flow correlation selection

5/21/2018 Flow Correlation Selection

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24th October 1997 - Revision: 0 Page 1 of 14

Information on Flow Correlations used withinPIPESIM

CONTENTS

1. TWO-PHASE FLOW CORRELATIONS ..............................................................................................2

1.1.APPLICABILITY.......................................................................................................................................... 2

1.2.DESCRIPTION OF CORRELATIONS...............................................................................................................2

1.2.1. Duns & Ros[4]

...................................................................................................................................2

1.2.2. Orkiszewski[11]

.................................................................................................................................. 2

1.2.3. Hagedorn & Brown[7]

....................................................................................................................... 3

1.2.4. Beggs & Brill Original[2]

.................................................................................................................. 3

1.2.5. Beggs & Brill Revised[2]

................................................................................................................... 3

1.2.6. Mukherjee & Brill[18]

........................................................................................................................3

1.2.7. Govier, Aziz & Fogarasi[1]

...............................................................................................................3

1.2.8. NoSlip ...............................................................................................................................................41.2.9. OLGAS-89

[24]....................................................................................................................................4

1.2.10. OLGAS-92[24]

.................................................................................................................................. 4

1.2.11. Ansari[20]

......................................................................................................................................... 4

1.2.12. BJA for Condensates[22]

.................................................................................................................. 4

1.2.13. AGA & Flanigan[3]&[6]

.................................................................................................................... 4

1.2.14. Oliemans[10] ....................................................................................................................................5

1.2.15. Gray[23]

........................................................................................................................................... 5

1.2.16. Xiao[21]

............................................................................................................................................ 5

1.3.MATCHING STUDY.....................................................................................................................................5

1.3.1. Overview of Analysis Work............................................................................................................... 5

1.3.2. Method of Analysis ...........................................................................................................................7

1.3.3. Overall Performance of Correlations............................................................................................... 8

2. SINGLE PHASE FLOW CORRELATIONS .......................................................................................10

2.1.APPLICABILITY........................................................................................................................................10

2.2.RECOMMENDATION ................................................................................................................................. 10

3. SLUG CORRELATIONS.......................................................................................................................10

4. REFERENCES ........................................................................................................................................ 12


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1. TWO-PHASE FLOW CORRELATIONS

1.1. Applicability

The two-phase flow correlations can be used as follows:-

Vertical and

Predominantly

Vertical Oil

Wells

Highly

Deviated

Oil Wells

Vertical Gas/

Condensate

Wells

Oil

Pipelines

Gas/

Condensate

Pipelines

Duns & Ros

Orkiszewski

Hagedorn & Brown

Beggs & Brill Revised

Beggs & Brill Original

Mukherjee & Brill

Govier, Aziz & Fogarasi

NoSlip

OLGAS-89 OLGAS-92

Ansari

BJA for Condensates

AGA & Flanigan

Oliemans

Gray

Xiao

1.2.

Description of Correlations

1.2.1.

Duns & Ros[4]

The Duns & Ros correlation was developed for vertical flowof gas and liquid mixtures

in wells. Equations were developed for each of three flow regions, (I) bubble, plug and

part of froth flow regimes, (II) remainder of froth flow and slug flow regimes, (III) mist

flow regime. These regions have low, intermediate and high gas throughputs respectively.

Each flow region has a different holdup correlation. The equations were based on

extensive experimental work using oil and air mixtures.

1.2.2.

Orkiszewski[11]

The Orkiszewski correlation was developed for the prediction of two phase pressure

drops in vertical pipe. Four flow regimes were considered, bubble, slug, annular-slug

transition, and annular mist. The method can accurately predict, to within 10%, the twophase pressure drops in naturally flowing and gas lifted production wells over a wide

range of well conditions. The precision of the method was verified when its predicted

values were compared against 148 measured pressure drops. Unlike most other methods,

liquid holdup is derived from observed physical phenomena, and is adjusted for angle of

deviation.


