SPE 120281

Evaluation of Twophase Flow Correlations and Mechanistic Models for Pipelines at Horizontal and Inclined Upward Flow Hong Yuan, SPE, and Desheng Zhou, SPE, IHS

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE Production and Operations Symposium held in Oklahoma City, Oklahoma, USA, 48 April 2009. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract In this study, commonly used two-phase flow pressure prediction correlations and mechanistic models for pipelines in petroleum industry are evaluated against experimental data. The experimental data were obtained from published papers.

Horizontal and upward two-phase flow are common in oil and gas production and transportation. During pipeline design and simulation, experimental data are usually unavailable to calibrate against correlations and models. In this situation, it is difficult to determine which correlation or model to use in predicting pressure gradient in pipelines.

Experimental data used in this study are from Kokal and Stanislav papers (Kokal and Stanislav, 1989) and from Chen et al. paper (Chen et al., 1997). For the Kokal and Stanislav papers, experimental data were gathered from 1-inch, 2-inch and 3-inch pipes with seven inclination angles. Oil and air were used as testing fluids. During the experiment, superficial liquid velocities range from 1.2 to 10 ft/s and superficial gas velocities range from 0.76 to 85 ft/s. For the Chen et al. paper, data were gathered from a 3-inch horizontal pipe at stratified-wavy flow. Kerosene and air were testing fluids.

Beggs-Brill, Dukler-Eaton-Flanigan, Dukler and Eaton correlations and Xiao mechanistic model are evaluated in this study.

The results of this study can be used as guidelines in choosing two-phase flow pressure prediction correlations and models in designing and analyzing horizontal and upward two-phase flow pipelines. Introduction

Horizontal and upward two-phase pipe flow is a common occurrence in oil and gas production and transportation. Although there are many pipeline correlations and mechanistic models around, during pipeline design and simulation, it is often difficult to determine which correlation or mechanistic model to use since correlations and mechanistic models were developed under specific conditions.

Correlations and mechanistic models evaluated in this study include Beggs-Brill (BB), Dukler-Eaton-Flanigan (DEF), Dukler (D), Eaton (E) and Xiao (Xiao). Below is a brief description of the correlations and Xiao Mechanistic model (Yuan and Zhou, 2008).

The Beggs-Brill correlation was developed from experimental data obtained in a small scale test facility. The facility consisted of 1-inch and 1.5-inch sections of acrylic pipe 90 ft long. Fluids used were air and water. The correlations were developed from 584 measured tests for all inclination angles (Brill and Beggs, 1991).

The Eaton correlation was developed from experimental data obtained from a flow system consisting of 2-inch and 4-inch horizontal lines. Correlations were for liquid holdup and two-phase friction factor (Brill and Beggs, 1991).

The Dukler correlation was based on similarity analysis and the friction factor and liquid hold up correlations were developed from field data (Brill and Beggs, 1991).

The Dukler-Eaton-Flanigan correlation uses Dukler correlation for friction calculation, Eaton correlation for liquid holdup calculation (Pipesoft-2TM Manual 2, 2007).

The Xiao model is a comprehensive mechanistic model developed for gas-liquid two-phase flow in horizontal and near horizontal pipelines. It has been evaluated against a data bank that includes field data culled from the A. G. A. database, and laboratory data published in the literature (Xiao et al., 1990).

In this study, above mentioned four correlations and one mechanistic model are evaluated against measured data from published papers to determine which correlations or model behave better at various pipe diameters, superficial velocities and inclination angles.

