters or properties. Flow regimes can either be identified through direct observation or indirect -5-
determination [23]. Direct observation involves the researcher visually interpreting an image of the flow to categorise it into a flow regime. Indirect or analytical determination is a twopart process. The researcher must firstly utilise a reliable experimental methodology to accurately measure characteristic flow parameters. This flow characteristic must then be objectively analysed to determine the flow regime [24]. This review finds that the most common practices for flow regime identification have been visual observation and analysis of void fractions. A summary of the various methods that have been adopted in the collated published experimental works, documented in Sections 3 and 4, is presented in Table 1. Subjectivity is perhaps the greatest issue when identifying flow regimes. Flow regime discrimination through visual observation, even with the aid of high speed cameras, is at the discretion of the researcher or operator. Even more advanced techniques based on flow characteristics such as void fractions that are inserted into Probabilistic Density Functions (PDFs), which intend to reduce subjectivity, still require the researcher to define the conditions at which each flow regime exists. This results in a level of subjectivity being retained. Delineation of flow regimes is further complicated by the transitions as the progression from one flow regime to the next is not instantaneous, rather it develops through intermediate regimes that exhibit mixed characteristics [25]. The axial location at which measurements or observations are made is an important factor that has seemingly been ignored in many of the examined experimental works. Sufficient flow time, and hence distance, must be permitted in order for the desired two-phase flow phenomena to fully develop. Studies have confirmed that the axial location of conductance probes had a significant influence on the adjudication of flow regimes [26-30]. This error is not exclusive to probes and is also applicable to all other flow regime identification and observation equipment.
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Consideration must also be given to the physical impacts of the selected measurement technique. The physical presence of the tool may impede on and thus directly impact the experimental flow path. This is of particular concern with flow in annulus as the available flow path is already limited. Sensors and their physical influence can be described as invasive or intrusive with Figure 2 illustrating their differences. An invasive device requires direct contact with the experimental medium whilst an intrusive device must be located within the experimental medium, impeding the flow path. The use of invasive electrodes may also lead to issues with corrosion and polarising effects [31]. For experimental studies on two-phase flows, avoiding both of these characteristics is highly recommended. The inlet conditions for two-phase flow experiments are determined by the adopted sparger design. A sparger disperses the gas flow into the test section as bubbles, ideally allowing for the development of flow regimes. Exclusion of a sparger results in influxes of large air bubbles into the system. It has been found in bubble columns that the sparger design and sparger hole diameters directly impact upon the gas holdup curve of the system [32-34]. The gas holdup curve describes the relationship between the gas holdup and superficial velocity, and can influence the flow regime that ensues. Mudde, et al. [11] examined uniform flows in bubble columns and reported that only a limited number of publications reported well defined and controlled inlet conditions. A similar observation is made in this review with only a limited number of the examined studies detailing the experimental inlet conditions, and so no comparisons could be made regarding their impact on flow regimes. Perhaps the most prohibitive limitation of all is the cost of the equipment required to facilitate the desired experimental method for identifying flow regimes. The compromise between simplicity, accuracy and affordability must often be managed by a research team in order to meet their objectives.
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Figure 2: Intrusive and invasive sensors, modified after Abdul Wahab, et al. [31].
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Table 1: Classification of experimental techniques used to identify flow regimes in gas-liquid systems. Method
Instrument types
Flow regime identification process
Visual
- Researcher observation
The flow regime is visually determined at the behest of the researcher
Observation
- Still photography
using either the naked eye or aided by some form of imagery.
- High speed camera - X-ray tomography Gas Holdup or Global Void Fraction
Image analysis - X-ray tomography
Measurement
Flow regimes are analytically determined using a Probabilistic Density Function of the measured void fractions. In this process, X-ray tomography is used to capture void fractions via image analysis rather than providing
- Neutron radiography imagery directly for visual delineation of the flow regime. - Electrical impedance tomography - Double wire mesh sensors Volumetric measurement - Quick-closing ball valve technique
The quick-closing ball valve technique physically captures the volume of liquid inside the test section, allowing for a direct measurement of the void
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fraction.
Local Void Fraction Measurement
- Conductance probes - Wire mesh sensor
Local flow regimes are analytically determined using a Probabilistic Density Function of the measured local void fractions. The global flow regime is subsequently determined from a combination of the local flow regimes.
Differential Pressure Measurement
- Differential pressure sensors
Differential pressure measurements can be used to determine flow regimes due to the differing densities, and hence pressure, exerted by the gas and liquid phases. Alternatively, the differential pressure measurements can be used to find volume averaged void fractions to then be analysed using a Probabilistic Density Function to determine the flow regime.
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2.1
Visual observation Visual observation, a direct measurement technique, is the simplest and most commonly
used method of identifying flow regimes and is believed to have been first attempted around 1960 [35, 36]. This is perhaps the most subjective approach with results determined at the discretion of the researcher thus resulting in very low levels of repeatability and replicability by others. Hewitt and Roberts [9] saw X-rays as a natural extension of visible light photography but this technique was not widely adopted by future researchers. This is likely due to advances in technology and the relatively long exposure times, comparative to photography, as well as safety requirements. Previous works have attempted to mitigate the issue of subjective visual interpretation in flow regime identification by including photographs or illustrations of the observed flow regimes. This is not an effective approach as results from these studies cannot easily be compared against one another. Although visual inspection cannot provide an objective classification of flow regimes, it is still a useful complement to modern techniques as it is simple, cost effective, non-intrusive and noninvasive. Photographs and high speed cameras can also be used to aid and improve the visual inspection process. High speed cameras are those with a frame rate greater than 250 frames per second [37]. Software is also available to analyse the documented flow patterns and calculate physical parameters such as bubble size and velocity [38]. Around 1980 the use of statistical parameters, specifically void fractions, was introduced as a means of identifying flow regimes. Analysing these parameters with Probability Density Functions (PDFs) allowed for identification of flow regimes from experimental data. Figure 3 presents typical plots of slug, churn, and annular flow classified using the PDF of time varying flow fraction in accordance with the rules set by Costigan and Whalley [39]. However, the rules regarding identification of flow regimes using the statistical parameters are at the behest of the researcher, retaining the possibility of a subjective analysis as well as -11-
complications when comparing results between studies [27]. Comparison with high speed video has found the PDF approach performs poorly when delineating between slug and churn flows but this is effective at discriminating between churn and annular flow regimes [40].
Figure 3: Typical Probabilistic Density Function (PDF) plots, sourced from OmebereIyari and Azzopardi [40]. The introduction of Artificial Neural Networks around 1990 is seen as a significant advance in the objective identification of flow regimes [41-43]. A much more objective process was achieved by classifying the flow regime indicators, obtained using non-intrusive impedance probes, with the Kohonen Self Organising Neural Network (SONN) [24]. SONN classification was originally performed using the PDF of the void fraction, Į, signals as an indicator. However, this approach had a major drawback in that a long period of observation was required to obtain reliable statistical parameters of the void fraction signal. This was later improved when the Cumulative PDF (CPDF) of the impedance void meter signals was used by Lee, et al. [44]. The CPDF is more stable due to it being an integral parameter and is also faster than the PDF methodology as it requires less input data. 2.2
Gas Holdup or Global Void Fraction In gas-liquid two-phase flow, the gas or liquid hold-up is the fraction of the available flow
channel volume occupied by the respective phase. Gas holdup is synonymous with the global
-12-
void fraction [45]. Recorded void fractions enable the use of PDFs in delineating between flow regimes [46-48]. One of the first approaches to capture void fractions and interpret flow regimes was to use tomography. A linearised X-ray system was employed by Jones and Zuber [46] to inspect flow regimes using void fraction fluctuations. However, the safety requirements necessary for the safe and proper handling of radiation are a major hindrance in the application of such techniques. Mishima and Hibiki [49] later used neutron radiography and image processing to measure void fractions. The process involved using aluminium alloy tubes to allow for a neutron beam to perpendicularly penetrate the pipe. This neutron beam was proportionately attenuated by the encountered hydrogen within the water phase along its path and able to project an image of the residing two-phase flow that could then be converted to an optical image [50, 51]. Schmidt, et al. [52] employed a gamma ray system following the same basic principles. Yamaguchi and Yamazaki [5] and Caetano, et al. [53] elected to use the quick-closing (ball) valve technique, with Caetano, et al. [53] reporting excellent repeatability in the obtained liquid hold-up measurements. This technique involves incorporating two valves at either end of the test section. The valves are closed and flow is diverted to a by-pass pipe when the desired flow rates have been reached and steady-state conditions have been established. Measurement of the enclosed liquid volume yields the liquid holdup when compared to the total available channel volume. The addition of markings to the outside of the test section can allow for a simple means of attaining the liquid volume once it has settled. Alternatively, the liquid can be drained and measured. In a two-phase flow the remaining volume is occupied by gas and hence the gas holdup or global void fraction is also obtained. The use of ball valves in pipe test sections is recommended due to the circular geometrical configuration. Inaccuracies in this method arise from potential changes to the -13-
flow pattern during the closing of the valves. It is also necessary to stop and restart the test for each desired set of flow rates which can be very time consuming. The effect of pressure upon the compressible gas phase has not been acknowledged in these studies and may influence the void fraction measurements acquired using this technique. Schlegel, et al. [54] and Smith, et al. [55] determined void fractions using electrical impedance tomography through electrical impedance void meters, shown in Figure 4(a). This technique is dependent on the electrical impedance of the gas-liquid phases and requires simultaneous measurements at multiple locations along the test section to obtain a global void fraction. A voltage output is acquired at each measurement area and then related to a void fraction in a relatively complex manner which is dependent on the existing flow pattern. Since the flow pattern must already be known, pressure differential measurements are also required in order to initially identify the flow patterns. The electrical impedance void meters can then be cross-calibrated against the differential pressure void fractions. This process was developed by Mi, et al. [56]. Schlegel, et al. [54] reported overall relative errors in the resultant void fraction measurements of less than 10% for void fractions between 0.2-0.4 and less than 5% for void fractions greater than 0.4. The accuracy of this technique was also reported by Prasser, et al. [57] to be 5% void fraction. This approach has a greater level of complexity but is non-intrusive, and does not obstruct the flow channel which would risk affecting the flow pattern.
