An assessment of gas void fraction prediction models in highly viscous liquid and gas two-phase vertical flows

Highlights

• Air-viscous liquid mixture used to investigate gas void fraction in vertical pipes.

• Influence of superficial phase velocities and liquid viscosity studied.

• 100 existing correlations evaluated using air-viscous liquid mixture database.

• Detailed assessment showed the overall best performing correlations.

• Churn/annular void fraction correlations developed which give improved predictions.

Abstract

Gas void fraction plays a significant role in determination of several multiphase flow parameters. Good insight of its behaviour coupled with accurate prediction is imperative for design of efficient equipment which has the potential to translate to higher production rates in the petroleum industry. Against the background of the prevalence of higher viscous and imminent application of highly viscous liquids in the petroleum industry, air-water and air-low viscous liquid mixtures dominate gas void fraction research in vertical pipes. In this work, gas-liquid (${\mu }_l=100-7000mPas$) mixtures are used to investigate the behaviour of gas void fraction in vertical pipes. The influence of superficial phase velocities and liquid viscosity are observed. Further, a combined database consisting of experimental and the reported data of Schmidt et al. (2008) is employed to evaluate the predictions of 100 existing correlations. The results indicate that the Hibiki and Ishii (2003) and Bestion (1990) correlations are the overall best and second-best performing correlations. In the absence good performing correlations for churn and annular flows, two correlations each, based on drift flux and slip ratio, are developed respectively. Predictions from these correlations show good agreement with the database and comparable performance with the overall best correlations.

Introduction

Simultaneous transportation of gases and liquids is critical to production in many industries. For this reason, gas-liquid two-phase flows are regularly employed in industries including food, civil, chemical, nuclear, power plants (Yin et al., 2018) and petroleum where they are employed in various applications (Wu et al., 2017). For instance, two-phase flow applications are found in process equipment (vapour-liquid contactors and/or absorbers, vapour generators, thermosyphon reboilers, and gas-liquid chemical reactors) in chemical industries (Fernandes et al., 1983). In the petroleum industry, two-phase flows are observed during transportation of oil and gas products through pipes from wells to processing facilities (Hewakandamby et al., 2014; Kim et al., 2018) while its characteristics are employed in the calculation of phase flow rates, pressure loss and liquid holdup in pipelines. Additionally, related parameters are essential to the design of production conduits, sizing of gas lines, gathering and separation systems, heat exchangers and gas condensate pipelines (Alamu, 2010).

Two-phase flows in vertical pipes can be classified on the basis of flow patterns observed. A large number of flow pattern classifications exists partly due to the subjective nature of identification methods and can also be attributed to the effects of flow conditions, pipe geometry, and fluid properties. Additionally, the application of current technologies such as wire mesh sensors is aiding more accurate identification of previously unknown flow characteristics (Abdulkadir et al., 2014a; Aliyu et al., 2017; Almabrok et al., 2016; Ambrose, 2015; Hernandez Perez et al., 2010; Peddu et al., 2018). Common flow patterns reported, however, are bubble, slug, churn (froth), annular (Hewakandamby et al., 2014).

Bubble flow is characterized by individual gas bubbles dispersed in a continuous phase liquid. This flow regime is often observed at low gas and liquid velocities. Some studies (Barnea, 1987; Taitel et al., 1980) have also reported dispersed bubble flow regime at high liquid velocities/flow rates, which can produce large turbulent forces and inhibit bubble coalescence. Slug flow occurs when gas velocity is increased beyond that generating bubble flow. This regime is characterized by the presence of large gas bubbles, known as Taylor bubbles, which occupy the entire cross section of the pipe except for a thin liquid film on the wall. Taylor bubbles form as a result of coalescence smaller bubbles as gas velocity increases. Further increases in the superficial gas velocity lead to the collapse of Taylor bubbles into an unstable flow (Wu et al., 2017). Churn flow is characterized by highly oscillatory, violently mixing of liquid and gas (Hewakandamby et al., 2014) while annular flow is fully developed at sufficiently high gas velocities and is characterized by a gas core flowing in the middle of the pipe with thin liquid film flowing at the inner periphery of the wall (Berna et al., 2014; Wu et al., 2017). Details of the flow regimes have been compiled by several authors including Alamu (2010), Bhagwat and Ghajar (2014) and Wu et al. (2017).

