A New Model for Predicting Liquid Holdup in Two-Phase. Flow under High Gas and Liquid Velocities

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1 A New Model or Predicting iquid Holdup in Two-Phase Flow under High Gas and iquid Velocities Zilong iu a,b,c, Ruiquan iao a,b,c,*, Wei uo a,b,c, Joseph X. F. Ribeiro a,b,c a. Petroleum Engineering College, Yangtze University, , Wuhan Campus, No. 111, Caidian Street, Caidian District, Hubei Province, China b. The Multiphase Flow aboratory o Gas it Innovation Centre, CNPC, , Wuhan Campus, No. 111, Caidian Street, Caidian District, Hubei Province, China c. The Branch o Key aboratory o CNPC or Oil and Gas Production, Yangtze University, Jingzhou 43403, China Abstract Existing liquid holdup models are generally based on low gas and liquid velocities. To extend the applicable range o existing liquid holdup prediction models and improve their prediction accuracy, a gas-liquid two-phase low experiment was carried out using a pipe with an inner diameter o 60 mm and length o 11.5 m. The supericial gas and liquid velocity ranges were 14.07~56.50 m/s and 0.05~1.46 m/s, respectively. The results indicate that the liquid holdup decreases with the increase in the supericial gas velocity and increases with the increase in the supericial liquid velocity. A new annular low model or calculating low liquid holdup in a horizontal pipe was developed and presented, considering the relationships between the riction actor ratio 1

2 o the liquid phase and the gas-liquid interace as well as the supericial Reynolds number o the gas and liquid. The predictions o the model were ound to be accurate with an average absolute error o 4.8%. Further, combining the approach o the Beggs-Brill model with that o the horizontal pipe model established in this paper, a new liquid holdup model that accounts or dierent angles is presented. It was observed the resultant model is also accurate and has an average absolute error o 10%. Keywords: Gas-liquid two-phase low; Annular low; Higher gas and liquid velocities; ow liquid holdup 1. Introduction Gas-liquid two-phase low exists widely in petroleum, chemistry, nuclear power, aerospace and other industries. In the petroleum industry, gas-liquid two-phase low oten occurs in oil and gas production wells and gathering pipelines, and its low characteristics have signiicant inluence on the production o reservoirs and the equipment on the ground. iquid holdup is not only an important parameter or the classiication o low patterns but also related to the calculation o the existing models o pressure drop. Gas-liquid two-phase low is more complicated than single-phase low. Similarly, determination o liquid holdup is also complex because there are many actors that inluence liquid holdup. Due to its complexity, most researchers initially used empirical models to predict liquid holdup [1-3]. However, empirical models are based on

3 experiments and applicable to experimental data within certain ranges o conditions. It is diicult, thereore, to generalize and apply the empirical models to other experimental and operational conditions. With the development o gas-liquid two-phase low mechanisms and computational luid dynamics (CFD), several investigators have studied mechanistic models that can predict the liquid holdup and subsequent pressure drop or dierent angles [4-11]. One o the most signiicant mechanistic models, which is based on the dynamics o slug low, was carried out by Zhang [8]. By using the entire ilm zone as the control volume, the momentum exchange between the slug body and the ilm zone was introduced into the momentum equations or slug low. Slug low shares transition boundaries with all the other low patterns. The equations o slug low are used not only to calculate the slug characteristics but also to predict transitions rom slug low to other low patterns. Slug liquid holdup is a critical slug low characteristic or predicting average liquid holdup. Wang et al. [1] developed a complex mechanistic model or slug liquid holdup, using an empirical proportionality parameter generated rom their data bank as a unction o the Froude number and the inclination angle. Al-Saran [13] postulated several mechanisms o gas entrainment and evolution within the slug body and proposed a new simple empirical slug liquid holdup closure relationship valid or dierent liquid viscosity. Hassanlouei [14] presented a methodology or calculation o a slug liquid holdup in a horizontal pipe. The advantage o this method is that the slug unit holdup can be calculated directly rom the solutions 3