-14-
Figure 4:Apparatus used in electrical impedance tomography, including (a) arch-type electrical impedance void meter [54] and (b) wire mesh sensor [58]. Wire mesh sensors are a form of electric resistivity tomography and another means of measuring void fractions that is also capable of reconstructing the three-dimensional structure of a two-phase flow. This is achieved with double wire mesh sensors that can also be used to calculate bubble velocity and total interfacial area concentrations from the measured bubble shapes. The sensor is able to operate using conductivity or permittivity based on the selected gas-liquid combination, typically air-water or air-oil respectively. Figure 4(b) displays the -15-
wire electrodes that are orthogonally positioned across two planes of the flow cross-section. The set of wires in one orientation act as electrical transmitters whilst the other set acts as electrical receivers. Conductivity or permittivity is measured within the gaps by alternately sending an excitation voltage to each of the sender electrodes [58]. The accuracy of this technique was reported to be 1-4% of the area-averaged void fraction [57]. Rapid calculations are possible with this tool, however, resolution is limited to approximately 3 mm [30]. Another significant concern regarding this measurement technique is the invasive and intrusive nature of the wire mesh sensors. Wire mesh sensors have been found to distort the shape of Taylor bubbles at low liquid flow rates and tend to underestimate the gas fraction in large bubbles. The two main intrusive effects are bubble break-up and bubble deceleration [59]. It must be noted that gas holdup can be influenced by the experimental setup used in the studies. The gas holdup curve, describing the relationship between the gas holdup and gas superficial velocity, is dependent upon the selected air sparger design and hole sizes [32-34]. 2.3
Local void fraction Juliá, et al. [24] conceptualised a means of identifying the Global Flow Regime (GFR)
using simultaneously obtained Local Flow Regime (LFR) data from three radially distributed local conductivity probes. A LFR identifies the flow regime present in a specific cross section of the flow path at a given moment in time where as a GFR describes the flow regime occurring throughout the system or pipe section. Combinations of the three local signals corresponded to different GFRs. The majority of two-phase flow experiments are conducted using air-water as the gas-liquid phases due to their convenience and safety. This allows for local void fraction measurements using the conductance technique. Conductance probes are invasive sensors that can provide estimates of local void fractions because tap water is electrically conductive whilst air is essentially resistant. Pure water is also essentially -16-
resistant and would not work in such experiments. Local void fractions are limited to one point in the test apparatus and so multiple probes or measurements are required. Once the relationship between electrical impedance and phase distribution has been established, the cross-sectional averaged void fraction can then be estimated [40]. Prasser, et al. [57] reported the accuracy of conductivity probes to be 5% void fraction. Optical fibre probes operate similarly to conductance probes but rely upon differences in refractive index rather than conductivity to measure local void fractions [60]. However, no studies have been seen to use optical fibre probes for the identification of flow regimes. Ghosh, et al. [61] compared the efficiency of parallel wire conductivity probes and ring conductivity probes in a vertical pipe, as shown in Figure 5. It was experimentally determined that the parallel wire probe is capable of identifying individual flow regimes whilst the ring probe is not. This was due to the geometric configuration of the ring probe wherein both of its electrodes are flush mounted on the walls of the pipe. Thus, throughout all of the different flow regimes, the ring probes were always partially or fully submerged in water and showed little variation in conductivity. So, in order for conductance probes to properly identify flow regimes they must be intrusive in addition to being invasive. Smith, et al. [55] stated that there are generally two main sources of uncertainty regarding the use of conductivity probes, namely the probe structure itself and the deformation of the interfaces of large bubbles on contact with the probe. Wire mesh tomography is a similar approach that utilises single layer wire mesh sensors to capture local void fractions. A study comparing the results of wire mesh tomography with an optical, or visual, method found theirs accuracies to be within 10% of one another [59]. This study was limited to the bubble flow regime and concluded that the accuracy of wire mesh tomography in counter-current flow is in the same order of magnitude as for stagnant and co-current bubble flow.
-17-
Figure 5: (a) Parallel wire conductivity probe and (b) ring conductivity probe, sourced from Ghosh, et al. [61]
2.4
Differential pressure measurement The physical mechanisms controlling pressure drop are intrinsically linked to local flow
patterns [2]. This makes differential pressure measurements an alternative flow characteristic to void fractions for identifying flow regimes. It must be noted that in experimental works, pressure measurements may be complicated by the potential presence of trapped gas within the pressure lines [24]. This can directly affect the pressure readings and hence the flow regime delineation. Differential pressure measurements can be also used to determine void fractions. The differential pressure method for determining volume-averaged void fractions is well known for its low cost, simplicity and ruggedness and is a viable option for the cross-calibration of more advanced sensors [62].
-18-
3 3.1
Summary of available data sets for two-phase flow in vertical pipes Co-current upward flow in vertical pipes A total of 22 publications that described flow regimes in upward, co-current, gas-liquid
flows in vertical pipes with diameters of 10 to 100 mm (see Table 2) and diameters larger than 100 mm (see Table 3) have been analysed. The delineation of these size categories is detailed in Section 3.3.1. Experiments in tube diameters less than 10 mm were not included in our analysis because in tubes narrower than 10 mm the capillary forces begin to dominate the gravitational force, producing a different set of unique flow regimes[63]. We did not include in this study the limited number of reports for downward concurrent gas-liquid flows in vertical pipes [64-66] because conditions that draw gas bubbles or slugs down with liquid flows are less common in industrial applications than upward flow conditions. Although most of the co-current upward flow studies used air with water, eight studies report co-current experiments in vertical pipes with hydrocarbon liquids or glycerol-water solutions [21, 52, 58, 67-71]. Three studies report experiments with nitrogen gas instead of air [52, 70, 71]. Figure 6 presents flow maps generated from flow regimes described in the air-water studies listed in Table 2 and Table 3. Figure 6a shows the approximate regions of gas and liquid superficial velocity that each flow regime exists within, for small-medium diameter pipe flows. Barnea, et al. [72] recorded slug flows within pipe diameters of 25 mm and 51 mm at comparatively high gas and liquid superficial velocities, where other experimental works recorded churn or even annular flows. This was likely due to the subjective identification of flow regimes and or a flaw in the adopted measurement technique. These experiments were reliant upon visual observation and basic conductance probes for flow regime identification, neither of which is capable of objective interpretations. Churn flow in particular can be difficult to distinguish through visual observation and could be misinterpreted as either slug or annular flow regimes. Identification of slug flows where an -19-
annular flow regime is expected by other researchers is inexplicable. Therefore, these recorded improbable slug flows have been excluded from further analysis in this review but have been highlighted in Figure 6a for clarity. Figure 6b shows the data for gas-liquid flows in large pipes (D>100 mm). Large diameter vertical pipes are incapable of sustaining the slug flow regime. However, observations of the slug flow regime are reported by Hills [73] who did not document their fluids’ physical properties. Oddie, et al. [70], Schlegel, et al. [54] and Smith, et al. [55] conducted studies using a similar pipe diameter, approximately 150 mm, and did not observe any slug flow regime. The remaining results shown in Figure 6b support the absence of the slug flow regime within large diameter pipes. Transition boundaries are poorly defined in Figure 6b, with significant overlap observed between all of the flow regime regions. In particular, the bubble to churn flow regime transition observed by Ohnuki and Akimoto [74] and Ohnuki and Akimoto [26] occurred at a significantly lower gas superficial velocity. This may be due to the axial location of the observation points in the experiments. The presented flow map data from Ohnuki and Akimoto [74] and Ohnuki and Akimoto [26] were recorded at length to diameter (L/D) ratios of 4.2 and 61.5 and temperatures of 35 and 30 degrees Celsius respectively. Previous studies have shown that flow regimes require a certain distance, measured as L/D ratios, to fully develop and this L/D ratio of 4.2 is unlikely to be sufficient [26-30]. Because the other researchers did not report their experimental L/D ratios or accurate pressures and temperatures, a consistent comparison cannot be made. Further to the aforementioned uncertainties, Ohnuki and Akimoto [26, 74] relied solely upon visual observation without the aid of a high speed camera, which may explain the observed discrepancy shown in Figure 6b. Omebere-Iyari, et al. [71] conducted experiments at very high pressures of 20 kPa and 90 kPa resulting in the annular flow regime developing at
-20-
comparatively very low gas superficial velocities. Their results account for all of the observed annular flows that occur below a gas superficial velocity of 5 m/s shown in Figure 6b. Table 2: Survey of published experiments of co-current upward gas-liquid flow regimes in vertical pipes with diameters 10 < D < 100 mm. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification techniques
࢛ࡳࡿ (m/s) ࢛ࡸࡿ (m/s) Akhiyarov et al.
Air
Oil
52.5
16
[67]
Visual obs. (still)
0.50 – 4 .0 0.10 – 1.0
Alruhaimani
Air
[68]
ND50
50.8
Mineral Oil
183
Visual obs. (video 1000
0.01 – 5.0
frame/s)
0.05 – 2.6
Barnea et al.
Air
Water
12.3
[75]
164
Visual obs., conductance
0.04 – 63.5
probe
3.8e-3 – 4.1 Barnea et al.
Air
Water
25
[72]
103 (excluding
Visual obs., conductance
19 improbable
probe
slug flow data points) 0.04 – 25 3.8e-3 – 2.6
-21-
Air
Water
51
63 (excluding
Visual obs., conductance
43 improbable
probe
slug flow data points) 0.16 – 25 2.6e-3 – 1.6 Furukawa and
Air
Water
19.2
Fukano [69]
73
Visual obs. (still
0.05 – 41
photography)
0.10 – 1.0 Air
Glycerol
19.2
53wt%
52
Visual obs. (still
0.03 – 5.6
photography)
0.10 – 1.0 Air
Glycerol
19.2
72wt%
72
Visual obs. (still
0.05 – 40
photography)
0.09 – 0.76 Govier and
Air
Water
16
11
Short [15]
Visual obs.
0.60 – 8.1 0.26 – 0.26 Air
Water
26
11
Visual obs.
0.84 – 4.1 0.27 – 0.27 Air
Water
38.1
13
Visual obs.
0.80 – 9.6 0.27 – 0.27 Air
Water
63.5
11
-22-
Visual obs.
0.52 – 4.6
0.26 – 0.26 Juliá et al. [24]
Air
Water
50.8
121
Visual obs., conductance
0.02 – 9.7
probe
0.03 – 2.5 Lucas et al. [29]
Air
Water
51.2
89
Wire mesh conductance
1.4e-3 – 0.52
sensor
0.02 – 6.3 Rosa et al. [76]
Air
Water
54.5
73
Visual obs., resistivity
0.12 – 29
probe
0.22 – 3.1 Schmidt et al.
Nitrogen
[52]
Luviskol in
54.5
Water
20
Visual obs.,
0.04 – 21
gamma ray,
4.6e-3 – 3.3
quickclosing valves
Spedding et al.
Air
Water
26
291
[25]
Visual obs., dP
0.35 – 37 7.7e-3 – 1.1
Szalinski et al.
Air
Water
67
[58]
Air
Silicone
67
-23-
29
Visual obs., wire mesh
0.05 – 5.7
conductivity &
0.20 – 0.71
permittivity
28
Visual obs., wire mesh
0.06 – 5.6
conductivity &
0.20 – 0.72
permittivity
Taitel et al. [8]
Air
Water
25
108
Visual obs.
0.04 – 27 2.7e-3 – 2.8 Air
Water
51
79
Visual obs.
0.01 – 19 0.02 – 3.6
Table 3: Survey of published experiments of co-current upward gas-liquid flow regimes in vertical pipes with diameters D > 100 mm. Study
Gas
Liquid
Pipe dia.