Measured flow characteristics such as gas void fraction (Cioncolini and Thome, 2012), liquid holdup and pressure gradient can also be used to categorize two-phase flows. In particular, gas void fraction, defined as the quantification of the in-situ phase fraction for the gas phase, is a dimensionless quantity which plays crucial roles in the accurate determination of several multiphase flow parameters (Parrales et al., 2018) including mixture density, pressure gradient and heat transfer (Azizi et al., 2016; Cioncolini and Thome, 2012). It is also useful in the classification of flow patterns in pipes (Barnea, 1987; Taitel et al., 1980). Indirectly, therefore, gas void fraction influences the accurate design of equipment for safety and enhanced production. Its significance, the need to understand its dynamic behaviour as well as factors which influence it has made it an intense subject of research spanning several decades and resulting in a long list of reported correlations for varied flow conditions and pipe configurations.

Against the backdrop of significant application of highly viscous liquids in industry, the behaviour of gas void fraction in vertical pipes has largely been studied using air-water with a considerable number of studies employing air-low viscosity mixtures. Reports from studies based on air-low viscosity mixtures establish, with evidence, that liquid viscosity influences flow characteristics including gas void fraction (Alamu, 2010; Parsi et al., 2015a). Despite these findings, there is generally a dearth of information and data obtained from highly viscous flow studies, especially for flows in vertical pipes. To successfully model gas void fraction in highly viscous flows, there is the need to understand its behaviour under this influence. Furthermore, most existing correlations were developed based on air-water and air-low viscosity liquid mixtures, hence their prediction capacities in high viscosity liquid systems need investigation to ascertain their reliability.

In an attempt to fill the information gap, this review highlights findings of relevant studies and reports the results of an experimental study with the same focus. Additionally, it also aims to establish the prediction accuracy of existing correlations when applied to highly viscous flows. Results from this study will provide the much need confidence in the application of these correlations and make the case for improvement or development of new ones where necessary.

Gas void fraction can be estimated for all flow regimes. Perhaps, this constitutes one of the major reasons for its intense investigation in multiphase flows. Research efforts have yielded several correlations for different flow regimes and inclinations. Recent contributions include the works of Vijayan et al. (2000), Coddington and Macian (2002), Woldesemayat and Ghajar (2007), and Godbole et al. (2011) and Cioncolini and Thome (2012). For the majority of reported studies, however, air-water mixtures constitute the main experimental fluids. Detailed information has been covered by Godbole (2009), Godbole et al. (2011), Mathure (2010), Bhagwat (2011), Oyewole (2013), and Tang et al. (2013). The few reported studies on the subject reported using gas-low/higher viscous liquids in vertical pipes are listed in Table 1.

As a result of intense study of gas void fraction, several correlations have been reported in literature. In this study, correlations which presented satisfactory performance are highlighted to aid comparison and discussion.

Gas void fraction correlations can be categorized into 4 groups; namely, flow pattern specific correlations, flow pattern independent correlations for vertical upward orientation, flow pattern independent correlations applicable to a variety of the flow orientations including vertical upward flow and correlations not developed for but applicable to vertical upward flow (Godbole, 2009). Flow pattern-specific correlations are developed for a specific flow pattern in vertical upward two-phase flow. Flow-regime independent correlations developed for vertical pipes comprise those correlations independent of flow pattern and developed only for upward vertical orientation. Flow regime independent correlations developed for multiple pipe orientations are correlations are independent of flow pattern and developed only for different angles of inclination including upward vertical orientation. Flow regime independent correlations not developed for but applicable to vertical pipes are correlations not developed specifically for vertical flow but are recommended by researchers for prediction of void fraction in vertical flow.