4 o the low ield equations with no need to use correlations. Zuber [15] irst proposed the drit-lux model to predict the liquid holdup or slug low, which has been well-researched and applied to gas-liquid two-phase pipe lows [16-1]. Some researchers used the two-luid model to calculate liquid holdup o stratiied and annular low regimes [-4]. The two-luid model was developed by establishing and solving a momentum equation or each phase with corresponding closure relationships, which are oten empirical in nature. Khaledi [5] perormed experiments with high density gas phase and oils o two dierent viscosities and the experimental results that were obtained were compared with the predictions rom a two-luid gas-liquid model, which was presented by Unander [6]. Dabirian [7] studied the eects o phase velocities and luid properties on the characteristics o stratiied low and proposed a closure relationship or the interacial riction actor to predict the liquid holdup. The mechanistic model is more accurate or liquid holdup prediction, but it usually incorporates a system o nonlinear equations. In addition, the mechanistic model also relies on some assumptions and empirical constants obtained by experiment. Due to the limitation o such experimental conditions, the supericial gas and liquid velocities or most gas-liquid two-phase low experiments reported in the literature is generally not very high. Most o the experimental data or liquid holdup based on gas-liquid two-phase low are derived rom the Tulsa University Fluid Flow Projects (TUFFP), where the supericial gas velocity range o the experimental loop in the laboratory is 4

5 0~44.8 m/s, while the supericial liquid velocity range is 0~1.83 m/s. Thereore, it is necessary to develop a prediction model or liquid holdup and pressure drop based on experimental data and take advantage o dierent models. To obtain an accurate model or prediction o liquid holdup at higher gas and supericial liquid velocities applicable to dierent angles, a two-phase low experiment with higher gas and liquid velocities was carried out on a multiphase low experimental platorm at Yangtze University where the supericial liquid velocity range was rom 0.05 to 1.46 m/s, and the supericial gas velocity range was rom to m/s. The low patterns in the experiment were observed and the inluence o dierent actors on the liquid holdup under the experimental conditions was obtained by analyzing the experimental data. Finally, a new model or predicting low liquid holdup (H <0.1) in horizontal pipes is presented. In addition, based on the Beggs-Brill model, a model or predicting the holdup at dierent angles was obtained under the condition o higher supericial gas and liquid velocities.. Experimental acility and measurement methods.1. Experimental acility The experiment was carried out on the multiphase low experimental platorm, which is the platorm o the gas lit test base o CNPC located in the School o Petroleum Engineering, Yangtze University. The diagram o the experimental device is shown in Figure 1. 5

6 iquid rom the mixing tank is pressurized by a pump. Ater pressure stabilization and measurement, the liquid is mixed with measured compressed gas, and the mixed media are introduced together into the test section. The liquid returns to the mixing tank ater separation rom the gas as they pass through the gas-liquid separator. The inner diameter o the test section used in the experiment is 60 mm. The length o the plexiglass pipe used to observe the low pattern is 7 m. The test section can be adjusted at an angle o 0~90. Pressure, temperature and pressure dierential sensors, as well as quick closing valves and other devices, are installed on the pipe section. The distance between the two quick closing valves is 9.5 m, including the 7-m Plexiglas tube and.5-m-long stainless steel tube. Control o the devices as well as extraction o data is done directly online at the control center. The test section is shown in Figure. To ensure the reliability o the experimental data, high-precision instruments are used. The liquid lowmeters installed are Endress+Hauser/80E5 and Endress+Hauser/80E50, while the gas lowmeter employed is Endress+Hauser/65F1H. All lowmeters measure the volume low rate during the experiment. The response time o the quick-closing valve is 0.3~0.5 s. The pressure and temperature sensors installed behind the quick-closing valve are used to measure the temperature and pressure in the test section. The measurement parameters and errors o each device are shown in Table 1. Air is the gas phase while water constitutes the liquid phase. The surace tension o 6