Data points
Flow regime
(mm)
࢛ࡿࡳ (m/s)
identification techniques
࢛ࡿࡸ (m/s) Farman Ali and
Air
Water
254
124
Yeung [62]
Visual obs. (video), dP
0.06 – 2.3 0.19 – 1.08
Hills [77]
Air
Water
150
44
Visual obs., dP
0.07 – 3.6 0.00 – 2.6 Oddie et al. [70]
Ohnuki and
Nitrogen Naptha
Air
Water
150
480
Akimoto [74]
-24-
14
Visual obs., gamma ray,
0.04 – 0.98
conductance probe
0.03 – 1.5
(parallel wire)
89
Visual obs. (still & video
0.02 – 0.77
200 frame/s)
9.8e-3 – 0.21
Ohnuki and
Air
Water
200
Akimoto [26]
58
Visual obs. (still & video
0.03 – 4.7
200 frame/s)
0.02 – 0.70 Omebere-Iyari et
Nitrogen Naptha
189
121
al. [71]
Conductance probe (ring)
0.09 – 15 3.9e-3 – 3.9
Schlegel et al.
Air
Water
150
63
[54]
Impendence probe (arch)
0.07 – 11 0.01 – 2.03
Smith et al. [55]
Air
Water
102
83
Visual obs. (video 10,000
0.01 - 21
frame/s)
0.02 – 2.0 Air
Water
152
129
Visual obs. (video 10,000
0.02 – 10
frame/s)
0.02 – 0.99 Sun et al. [78]
Air
Water
101.6
10
Conductance probe (4
0.05 – 0.51
sensor)
0.06 – 1.0
-25-
Figure 6: Flow maps for upward co-current air-water flow in vertical pipes, including (a) small pipes with diameter 12.3 < D < 67 mm (with improbable slug flow regime data points -26-
recorded by Barnea, et al. [72] in pipe diameters of: 25mm, shown as +, and 51mm, shown as ×), and (b) larger pipes with diameters D > 100 mm. The data points are taken from the literature and listed in Tables 2 and 3. 3.2
Counter-current flow in vertical pipes Despite the existence of numerous experimental investigations on the flow regimes of co-
current two-phase flow, there are few studies available on the flow regimes of counter-current flows in pipes [5, 61, 79-82]and no experimental studies on flow regimes of counter-current flows in annuli. Besagni, et al. [83] experimentally investigated the influence of two inner pipes on counter-current flow in a bubble column, however this study is not directly relevant to the focus of this review paper due to the difference in geometry. The majority of the available experimental investigations of counter-current flows in vertical pipes focus on identifying the onset of flooding or counter-current flow limitation (CCFL). Table 4 summarises the available experimental studies on flow regimes of counter-current gas-liquid flows in vertical pipes. The flow regime data are shown in Figure 7. It must be noted that at low gas and liquid flow rates in a continuous gas medium an annular or falling liquid film flow would be expected, however all of the identified experiments have been conducted within a continuous liquid phase. Figure 7 shows extensive overlapping of the identified flow regimes. Kim, et al. [82] only investigated the slug to churn flow transition. Results from the experiments of Yamaguchi and Yamazaki [5] cannot be analysed nor comparatively examined, as a broad range of experimental conditions, pressure and temperature, was reported for the two investigated pipe diameters and so the exact fluid properties are unknown. The flow map data published by Ghiaasiaan, et al. [80] was solely dependent upon unaided visual observation whilst Ghiaasiaan, et al. [81] investigated two-phase flows with significantly different fluid -27-
properties. The results published by Ghosh et al. [61, 79] are likely to be the most reliable as they adopted multiple flow regime identification techniques. Overall, the poor performance of this collated flow map can be attributed to the limited number of available experimental results, and the results that are available being for significantly different experimental conditions and fluid properties. Table 4: Survey of published experiments of counter-current upward gas-liquid flow regimes within a continuous liquid phase in vertical pipes with diameters 10 < D < 100 mm. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification techniques
࢛ࡳࡿ (m/s) ࢛ࡸࡿ (m/s) Kim, et al. [82]
Air
Water
20
86
Visual obs. (video)
0.02 – 2.7 5.0e-3 – 0.15 Ghiaasiaan et al.
Air
Water
19
60
[80]
Visual obs.
0.10 – 1.7 7.5e-3 – 0.14
Ghiaasiaan et al.
Air
Mineral oil
19
94
[81]
Visual obs.
0.01 – 1.7 1.4e-3 – 0.22 Air
Paraffinic
19
66
oil
Visual obs.
0.01 – 2.2 1.4e-3 – 0.07
Ghosh et al. [61]
Air
Water
25.4
-28-
18
Visual obs. (still & video)
0.19 – 4.9
6.4e-3 – 0.06 Ghosh et al. [79]
Air
Water
25.4
159
Conductance probe (ring,
0.20 – 5.2
parallel wire)
7.0e-3 – 0.15 Yamaguchi and
Air
Water
40
141
Visual obs.
4.0e-3 – 1.6
Yamazaki [5]
3.8e-6 – 0.29 Air
Water
80
74 7.3e-3 – 1.4 1.0e-5 – 0.54
-29-
Visual obs.
Figure 7: Flow maps for counter-current flow within a continuous liquid phase in vertical pipes with diameters 19 < D < 80 mm. The negative sign on the liquid superficial velocity in the vertical axis indicates downward flow. The data points are taken from the literature and listed in Table 4. 3.3
Effect of Pipe Geometry The effect of pipe geometry on flow regimes has been studied extensively in co-current
upward flows in vertical pipes. This flow configuration is the most well studied and hence provided the greatest depth of information for an investigation into the influence of pipe geometry. ϯ͘ϯ͘ϭ ĨĨĞĐƚŽĨWŝƉĞŝĂŵĞƚĞƌ Mishima and Hibiki [49] considered upward co-current flows within very small pipe diameters ranging from 1 to 4 mm, described by the authors as capillary tubes. Two-phase
-30-
flows in such pipe sizes produce special flow regimes due to the capillary forces influencing the shape of the gas bubbles. Pipes of inner diameters smaller than 5 to 9 mm can be defined as capillary tubes in which capillary pressure replaces gravity as the dominant force [63]. This review paper will focus on pipes, with diameters greater than 10 mm. Taitel, et al. [8] experimentally investigated upward co-current flows in vertical pipes with internal diameters of 21 and 51 mm. The study found that the bubble flow regime did not exist for the smaller, 21 mm, pipe, which was explained by bridging of bubbles in the small pipe diameter and therefore, forming Taylor bubbles. Taitel, et al. [8] showed that at low liquid flow rates, when the rise velocity of gas bubbles, U 0 = 1.53 ª¬ g ( ρ L − ρ G ) σ / ρ L2 º¼
1/ 4
[84] is greater than the rise velocity of a Taylor
bubble, UG ≅ 0.35 gD [85], the bubble flow regime does not occur. This is because the rising bubbles approach, from behind, and coalesce with the larger bubble, increasing its size and resulting in a Taylor bubble and, therefore, the slug flow regime. Conversely, if the rise velocity of the Taylor bubble is greater than the velocity of the gas bubbles then coalescence does not occur as the forces at the nose of the Taylor bubble disperse the smaller bubbles [8]. Therefore, the critical pipe diameter, below which bubble flow regime does not exist can be determined by equating the rise velocity of the gas bubbles and Taylor bubbles [8],
D critical = 19.1
( ρ L − ρ G )σ
(1)
g ρ L2
For an air-water system close to the atmospheric pressure, Eq. (1) results in a critical internal pipe diameter of 50 mm. Pipes and annuli of hydraulic diameters between 10 to 100 mm will be defined in this paper as small to medium diameter pipes and annuli. Kataoka and Ishii [86] defined a critical diameter above which, Taylor bubbles and therefore the slug flow regime cannot exist due to interfacial instability. This critical diameter -31-
was defined as D = 40 σ / g ( ρ L − ρG ) ͕which results in a diameter of approximately 108 mm
for an air-water system at an atmospheric condition. Schlegel, et al. [54] experimentally demonstrated that Taylor bubbles in such configurations are unable to bridge the pipe and achieve stability. Smith, et al. [55] conducted studies on co-current upward flows in larger pipes with inner diameters of 102 and 152 mm. Slug flows were absent from both of the produced flow maps. Figure 6b supports this theoretical pipe size limitation of 108 mm for the existence of slug flow through the absence of any experimentally observed slug bubbles, with the exception of the results produced by Hills [73]. Slug flow was documented by Hills [77] in a pipe diameter of 150 mm, which is much larger than the limitation for slug flow that any other researchers have theoretically predicted or experimentally observed. For the purposes of this paper the maximum pipe size for the existence of the slug flow regime, acknowledged as the limit between medium and large sized pipes, will be taken as 100 mm. The effect of pipe diameter on vertical counter-current two-phase flows was analysed by Yamaguchi and Yamazaki [5] using pipes of 40 and 80 mm diameters. The bubble flow regime appeared to exist at similar air-water flow rates in both pipes. However, the annular flow regime could not be attained within the 80 mm pipe. This was attributed to the considerable volume of air escaping through the liquid exit of the apparatus. This is an experimental issue and no conclusions can be made. At higher volumetric flux densities, it was found that void fractions were significantly greater within the 40 mm pipe, compared to the 80 mm, for the same liquid and gas volumetric flux densities. This difference in void fractions was seen to decrease as the absolute volumetric flux density decreased. Literature on vertically downward two-phase flow is sparse in comparison to its upward counterpart, however, an investigation into the effects of pipe diameter was conducted by Barnea, et al. [64] in pipes of 25 and 51 mm diameters. The transition to bubble flow from slug flow regime at high liquid flow rates (dispersed bubble flow) within the 25 mm pipe was -32-
similar to that seen for the vertical upward flow case. However, the same transition within the 51 mm pipe occurred at relatively lower liquid flow rates, subsequently reducing the range of the slug flow regime. ϯ͘ϯ͘Ϯ ĨĨĞĐƚŽĨWŝƉĞĞǀŝĂƚŝŽŶ Although this review is focused on vertical two-phase flows, it is important to understand the effect on flow patterns caused by deviation from a vertical configuration. Barnea, et al. [72] investigated the effect of pipe inclination from 0 to 90° on co-current upward flow regimes and they reported that slight deviations from vertical had little effect on flow patterns while small inclination from horizontal can significantly influence the flow regime. The smallest deviation from vertical that was published in their study was 40°, and so the description of a slight deviation cannot be quantified. Spedding, et al. [87] were able to consider even smaller angles and found that pipe deviations of as small as 3.5° had a significant influence on co-current upward flow regimes at gas flow rates of smaller than 10 m/s. The inclination was found to generate a preferential build-up of liquid on the lower pipe wall, developing anisotropy and eventually blow through slug. This blow through slug is best described as a slug bubble that occurs due to a gradual ramp up of the void fraction behind the liquid build-up, eventually a slug bubble is formed that displaces the accumulated liquid. Oddie, et al. [70] investigated a minimum deviation of 5° for co-current upward flows and their results showed that the flow regimes were barely effected. Ghiaasiaan, et al. [80] investigated counter-current flows in deviations as low as 8° and found that this led to the development of stratified flow. This deviation also caused the slug flow regime to persist at a considerably higher gas flow rate when compared to the vertical case. The critical observation here is that when the pipe deviation significantly impacts the flow regimes, the influence is seen through a change in the regimes themselves. Stratified and anisotropic flow behaviour are non-existent in vertical two-phase flows. As such, imperfect -33-
experimental setups containing significantly deviated vertical test sections should be readily identified, and subsequently ignored, due to the existence of atypical flow behaviour. 3.4
Effect of fluid properties on flow regimes in vertical pipes
ϯ͘ϰ͘ϭ sŝƐĐŽƐŝƚLJ Investigations into the effect of fluid physical properties are complicated by the intrinsic difficulty of isolating and manipulating individual fluid properties. Most of the studies on the effect of fluid physical properties on flow regimes focus on the effect of liquid viscosity. A summary of the fluid properties utilised in the available investigations on the effect of liquid viscosity on the flow regime transition in pipes is presented in Table 5. Ghiaasiaan, et al. [81] investigated the effect of increased liquid viscosity on countercurrent flows in small diameter pipes with mineral oil and paraffinic oil, which increased the viscosity from that of water by a factor of 35 and 185, respectively. It was found that the increasing viscosity resulted in flow regime transitions occurring at significantly lower gas and liquid superficial velocities. Table 5: Summary of experimental studies on the effect of fluid properties on flow regimes of gas-liquid flows in pipes. Author
Experimental Parameters
Liquid Properties
Fluids
Pipe
ȡL
ȝL
ȝL/ ȡL
ıL
Diameter
(kg/m3)
(mPa.s)
(St)
(N/m)
(mm) Counter-current Flow in Pipes Ghiaasiaan, et al.