Correlations can further be categorized into four groups based on the approach employed for development; namely, empirical (semi-empirical), ${\text{K}\alpha }_{\text{H }}$, mechanistic, slip ratio and drift flux. The empirical approach fits curves to data obtained from experiments and makes predictions using the mathematical expressions which describe the fitted curve. The ${\text{K}\alpha }_{\text{H}}$ methods predict void fraction by multiplying the homogenous model ($\alpha =v_{sg}/v_{sg}+v_{sl}$) with an empirically determined constant, K (Cioncolini and Thome, 2012). Mechanistic correlations, on the other hand, are based on mathematical theories which are based on flow phenomena. The drift-flux model, is based on the interaction of two-phase and physics of the flow. It represents the mean value of the local void fraction averaged across the pipe cross-section and in essence, is the same as that of $\alpha$ when measured using the quick closing valve method. Hence, the cross-sectional averaged void fraction $\alpha$ can be interchangeably used with $\alpha$. Slip ratio correlations specify establish the empirical relationship for predicting the slip between phases (Cioncolini and Thome, 2012). Majority of correlations reported for void fraction prediction are based on the drift-flux approach (Cioncolini and Thome, 2012).

For this study, the first categorization is adopted for analysis. Correlations which presented good performances in this study are briefly discussed. Also, a summarized detail of the correlations discussed is provided in Appendix A.1. Details of these approaches as well as others, not covered in this study, are adequately discussed by the aforementioned authors.

Gomez et al. (2000), as reported by (Godbole, 2009), proposed a mechanistic model for prediction of liquid holdup (gas void fraction) in bubble flow as part of their work to develop a unified model for the prediction of flow pattern, liquid holdup and pressure drop for all flow patterns from horizontal to vertical two-phase flow. They introduced the inclination angle to modify the Hasan and Kabir (1988) bubble flow correlation in order to extend the range of inclinations. The drift velocity proposed by Harmathy (1960) was adopted. The ${\text{C}}_{\text{o}}$ value used was 1.15.

Nicklin and Davidson (1962) studied flow pattern transition in upward vertical slug flow using air and water mixtures as fluids and presented a drift flux correlation for void fraction. The authors estimated a distribution parameter, ${\text{C}}_{\text{o}}$ of 1.2. Ellis and Jones (Ellis and Jones, 1965; Godbole, 2009) adopted an empirical correlation for void fraction development for the slug flow regime. Bonnecaze et al. (1971) studied void fraction and pressure drop in slug flow using gas and oil in inclined ($\pm 10°$ to horizontal) pipes and used 152 experimental data points to develop a ${\text{K}\alpha }_{\text{H}}$ correlation for void fraction prediction. Kataoka and Ishii, 1987a, Kataoka and Ishii, 1987b demonstrated that the conventional drift flux model for pool void fraction to relatively large pipes was only limited to low gas fluxes and proposed a drift flux correlation for larger systems (Aliyu et al., 2017). Their correlation accounted for the effect of the gas and liquid phase properties, diameter and pressure. The authors compared their model with air-water, air-glycerin and steam-water void fraction data of 13 other researchers. Good results were achieved with nearly all predicted data points falling within the $\pm$ 20% error index (Godbole, 2009). The proposed mechanistic correlation presented by Gomez et al. (Godbole, 2009) for slug flow is similar to that of Fernandes et al. (1983) and is applicable to inclinations from 0 to + 90$°$. The correlations of Kataoka and Ishii, 1987a, Kataoka and Ishii, 1987b, Nicklin and Davidson (1962) and Bonnecaze et al. (1971) predicted more than 80% of entire data used by Godbole (2009) in his study. The correlation of Gomez et al. (2000) (as presented by Godbole, 2009) predicted 80% of the overall data. Godbole (2009) asserts that the Bonnecaze et al. (1971) and Nicklin and Davidson (1962) correlations are approximately the same for vertical upward orientation. Hence, identical performance is to be expected. These two correlations performed best for overall slug flow data used by Godbole (2009).

Kabir and Hasan (1990) applied the drift-flux model to develop a correlation for gas void fraction. The authors used a ${\text{C}}_{\text{o}}$ value of 1.15. Godbole (2009) reported a good performance for the correlation when it was evaluated. It predicted as high as 91.3% experimental data points within the 15% error index. At the suggestion of Mao and Dukler (1993) that slug flow correlations could predict churn flow data, Godbole (2009) evaluated the Nicklin and Davidson (1962) and Orell and Rembrand, 1986; (Godbole, 2009) correlations with his churn flow data. The authors found that Nicklin and Davidson (1962) performs better than the churn flow correlations, predicting more than 80% of experimental data in the 10% error index.