7 the water is Nm -1 (3.58 ). The densities o water and air are 1000 kg/m 3 and 1.05 kg/m 3 (0.101 MPa), respectively, while their respective viscosities are 1 mpa s and mpa s (0 )... Experimental measurements Numerous researchers have reported various development lengths (/D ratios) or ully developed low. Omebere [8] demonstrated that /D=40 is suicient or a reasonably well-developed churn-turbulent low using probability density unctions o the void raction that showed the same shapes or this value and higher. Additionally, some o the reported experimental observations are or temporary or developing low patterns as described by Brennen [9]. Aliyu et al. [30] observed ully developed low in a pipe position with /D=46 or annular low in upward vertical pipes. In the literature, no previous study provides conclusive experimental evidence or estimates o the minimum required length or the low development section. In this study, we provide approximately.4 m or the low to develop, /D=40, and our observations show that low almost reaches development at this stage; thereore, the liquid holdup measurements could proceed. In the experiment, a constant liquid low rate was maintained, while the gas low rate was adjusted. When the system was steady, the data were recorded, and the experimental low pattern was observed. The experimental data were recorded every 5 seconds or 3 minutes, and inally the average value o each measurement parameter 7

8 was obtained. Ater the data recording was completed, the quick-closing valve was closed, and the liquid holdup was measured. The measurement method o liquid holdup was to test the volume o residual liquid in the test section, and the ratio o the volume o the residual liquid to the volume o the whole pipe was used as the average liquid holdup o the experiment. The range o measurement parameters in the experiment is shown in Table. 3. Experimental results and analysis 3.1. Experimental low pattern Under the experimental conditions, the low patterns observed in the horizontal pipe were slug and annular low, attributed to the high supericial gas and liquid velocities. Experimental data points, indicating the observed low patterns, plotted on the low pattern maps presented by Mandhane [31], Taitel-Dukler [3] and Zhang are shown in Figure 3. It can be seen that when the supericial gas velocity is approximately 1 m/s, the slug low transitions to annular low. With the increase in the supericial liquid velocity, the supericial gas velocity needed when the slug low changes into annular low increases gradually. It can also be observed that the experimental data all near the transition boundary between slug low and annular low in the three low pattern maps. It is ound that the Mandhane low pattern map agrees best with the experimental data. In addition, slug low, churn low and annular low were observed in the inclined and vertical pipe. The experimental data points plotted on the low pattern map o Kaya [33] 8

9 or vertical pipes are presented in Figure 4. It can be seen rom Figure 4 that the area o churn low decreases with increasing supericial liquid velocity. It can also be observed that the low pattern map o Kaya is consistent with the experimental data. 3.. iquid holdup vs. supericial velocity and inclination The variation in liquid holdup with the supericial gas and liquid velocities is shown in Figure 5. From the horizontal to the vertical, the liquid holdup decreases with the increase in supericial gas velocity. When the supericial gas velocity is greater than 35 m/s, with the increase in supericial gas velocity, the liquid holdup decreases little. When the supericial gas velocity is high enough, the low pattern changes into annular low, the liquid holdup is very low, and the inluence o increasing gas velocity on liquid holdup is not obvious. The Figure also shows that the liquid holdup increases with the increase in the supericial liquid velocity at the same supericial gas velocity. The variation in liquid holdup with the inclination angle is shown in Figure 6. The liquid holdup increases with the increase in the angle at the same supericial gas and liquid velocity and reaches the maximum value when the inclination angle is 45. The liquid holdup decreases slightly, but the change is small with the increase in the angle. This eect may be due to the inluence o gravity and viscosity, which can be seen in the literature study o Beggs [1]. When the inclination angle is less than 45, the inluence o angle on the liquid holdup decreases with the increase in the supericial gas 9