Air-Water
19
996
1
0.010
0.072
Air-Mineral Oil
19
843.1
35.2
0.418
0.014
[80] Ghiaasiaan, et al.
-34-
[81]
Air-Paraffinic Oil
19
871.4
185
2.124
0.013
Co-current Upward Flow in Pipes Furukawa and
Air-Water
19.2
1000
1
0.010
0.072
Fukano [69]
Air-Glycerol
19.2
1125
6.4
0.057
0.065
19.2
1172
17.2
0.147
0.062
Air-water
19
995
0.848
0.009
0.071
Air-Glycerol
19
1121
4.48
0.040
0.065
54.5
982-
900-
8.227-
0.072
1094
7000
71.283
53wt% Air-Glycerol 72wt% Da Hlaing et al.[21]
50wt% Schmidt et al.[52]
Air-Luviskol in Water
Szalinski et al.
Air-Water
67
1000
1
0.01
0.072
Air-Silicone
67
900
5.3
0.059
0.020
Gas-Oil
52.5
884
100-500
1.131
0.036
Air-Water
50.8
1000
1
0.01
0.072
Air-ND50 Mineral
50.8
884
127-586
1.437-
0.036
[58]
Akhiyarov, et al. [67] Alruhaimani [68]
Oil
6.629
Furukawa and Fukano [69] attempted to isolate the liquid dynamic viscosity in their work on co-current upward flows in small diameter pipes by adding glycerol to water. This procedure provided a six and seventeen-fold increase in liquid viscosity from water whilst retaining similar densities and surface tensions. Their results showed that the bubble to slug -35-
flow transition boundary shifts towards a lower superficial gas velocity with increasing liquid viscosity. The transition to the churn flow regime, denoted as froth and froth-annular, shifts towards a higher superficial gas velocity with increasing liquid viscosity. The occurrence of a falling film, annular flow regime, appeared to be independent of the liquid viscosity. Da Hlaing, et al. [88] also investigated the effect of liquid viscosity in co-current upwards flows within small diameter pipes, 19 mm. Water and a 50 vol. % glycerol solution were used as the working liquid with dynamic viscosities of 0.848 and 4.48 mPa s. They observed a pronounced shift in the bubble to slug transition to higher gas superficial velocities due to the formation of fewer bubbles in the higher viscous liquid. However, the slug to churn and churn to annular transitions remained largely unaffected by the increased fluid viscosity. This was assigned to the dominant effect of high turbulent flow at the high gas flow rates at which these transitions occur. Szalinski, et al. [58] conducted a comparative study of flow regimes in co-current upward flows within 67 mm diameter pipes using air-water and air-oil, with a liquid viscosity of approximately five times greater than that of water. This study also reported opposing results to those of Furukawa and Fukano [69] regarding the effect of viscosity on the bubble-slug and churn-annular transitions. Their experimental results indicated that the bubble to slug flow transition occurred at greater gas superficial velocities with increasing liquid viscosity and the churn to annular flow transition occurred at lower gas superficial velocities with increasing viscosity. It was reported that there was more coalescence, and hence larger gas bubbles in the air-water flows than the air-oil flows. In another study Schmidt et al.[52] investigated the effect of liquid viscosity on upward vertical gas-liquid flows in a tube with 54.5 mm inner diameter and mixtures of nitrogen and solutions of polyvinylpyrrolidone in water with dynamic viscosities in the range of 900!7000 mPa s. They observed a decrease in the gas holdup with increasing the liquid viscosity from -36-
1 to 480 mPa s. They also compared the flow map for liquid viscosity of 1600 mPa s with the air-water flow map of Taitel, et al. [8] and concluded that the transition to annular regime occurred at lower gas superficial velocities in the viscous liquid. Akhiyarov, et al. [67] conducted experiments on gas-oil flows in vertical pipes with internal diameter of 52.5 mm and oil viscosities of 100-500 mPa s to assess the performance of the available mechanistic models to predict the pressure gradient and liquid holdup. No comparison was reported on the effect of liquid viscosity on the liquid holdup and flow regimes. Alruhaimani [68] also performed a comparative study for co-current upward flows in medium diameter pipes. Air-water and various compositions of air-oil were used. They did not observe any viscosity effect on bubble-slug and slug-churn transitions. However, the transition to the annular flow regime occurred at a lower superficial gas velocity as the liquid viscosity increased. The lack of consensus regarding the effect of fluid viscosity ranges outside of experiments on liquid viscosity on flow regime transition in vertical two-phase pipe flow. Early work in bubble columns/pipes also observed contradictory results for varying fluid viscosities on gas holdup which is an indirect indication of flow regimes. For example Weiss, et al. [89] observed an increase in gas holdup with increasing liquid viscosity from 0.92 mPa s to 1670 mPa s in a 15.1 mm pipe. Eissa and Schügerl [90] observed a dual effect of liquid viscosity on gas holdup in a bubble column with 15.9 cm diameter. They found an initial increase in gas holdup for liquid viscosity below 3 mPa s, a decrease between 3 and 11 mPa s and an almost constant gas holdup at viscosities greater than 11 mPa s. This dual effect of liquid viscosity was also observed by Kuncová and Zahradník [91] who studied the effect of liquid viscosity on gas
-37-
holdup in a bubble column with 15.2 cm diameter by using saccharose solutions to achieve viscosities ranging from 1.4 mPa s to 110 mPa s. They observed an increase in gas holdup for liquid viscosities smaller than 3 mPa s and significant reduction in gas holdup in liquids with viscosities greater than 3 and smaller than 30 mPa s. Recent research by Besagni, et al. [33] into the effect of viscosity in bubble columns also reported similar findings. The reduced gas holdup in high viscous liquids, viscosity greater than 3 mPa s, is explained by the increase in bubble coalescence due to the effect of wake with stable vortex [92]. Therefore, in gas-liquid flows with high liquid viscosities gas holdup reduces due to the higher coalescence rate. This results in a shift in bubble-slug transition towards higher gas velocities whereas the transition to churn flow regime occurs in smaller gas velocities due to the formation of large bubbles. This is in agreement with the prediction of Mishima and Ishii [6] for the churn to annular regime transition. The experimental results of Da Hlaing et al.[21], Schmidt et al.[52], Szalinski et al. [58] for bubble-slug transition in viscous liquids is in agreement with the above explanation for the effect of liquid viscosities greater than 3 mPa s unlike the results of Furukawa and Fukano [69] and Alruhaimani [68] for bubble-slug and slug-churn regime transitions. The conflicting results for flow regime transition in the above studies may be attributed to varying surface tension and/or different pipe sizes. These inconsistent results highlight the need for a better experimental design to investigate the effect of fluid physical properties by controlling other effective parameters. ϯ͘ϰ͘Ϯ ^ĂůŝŶŝƚLJ Salts are known to inhibit bubble coalescence beyond a concentration called the critical salt concentration, which is unique for each salt [93-98]. To explore this further, we performed experiments that investigated the effect of sodium chloride at different
-38-
concentrations on bubble coalescence and size in a bubble column. Results were captured using a high-speed camera at a frequency of 5000 frames per second. The bubble size at different salt concentrations was determined through image analysis by utilising ImageJ software. The Sauter mean bubble diameter, D32, was calculated as [99],
¦ (4 A / π ) , ¦ (4 A / π ) 3/2
D 32 =
(2)
p
p
where Ap is the projected bubble area. Figure 8 shows the effect of salt concentration on bubble size. The results indicate that bubble size decreases with increasing salt concentration. This effect is more pronounced at a concentration of approximately 0.13 Molar, which is close to the critical salt concentration of sodium chloride. Gas holdup, which is an indirect method for measuring bubble size, was reported to increase with salt concentration owing to the inhibiting effect of salt on bubble coalescence [96, 100]. Different mechanisms including colloidal forces, Gibbs-Marangoni effect, and ion specific effect have been proposed to explain the inhibiting effect of salts on bubble coalescence which have been reviewed by Firouzi, et al. [101]. To our knowledge there is no direct data available on the effect of salinity on flow regimes of gas-liquid two-phase flows with the exception of the recent study by Besagni and Inzoli [102] in a large bubble column (240 cm inner diameter) where flow regimes are mainly defined as homogenous (characterised by small and uniformly distributed bubbles) and heterogeneous (characterised by bubbles from different sizes due to high interactions between bubbles). Besagni and Inzoli investigated the effect of sodium chloride on these flow regime of counter-current air-water flows. Their experimental results indicated the stabilising effect of electrolytes with concentration up to the critical/transition concentration on the homogenous regime due to the inhibiting effect of salts on bubble coalescence.
-39-
Based on the available data on the stabilising effect of inhibiting salts, we postulate that at concentrations above the critical salt concentration, the transition from bubble to slug and slug to churn/annular can be significantly delayed compared with that in fresh water. This is in agreement with the empirical expression for the critical void fraction at the bubble-slug transition, αc = 0.55− 2.37 Db D , proposed by Guet, et al. [103] based on an interpolation of
Song et al. [104] experiments in a 25 mm diameter pipe. Here, the critical void fraction for the bubble-slug transition, αc , increases with decreasing bubble size, Db. Therefore, the bubble-slug transition occurs at a higher gas velocity (flow rate).