2 SPE 120281

Description of Experimental Data and Simulation Tool Experimental data. Experimental data are obtained from published papers (Kokal and Stanislav, 1989 and Chen, et al., 1997). In the Kokal and Stanislav papers, experiments were conducted with an 80.2 ft long acrylic pipe installed on an inclinable test section. Three different pipe diameters (1 inch, 2 inch and 3 inch) at seven inclination angles (0o, -1o, +1o, -5o, +5o, -9o and +9o) were studied. The fluids used were air and oil. The oil has a density of 53.56 lbm/ft3 and a viscosity of 7 cp at an average temperature of 73.4 oF and pressures of 33.4 50.8 psi. Superficial liquid velocities range from 0.1 to 10 ft/s and superficial gas velocities range from 0.26 to 85 ft/s during the experiments. Pressure gradients were measured by pressure transducers with accuracy of +/-0.000221 psi. For each pipe diameter and inclination angle, experimental results were plotted as pressure gradient vs. superficial gas velocity at various superficial liquid velocities. Experimental results used in this study are from 1-inch, 2-inch and 3-inch pipes at inclination angles of 1o, 5o and 9o, as well as at horizontal. Results at inclination angles of -1o, -5o and -9o were used in a previous study (Yuan and Zhou, 2008). In the Chen et al. paper, flow behavior in a 3-inch diameter, 1378-ft long pipeline was studied. The test section was 76-ft long and kerosene and air were used as testing fluids. Pressure drops were measured at stratified-wavy flow. Superficial liquid velocities are 0.022, 0.065 and 0.152 ft/s and superficial gas velocities range from 12 to 94.5 ft/s during the experiments.

In order to read the data, plots from the original papers were enlarged to the maximum possible size, and then detailed scale was drawn in the enlarged plots.

Simulation Tool. Commercial software is used to simulate the experimental test sections.

The software is a steady state flow simulator for single pipes as well as complex network systems. The software can handle various fluid types and flow can be single-phase or multi-phase. There are 12 correlations and mechanistic models available in the software for pipeline simulation, and they are capable of predicting flow patterns, liquid holdups, temperature gradients, pressure gradients, etc. (Pipesoft-2TM Manual 2, 2007).

In this study, simulation results from four correlations and one mechanistic model are used to compare with the experimental data.

Simulations are conducted using black oil fluid model for superficial liquid velocities ranging from 0.022 to 10 ft/s and superficial gas velocities ranging from 0.76 to 94.5 ft/s. A summary of the geometrical and operational parameters used in the experiments and in the simulation are given in Table 1.

Results and Discussion Simulation results are compared with measured data by using percent errors. The error is calculated by Eq. 1.

( ) ( )( ) errLDP

LDP

LDP

m

cm=

100 , (1)

where ( )

mLDP is measured pressure gradient, ( )

cLDP is calculated pressure gradient and err represents percent error.

A negative value of percent error indicates that calculated pressure gradient is greater than measured pressure gradient, that it, a correlation or model over predicts pressure gradient. A positive value of percent error means that a correlation or model under predicts pressure gradient.

An absolute average error is calculated by averaging the absolute values of percent errors at various superficial gas velocities for each superficial liquid velocity.

Percent errors for 1-inch pipe at superficial liquid velocity of 3 ft/s is given in Table 2. Absolute percent errors for 1-inch pipe at various inclination angles are given in Table 3, for 2-inch pipe given in Table 4 and for 3-inch pipe given in Table 5.

Simulation results and measured data are plotted as superficial gas velocity vs. pressure gradient at certain superficial liquid velocities. Symbols alone represent measured data and symbols with lines represent simulation results as indicated in the figures of this paper.

Fig. 1 and Fig. 2 are results of 1-inch horizontal pipe. Fig. 1 shows simulation results and experimental data at superficial liquid velocity of 3 ft/s. As shown in the figure, Xiao and Dukler give better prediction than other correlations. Percent errors of each correlation and Xiao model for superficial liquid velocity of 3 ft/s at various superficial gas velocities are given in Table 2. As shown in the table, Xiao has the minimum absolute average percent error (15.04), followed by Dukler (21.63). Dukler-Eaton-Flanigan over predicts pressure gradients for superficial gas velocities greater than 1.48 ft/s and Beggs-Brill over predicts pressure gradients for superficial gas velocities greater than 0.75 ft/s, and the percent errors increase with increasing superficial gas velocity. Eaton over predicts pressure gradients at superficial gas velocity less than 1.48 ft/s and under predicts pressure gradients at larger superficial gas velocities, and percent errors are very big at very small superficial gas velocities. Fig. 2 shows simulation results and experimental data at superficial liquid velocity of 2 ft/s. For superficial gas velocities less than 2 ft/s, all correlations over predict pressure gradients, especially Eaton that gives percent errors greater than 100. For superficial gas velocities greater than 2ft/s, Eaton under predicts pressure gradients while all other correlations still over predict pressure gradients. Dukler and Xiao behave better than other correlations.