10 velocity Prediction o liquid holdup by empirical and mechanistic models The Beggs-Brill (B-B) empirical model and Kaya mechanistic model are used to predict the experimental liquid holdup data. The Kaya model is applicable to deviated pipes and not suitable or horizontal pipes. Thereore, the Kaya model was used to predict the liquid holdup at the angle rom 15 to 90, while the B-B model was used to predict the liquid holdup at the angle rom 0 to 90. The comparison between the two dierent models predicted values with the experimental data o the liquid holdup shown in Figure 7. When the liquid holdup is low, the prediction o the liquid holdup rom these two models is not accurate. The prediction average relative error and the average absolute error were determined as ollows: Average relative error: E = 1 1 n H H n cal exp ( ) 100 (1) H 1 exp Average absolute error: E = 1 n H H n cal exp ( ) 100 () H 1 exp where H cal is the liquid holdup that was predicted by the model and exp H is the liquid holdup measured in the experiment. The liquid holdup errors o H <0.1 and H >0.1 are shown in Table 3. It can be seen 10

11 that when H <0.1, the prediction values o the two models are greater than the experimental value. The average absolute error shows that the errors o the two models are high and more than 40%. When H >0.1, the errors o the two models are lower, and the predicted values are lower than the experimental value. From the error o all the data, it can be seen that the errors o the two models are relatively high. However, the perormance o the B-B model is better than that o the Kaya model; the errors o the B-B model are 15.6% and 5.8%. The errors o the two models at dierent angles are shown in Table 4. It can be observed that the errors o the two models decrease with the increase in angle. The perormance o the B-B model is relatively better. When the angle is greater than 45, the B-B method is more accurate, and the error is approximately 10%. However, the error is high: when the angle is less than 45, all the errors are greater than 40%. 4. Model development and evaluation From the error analysis, the error o the B-B model is high when the liquid holdup is less than 0.1. However, the liquid holdup prediction at dierent angles o the B-B model is based on the calculation o the liquid holdup o the horizontal pipe. Thereore, development o a low liquid holdup correlation capable o predicting values is less than 0.1 in the horizontal pipe is necessary. When the liquid holdup is low, the low pattern o horizontal pipe is stratiied low or annular low. However, no stratiied low was observed in this experiment. Thereore, the low liquid holdup (H <0.1) model was 11

12 developed based on annular low. Hart [34] proposed the "apparent rough surace" (ARS) model. Badie [35] validated the two models by using the experimental data and ound the importance o liquid holdup prediction to the accuracy o pressure drop prediction. Meng [] added the concept o droplet entrainment on the basis o the "double-circle" model that was developed by Chen [36] and presented a new model. Fan [3] presented a two-luid model that requires the initial value calculated by the ARS model proposed by Hart. Xu [4] combined the research results o Meng and Fan, presenting a new model or calculating the low holdup and veriying it with the laboratory data rom the experiments o Meng and Fan Development o a liquid holdup model or the horizontal pipe The liquid phase in annular low exists in two orms: a liquid ilm lowing along the pipe wall and the droplets entrained in the gas core. The shape o the liquid in annular low is shown in Figure 8. The study ollows the approach o Xiao [5], who presented an annular low model with an average liquid ilm thickness around the pipe wall. The model was developed based on the momentum equation in the liquid ilm and the gas core. Momentum equation o gas core: dp -A( G ) G -isi - G AG gsin = 0 d (3) 1

13 where dp d is the pressure gradient o the gas phase, Pa; A G is the cross-sectional G area inside the pipe o the gas phase, m ; Si is the perimeter o the interace, m; gravity acceleration, m/s ; and is the inclination angle,. Momentum equation o liquid ilm: i is the shear stress o the interace,n/m; G is density o the gas, kg/m 3 ; g is the dp -A( ) - S isi - A gsin = 0 d (4) where dp d is the pressure gradient o the liquid phase, Pa; A is the cross-sectional area inside the pipe o the liquid phase, m ; is the shear stress o liquid ilm and wall, N/m; and is the density o the liquid, kg/m 3. I the pressure drop gradient in the gas is equal to that in the liquid, we can combine Eq. (3) and (4) to obtain the ollowing combined momentum equation: S A - S A A A ( ) gsin = 0 (5) i i p G G G where A is the cross-sectional area inside the pipe o the liquid phase, m. The shear stresses are v (6) ( v v) i (7) G G i i where and i are the liquid phase riction actor and the interacial riction actor, m ; v is the average liquid velocity, m/s; v is the average gas velocity, m/s; and v i 13