-40-
Figure 8: The Sauter mean diameter, D32, of bubbles as a function of salt concentration at QG= 0.46 L/min. 4
Summary of experimental data for co-current flow in vertical annuli Available experimental studies on flow regimes in annuli indicate that despite the
existence of similar flow regimes as in pipes, there are small differences in distribution of gas and liquid phases, which characterise different flow regimes, in these two geometries. This difference is more pronounced in the slug flow regime. Table 6 and Figure 9 show the -41-
experimental conditions and data in annuli for upward co-current flows. Some studies reported an asymmetric structure of Taylor bubbles in annular geometries [53, 105, 106]. Hasan and Kabir [107] observed Taylor bubbles with a sharper nose which causes the bubbles to rise faster. Annular flow configurations are described by the inside diameter (ID) of the outside pipe or casing, DC, and the outside diameter (OD) of the inside pipe or tubing, DT. The effect of annular eccentricity was examined by Kelessidis and Dukler [105], who compared co-current upward flows between concentric annuli and annuli with 50% eccentricity using 76.2 mm ID casing and 50.8 mm outside diameter (OD) tubing. It was found that the eccentricity had minimal effect on the global flow regimes. However, local flow regimes were observed to develop more readily at lower gas flow rates in the larger rather than smaller annulus. This anisotropy was applicable to all of the flow regime transitions, with transitions always occurring first in the larger annulus then the smaller one, as the gas flow rate increased. In another experimental study by Caetano, et al. [53] using concentric and fully eccentric annuli with 76.2 mm ID casing and 42.2 mm OD tubing, no major difference was observed for the churn to annular flow regime transition in concentric and eccentric annuli. However, bubble-slug and bubble-dispersed bubble flow regimes were observed at respectively smaller and larger gas flow rate compared with that in a concentric annulus.
-42-
Table 6 Survey of published experiments of co-current upward gas-liquid flow regimes in vertical annuli with small hydraulic diameters DH < 50 mm where the hydraulic diameter DH=DC-DT. Study
Gas
Liquid
Pipe dia.
Number of
Flow regime
(mm)
data points
identification
࢛ࡿࡳ (m/s)
techniques
࢛ࡿࡸ (m/s) Kelessidis and Dukler
Air
Water
DH: 25.4
85
DC: 76.2
0.02 – 19
DT: 50.8
1.0e-3 – 1.8
DH: 34.0
100
DC: 76.2
0.01 – 23
DT: 42.2
2.1e-3 – 3.1
Kerose
DH: 34.0
170
ne
DC: 76.2
0.03 – 23
DT: 42.2
2.7e-3 – 2.4
DH: 25.4
Results from
Conductance probe
DC: 50.8
three annuli
(parallel plate)
DT: 25.4
published in
[105]
Caetano et al. [53]
Air
Air
Das et al. [106]
Air
Water
Water
Visual obs.
Visual obs.
Visual obs.
a single flow Air
Water
DH: 25.4 DC: 38.1 DT: 12.7
Air
Water
DH: 12.7
-43-
Conductance probe map with no (parallel plate) distinctions made. Conductance probe
DC: 25.4
307
DT: 12.7
0.04 – 8.7
(parallel plate)
0.10 – 2.6
Sun et al. [108]
Jeong et al. [109]
Ozar et al. [110]
Julia et al. [27]
Air
Air
Air
Air
Air-
DH: 19.0
132
Visual obs.,
Water
DC: 38.1
0.02 – 0.90
Impendence probe
DT: 19.1
0.37 – 2.7
Air-
DH: 19.0
19
Conductance probe (4
Water
DC: 38.1
0.04 – 3.9
sensor)
DT: 19.1
0.24 – 3.3
Air-
DH: 19.0
19
Water
DC: 38.1
0.05 – 5.5
DT: 19.1
0.25 – 3.4
Air-
DH: 19.0
72
Conductance probe (4
Water
DC: 38.1
0.02 – 20
sensor)
DT: 19.1
0.21 – 3.4
-44-
Visual obs.
Figure 9: Flow maps for co-current flow in vertical annuli with small hydraulic diameters 19 < DH < 34 mm. The data points are taken from the literature and listed in Table 6. 5
Evaluation of flow maps based on non-dimensional parameters Wallis [111] was the first to present flow regimes on a flow map co-ordinate system using
superficial velocities of gas and liquid as its axes. This flow map coordinate is still most commonly used due to its simplicity. However, its presented results are also limited by this simplicity as they may not be reliably related to two-phase flows under dissimilar conditions. In order for a widely applicable solution to be found, non-dimensional parameters should be used to include the effect of fluid physical properties, geometry, and the velocity or flow rate.
-45-
Troniewski and Ulbrich [112] identified three groups of parameters that could be used as co-ordinates for flow maps, namely phase velocities or fluxes (i.e. gas superficial velocity), quantities representing homogenous transformations of the phase velocities or fluxes (i.e. mixture superficial velocity), and parameters including physical properties of phases (i.e. Reynolds number). The authors highlighted the latter as being the most likely to provide a universal solution. Table 7 examines the fluid properties that may affect two-phase gas-liquid flow and summarises their inclusion within dimensionless parameters. In order to include all of the fluid properties a combination of dimensionless parameters may be required. Chen [38] suggested that the Weber number, describing the inertial force of a flow in relation to its surface tension, may be the best parameter to deduce general correlations. However, it must be highlighted that the study by Chen [38] was focussed on capillary tubes of D < 5 mm. Since flows in pipes of diameters greater than 9 mm are dominated by gravity rather than capillary pressure and hence surface tension, it is expected that the Reynolds and Froude numbers will be of greatest importance [63]. Reynolds number is similar to the Weber number but considers the inertial force of the flow in relation to the viscous force instead of the surface tension force. The Froude number describes the inertial force of the flow against the gravitational force. Abdelsalam, et al. [22] proposed a flow map coordinate based on a new dimensionless number called slippage number (SL) and the mixture Froude number (FrM). S L takes into account the slippage between phases and is defined as the ratio of the gravitational force difference between slip and no-slip (homogenous) conditions. The proposed flow map coordinates were tested against experimental data of different studies for air-water and air-oil systems for a range of liquid visocity of 0.001 to 0.589 Pa.s, pipe diameters of 25 to 152 mm and inclinations of 1 to 90°. It was shown that S L decreases exponentionally with FrM and the smallest and greatest S L represent bubble and annular flow regimes. The proposed -46-
coordinates do not include viscosity and surface tension of the fluids as well as flow inclination, however, the liquid holdup (HL), which is an indication for identifying flow regimes, includes the influence of these parameters. S L requires the value of the liquid holdup at each gas and liquid flowrates which, is not always provided in the experimental studies of flow regimes. Unfortunately, the majority of studies did not document liquid holdup data for each flow map data point and so this set of proposed flow map coordinates could not be tested. Table 7: Flow regime map co-ordinates in vertical pipes Flow map coordinates
Author(s)
uLS vs. uGS
Wallis [111]
D
uGS
uLS
3
3
3
3
3
3
3
ȡG
ȡL
3
3
3
3
3
3
3
3
3
3
3
3
3
ȝG
ȝL
ı
Govier and
uLS vs.
uGS uLS
Leigh Short [15] Griffith and
u FrM2 vs. GS uM
3
Wallis [16] Moissis [113] Hewitt and
2 2 ρLuLS vs. ρGuGS
Roberts [17]
1/4
1/4
uLS ( sLσ S ) vs. uGS ( sLσ S )
sG1/3 Aziz, et al.
3
[114]
FrM
vs.
µS 3
( S Lσ S )
1
4
WeLS vs. WeGS
uSG uSL
Oshinowo and 3
3
Charles [19] Rezkallah and Zhao [20]
-47-
3
3
3
Da Hlaing, et
ReLS vs. ReGS
3
3
3
3
3
3
3
3
3
3
3
3
al. [21]
( ρ M − ρ H ) gD vs. 2 ρ G u SG
ρL Fr Abdelsalam, et ρ L − ρG M al. [22]
uM = uGS + uLS ρM = ρ L H L + ρG (1 − H L ) & ρH = ρL
uLS u + ρG GS uM uM
FrM = uM / Dg
WeGS =
2 ρGuGS D ρ u2 D & WeLS = L LS σ σ
ReGS =
ρGuGS D ρu D & ReLS = L LS µG µL
sL , σS
and
µS
are the liquid specific density, surface tension and viscosity and
sG is the gas
superficial density
Previous attempts to create a universally applicable flow pattern map through the use of non-dimensional parameters have been limited and were only verified against limited experimental data sets [22, 88]. Here, the suggested non-dimensional numbers listed in Table 7 were examined against the compiled experimental flow regimes. Flow maps presented in non-dimensional space were visually inspected against the popular superficial velocity space to gauge the success of the dimensionless solution. Ideally the selected parameters would result in plots containing clearly defined flow regime transition boundaries that align themselves similarly, regardless of experimental conditions and fluid properties. This would allow for the production of a widely applicable flow pattern map.
-48-
The majority of published experimental work did not report the utilised fluid properties nor laboratory conditions, and as such it was necessary to make some assumptions to complete this analysis. Standard laboratory conditions (room temperature of 25°C and atmospheric pressure) were assumed where necessary to make this analysis possible. The range of observed experimental conditions and fluid properties that will be considered are presented in Table 8. Table 8: Range of experimental pipe sizes and fluid properties.
uGS
uLS
ʌ'
ʌ>
ʅ'
ʅ>
ʍ
;ŵŵͿ
(m/s)
(m/s)
;ŬŐͬŵϯͿ
;ŬŐͬŵϯͿ
;ŵWĂ͘ƐͿ
;WĂ͘ƐͿ
;EͬŵͿ
Ϭ͘ϬϬϭϰ
Ϭ͘ϬϬϮϭ
Ϭ͘ϬϭϴϬͲ
Ϭ͘ϬϬϭͲ
Ͳϲϯ͘ϱ
Ͳϲ͘ϯ
Ϭ͘Ϭϭϵϴ
ϰ͘ϯϮ
ϭϮ͘ϯͲϲϳ
ϭ͘ϭͲϮ͘Ϭϯ
ϴϴϰͲϭϭϳϮ
Ϭ͘ϬϮϮͲϬ͘ϬϳϮ
Having considered the available experimental data, it was decided that results from cocurrent upward flows in small-medium diameter vertical pipes were the most suitable for the development of a dimensionless solution. A summary of the studies that have been utilised is presented in Table 2. Due to the complex nature of two-phase flows, the calculation of dimensionless flow map coordinates has been based on superficial velocity as shown in Table 7. Theoretically, mass flow rates would provide a better interpretation of the flow phenomena, however, this would require detailed void fraction data corresponding to the superficial flow rates. This information has not been made available in the examined studies and in most cases, has not been recorded. Based on the parameters considered in Table 7 and a visual assessment of the produced flow maps, the Reynolds number solution, ReLS vs. ReGS, is recommended and presented in Figure 10. In addition to our visual assessment of flow maps, liquid viscosity which has a pronounced effect on flow regimes is taken into account in
-49-
our recommended flow map. Flow maps in different coordinates listed in Table 7 are shown in the appendix.