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1.2.3. Hagedorn & Brown[7]

The Hagedorn and Brown correlation was developed following an experimental study of

pressure gradients occurring during continuous two-phase flow in small diameter

vertical conduits. A 1,500 ft experimental well was used to study flow through 1, 1,

and 1 nominal size tubing. Tests were conducted for widely varying liquid flowrates,

gas-liquid ratios and liquid viscosities. All of the correlations involve only dimensionless

groups, which is a condition usually sought for in similarity analysis but not always

achieved.

1.2.4.

Beggs & Brill Original[2]

The Beggs & Brill correlation was developed following a study of two-phase flow in

horizontal and inclined pipes. The correlation is based upon a flow regime map which is

first determined as if the flow was horizontal. A horizontal holdup is then calculated by

correlations, and this holdup is corrected for the angle of inclination. The test system

included two 90 ft long acrylic pipes, winched to a variable elevation in the middle, so as

to model incline flow both upwards and downwards at angles of up to 90.

1.2.5.

Beggs & Brill Revised[2]

The following enhancements to the original method are used; (1) an extra flow regime of

froth flow is considered which assumes a no-slip holdup, (2) the friction factor is changed

from the standard smooth pipe model, to utilise a single phase friction factor based on the

average fluid velocity.

1.2.6.

Mukherjee & Brill[18]

The Mukherjee & Brill correlation was developed following a study of pressure drop

behaviour in two-phase inclined flow. For bubble and slug flow, a no-slip friction factor

calculated from the Moody diagram was found adequate for friction head loss

calculations. In downhill stratified flow, the friction pressure gradient is calculated based

on a momentum balance equation for either phase assuming a smooth gas-liquid

interface. For annular-mist flow, a friction factor correlation was presented that is a

function of holdup ratio and no-slip Moody friction factor. Results agreed well with the

experimental data and correlations were further verified with Prudhoe Bay and North Sea

data.

1.2.7. Govier, Aziz & Fogarasi[1]

The Govier, Aziz & Fogarasi correlation was developed following a study of pressure

drop in wells producing gas and condensate. Actual field pressure drop v. flowrate data

from 102 wells with gas-liquid ratios ranging from 3,900 to 1,170,000 scf/bbl were

analysed in detail. The phase conditions in the well bore were determined by standard

flash calculations. Pressure-gradient data for flow under single-phase conditions were

compared with conventional predictions, and found generally to confirm them. For thetest in which two-phase conditions were predicted throughout the well bore, the field data

were compared with several wholly empirical prediction methods, with a previously

proposed method, and with a new prediction method partly based on the mechanics of

flow. The new prediction method incorporates an empirical estimate of the distribution of

the liquid phase between that flowing as a film on the wall and that entrained in the gas

core. It employs separate momentum equations for the gas-liquid mixture in the core and

for the total contents of the pipe.


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1.2.8. NoSlip

The NoSlip correlation assumes homogeneous flow with no slippage between the phases.

Fluid properties are taken as the average of the gas and liquid phases and friction factors

are calculated using the single phase Moody correlation.

1.2.9. OLGAS-89[24]

OLGAS is based in larger part on data from the SINTEF two-phase flow laboratory near

Trondheim, Norway. The test facilities were designed to operate at conditions that

approximated field conditions. The test loop was 800m long and of 8 diameter.

Operating pressures between 20 and 90 barg were studied. Gas superficial velocities of up

to 13 m/s, and liquid superficial velocities of up to 4 m/s were obtained. In order to

simulate the range of viscosities and surface tensions experienced in field applications,

different hydrocarbon liquids were used (naptha, diesel, and lube oil). Nitrogen was used

as the gas. Pipeline inclination angles between 1 were studied in addition to flow up or

down a hill section ahead of a 50m high vertical riser. Over 10,000 experiments were run

on this test loop during an eight year period. The facility was run in both steady state and

transient modes. OLGAS considers four flow regimes, stratified, annular, slug and

dispersed bubble flow and uses a unique minimum slip criteria to predict flow regimetransitions.