Correlations which offered good performances at this flow regime include those of Lockhart and Martinelli (Godbole, 2009), Fauske (1961), Smith (1969), Gomez et al. (Godbole, 2009) and Beggs (1972). The Lockhart and Martinelli correlation, as presented by (Godbole, 2009), is a slip ratio correlation. Woldesemayat (2006) reported the capacity of this correlation to predict void fraction in annular flow. The Fauske (1961) correlation also employed a slip ratio method to develop a gas void fraction correlation based on a steam-water system for a quality range from 0.01 to 1 using diameters of 0.003175 m, 0.006833 m and 0.0127 m. Pressures during the experiment ranged from 0.28 to 2.48 MPa(40 to 360 psia) respectively. Smith (1969) also proposed a slip ratio correlation for prediction of void fraction in annular flow. For annular flow, the Gomez et al. (2000) correlation (presented by Godbole, 2009) was mechanistic in nature and a similar approach to that of Kabir and Hasan (1990). This correlation accounted for liquid entrainment. The expression for liquid entrainment, proposed by Wallis (1969) was adopted for this correlation. The correlation presented by Beggs (1972) for void fraction prediction was empirical in nature and applicable to all inclinations.

Schmidt et al. (2008) studied flow pattern and gas void fraction by conducting adiabatic experiments using mixtures of nitrogen and solutions of Polyvinylpyrrolidone (Luviskol) in water with dynamic viscosities from 900 to 7000 mPa s and a pipe with ID 0.054 m. Mass flux and quality varied from 8 to 3500 kg/m²/s and 0–82% respectively. Superficial gas and liquid velocities were 0–30 m/s and 0.005–3.4 m/s respectively. For comparison, reference measurements were taken for mixtures of Nitrogen and water (1 mPa s). Two new correlations, based on slip ratio and drift flux methodologies respectively, were developed using 87 selected data points. Overall predictions of the correlations for the entire data agreed very well with the experimental data. Thom (1964) suggested a slip correlation for vertical upward flow of boiling water. The author presented the variation of void fraction with quality. Baroczy (1966) formulated a slip ratio correlation using vertical flow data. Czop et al. (1994) conducted experiments using 0.0198 m diameter vertical helical tubes with water and SF₆ as the working fluids. They developed a ${\text{K}\alpha }_{\text{H}}$ correlation based on the data obtained. Predictions of their correlations agreed well with the experimental data (40 data points) within $\pm$ 10%. The Dimentiev et al. (1959) correlation is a pool void fraction correlation for large diameter pipes and steam-water mixtures. The accuracy of the correlation was not stated by the author. Dix (1971) developed a drift flux correlation based on vertical upward flow data sets from a boiling water reactor. The correlation was one of the top three correlations in a comparative study Chexal et al. (1992) carried out using approximately 1500 data points obtained from a vertical upward steam – water system. The author presented a $C_o$ which is a function of phase superficial velocities. Takeuchi et al. (1992) developed a drift flux correlation for vertical two-phase flow. Accuracy of the correlation was not provided by the authors. It also presented good performance when subjected to the air-water data of Sujumnong (1997) (Godbole, 2009) and gave good performance in the 15% (more than 85%) and 10% (more than 75%) error indices respectively.

Bhagwat and Ghajar (2014) proposed two separate sets of equations for the distribution parameter and drift velocity for the drift flux correlation for gas void fraction prediction. The new expressions were defined as functions of several two-phase parameters. 8255 data points collected from more than 60 sources consisting of air-water, argon-water, natural gas-water, air-kerosene, air-glycerin, argon-acetone, argon-ethanol, argon-alcohol, refrigerants (R11, R12, R22, R134a, R114, R410A, R290, and R1234yf), steam-water as well as air and oil mixtures. The authors demonstrated successful prediction of experimental data obtained using hydraulic pipe diameters ranging between 0.5 and 305 mm, pipe orientations of −90$°\le \theta \le +$ 90$°$, liquid viscosities ranging from 0.0001 to 0.6 Pa s, system pressures from 0.1 to 18.1 MPa and two-phase Reynolds numbers from 10 to $5\times {10}^6$. Further, comparison with existing top performing correlations revealed the correlation gives better performance over the entire range of void fraction. The correlation appears to predict well at various viscosities.