SPE 120281 3

Fig. 3 shows results of 1-inch pipe at inclination angle of 1o and superficial liquid velocity of 4.5 ft/s. Dukler and Xiao give smaller percent errors than other correlations. Dukler-Eaton-Flanigan and Beggs-Brill over predict pressure gradients while Eaton under predicts pressure gradients at larger superficial gas velocities and over predicts pressure gradients at small superficial gas velocities.

In Fig. 4 and Fig. 5 are results of 1-inch pipe with 5o inclination angle at superficial liquid velocities of 2 ft/s and 7 ft/s respectively. At superficial liquid velocity of 2 ft/s, Dukler-Eaton-Flanigan, Xiao and Beggs-Brill give percent errors less than 10, while at superficial liquid velocity of 7 ft/s, Dukler and Xiao give percent errors within 10.

Fig. 6 and Fig. 7 are results of 1-inch pipe at 9o inclination angle. In Fig. 6 (VSL = 2 ft/s), Dukler-Eaton-Flanigan and Xiao behave better than other correlations with percent errors less than 10. Beggs-Brill over predicts pressure gradients and Eaton under predicts pressure gradients. In Fig. 7 (VSL = 7 ft/s), Dukler and Xiao behave better than other correlations. For superficial gas velocities above 3 ft/s, Xiao, Beggs-Brill and Dukler-Eaton-Flanigan over predict pressure gradients while Dukler and Eaton under predict pressure gradients.

Fig. 8 and Fig. 9 are results of 2-inch horizontal pipe with superficial liquid velocities of 3 ft/s and 4.5 ft/s respectively. Xiao and Dukler give better predictions with percent errors less than 10. Dukler-Eaton-Flanigan and Beggs-Brill over predict pressure gradients. Eaton under predicts pressure gradients at larger superficial gas velocities and over predicts pressure gradients at small superficial gas velocities.

Fig. 10 and Fig. 11 are results of 2-inch pipe at 1o inclination angle with superficial liquid velocities of 3 ft/s and 6.56 ft/s respectively. All correlations show similar behavior as for the horizontal cases given in Fig. 8 and Fig. 9.

Fig. 12 and Fig. 13 are results of 2-inch pipe at 5o inclination angle. In Fig. 12 (VSL = 1.64 ft/s), Dukler-Eaton-Flanigan behaves the best with an absolute percent error within 10 followed by Xiao and Beggs-Brill which have percent errors of 11.18 and 11.87 respectively. Dukler over predicts pressure gradients at superficial gas velocities greater than 10 ft/s and under predicts pressure gradients at superficial gas velocities less than 10 ft/s. Eaton over predicts pressure gradients at superficial gas velocities below 3 ft/s. Fig. 13 (VSL = 3.28 ft/s) shows that Xiao behaves the best followed by Dukler-Eaton-Flanigan and Dukler. Beggs-Brill and Dukler-Eaton-Flanigan over predict pressure gradients from superficial gas velocity around 5 ft/s.

Fig. 14 and Fig. 15 are results of 2-inch pipe at 9o inclination angle. In Fig. 14 (VSL = 3.28 ft/s), from superficial gas velocity around 5 ft/s, Beggs-Brill, Dukler-Eaton-Flanigan and Xiao over predict pressure gradients while Dukler and Eaton under predict pressure gradients. At small superficial gas velocities, Dukler-Eaton-Flanigan and Xiao behave very well. In Fig. 15 (VSL = 6.56 ft/s), Beggs-Brill over predicts pressure gradients. Dukler-Eaton-Flanigan behaves very well at small superficial gas velocities and over predicts pressure gradients for superficial gas velocities above 5 ft/s. Dukler and Eaton under predict pressure gradients except for superficial gas velocities below 3 ft/s where Dukler behaves fine while Eaton over predicts pressure gradients substantially.