14 is the gas-liquid interace velocity, m/s. The area o each phase can be expressed approximately as unctions o pipe cross sectional area and liquid holdup: A ApH (8) A A (1 H ) (9) G p where H is the liquid holdup. Then, we can obtain that: v G( vg v) SAp (1 H) i Si Ap ApH Ap (1 H)( G ) gsin 0 (10) When the pipe is horizontal, and Eq. (10) can be simpliied as v 1 i GSi v vg 1 H S vg (1 ) 0 (11) The average gas and liquid velocities are v G vsg 1 H (1) v v H sl (13) where v sg is the supericial gas velocity, m/s, and v sl is the supericial liquid velocity, m/s. The gas-liquid interace velocity is diicult to obtain. Many researchers assume that the gas-liquid interace velocity equals the average liquid velocity, v v. i We deine the parameter a 1 H H, where a H. Eq. (11) can be transormed 1 a 14

15 into v S v vsg S vsg sl i G i sl (1 a) ( a ) 0 (14) According to the geometry o the low pattern, the ollowing equations can be obtained: S D (15) S ( D ) (16) where D is the internal diameter, m, and is the liquid ilm thickness, m. i According to the assumption that the liquid ilm thickness on the wall o the annular low is the same, the relation below was given by Fan between the liquid ilm thickness and the liquid holdup: D(1 1 H ) (17) By substitution, v a v sl 0.5 ( (1 H) 1) sg ig (18) Finally, the implicit equations o liquid holdup are obtained: v H H H sl 0.5 ( (1 ) 1)(1 ) vsg ig (19) Eq. (19) shows that the key to calculating the liquid holdup is to calculate the riction coeicient ratio between the liquid phase and the gas-liquid interace i. Hart (1989) 15

16 reported the relationship between i and the supericial liquid Reynolds number. According to the experimental results: i =108R 0.76 esl (0) According to the experimental data, i can be calculated by Eq. (19), and then the corresponding supericial gas and liquid Reynolds number can also be calculated. The ratio o the riction coeicient between the liquid phase and the gas-liquid interace i o dierent supericial gas and liquid Reynolds number as shown in Figure 9. It can be seen rom the igure that i changes not only with the supericial liquid Reynolds number but also with the supericial gas Reynolds number. Thereore, in the reerence orm o Eq. (0), we can give the ollowing equations: i xr y esl R z esg (1) where vd R sl esl is the supericial liquid Reynolds number; R esg v D g sg is the G supericial gas Reynolds number; G is the gas viscosity, mpa s; and is the liquid viscosity, mpa s; By itting the experimental data, the parameters obtained are as ollows: x=0.5756, y=0.537, z=

17 4.. Evaluation o the new horizontal low liquid holdup model The calculation procedure or the new horizontal low liquid holdup model is as ollows: (1) Select an initial value or the liquid holdup (H =0.1). () Use Eq. (19) to calculate a new liquid holdup H new. (3) I H new - H >0.0001, then H =H new. Repeat step (), until H new - H < There are 49 groups o data or which the liquid holdup is H <0.1 in the horizontal pipe. A comparison between the prediction o 6 existing models, presented by B-B, M-B, Hart, Xiao, Chen, and Fan, as well as the present model and experimental data, is shown in Figure 10. The igure shows that the B-B, Xiao, Fan, Chen and Hart models over-predict the experimental values. The average relative error and the average absolute error are all greater than 70%. The perormance o the M-B model is good, and the average relative error is 17.8%. The average absolute error is 19.3%, but the error is relatively high. On the other hand, the present model gives better predictions than the existing models. The absolute error o the present model is within 0%, the average absolute error is 4.8%, and the average relative error is 0.6% Prediction and evaluation o the new liquid holdup model with dierent inclination angles at high velocity The model that has been presented modiies the B-B model when the angle is less than 45 and the liquid holdup is less than 0.1. The procedure or predicting the liquid 17