Armand (1946) (Godbole, 2009) employed a ${\text{K}\alpha }_{\text{H}}$ approach to develop a gas void fraction. Hart et al. (1989), Flanigan (1958) and Wallis (1969) used a general equation to develop their correlation for predicting gas void fraction. Turner and Wallis (1965) adopted a slip ratio methodology to develop their void fraction correlation.

The rest, including Mattar and Gregory (1974), Woldesemayat and Ghajar (2007), Lahey and Moody (1977), Ishii (1977) (Godbole, 2009), Ohkawa and Lahey (1980) (Godbole, 2009), Jowitt et al. (1984), Bestion (1985), Pearson et al. (1984) (Azizi et al., 2016), Hughmark (1965), Gregory and Scott (1969), Toshiba (Coddington and MaCain, 2002; Woldesemayat and Ghajar, 2007), Shipley (1982) (Bhagwat and Ghajar, 2014), Hibiki and Ishii (2003), Mishima and Hibiki (1996), presented new equations for distribution parameter as a function of inner diameter. Clark and Flemmer (1985) (Bhagwat and Ghajar, 2014), and Beattie and Sugawara (1986) (Bhagwat and Ghajar, 2014) also utilized the drift flux method for correlation development.

Mattar and Gregory (1974) employed air-oil mixtures, the correlation was designed to be capable of predicting gas void fraction (GVF) from horizontal to $\pm$ 10$°$ inclined flows (Mathure, 2010; Mattar and Gregory, 1974; Woldesemayat and Ghajar, 2007). Lahey and Moody (1977) (Godbole, 2009) presented a drift flux correlation known as the “ramp model”. Accuracy of correlation was not determined initially by the authors. Ohkawa and Lahey (1980) (Godbole, 2009) proposed a correlation for void fraction in countercurrent flow limited (CCFL) conditions. Accuracy of correlation was not determined initially by the authors. Bestion (1985) presented a drift flux correlation with a modified expression for drift velocity and a distribution parameter of 1. When compared with the experimental data of Coddington and Macian (2002), the author observed overprediction above the value of 0.6. Its absolute error in prediction was 0.049. Shipley (1982) (Bhagwat and Ghajar, 2014) presented a drift flux correlation. It can be noticed that the expression for drift velocity does not account for the effect of fluid properties. Ishii (1977) (Godbole, 2009) presented a drift flux correlation. Accuracy of correlation was not determined initially by the authors. When compared with the data of Coddington and Macian (2002), it predicted it with an absolute error of 0.048. The correlation was found to present good performance when subjected to the air-water data of Sujumnong (Godbole, 2009), and gave the best performance in the 15% (94.2%) and 10% (86.5%) error indices respectively. It also presented the best performance for 10% (85.7% data points) and 15% (92.2% data points) error bands for air-glycerin mixtures.

Jowitt et al. (Godbole, 2009; Jowitt et al., 1984) suggested a drift flux correlation. The correlation predicted the void fraction data in the study of Coddington and Macian (2002) with an average absolute error of 0.057. It was also observed that the correlation showed overprediction for void fraction data for values equal to and greater than 0.5. Hibiki and Ishii (2003) developed three flow regime dependent correlations for bubble, slug and annular flow respectively. The authors employed drift velocity expressions suitable for slug flow, which captures the effect of pipe diameter and phase densities. Mishima and Hibiki (1996) presented a correlation based on the drift flux methodology. The drift velocity they employed does not account for the effect of fluid properties. Beattie and Sugawara (1986) (Bhagwat and Ghajar, 2014) presented a drift flux model essentially developed for two-phase flow of steam-water through large diameter pipes and is modelled as a function of two-phase friction factor (ftp).

Hughmark (1965) presented a drift flux correlation with a $C_o$ value of 1.2. There is the noticeable absence of drift velocity parameter (as reported by Woldesemayat and Ghajar (2007) and Mathure (2010)). Using carbon dioxide and water mixtures and a pipe ID of 0.75 and 1.5 inches (Nobakht Hassanlouei et al., 2012), Gregory and Scott (1969) developed a drift flux correlation based on the work of Nicklin and Davidson (1962) and determined a $C_o$ value of 1.19. The authors presented no drift velocity in their correlation (Mathure, 2010; Woldesemayat and Ghajar, 2007).