Fig. 16 and Fig. 17 are results of 3-inch horizontal pipe and the experimental data are from Chen et al. paper. Both figures show that Eaton over predicts pressure gradients with percent errors greater than 400. In Fig. 16 (VSL = 0.022), Xiao and Beggs-Brill behave better than other correlations. In Fig. 17 (VSL = 0.152), Dukler-Eaton-Flanigan behaves the best. Xiao behaves very well at superficial gas velocity below 30 ft/s and then begins over predicting pressure gradients. The reason of the sudden change in Xiao model is that the model predicts annular flow pattern while the experiments indicated stratified-wavy flow.

Fig. 18 is the results of 3-inch horizontal pipe at superficial liquid velocity of 3.28 ft/s. Xiao and Dukler give better predictions than other correlations with average absolute percent errors of 6.21 and 11.05 respectively. Beggs-Brill and Dukler-Eaton-Flanigan over predict pressure gradients. Eaton over predicts pressure gradients at superficial gas velocity below 7 ft/s and then under predicts pressure gradients as superficial gas velocity above 7 ft/s.

Fig. 19 is the results of 3-inch pipe at 1o inclination angle with superficial liquid velocity of 3.28 ft/s. Similar trend as in Fig. 18 is observed.

Fig. 20 and Fig. 21 are results of 3-inch pipe at 5o inclination angle. It seems that all correlations tend to under predict pressure gradients at lower superficial gas velocities and under predict pressure gradients at higher superficial gas velocities. The results are inconclusive since the data begin harder to read from inclination angle 5o.

Fig. 22 shows the comparison of experimental data with Xiao model for 1-inch pipe at all inclination angles with superficial liquid velocity at 4.5 ft/s. At superficial gas velocity below 10 ft/s, Xiao model predicts quite well, but over predicts at superficial gas velocities above 10 ft/s.

In general, errors are higher at lower superficial liquid velocities. The reasons could be the following. At small superficial liquid velocities, pressure gradients are small. In this case, even a small difference in the pressure gradient values will create a large error value since the denominator in Eq. 1 is small. Additionally, measurement errors also increase with decreasing pressure gradient due to the accuracy level of the pressure transducers.

For 1-inch horizontal pipe, Dukler and Xiao behave better than other correlations. At superficial gas velocities below 3 ft/s, all correlations and Xiao model behave fine with the exception of Eaton which over predicts pressure gradients substantially at small superficial gas velocities. At superficial gas velocities greater than 3 ft/s, Xiao behaves the best. For 1-inch pipe at 5o and 9o inclination angles, Xiao behaves the best followed by Dukler. Dukler surpasses Xiao at superficial liquid velocities greater than 3 ft/s. For 1-inch pipe, Xiao behaves the best in general. At superficial liquid velocities greater

4 SPE 120281

than 3 ft/s, Dukler also behaves very well. Eaton over predicts pressure gradients for superficial gas velocities below 3 ft/s and over predicts for larger superficial gas velocities.

For 2-inch pipe at 0o and 1o inclination angles, Xiao and Dukler behave better than other correlations. For 2-inch pipe at 5o and 9o inclination angles, Xiao behaves the best for all superficial liquid velocities and Dukler begins behaving well at superficial liquid velocities greater than 3 ft/s. Dukler-Eaton-Flanigan and Beggs-Brill behave well at superficial liquid velocities below 3 ft/s. For 2-inch pipe, Xiao behaves the best. At superficial liquid velocities greater than 3 ft/s, Dukler also behaves well and at superficial liquid velocities less than 3 ft/s, Dukler-Eaton-Flanigan and Beggs-Brill behave well for 5o and 9o inclination angles.

For 3-inch pipes, Xiao behaves the best in general for the limited data. Conclusions From the simulation results and available experimental data, following conclusions are reached.

Xiao model behaves better than other correlations. Dukler correlation behaves well at superficial liquid velocities greater than 3 ft/s. Dukler-Eaton-Flanigan and Beggs-Brill behave well for 5o and 9o inclination angles with superficial liquid velocities below

3 ft/s. Eaton is always over predicts pressure gradients at small superficial gas velocities and superficial liquid velocities and the

error values get bigger as the superficial gas velocities and superficial liquid velocities getting smaller.