18 holdup with the modiied B-B model is presented in Figure 11. The average relative error and average absolute error o the new model are shown in Table 5. The table shows that compared with the B-B model, the error o the new model in 0~30 is clearly reduced, and the average absolute error is approximately 10%. Overall, the predicted average relative error and average absolute error o the new model are % and 10%, and the prediction accuracy is improved compared with the B-B model and the Kaya model. The new model is useul or predicting the liquid holdup o gas and liquid at high velocities. 5. Conclusions To obtain an accurate two-luid model or the prediction o liquid holdup or all inclinations at high gas and liquid velocities, 548 liquid holdup data points were obtained rom the multiphase low experimental laboratory o the Yangtze University rom the study. The ollowing conclusions can be reached. (1) Under a certain supericial liquid velocity, the liquid holdup decreases with the increase in supericial gas velocity, while the liquid holdup increases gradually with the increase in supericial liquid velocity. The liquid holdup increases with the increase in the angle and reaches the maximum value at the angle o 45. Then, with the increase in the angle, the liquid holdup changes little, slightly decreased. With the supericial gas velocity increase, the eect o angle on liquid holdup decreases when inclination o angle is less than

19 () A new two-luid model or predicting liquid holdup or annular low in horizontal pipes has been presented. Predictions o the model are ound to be accurate and agree with experimental data. The average absolute error is 4.8%. In addition, a modiied B-B model or calculating the liquid holdup at dierent angles is also presented. The error o the new model is lower, and the average absolute error is 10%. Both models are applicable to high gas and liquid velocities. Acknowledgments The authors are grateul to everyone at the Branch o Key aboratory o CNPC or Oil and Gas Production and Key aboratory o Exploration Technologies or Oil and Gas Resources or their assistance. This work was supported by the National Natural Science Found Project (No ) and National Key Scientiic and Technological Project (016ZX , 017ZX ). Reerences 1. Beggs, D. H., and Brill, J. P. An experimental study o two-phase low in inclined pipes, Journal o Petroleum Technology, 5(5), pp (1973).. Mukherjee, H., and Brill, J. P. iquid holdup correlations or inclined two-phase low, Journal o Petroleum Technology, 35(5), pp (1983). 3. Eaton, and Alan, B. The prediction o low patterns, liquid holdup and pressure losses occurring during continuous two-phase low in horizontal pipelines, Journal o Petroleum Technology, 19(6), pp (1967). 19

20 4. Barnea, D. A uniied model or predicting low-pattern transitions or the whole range o pipe inclinations, International Journal o Multiphase Flow, 13(1), pp. 1-1 (1987). 5. Xiao, J. J. A Comprehensive Mechanistic Model or Two-Phase Flow in Pipelines, M.S. Thesis, U. o Tulsa, Tulsa, OK (1990). 6. Kaya, A. S., Sarica, C. and Brill, J. P. Mechanistic modeling o two-phase low in deviated wells, Spe Production and Facilities, 16(3), pp (1999). 7. Gomez,., Shoham, O., Schmidt, Z., Chokshi, R., Brown, A. and Northug, T. A uniied mechanistic model or steady-state two-phase low in wellbores and pipelines, Ediciones El País (1999). 8. Zhang, H. Q., Wang, Q., Sarica, C. and Brill, J. P. Uniied model or gas-liquid pipe low via slug dynamics: part 1 model development, Journal o Energy Resources Technology, 15(4), pp (003). 9. Khasanov, M. M., Krasnov, V., Khabibullin, R., Pashali, A. and Guk, V. A simple mechanistic model or void-raction and pressure-gradient prediction in vertical and inclined gas/liquid low, Spe Production & Operations, 4(1), pp (009). 10. Saari, H. and Dalir, N. Calculation o pressure drop inside condensing vertical pipes in new inlet pressures using a new modiied three-luid model, Scientia Iranica, 0(3), pp (013). 11. Firouzi, M., Towler, B. F. and Ruord, T. E. Mechanistic Modelling o 0