Clark and Flemmer (1985) (Bhagwat and Ghajar, 2014) analyzed the Zuber and Findlay (1965) drift flux model for both upward and downward flows. Air-water mixtures were used in experiments with a pipe diameter of 0.1 m. The authors performed regression on results using Wallis (1969) equation and found bubble rise velocity approximately equal to 0.25 m/s which is in good agreement with Harmathy (1960) equation. They obtained a $C_o$value of 1.165 the best fit for all data in bubbly flow for downward flow and $C_o$ value of 1.07 for bubble upward flow. Their result was found in contrast to that of Zuber and Findlay (1965) who proposed the same value for the different conditions. For slug flow, Clark and Flemmer (1985) (Bhagwat and Ghajar, 2014) suggested a drift velocity similar to that of Nicklin et al. (1962). They observed a certain relationship between the distribution parameter and gas void fraction for slug flow. The expression for the distribution parameter $C_o$ in terms of void fraction was given as, ${\text{C}}_{\text{o}}=1.521\left(1-3.67\alpha \right)$. However, they claimed that this linear relation between $C_o$ and gas void fraction may not be valid for some pipe geometries since dependence on $C_o$ on void fraction may vary for different pipe diameters. The reliability of this expression is open to question since the correlation was not compared with another data and the percentage accuracy of the void fraction correlation was not provided (Bhagwat, 2011).

Two correlations, originally developed by Cai et al. (1997) (Bhagwat and Ghajar, 2012) for predicting void fraction for vertically downward flows were evaluated by Bhagwat and Ghajar (2012) using data obtained for vertically upward flows with success. These were also integrated into study for assessment. Though Nicklin et al. (1962) was developed for slug flow, Woldesemayat and Ghajar (2007) observed that it predicted 75% of their data points for all their data sets, indicating that it has more potential than just to predict for slug flows only.

Detailed information has been covered by Godbole (2009), Godbole et al. (2011), Mathure (2010), Bhagwat (2011), Oyewole (2013), and Tang et al. (2013).

A number of comparative studies have been made to evaluate the reliability of correlations at different flow conditions. This has often been the case when new data, obtained at novel conditions, become available.

Majority of the comparative studies have been implemented for horizontal pipes (Dukler et al., 1964; Marcano, 1973; Abdul-Majeed, 1996; Hoogendoorn, 1959). Dukler et al. (1964) implemented the first comparison. In their investigation, 706 void fraction data points of Hoogendoorn (1959) which had viscosities range between 3 and 20 mPa s were used for the exercise. Void fraction correlations considered included Hoogendoorn (1959), Hughmark (1962) and Lockhart and Martinelli (1949). Using statistical tools such as arithmetic mean deviation and standard deviation, the authors showed that the Hughmark (1962) correlation performed better than the others. Marcano (1973) performed a similar exercise on the correlations of Lockhart and Martinelli (1949), Hughmark (1962), Dukler et al. (1969), Eaton et al. (1967), Guzhov et al. (1967) and Beggs (1972) using the reported data of Eaton (1966) and Beggs (1972). The authors found that correlations of Eaton et al. (1967) and Beggs (1972) performed well due to the fact the data used for the comparison was the data from which these correlations were developed. Further, the correlations of Dukler et al. (1969) and Lockhart and Martinelli (1949) were found to present satisfactory results.

Palmer (1975) compared the correlations of Beggs (1972), Flanigan (1958) and Guzhov et al. (1967) for inclinations between 4.2 and 7.5°. Using the percent error, average percent error and standard deviation, the authors concluded that the Beggs (1972) correlation presented good prediction of the void fraction for uphill flow.