1.2.10.OLGAS-92[24]

This is a revision of OLGAS-89

1.2.11.

Ansari[20]

The Ansari model was developed as part of the Tulsa University Fluid Flow Projects

(TUFFP) research program. A comprehensive model was formulated to predict flow

patterns and the flow characteristics of the predicted flow patterns for upward two-phase

flow. The comprehensive mechanistic model is composed of a model for flow pattern

prediction and a set of independent models for predicting holdup and pressure drop in

bubble, slug, and annular flows. The model was evaluated by using the TUFFP well

databank that is composed of 1775 well cases, with 371 of them from Prudhoe Bay data.

1.2.12.BJA for Condensates[22]

Baker Jardine & Associates have developed a correlation for two phase flow in gas-

condensate pipelines with a no-slip liquid volume fraction of lower than 0.1 . This

model represents no major advance in theory, but rather a consolidation of various

existing mechanistic models, combined with a modest amount of theoretical development

and field data testing. The model uses the Taitel Dukler flow regime map and a modified

set of the Taitel Dukler momentum balance to predict liquid holdup. The pressure loss

calculation procedure is similar in approach to that proposed by Oliemans, but accounts

for the increased interfacial shear resulting from the liquid surface roughness.

1.2.13.AGA & Flanigan[3]&[6]

The AGA & Flanigan correlation was developed for horizontal and inclined two phase

flow of gas-condensate gathering systems. The Taitel Dukler flow regime map is used

which considers five flow regimes, stratified smooth, stratified wavy, intermittent,

annular dispersed liquid, and dispersed bubble. The Dukler equation is used to calculate


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the frictional pressure loss and holdup, and the Flanigan equation is used to calculate the

elevational pressure differential.

1.2.14.

Oliemans[10]

The Oliemans correlation was developed following the study of large diameter

condensate pipelines. The flow regime is predicted using the Taitel Dukler flow regime

map, and a simple model, which obeyed the correct single phase flow limits wasintroduced to predict the pressure drop. The model was based on a limited amount of data

from a 30, 100 km pipeline operating at pressures of 100 barg or higher.

1.2.15.

Gray[23]

This correlation was developed by H E Gray of Shell Oil Company for vertical flow in

gas and condensate systems which are predominantly gas phase. Flow is treated as

single phase, and dropped out water or condensate is assumed to adhere to the pipe wall.

It is considered applicable for vertical flow cases where the velocity is below 50 ft/s, the

tube size is below 3, the condensate ratio is below 50 bbl/mmscf, and the water ratio is

below 5 bbl/mmscf.

1.2.16.

Xiao[21]

The Xiao comprehensive mechanistic model was developed as part of the TUFFP

research program. It was developed for gas-liquid two-phase flow in horizontal and

near horizontal pipelines. The model is able first to detect the existing flow pattern, and

then to predict the flow characteristics, primarily liquid holdup and pressure drop, for the

stratified, intermittent, annular, or dispersed bubble flow patterns. The model was tested

against a pipeline data bank. The data bank included large diameter field data culled from

the AGA multiphase pipeline data bank, and laboratory data published in literature. Data

included both black oil and compositional fluid systems. A new correlation was proposed

which predicts the internal friction factor under stratified flow.

1.3.

Matching Study

Baker Jardine conducted a major data matching study to identify the most suitable two

phase flow correlations for each category of problem.

1.3.1.