21 Counter-Current Slug Flows in Vertical Annuli, SPE Asia Paciic Unconventional Resources Conerence and Exhibition. Society o Petroleum Engineers (SPE) (015). 1. Wang, S., Zhang, H. Q., Sarica, C. and Pereyra, E. A mechanistic slug-liquid-holdup model or dierent oil viscosities and pipe-inclination angles Spe Production & Operations, 9(4), pp (014). 13. Al-Saran, E., Kora, C. and Sarica, C. Prediction o slug liquid holdup in high viscosity liquid and gas two-phase low in horizontal pipes, Journal o Petroleum Science & Engineering, 133, pp (015). 14. Hassanlouei, R. N., Firouzar, H., Kasiri, N. and Khano, M. H. A simple mathematical model or slug liquid holdup in horizontal pipes,scientia Iranica, 19(6), pp (01). 15. Zuber, N. and Findlay, J. A. Average volumetric concentration in two-phase low systems, Journal o Heat Transer, 87(4), pp (1965). 16. Shi, H., Holmes, J. A., Durlosky,. J., Aziz, K., Diaz,. and Alkaya, B. Drit-lux modeling o two-phase low in wellbores, Spe Journal, 10(1), pp (005). 17. Choi, J., Pereyra, E., Sarica, C., Park, C. and Kang, J. M. An eicient drit-lux closure relationship to estimate liquid holdups o gas-liquid two-phase low in pipes, Energies, 5(1), pp (01). 18. Adekomaya, O. A. An improved version o drit-lux model or predicting pressure-gradient and void-raction in vertical and near vertical slug low, Journal o 1

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23 6. Unander, T. E., Smith, I. E. and Nossen, J. Improved holdup and pressure drop prediction or multiphase low with gas and high viscosity oil, International Conerence on Multiphase Production Technology (013). 7. Dabirian, R., Padsalgikar, A., Mohammadikharkeshi, M., Mohan, R. S. and Ovadia - Shoham. The Eects o Phase Velocities and Fluid Properties on iquid Holdup under Gas-iquid Stratiied Flow, Spe Western Regional Meeting (018). 8. Omebere-Iyari, N. K., Azzopardi, B. J., ucas, D., Beyer, M. and Prasser, H. M. The characteristics o gas/liquid low in large risers at high pressures, International Journal o Multiphase Flow, 34(5), pp (008). 9. Brennen, C. E. Fundamentals o Multiphase Flow, Fundamentals o multiphase low. Cambridge University Press (009). 30. Aliyu, A. M., Baba, Y. D., ao,., Yeung, H. and Kim, K. C. Interacial riction in upward annular gas liquid two-phase low in pipes, Experimental Thermal & Fluid Science, 84, pp (017). 31. Mandhane, J. M., Gregory, G. A. and Aziz, K. A low pattern map or gas liquid low in horizontal pipes, International Journal o Multiphase Flow, 1(4), pp (1974). 3. Taitel, Y. and Dukler, A. E. A model or predicting low regime transitions in horizontal and near horizontal gas liquid low, Aiche Journal, (1), pp (1976). 3

24 33. Kaya, A. S., Sarica, C. and Brill, J. P. Mechanistic modeling o two-phase low in deviated wells, Spe Production and Facilities, 16(3), pp (1999). 34. Hart, J., Hamersma, P. J. and Fortuin, J. M. H. Correlations predicting rictional pressure drop and liquid holdup during horizontal gas-liquid pipe low with a small liquid holdup, International Journal o Multiphase Flow, 15(6), pp (1989). 35. Badie, S., Hale, C. P., awrence, C. J. and Hewitt, G. F. Pressure gradient and holdup in horizontal two-phase gas liquid lows with low liquid loading, International Journal o Multiphase Flow, 6(9), pp (000). 36. Chen, X. T., Cal, X. D. and Brill, J. P. Gas-liquid stratiied-wavy low in horizontal pipelines, Journal o Energy Resources Technology, 119(4), pp (1997). Biographies Zilong iu obtained both his B.Sc. degree ( ) and M.Sc. degree ( ) in Petroleum Engineering College at Yangtze University, China. He is currently pursuing his PhD in Oil and Gas Transportation and Storage at Yangtze University, Wuhan, China. His main research interest is multiphase low and gas lit. *Ruiquan iao is a proessor o Petroleum Engineering at Yangtze University, China. He received his PhD degree (00) rom Huazhong University o Science and Technology, China. He has published over 100 research papers. His research interests include multiphase low, oil and gas ield development, gas lit and control science and engineering. * Corresponding author. Tel.: Fax: address: liaoruiquan@63.net Post address: Wuhan Campus, No. 111, Caidian Street, Caidian District, Hubei Province, China 4