Mandhane et al. (1975) utilized the 2700-point void fraction data hosted in the University of Calgary multiphase pipe flow data bank to evaluate 12 correlations: Lockhart and Martinelli (1949), Hoogendoorn (1959), Eaton et al. (1967), Hughmark (1962), Guzhov et al. (1967), Chawla (1969), Beggs (1972), Dukler et al. (1969), Scott (1962), Agrawal et al. (1973), Hughmark (1965) and Levy (1960). Root mean-square error (RMSE), mean absolute error (MAE), simple mean error, mean-percentage absolute error (MPAE) and mean percentage error (MPE) were the statistical tools used for the assessment. Best performing correlations were identified for the various flow regimes.

Spedding et al. (1990) (Woldesemayat and Ghajar, 2007) evaluated 60 correlations using the data of Spedding and Nguyen (1976) for an upward angle of 2.75° from the horizontal. 30% of data points predicted within the error was the criteria for satisfactory performance. Nicklin et al. (1962) was found to give satisfactory predictions for bubble and slug flows at all inclined angles. The correlations of Bonnecaze et al. (1971), Premoli et al. (1971) and Lockhart and Martinelli (1949) were reported to give satisfactory predictions for some flow patterns independent of inclination angle. Lockhart and Martinelli (1949) and Spedding and Chen (1984) performed well for slug and annular flow respectively.

Abdul-Majeed (1996) simplified the mechanistic model of Taitel and Dukler (1976) thereby obtaining a new correlation. He compared the predictions of 12 correlations with the experimental data obtained from his 51-mm diameter horizontal pipe. Statistical tools used for the comparison were the average percent error (APE), absolute average percent error (AAPE) and the standard deviation. He demonstrated that the correlation satisfactorily predicts void fraction in stratified, slug and annular flow regimes better compared to the Taitel and Dukler (1976) correlation specifically developed for stratified flow.

Spedding (1997) implemented an extensive comparison on more than 100 void fraction correlations using the air-water data of Spedding and his co-workers (1989; 1979; 1993; 1991; 1976) for all inclinations ($-90°\text{ to}+90°$) (Woldesemayat and Ghajar (2007). The authors concluded that no correlation could handle all flow regimes and angle of inclination satisfactorily. Different void fraction correlations were recommended for the various flow regimes and inclinations.

To implement a horizontal and upward vertical comparison, Diener and Friedel (1998) used 24,000 experimental data points to evaluate 13 correlations. The average predictive accuracy of the correlations was established the scatter logarithmic ratios, scatter of absolute deviations, average logarithmic ratios and mean density. The first correlation of Rouhani and Axelsson (1970) was recommended as exhibiting an accurate predictive capability.

For vertical pipes, comparison of predictions for gas void fraction has been investigated by a few researchers including Godbole (2009), Woldesemayat and Ghajar (2007) and in recent times, Bhagwat and Ghajar (2012). Godbole (2009) comprehensively evaluated 52 existing correlations using experimental data and data obtained from literature. He observed that no correlation was could predict the data of Schmidt et al. (2008) satisfactorily. He attributed this failure to the fact that all the correlations were developed based on low viscosities. Woldesemayat and Ghajar (2007) compared the performance of 68 void fraction correlations using a dataset of 2845 data points covering a wide range of parameters. The analysis showed that most of the correlations developed are very restricted in terms of handling a wide variety of data sets. Based on the observations made, an improved void fraction correlation which could acceptably handle all data sets regardless of flow patterns and inclination angles was suggested. In recent times, using a large dataset, a wide range of flow conditions and pipe geometries, Bhagwat and Ghajar (2012) (Ghajar and Bhagwat, 2013) presented a flow pattern independent void fraction correlation. The authors claim the correlation is accurate for all inclinations, diameters from 0.5 to 305 mm and viscosities from 0.0001 Pa s to 0.6 Pa s for system pressures from 0.1 MPa to 18.1 MPa. The correlation was verified with 8255 data points collected from more than 60 sources and was determined to perform consistently accurate and satisfactorily over the collected data. Abdulkadir et al. (2014a) compared 13 correlations with air-silicone data. Morooka et al. (1989) was adjudged the best correlation based on RMS error while Kawanishi et al. (1990) was found to be the best based on percentage error. McNeil and Stuart (2003) as well as Schmidt et al. (2008) reported that the existing correlations compared could not accurately predict their data. However, it should be noted that their conclusion was based on comparison of very few correlations.