Figure 10: Recommended dimensionless solution, ReLS vs. ReGS, for co-current upward flow in small-medium diameter vertical pipes and annuli, 10 < D < 100mm.
6
Theoretical prediction of flow regime transitions This section reviews the empirical models, which are the most popular, and tested against
experimental data, for predicting the transition of flow regimes. Note that these transitions were developed for co-current, upward flow in vertical pipes, which is the most well-studied of the vertical two-phase flow configurations. -50-
6.1 Transition from bubble to slug flow regime The transition from bubble to slug flow regime occurs due to the agglomeration and coalescence of bubbles in the bubble flow regime at low liquid flow rates. Taitel, et al. [8] showed that this transition in a vertical co-current upward flow takes place when the gas void fraction, Į, is greater than 0.25. Substituting this value for the gas void fraction into the equation for rise velocity of bubbles relative to the average liquid velocity defines the bubble to slug transition as,
uLS = 3uGS −0.75u∞ ,
(3)
where ݑஶ describes the rise velocity of fairly large bubbles which is quite insensitive to bubble size [84], 1/4
ª g ( ρL − ρG ) σ º u∞ = 1.53 « » . ρL2 ¬ ¼
(4)
McQuillan and Whalley [115] followed the same approach for predicting the transition between bubble and slug flow regimes. Barnea [116] also followed the same approach and modified the bubble to slug transition model to include pipe inclination. Mishima and Ishii [6] considered α = 0.3 as the criterion for the transition from bubble to slug flow and proposed a model to predict this transition by employing the drift velocity for bubble flow, 1/4
§ 3.33 · 0.76 § σ g ( ρL − ρG ) · uLS = ¨ −1¸ uGS − ¨ ¸ , ρL2 C0 © © C0 ¹ ¹ in which C0 is the approximate ratio of the centreline velocity to the average velocity and is defined as C 0 = 1.2 − 0.2
ρg for round tubes. Hasan and Kabir [117] followed the same ρL
-51-
(5)
approach and proposed their own model to predict the bubble-slug transition by considering
α = 0.25 as the transition criterion. § 4 · u u LS = ¨ − 1 ¸ u GS − ∞ , C0 © C0 ¹
in which
(6)
C0 =1.2 .
At high liquid flow rates Taitel, et al. [8] suggested that the bubble coalescence and agglomeration will be overcome by the breakup of bubbles due to the turbulence of the high liquid flow rate. As a result, dispersed bubble flow occurs at high liquid flow rates wherein gas bubbles remain dispersed due to turbulence. These small bubbles can exist at void fractions up to 0.52 at higher water flow rates. Taitel, et al. [8] proposed the bubble-dispersed bubble transition by employing the theory of breakup of immiscible fluids by turbulence forces, given by Hinze [118] as, 0.54
0.43
uLS = 3.97 D
§σ · ¨ ¸ © ρL ¹
0.071
§ ρL · ¨ ¸ © µL ¹
0.45
§ g ( ρL − ρG ) · ¨ ¸ σ © ¹
− uGS .
(7)
It has been assumed that at high enough gas concentration, bubbles coalesce again to form slug or churn flow regimes. A gas void fraction of 0.52 was considered as the transition between dispersed bubble and slug/churn flow regime, which yields,
uLS = 0.92uGS
(8)
This model was later improved by [119] to consider the relatively small effect of the gas void fraction on the coalescence and breakup of bubbles [120]. 0.4σ § ρL · 2 ¨ ¸ g ( ρ L − ρG ) © σ ¹
0.6
− 0.2 § 2 § DρL · · ¨ 0.046 ¨ ¸ ¸ ¨ D © µL ¹ ¸ © ¹
0.4
-52-
u 1.12 = 0.725 + 4.15 α . M
(9)
where the average velocity,
u M , is defined as uM = uLS + uGS . Substituting a void fraction of
0.52 into Eq. (9) and solving this nonlinear algebraic equation for the liquid superficial velocity results in, 0.54
0.43
uLS = 6.14D
§σ · ¨ ¸ © ρL ¹
0.071
§ ρL · ¨ ¸ © µL ¹
0.45
§ g ( ρL − ρG ) · ¨ ¸ σ © ¹
− uGS .
(10)
Mishima and Ishii [6] made no distinction between bubble and dispersed flow regimes. McQuillan and Whalley [115] employed the empirically modified model proposed by Taitel and Dukler [121] for horizontal pipes, to predict the bubble to dispersed bubble transition in vertical pipes. It was postulated that at high liquid flow rates, the effect of slip between two phases is negligible and the turbulence is caused only by the bulk flow. Therefore, the modified expression for the horizontal pipes should be independent of the pipe inclination and can be used for vertical pipes as well. The correlation suggests that the transition is independent of the gas flow rate and dispersed flow regime exists if,
uLS =
6.8
0.11
ª gσ ( ρL − ρG ) º¼
ρL0.44 ¬
0.28
§ D· ¨ ¸ © µL ¹
.
(11)
McQuillan and Whalley [115] considered a gas void fraction of 0.74 as limit for stability of dispersed bubbles and transition to slug/churn flow regime which yields,
uLS = 0.35uGS .
(12)
6.2 Slug to churn flow transition Accurate prediction of the transition from slug to churn flow regime is difficult as there is no clear definition of the churn flow regime. Different mechanisms have been proposed for the transition from slug to churn flow regime. These include flooding, bubble coalescence, wake effect and entrance effect [8]. Taitel, et al. [8] proposed that the churn flow regime is -53-
an entrance related phenomenon. It was suggested that the entry length, lE, in which churn flow can form before a stable slug flow occurs, depends on the gas and liquid flow rates and pipe diameter. An expression was proposed to evaluate the required entrance length to form stable slugs,
§ u · lE = 40.6¨ M + 0.22¸ , ¨ gD ¸ D © ¹
(13)
Rearranging Eq. (13) results in an equation for the superficial liquid velocity at which the slug-churn transition occurs,
§l / D · uLS = gD ¨ E − 0.22 ¸ − uGS . © 40.6 ¹
(14)
Mishima and Ishii [6] suggested that just before the slug-churn transition, the nose of the following bubble touches the tail of the proceeding bubble and therefore, the liquid slug becomes too unstable to support the bridge between two consecutive Taylor bubbles due to the strong wake effect. This condition was mathematically described as when the mean void fraction, Įmean, within the entire flow reaches the void fraction within the slug-bubble section, Įbs, where, ª º gD ( ρ L − ρG ) « » ( C0 − 1) uM + 0.35 « » ρL » α bs = 1 − 0.813 « 1/18 » « 3 § · « u + 0.75 gD ( ρ L − ρ G ) ¨ ª« ρ L D ( ρ L − ρ G ) º» ¸ » M 2 ¨ ¸ « ρL µL ¼ ¹ »¼ ©¬ ¬
0.75
(15)
and,
αavg =
uGS C0uM + 0.35
gD ( ρL − ρG )
.
(16)
ρL
-54-
In the model proposed by Barnea [116] for the entire range of pipe inclination it was suggested that the slug to churn transition takes place due to the coalescence of bubbles within the liquid slug and, therefore, destruction of the liquid slug. Mathematically, it was described as when the average void fraction in the liquid slug reaches the maximum bubble volumetric packing, 0.52, and bubbles become close enough to each other to collide and coalesce. This model postulates that the gas bubbles in the liquid slugs behaves similar to bubbles in the dispersed flow regimes. Tengesdal, et al. [122] proposed a model based on the drift flux approach to predict the transition from slug to churn flow regimes,
α=
uGS 1.2uM + 0.35
gD ( ρL − ρG )
.
(17)
ρL
This work considered the void fraction of 0.78, which was experimentally observed by Owen [123], as the void fraction in which this transition occurs. By substituting α = 0.78 into Eq. (17) and rearranging, the resultant prediction of slug-churn transition is,
uLS = 0.0684uGS −
0.35 gD ( ρL − ρG ) . 1.2 ρL
(18)
McQuillan and Whalley [115] attributed the slug to churn transition to the flooding of the liquid film around a Taylor bubble in the slug flow regime. They employed the semiempirical correlation suggested by Wallis [124] to predict the gas and liquid flow rates at the flooding point in pipes, * 1/2 * 1/2 (uGS ) + m (uLS ) =C,
(19)
-55-
where the empirical constants m = 1 and 0.725 C 1 depend on the pipe entrance conditions. McQuillan and Whalley [115] considered C as 1. The dimensionless superficial *
*
velocities of the gas, uGS , and liquid, u LS , are defined as,
u *KS = u KS
ρK gD ( ρ L − ρ G )
K = G, L .
(20)
McQuillan and Whalley [115] proposed that the gas and liquid superficial velocities in the flooding model be replaced by the Taylor bubble superficial velocity, § 4δ ubS = ¨1 − D ©
gD ( ρ L − ρG ) · ·§ ¸, ¸ ¨¨1.2uM + 0.35 ¸ ρL ¹© ¹
and the liquid film superficial velocity,
(21)
uFS = ubS −uM . The film thickness, į, can be calculated
by Nusselt’s expression for a laminar falling film as, 1/3
§ 3uFS DµL · δ = ¨¨ ¸¸ . © 4 g ( ρ L − ρG ) ¹
(22)
Jayanti and Hewitt [125] identified the assumption of a laminar liquid film around the Taylor bubble as a shortcoming in the model by McQuillan and Whalley [115]. To address this concern, the superficial liquid film velocity,
uFS can be correlated to a constant film
thickness as a result of the balance between the effect of gravity on the liquid in the film and the wall shear forces for sufficiently long bubbles [126]. This can be expressed as [12, 120], 1/ CM
uFS
½ ° ° ° 4δ µL ° δ 1−CM = ® 1/3 ¾ D 4ρ L ° § · ° µL2 C ° K ¨ g ρ −ρ ¸ ° G)¹ ¯ © ( L ¿
,
(23)
-56-
where CM and CK were analytically determined to be 0.3333 and 0.9086 for laminar flow and recommended to be 0.6666 and 0.0682 for turbulent flow. As already mentioned, the value of C in the flooding model depends on the pipe entrance condition. Therefore, different C values were investigated to find the best model to predict the slug to churn transition. A value of C = 1 resulted in the best match compared with the experimental data points. Therefore, the following is proposed as the best model to predict the slug-churn transition, § ¨ ¨ µL ¨ ¨ ρ L gD 3/ 2 ∆ρ ¨ ¨ ©
1/ 2
δ 1/C
M
1/ C M
§ § µ 2 ·1/3 · ¨ CK ¨ L ¸ ¸ ¨ © g ∆ρ ¹ ¸ © ¹
§ ©
where ∆ρ = ( ρ L − ρG ) and αb = ¨1−
· ¸ ¸ ¸ ¸ ¸ ¸ ¹
1/2
§ ρG ρG · + ¨¨ 1.2u M α b + 0.35ε b ¸ gD∆ρ ρ L ¸¹ ©
= 1,
(24)
4δ · ¸ . The statistical analysis for this model as well as D¹
other models discussed in this section is summarised in Table 9.