25 Wei uo is a lecturer o Petroleum Engineering at Yangtze University, China. He has worked as engineering in Gas lit technology center in PetroChina Tuha Oilield Company rom 009 to 01. He received his PhD degree (01-015) rom Yangtze University, China. He has published over 10 research papers. His research interests include gas lit design method, multiphase low and oil well inlow perormance. Joseph Xavier Francisco Ribeiro obtained both his B.Sc. degree ( ) and M.Sc. degree ( ) in Mechanical Engineering at the Kwame Nkrumah University o Science and Technology, Ghana. He is currently pursuing his PhD in Oil and Gas Transportation and Storage at Yangtze University, China. His main research interest is multiphase low. Figures and tables 1. Water meter;. Filter; 3. Accumulator; 4. Pressure sensor; 5. iquid low meter; 6. Control center; 7. Quick close valve; 8. Dierential pressure sensor; 9. Pressure sensor; 10. Gas-iquid mixture; 11. Temperature sensor Figure 1. Multiphase low test device Figure. iquid holdup test section 5

26 Figure 3. Test points on dierent horizontal low pattern maps (black represents the Mandhane low pattern map; blue color represents the Taitel-Dukler low pattern map; red represents the Zhang low pattern map) 6

27 Figure 4. Test points on the Kaya low pattern map 7

28 Figure 5. iquid holdup vs. supericial gas velocity with dierent inclinations (rom horizontal to vertical) Figure 6. iquid holdup vs. angle o inclination (a) Beggs-Brill model (b) Kaya model Figure 7. Comparison o dierent models predicting liquid holdup with experimental data 8

29 Figure 8. The morphology o gas-liquid two-phase low in the pipe Figure 9. The ratio o riction coeicient between the liquid phase and the gas-liquid interace ( vs. supericial gas Reynold number ( R esg ) and supericial liquid Reynold number ( R esl ) i ) 9

30 (a) (b) Figure 10. Comparison o prediction o liquid holdup in dierent models and experimental values. (a) B-B, M-B, Fan, Xiao, Chen, and Hart models; (b) present model Figure 11. Calculation low chart or the new model 30

31 Table 1. Measurement parameters and errors o the experimental devices Equipment Measuring Range Measurement Error Pressure 0~3.5 MPa ±0.1% Temperature 0-90 ±0.5% iquid Flow Rate ~0 m 3 /h ±0.3% Gas Flow Rate 160~000 m 3 /h ±1% Table. Range o parameters under the experimental conditions Experimental Conditions Supericial iquid Velocity (m/s) 0.05~1.46 Supericial Gas Velocity (m/s) 14.07~56.50 Pressure (MPa) 0.03~0.46 Temperature ( ) 4.0~0.83 iquid Holdup 0.007~0.39 Angle o Upward Inclination ( ) Total Number o Data Points Table 3. Errors o the B-B model and Kaya model Model H <0.1 H >0.1 All Data E 1 (%) E (%) E 1 (%) E (%) E 1 (%) E (%) 31

32 B-B Kaya Table 4. The errors o B-B model and Kaya model at dierent angles Model Angle ( ) B-B E 1 (%) E (%) Kaya E 1 (%) _ E (%) _ Table 5. B-B model errors or dierent angles Angle o inclination ( ) ~90 E 1 (%) E (%)