Nomenclature VSL = superficial liquid velocity, ft/s VSG = superficial gas velocity, ft/s DP/L = pressure gradient, psi/ft (DP/L)c = calculated pressure gradient, psi/ft (DP/L)m = measured pressure gradient, psi/ft err = error, % Acknowledgments The authors would like to thank IHS Global Inc. for permission to publish this paper. References 1. Kokal, S.L. and Stanislav, J.F.: An Experimental Study of Two-Phase Flow in Slightly Inclined Pipes I. Flow Patterns,

Chemical Engineering Science, Vol. 44, No. 3, pp. 665-679, 1989. 2. Kokal, S.L. and Stanislav, J.F.: An Experimental Study of Two-Phase Flow in Slightly Inclined Pipes II. Liquid Holdup and

Pressure Drop, Chemical Engineering Science, Vol. 44, No. 3, pp. 681-693, 1989. 3. Chen, X.T., Cai, X.D. and Brill, J.P.: Gas-liquid Stratified-wavy Flow in Horizontal Pipelines, Journal of Energy Resources

Technology, Vol. 119, No. 4, pp. 209-216, 1997. 4. Yuan, H. and Zhou, D.: Evaluation of Two-phase Flow Correlations and Mechanistic Models for Pipelines at Inclined

Downward Flow paper SPE 117395 presented at the SPE Eastern Regional/AAPG Eastern Section Joint Meeting held in Pittsburgh, Pennsylvania, USA, 1115 October 2008.

5. Brill, J. P. and Beggs, H. D., Two-Phase Flow in Pipes, Sixth Edition, Third Printing, January 1991, Tulsa, OK. 6. Pipesoft-2TM Multi-phase Fluid Flow Network Simulator, Manual 2, Copyright 2001 2007, IHS. 7. Xiao, J.J., Shoham, O. and Brill, J.P.: A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines, paper SPE

20631 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, 23-26 September. SI Metric Conversion Factors bbl 1.589 873 E-01 = m3 ft 3.048* E-01 = m psi 6.894 757 E+00 = kPa in. 25.4* E+00 = mm *Conversion factor is exact.

SPE 120281 5

Table 1. Parameters used in experiments and in simulation Kokal and Stanislav Chen, et al. Experiments Simulation Experiments Simulation Pipe ID, in. 1, 2, 3 1, 2, 3 3 3 Pipe Length, ft 80.2 80.2 76 76 Pipe roughness, ft didnt specify 3.28x10-5 didnt specify 3.28x10-5 Inclination angle 0o, 1o, 5o, 9o 0o, 1o, 5o, 9o 0o 0o Oil density , lbm/ft3 53.56 53.56 49.95 49.95 Oil viscosity, cp 7 7 1.64 1.64 Pressure, psi 33.4 50.8 40 at inlet 14.5 14.5 at inlet Temperature, oF 73.4 73.4 at inlet 61 61 at inlet Table 2. Percent errors of correlations and Xiao model

for 1-inch horizontal pipe at VSL = 3 ft/s VSG (ft/s) BB DEF D E Xiao

0.28 6.6 13.5 9.3 -174.1 12.7 0.43 2.5 10.4 10.5 -96.1 12.1 0.75 0.4 9.0 15.4 -20.3 16.3 1.48 -17.0 0.2 11.1 11.7 14.0 3.05 -12.7 -5.7 14.7 30.2 16.5 5.91 -22.8 -26.8 2.7 34.8 7.3 9.84 -30.8 -48.1 -1.6 30.7 -1.1

18.04 -50.3 -51.7 -45.9 11.5 -21.1 32.81 -50.1 -47.5 -22.4 7.8 -18.1 49.21 -80.7 -67.4 -82.7 -12.7 -31.2

Abs. avg. err. 27.38 28.04 21.63 42.98 15.04 Table 3. Absolute average percent errors of correlations and Xiao model for 1-inch pipe

0o inclination angle VSL (ft/s) BB DEF D E Xiao

3 27.38 28.04 21.63 42.98 15.04 4.5 29.70 32.14 6.69 42.40 12.29

7 36.36 43.17 9.85 43.10 17.08 10 37.69 36.08 16.86 49.98 22.60

1o inclination angle 4.5 20.97 25.13 6.76 41.94 11.02

5o inclination angle VSL (ft/s) BB DEF D E Xiao

2 9.12 7.00 25.67 20.85 7.05 3 9.18 9.64 13.96 36.47 5.77

4.5 20.41 22.19 9.52 37.53 6.67 7 23.26 28.90 5.64 30.40 9.44

10 31.88 28.90 10.60 41.09 17.92 9o inclination angle

VSL (ft/s) BB DEF D E Xiao 2 11.58 2.98 29.56 18.17 6.19 3 27.34 21.33 24.43 14.18 11.62