6.3 Churn to annular flow transition: The transition to annular flow might be the most important transition to predict because this transition represents the transition from a liquid continuous phase to a gas continuous phase. Consequently, the pressure gradient undergoes a step change at this transition. Taitel, et al. [8] predicted the gas superficial velocity at which the churn to annular transition occurs as the minimum gas velocity required to prevent the entrained droplets from falling. Therefore, balancing the buoyancy and drag forces acting on a droplet results in, 1/4
§ σ g ( ρL − ρG ) · uGS = 3.1¨ ¸ . ρG2 © ¹
(25)
-57-
Mishima and Ishii [6] proposed the criteria for churn to annular transition based on two different mechanisms, namely flow reversal in the liquid film around large bubbles and destruction of the liquid slug or large wave that can be sustained as small droplets in a gas core. This mechanism is applicable to flows in large diameters pipes,
σ g ( ρ L − ρG ) Nµ−0.4
D>
L
( (1 − 0.11C0 ) C0 )
2
.
(26)
where, N µL =
µL
(
ρ Lσ σ g ( ρ L − ρG )
1/2
)
.
(27)
For small pipes, the following correlation was proposed to predict the transition from churn to annular flow regimes,
uGS =
gD ( ρL − ρG )
ρG
(α − 0.11) ,
(28)
where the void fraction needs to satisfy Eq. (15). For flows in large pipes where the second mechanism is applicable, the transition to the annular regime can be predicted by determining the onset of entrainment. Therefore, 1/4
−0.2
uGS > NµL
§ σ g ( ρL − ρG ) · ¨ ¸ . ρG2 © ¹
(29)
Lastly, McQuillan and Whalley [115] proposed an inequality to predict the existence of the annular flow regime by considering zero liquid superficial velocity in the flooding equation,
uGS
ρG gD ( ρ L − ρ G )
≥ 1.
(30)
-58-
6.4 Validation of the Existing Models In order to determine the most accurate theoretical model for each flow regime transition, the discussed models were assessed against the collated experimental results. Flow map data from co-current upward flows in pipes and annuli with diameters ranging from 12.3 to 67 mm were used for this assessment. To ensure consistency in the analysis, the physical fluid properties applied in each model are consistent with the experimental studies. Only through examination of the developed models against a large collated database is it possible to verify their effectiveness. This work has taken 20 experimental studies generating over 2500 data points in order to assess the transition models of Taitel, et al. [8], Barnea [116], McQuillan and Whalley [115], Mishima and Ishii [6], Tengesdal, et al. [122] and Eq.(24). The latter has been proposed in this work as an improvement for the slug to churn transition criterion proposed by McQuillan and Whalley [115]. To validate the models, the number of conforming and non-conforming points for each transition boundary was determined. In order to assess each experimental data point, a critical superficial liquid velocity was calculated for each given superficial gas velocity (or vice versa if a superficial gas velocity provided the transition criterion, for example in the churn-annular model by McQuillan and Whalley [115] given in Eq.(30). An example of the analysis can be seen in Figure 11, where all slug and churn data points in small pipes are shown first, along with the critical transition values using the model of Mishima and Ishii [6], before the filtering out of all conforming values as shown in Figure 11 (b). In this study, non-conforming points are those data points reported in the literature to be of one flow regime, but predicted to be another by a given transition model.
-59-
Figure 11: An example of the statistical analysis using the Mishima and Ishii [6] slugchurn transition model showing (a) the full experimental slug and churn regimes for pipe diameters smaller than 50 mm and (b) non-conforming points (i.e. slug flow observed in the region that predicted to be churn and vice versa).
-60-
Table 9 shows the results of this analysis, highlighting the best performing models for each flow regime. This statistical analysis shows that for the bubble-dispersed transition, Eq. (10) proposed by Barnea [116] produced the best results. For the bubble-slug transition, the same model used by both Taitel, et al. [8] and Barnea [116] given by Eqs. (3) and (4) outperformed the work of Mishima and Ishii [6]. The slug-churn transition presents a more challenging analysis with empirical constants often used for tuning purposes. Here, the model proposed by Taitel, et al. [8] is dependent on the L/D ratio. For the purposes of this analysis, a set ratio of 250 was assumed for all cases as this information was not often available in literature. This limits the validity of this particular transition criterion, and as such, the model proposed by Barnea [116] provides a more general solution. The modification proposed in this work for the model of McQuillan and Whalley [115] for the slug-churn transition improved the transition prediction from 69% to 76% of conforming data points. For the final transition from churn to annular flow, it was found that the model proposed by Mishima and Ishii [6] was able to best capture the experimental data. Figure 12 presents the best performing models overlain upon the collated experimental flow map data used for their assessment. Table 9: Analysis of conforming and non-conforming experimental data points for smallmedium and annuli pipes with respect to transition models discussed in Section 6. ŝƐƉĞƌƐĞĚ ďƵďďůĞƚŽ
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-62-
Figure 12: Comparison of the best flow regime transition models with the experimentally identified flow regimes. 7
Development of numerical methods for the prediction of flow regime transitions This review has demonstrated that multiphase flow in pipes and annuli is sensitive to a
number of material, geometrical, and operational parameters. This makes comprehensive experimental investigation of the relevant phenomena difficult. Further, many of the experimental studies that have been reviewed exhibit incongruent or contradictory findings. In spite of these challenges, a range of criteria has been developed for the description of the various multiphase flow regimes and their transitions, but these are constrained by their empirical basis.
-63-
Numerical methods represent one possibility for improving the description of the various regimes of multiphase flow in industrial-scale pipes and annuli. These techniques are typically founded in the discretisation of widely-accepted analytical systems of equations, which are then solved using computers. Prominent examples in engineering include the finite element method (FEM) for structural mechanics and computational fluid dynamics (CFD) for vehicle aerodynamics. Some of the major benefits of such numerical methods is that they are deterministic, readily able to explore a wide range of problem parameters, and relatively inexpensive to use once developed. As an extension to CFD, the use of computational multiphase fluid dynamics (CMFD) has become common practice in a number of industrial sectors such as nuclear, thermalhydraulics, and petrochemical [127]. This first started with the introduction and development of the two-fluid model (TFM) in the 1970 - 80s, which acted as a key driver in the removal of limitations associated with the use of empirically determined parameters for 1D modelling [128-130]. The use of high resolution 3D simulation has allowed for more accurate closure relations in 1D models and insights into transition mechanisms which had previously not been possible. Additionally, the development of interface tracking methods (ITM) provides researchers with the ability to further reduce modelling assumptions, particularly those associated with flow topology and momentum interactions between phases [131]. This section describes and presents examples of how numerous simulation methods have been applied to capture multiphase flow regimes and their development. A detailed description of the governing equations and their discretisation is not attempted here. For more information the interested reader is pointed towards texts such as those by Prosperetti [132] and Martin [133]. Instead, it is the intention that this section elucidates the potential for numerical methods to contribute to the state of knowledge in multiphase flows and highlights the aspects in need of further research. -64-
7.1 Numerical Methods The TFM has seen extensive use in commercial codes including OLGA [134] in the oil and gas industry or the more recent PeTra [135], as well as in general simulation software such as ANSYS Fluent and CFX. The method relies on phases being treated as interpenetrating continua [132], and in this sense, continuity equations for each phase are solved throughout a fixed, or Eulerian numerical domain. This can be expressed by weighted continuity equations [131],
∂t Įi ȡi +∇⋅ ( Įi ȡiui ) = 0 ,
(31)
∂t (αi ρi ui ) + ∇⋅ (αi ρi ui × ui ) = −αi∇p +∇⋅ (αiTi ) + αi ρi g + Fiinter
(32)
where, the subscript i indicates the phase (gas/liquid/oil) present in the system, ߙ is the void fraction of phase i with
¦α i
i
int er = 1 , and Fi represents the interfacial forces that are used to
couple interactions between phases. Additionally,
Ti represents the viscous stress tensor
while ࢛ ǡ ߩǡ and g represent the fluid velocity, density, pressure and gravitational acceleration, respectively. It is noted that closure relations need to be incorporated to account for the phase interactions including drag, lift, wall lubrication, virtual mass and turbulent dispersion forces within Fi
int er
. For a detailed description of the available correlations for
these forces, the reader is referred to [133, 136-138]. The ITMs discussed here are generally implemented on an Eulerian grid, however, these methods only solve one set of continuity equations. The ITMs can be divided further into volume-tracking or front-tracking methods. The volume-tracking methods were developed from the marker-and-cell approach proposed by Harlow [139]. In these methods, for example volume-of-fluid (VoF) [140], level-set (LS) [141] or Phase Field (PF) [142], an order parameter is advected through the flow field to track the location of each phase present in the -65-
system. Thus, the volume of each phase is effectively being tracked and the interface can be re-constructed from this information. These methods typically solve a single set of continuity equations weighted by the phase fraction or order parameter, which is tracked by a marker function of the form,
∂t Į + u ⋅∇Į = 0
(33)
The implementation of interfacial interactions, such as surface tension, on an Eulerian grid is performed via a volumetric force in the momentum equation to account for the likelihood of the interface location to be ‘off-grid.’ In this sense the force is applied to a regularised region about the interface, rather than as a force at the interface point only. There are two ways in which the surface tension force can be derived. Firstly, one can consider a geometric argument, in which the force acts to minimise the interfacial area. Alternatively, one can also look at the system from a chemical potential perspective in which the force acts to minimise the free energy functional of the system [142]. In addition to the previously mentioned TFM (also referred to as the Euler-Euler approach or multifluid model if more than two phases are present) and interface tracking techniques, another important class of two-phase solvers is the Euler-Lagrange method. Here, the dispersed phase is no longer captured on an Eulerian grid, but the position of each particle or bubble is tracked and propagated using Newton’s laws of motion. The behaviour of the individual bubbles is then coupled to the bulk media, which is solved through the Reynoldsaveraged Navier Stokes (RANS) equations. The bulk media can be resolved with varying techniques including the finite volume and lattice Boltzmann methods [143]. In multiphase pipe flows, various flow regimes are observed in which the gas-liquid interface acquires characteristic topologies that affect the phase interactions. As such, the traditional form of methods such as the one-, two- or three-dimensional TFM, which require -66-
correlations to describe the phase interactions, become dependent on the flow regime [144]. This means that a priori knowledge is required to describe how the flow will manifest before predictions and or simulations are conducted and, therefore, the importance of flow regime maps is realised. Contrary to this, recent works have developed hybrid models that effectively couple the TFM with either a population balance model (PBM) or an ITM in an attempt to eliminate the dependency on prior knowledge of the flow regime. The commercial CFD code, CFX for example has implemented an inhomogenous multiple size group (MUSIG) model [145-147] that has been reported to capture flow regimes consistent with the work of Taitel, et al. [8] on vertical co-current flow. One criticism of experimentally generated flow maps is the level of subjectivity that arises in determining the current flow regime. To cater for this, Krepper, et al. [147] looked to use more objective criteria when analysing co-current vertical flows by measuring the bubble size distributions and radial gas volume fraction profiles. This was performed in both their experimental setup and CFD simulations. They were able to show that their model could quite accurately capture bubble size distributions correlating to the transition from bubble to slug flow. Parvareh, et al. [148] used the VoF technique to capture the liquid-gas interface development in co-current flow for both horizontal and upwards vertical flow configurations. Experimental work was performed in small diameter pipes of 2 cm diameter and 4 m length. In the tested cases, the researchers were able to qualitatively match simulation and experimental results for slug, churn and annular flows, but only a limited discussion of the numerics was given. Dakshinamoorthy [149] followed the approach of coupling the TFM with the VoF technique to analyse flow in a large vertical pipe (ID of 189 mm) with a superficial liquid velocity of 0.05 m/s and varying superficial gas velocities from 0.1 to 1.0 m/s. In this study, -67-
the authors were able to qualitatively identify flow regimes consistent with experimental results and without the need for pre-identification. It is noted that slight trouble in identifying a pure bubble regime was observed, with small regions of high void fraction possibly indicating a move to intermittent slug flow, again highlighting the difficulty that can arise in determining specific transition points. Quantitatively the same study compared both pressure drop and void fraction profiles for the slug and annular flow cases that showed reasonable agreement with experimental measurements. The following sections discuss the aforementined simulation techniques for simulation of different flow regimes.