In summary, literature remains dominated by studies which employed air-water as well as air-low viscosity liquids as experimental fluids. Data obtained from these experiments have been employed for the development of gas void fraction correlations. This has fueled concerns about the ability of existing correlations to provide accurate prediction for highly viscous gas-liquid flows (Godbole, 2009; McNeil and Stuart, 2003; Schmidt et al., 2008) due to limitations including flow pattern dependency and empiricism (Godbole et al., 2011). Empiricism comes into play because some of correlations have been developed and validated with data limited to some specific flow conditions (e.g. pipe configuration and orientation, flow pattern, and gas-liquid combination) (Godbole et al., 2011). Furthermore, the influence of liquid viscosity on gas void fraction has been established with evidence. Research reports of authors whose work has yielded some data and insight to the discussions are listed in Table 1. Due to scarcity of highly viscous data this knowledge is still limited to information obtained with low viscous liquids. Knowledge of the behaviour this important parameter under the influence of high liquid viscosity would translate to more accurate prediction of other equally important flow parameters including pressure gradient and additionally contribute to safe and efficient equipment design. The full extent of its influence needs to be investigated. In addition, there is a plethora of existing correlations for gas void fraction, majority of which were developed based on air-water as well as air/gas – low viscous liquid data. Before improved correlations can be developed for highly viscous flow conditions, there is the need to scrutinize existing ones. Evaluations of such nature provide strong basis and direction for targeted improvements during development of new correlations of modification of old ones.

In this work, the influence of high liquid viscosity on gas void fraction is investigated and reported. In addition, using the combined experimental data and the reported data of Schmidt et al. (2008), predictions of 100 existing correlations are compared with combined experimental data and the best performing correlations identified. Further, based on the database employed, two new gas void fraction correlations are developed for churn and annular flows respectively. Results of evaluation indicated that predictions from these correlations agree very well with the experimental data and their performances is observed to rival than the top performing existing correlations.

In the absence of a universal definition for satisfactory performance for correlations prediction assessment, the user-defined approach adopted Godbole et al. (2011) and Bhagwat and Ghajar (2012) is utilized in this study. The correlations were evaluated against the entire experimental dataset, four specified ranges of the void fraction and the different flow patterns. To identify the best performing correlations, four levels of assessment were pursued. Accuracy of correlations were judged in terms of percentage of experimental data predicted within a selected error index and RMS error.

The first level of assessment, which is assessment of the entire data is perfunctory, since it overlooks the strengths and weaknesses of the correlations in specific ranges of void fraction. The number of experimental data points is not uniformly distributed throughout the entire void fraction range of $0<\alpha <1$ (in this study, majority are in the annular flow regime) hence, relying solely on overall performances could lead to a biased interpretation. Subsequently, a second level of assessment, which is the analysis of correlations at various viscosities. This is important to gain insight into the reliability of the prediction capacities of the correlations at varied viscosities. The third assessment level was to examine the predictions of correlations at smaller void fraction ranges, by dividing the entire void fraction range into four categories: $0<\alpha \le 0.25$, $0.25<\alpha \le 0.5$, $0.5<\alpha \le 0.75$, $0.75<\alpha \le 1.0$. Dividing the analysis into specific void fraction ranges would also reveal the most accurate correlations for each specific range, thus allowing access to correlations with higher accuracies in specific void fraction range of interest. The previous authors reported that the void fraction in the range typically 0–0.25 is sensitive to the increase in the gas flow rate and also the percentage error in the prediction is large due to low values of the void fraction, hence a less restrictive criterion was used for the lowest of the four specified void fraction ranges (Bhagwat, 2011). Due to better accuracies involved in the measurement and the high values of the void fraction typically in a range of 0.75 < $\alpha$ < 1, the associated percentage error was expected to be small and hence a stringent criterion was set in this range for the satisfactory performance of the void fraction correlations. Finally, the fourth level of assessment is taking the “best” correlation identified from the first three levels of assessment and comparing it with the performances of the flow pattern specific void fractions. The criteria for assessment are summarized in Table 2.

Out of the 100 void fraction correlations considered, 47 are mentioned in this article because they were found to compare satisfactorily with the compiled experimental results. It is to be noted that, in the work of the previous authors, only three levels of assessment were investigated because viscosity was not a parameter to be examined.