4.5 18.55 18.22 8.35 31.69 7.00 7 28.41 35.55 4.52 26.40 12.90

6 SPE 120281

Table 4. Absolute average percent errors of correlations and Xiao model for 2-inch pipe

0o inclination angle VSL (ft/s) BB DEF D E Xiao

3 27.41 27.88 6.78 83.46 3.60 4.5 26.41 32.42 5.51 142.33 5.28

1o inclination angle 3 15.29 13.16 5.99 96.11 3.43

6.56 23.58 29.78 4.73 76.61 12.14 5o inclination angle

VSL (ft/s) BB DEF D E Xiao 1.64 11.87 8.24 32.18 29.53 11.18 3.28 12.25 10.83 11.89 52.21 6.40 6.56 14.91 7.27 5.41 87.46 3.92

9o inclination angle VSL (ft/s) BB DEF D E Xiao

1.64 7.50 10.16 36.29 9.87 13.34 3.28 8.40 7.75 17.61 37.73 6.16 6.56 14.33 11.46 10.14 61.49 3.44

Table 5. Absolute average percent errors of correlations and Xiao model for 3-inch pipe

0o inclination angle VSL (ft/s) BB DEF D E Xiao

0.022 21.21 45.54 40.26 810.17 12.11 0.065 26.85 23.36 66.62 426.68 7.09 0.152 54.41 17.76 137.43 479.65 49.74

1.64 48.92 25.32 28.22 193.38 8.37 3.28 37.68 34.26 11.05 116.57 6.21

1o inclination angle 1.64 17.86 8.74 17.43 66.56 3.98 3.28 25.03 20.78 6.74 69.98 4.02

5o inclination angle VSL (ft/s) BB DEF D E Xiao

1.64 14.50 11.00 21.15 5.79 19.05 2.62 21.21 18.49 28.40 14.62 23.50

VSL = 3 ft/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 10 20 30 40 50 60

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEF

D

E

XIAO

VSL = 10 ft/s

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 2 4 6 8 10 12VSG ft/s

DP

/L p

si/ft

Exp. data

BB

DEFD

E

Xiao

Fig. 1 Pressure gradient vs. VSG at VSL = 3 ft/s Fig. 2 Pressure gradient vs. VSG at VSL = 10 ft/s for 1-inch horizontal pipe. for 1-inch horizontal pipe.

SPE 120281 7

VSL = 4.5 ft/s

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 5 10 15 20 25 30 35 40VSG ft/s

DP/

L ps

i/ft

Exp. dataBB

DEFD

EXIAO

VSL = 2 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 5 10 15 20

VSG ft/s

DP

/L p

si/ft

Exp. data

BB

DEF

D

E

Xiao

Fig. 3 Pressure gradient vs. VSG at VSL = 4.5 ft/s Fig. 4 Pressure gradient vs. VSG at VSL = 2 ft/s for 1-inch pipe at 1o inclination angle. for 1-inch pipe at 5o inclination angle.

VSL = 7 ft/s

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 5 10 15 20 25VSG ft/s

DP/

L ps

i/ft

Exp. data

BB

DEF

D

E

Xiao

VSL = 2 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 5 10 15 20

VSG ft/s

DP/L

psi

/ft

Exp. data

BBDEF

DE

Xiao

Fig. 5 Pressure gradient vs. VSG at VSL = 7 ft/s Fig. 6 Pressure gradient vs. VSG at VSL = 2 ft/s for 1-inch pipe at 5o inclination angle. for 1-inch pipe at 9o inclination angle.

VSL = 7 ft/s

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 5 10 15 20 25

VSG ft/s

DP/

L ps

i/ft

Exp. data

BBDEF

D

E

Xiao

VSL = 3 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEF

D

E

XIAO

Fig. 7 Pressure gradient vs. VSG at VSL = 7 ft/s Fig. 8 Pressure gradient vs. VSG at VSL = 3 ft/s for 1-inch pipe at 9o inclination angle. for 2-inch horizontal pipe.