7.2 Bubbly Flow Modelling of dispersed bubbly flow in pipes is typically approached using either the TFM or an Euler-Lagrangian technique. In order to model this flow regime with an ITM alone, a high-resolution grid is required to fully resolve the bubble motion which leads to excessive computations for practically sized scenarios. However, this approach is often used for direct numerical simulation (DNS) of a finite number of bubbles in order to derive correlations also known as closure models, for the interfacial forcing terms, such as drag and lift. These forces need to be modelled as sub-grid-scale interactions in both the TFM and Euler-Lagrange methods [138, 150, 151]. The TFM was validated by Rzehak and Krepper [152] against experimental void fraction and mean fluid superficial velocities of the bubble flow regime in upward flows through ANSYS CFX. It is noted that extensive validation with experimental data is still required for closure models under a wide range of flow conditions (e.g. counter-current flows) and configurations (e.g. inclined or annular pipe geometry, different pipe sizes). This can
-68-
potentially limit the TFM, but the possibility of formulating these correlations from CFD experiments is one option to streamline the process.
7.3 Slug Flow Capturing the bubble to slug regime transition can be quite complex using the TFM as the bubble size tends to be predefined in order to apply closure models. Therefore, MUSIG solvers along with PBMs have been developed to account for bubble coalescence and breakup. Such models were used by Lucas et al. [146] and further developed by Das et al. [153] to simulate the transition from bubbly to slug flow regimes in upwards vertical pipes and annular geometries, respectively. These studies highlighted the importance of capturing the radial position of different sized bubbles in predicting the transition point as a function of pipe length over diameter. The simulation results showed that small bubbles moved closer to the wall, but after coalescence they shifted towards the centre of the pipe. The application of ITMs such as the VoF, LS and PF techniques have been utilised in the literature to resolve the shape, velocity and liquid film parameters of Taylor bubbles to assist in the understanding of the slug flow regime. Additionally, these techniques have been used to analyse the wake region of the liquid slug in which smaller bubbles are typically found. Taha and Cui [154] used the VoF technique within the ANSYS CFX platform to analyse all of these parameters. They used a vertical pipe with a 19 mm diameter and concluded ranges of dimensionless numbers for which varying shape profiles, rise velocities and wake behaviour could be expected. In the study, the bubble rise velocity, in the form of the bubble Froude number, was shown to be a function of the surface tension. The results were consistent with experimental data from the literature with Eötvös numbers ranging from five to 500. Additionally, the inverse viscosity number (ܰ ) was found to be correlated to the length of the bubble wake, with numerical results presented for ܰ between 100 and -69-
750.These such relations can be essential to close the system of equations in 1D mechanistic models.
7.4 Churn/Annular Flow With a continued increase in gas velocity, Taylor bubbles become unstable and the flow within a pipe breaks down into the churn regime. Da Riva and Del Col [155] used the VoF technique and the ANSYS CFX simulation software in order to simulate the churn flow regime and its transition mechanisms in small diameter pipes (ID of 32 mm). Deforming bubbles in the churn flow regime introduce a great level of complexity in modelling via the TFM due to the lack of robust closure models for this regime. A DNS approach is also complicated due to the variation in bubble size and the requirement of a finely-resolved solution to capture the break-up of small bubbles. Montoya et al. [156] proposed that perhaps a hybrid model would be effective to capture the sub-grid-scale behaviour, however, this required the development of accurate break-up and coalescence models. Further increase in gas flow leads to the annular flow regime in which gas flows in the core of the pipe carrying entrained liquid droplets and surrounded by a thin liquid film. A simplified view of annular flow tends to be particularly well suited for interface tracking methods with a high level of separation. However, similar to the churn flow regime, there is a range of scales evident in the system and to accurately capture the behaviour of entrained droplets would require a high computational grid resolution using an ITM alone. Such a problem was addressed by Liu, et al. [157] where a two-phase, two-component numerical model was proposed to analyse vertical upwards annular flow in a small diameter pipe (ID of 31.8 mm). This study used a two-fluid-type mixture model in the gas core and a VoF method to differentiate the gas core from the liquid film. Good predictions were found for the pressure gradient, wall shear stress, film thickness and the film flow flux and the parameters
-70-
associated with the wave-like behaviour in the liquid film. This presents an interesting technique for capturing the various scales present in two-phase flows, however, a complete understanding of deposition and entrainment of liquid droplets is required for varying flow configurations. Despite a large body of existing literature in the simulation of flow regimes, complete validation of these models across a large range of flow geometries has not yet been achieved. This indicates potential work in the future to develop either robust coupling methods to capture bubble size of varying scales or improved closure relations to model the complex phase interactions. 8
Conclusions and outlook
This critical review of the published experimental data for gas-liquid flow maps in vertical pipes and annuli has highlighted the complications behind the accurate prediction of two-phase flow regime. Examination of the experimental methods adopted for the identification of bubbles, slug, churn and annular flow regimes identified subjectivity as being the greatest hindrance to the acquisition of reliable results. Measurement tools may also impede upon the development of flow phenomenon, and so objective, non-intrusive and noninvasive measurement techniques are required. However, this may be unachievable and a more feasible approach is to adopt multiple measurement techniques for validation. Review of the critical factors of pipe geometry (diameters, deviation from vertical), fluid properties (density, viscosity, interfacial tension, salinity) and flow conditions found that the effect of liquid viscosity upon flow transitions is a polarising topic with plenty of room for clarification. Alternative flow map coordinates were tested in an attempt to create a universal map which can be applied to any industrial application regardless of fluid type and experimental conditions.
-71-
Transition criteria were assessed against a large collated data set consisting of over 2500 flow map data points from 20 experimental studies of co-current upward flows in vertical pipes and annuli of diameters ranging from 12.3 to 67 mm. The statistical analysis identified the most reliable flow regime transition models as being: (i) Barnea [116] for dispersed bubble to bubble flow, (ii) Taitel, et al. [8] for bubble to slug flow, (iii) Barnea [116] for slug to churn flow, and (iv) Mishima and Ishii [6] for churn to annular flow regime. Although an abundance of experimental flow regime studies have been reviewed, it is observed that important information regarding the flow regimes is often ignored. In particular, the void fraction, or gas holdup, that is considered in developed transition criteria is rarely documented. Future experimental work should take into consideration the inputs required for computational modelling, thus improving comparability and the validation of results. Computational fluid dynamics techniques also need to be further developed in order to capture the complex behaviour of individual bubbles and thus better understand the interaction between the gas and liquid phases in different flow regimes.
-72-
Nomenclature
Ap
Projected bubble area (m2)
* uKS
Dimensionless phase superficial velocity
C
Empirical constant
uLS
Liquid superficial velocity (m/s)
CK
Empirical constant
* u LS
Dimensionless liquid superficial velocity
CM
Empirical constant
uM
Mixture superficial velocity (m/s)
C0
Approximate ratio of centreline
u∞
Rise velocity of fairly large bubbles
velocity to average velocity
(m/s)
(dimensionless)
D
Pipe inner diameter (m)
Greek symbols
Db
Bubble diameter (m)
α
Void fraction (dimensionless)
DC
Casing inner diameter (m)
αavg
Average void fraction (dimensionless)
Dcritical
Critical pipe inner diameter (m)
αb
Bubble void fraction (dimensionless)
DH
Hydraulic diameter (m)
α bs
Bubble-slug void fraction (dimensionless)
DT
Tubing outer diameter (m)
αmean
Mean void fraction (dimensionless)
D32
Sauter mean bubble diameter (m)
δ
Liquid film thickness (m)
Fi inter
Interfacial forces (N/m2)
εc
Critical void fraction (dimensionless)
-73-
HL
Liquid holdup (dimensionless)
µG
Gas viscosity (mPa.s)
lE
Entry length (m)
µL
Liquid viscosity (mPa.s)
m
Empirical constant
µS
Liquid specific viscosity (dimensionless)
N µl
Liquid viscosity number
ρG
Gas density (kg/m3)
sG
Gas specific density
ρH
Homogenous or no-slip density (kg/m3 )
ρL
Liquid density (kg/m3)
(dimensionless)
sL
Liquid specific density (dimensionless)
SL
Slippage number (dimensionless)
ρM
Mixture density (kg/m3)
Ti
Viscous stress tensor
σ
Surface tension (N/m)
σS
Liquid specific surface tension
(dimensionless)
U0
Bubble rise velocity (m/s)
(dimensionless)
UG
Taylor bubble rise velocity (m/s)
Non-dimensional parameters
ubS
Taylor bubble superficial velocity
FrM
= uM / Dg
ReGS
=
ρGuGS D µG
ReLS
=
ρLuLS D µL
(m/s)
uFS
Liquid film superficial velocity (m/s)
uGS
Gas superficial velocity (m/s)
-74-
* uGS
Dimensionless gas superficial
WeGS
velocity
uKS
Phase superficial velocity (m/s)
WeLS
-75-
=
2 ρGuGS D σ
2 D ρLuLS = σ
Acknowledgements
This project received industry funding through The University of Queensland’s Centre for Coal Seam Gas (www.ccsg.uq.edu.au). TM would like to acknowledge the support of the Australian Government Research Training Program Scholarship during the development of this work. References
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Appendix
Flow maps of co-current upward vertical flows in pipe of diameters between 12.3 and 67 mm plotted with alternate coordinates as presented in Table 7.
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Highlights
• • •
Critical review and analysis of 3947 flow regime data points for vertical flows. Assessment of the available models for prediction of upward flow regime transition. Generation of a universal flow map for upward flows based on Reynolds numbers.
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