8 SPE 120281

VSL = 4.5 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0 5 10 15 20

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEFD

E

Xiao

VSL = 3 ft/s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 2 4 6 8 10

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEF

D

E

Xiao

Fig. 9 Pressure gradient vs. VSG at VSL = 4.5 ft/s Fig. 10 Pressure gradient vs. VSG at VSL = 3 ft/s for 2-inch horizontal pipe. for 2-inch pipe at 1o inclination angle.

VSL = 6.56 ft/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 5 10 15 20 25 30 35VSG ft/s

DP/

L ps

i/ft

Exp. dataBB

DEF

DE

Xiao

VSL = 1.64 ft/s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 5 10 15 20 25 30 35 40

VSG ft/s

DP/L

psi

/ftExp. data

BB

DEF

D

E

XIAO

Fig. 11 Pressure gradient vs. VSG at VSL = 6.56 ft/s Fig. 12 Pressure gradient vs. VSG at VSL = 1.64 ft/s for 2-inch pipe at 1o inclination angle. for 2-inch pipe at 5o inclination angle.

VSL = 3.28 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 5 10 15 20 25 30 35

VSG ft/s

DP

/L p

si/ft

Exp. data

BBDEF

D

EXiao

VSL = 3.28 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30 35 40

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEF

DE

Xiao

Fig. 13 Pressure gradient vs. VSG at VSL = 3.28 ft/s Fig. 14 Pressure gradient vs. VSG at VSL = 3.28 ft/s for 2-inch pipe at 5o inclination angle. for 2-inch pipe at 9o inclination angle.

SPE 120281 9

VSL = 6.56 ft/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 5 10 15 20VSG ft/s

DP/L

psi

/ft

Exp. dataBB

DEFD

EXiao

VSL = 0.022 ft/s

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0 10 20 30 40 50VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEF

D

E

Xiao

Fig. 15 Pressure gradient vs. VSG at VSL = 6.56 ft/s Fig. 16 Pressure gradient vs. VSG at VSL = 0.022 ft/s for 2-inch pipe at 9o inclination angle. for 3-inch horizontal pipe.

VSL = 0.152 ft/s

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0 5 10 15 20 25 30 35 40VSG ft/s

DP/L

psi

/ft

Exp. data

BBDEF

DE

Xiao

VSL = 3.28 ft/s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 5 10 15 20VSG ft/s

DP/L

psi

/ftExp. data

BB

DEF

DE

Xiao

Fig. 17 Pressure gradient vs. VSG at VSL = 0.152 ft/s Fig. 18 Pressure gradient vs. VSG at VSL = 3.28 ft/s for 3-inch horizontal pipe. for 3-inch horizontal pipe.

VSL = 3.28 ft/s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 2 4 6 8 10 12 14 16VSG ft/s

DP/L

psi

/ft

Exp. data

BBDEFD

EXiao

VSL = 1.64 ft/s

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0 5 10 15 20 25 30 35

VSG ft/s

DP/L

psi

/ft

Exp. data

BB

DEFD

E

Xiao

Fig. 19 Pressure gradient vs. VSG at VSL = 3.28 ft/s Fig. 20 Pressure gradient vs. VSG at VSL = 1.64 ft/s for 3-inch pipe at 1o inclination angle. for 3-inch pipe at 5o inclination angle.

10 SPE 120281

VSL = 2.62 ft/s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25 30 35VSG ft/s

DP/L

psi

/ft

Exp. dataBB

DEFD

EXiao

1-in., All Inclination Angles, VSL = 4.5 ft/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 5 10 15 20 25

VSG ft/s

DP/L

psi

/ft

1 Exp. data1 Xiao5 Exp. data5 Xiao9 Exp. data9 Xiao

Fig. 21 Pressure gradient vs. VSG at VSL = 2.62 ft/s Fig. 22 Comparison of Eaton correlation prediction with

for 3-inch pipe at 5o inclination angle. measured data for 1-inch pipe, all inclination angles at VSL = 4.5 ft/s.