Overview of Analysis Work

Typically each dataset had around 10 data points. The following volume and range of

data was analysed:-


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Oil Wells

Number of Fields 8

Number of Wells 35

Range of Well Depth (feet) 1,782 - 10,007

Range of Nominal Tubing Diameter (inches) 2.5 - 7

Range of Mean Deviation Angle (degrees) 0 - 49

Range of Gross Liquid Flowrate (STbbl/day) 199 - 16,726

Range of Downhole Pressure (psia) 848 - 4,194

Range of Wellhead Pressure (psia) 98.5 - 956

Range of Bottom Hole Temperature (F) 86 - 254

Range of Watercut (%) 0.1 - 98.55

Range of GOR (Scf/STbbl) 60 - 1,077

Range of API 20.7 - 41

Range of Lift Gas Flowrate (MMScf/day) 0 - 4.89

Condensate Wells

Number of Fields 2Number of Wells 3

Range of Well Depth (feet) 11,560 - 17,710

Range of Nominal Tubing Diameter (inches) 3 - 4.5

Range of Mean Deviation Angle (degrees) 0

Range of Gas Flowrate (MMScf/day) 3.78 - 18.06

Range of Downhole Pressure (psia) 2,032 - 14,228

Range of Wellhead Pressure (psia) 1,213 - 9,649

Range of Bottom Hole Temperature (F) 202 - 377

Range of Watercut (%) 0 - 3

Range of GOR (Scf/STbbl) 5,149 - 10,831

Oil Pipelines

Number of Pipelines 4

Range of Pipeline Length (miles) 0.97- 8

Pipeline Diameters (inches) 6

Range of Gross Liquid Flowrate (STbbl/day) 2,189 - 11,588

Range of Inlet Pressure (psia) 439 - 1,734

Range of Outlet Pressure (psia) 258 - 1,415

Range of Inlet Temperature (F) 77 - 162

Range of Watercut (%) 0 - 12.3

Range of GOR (Scf/STbbl) 248 - 1,545

Range of API 21.5 - 39.4

Range of Gas Flowrate (MMScf/day) 1.98 - 10.29


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Gas/Condensate Pipelines

Number of Pipelines 3

Range of Pipeline Length (miles) 38 - 226

Range of Pipeline Diameter (inches) 20 - 32

Range of Gross Liquid Flowrate (STbbl/day) 0 - 1,521

Range of Inlet Pressure (psia) 848 - 2,103Range of Outlet Pressure (psia) 272 - 1,291

Range of Inlet Temperature (F) 70 - 117

Watercuts (%) 0

Range of GOR (Scf/STbbl) 24,400 - 1,250,000

Range of API 51 - 70

Range of Gas Flowrate (MMScf/day) 37.8 - 1,116

1.3.2. Method of Analysis

Each data point was individually modelled using the various correlations which have

been built into Baker Jardines steady state simulation program PIPESIM. The entered

values were obtained from well/pipeline tests, reservoir fluid analysis, and drillingsurveys/pipeline measurements.

For wells, the flow of fluid was modelled from the bottom hole to the well head where

possible. In some cases the flowing bottom hole pressure was not available, and in those

circumstances, the flow was modelled from the reservoir to the well head using a straight

line productivity index which had been estimated by the operator.

Similarly, pipelines were modelled using a reference inlet and outlet point.

In the case of dP prediction, the bottom hole (or reservoir), or pipeline inlet pressure was

calculated, and the calculated pressure drop (dPcalc= predicted inlet pressure - measured

outlet pressure) was compared to the measured pressure drop (dPmeas= measured inletpressure - measured outlet pressure). The %error for each point was then calculated as

follows:-

%error = ((dPcalc- dPmeas)/dPmeas) x 100%

The mean and standard deviation of this %error were calculated for each data set and the

correlations were rated in accordance with the following table:-

Designation Error Range (%) Maximum Standard Deviation (%)

Very Good -5.0 to +5.0 5.0

Good -10.0 to +10.0 10.0Moderate -20.0 to +20.0 10.0

Poor Outside of the above error ranges

In the case of flowrate prediction, the measured pressure values were entered, and the

flowrate was solved by iteration. The predicted flowrate was then compared to the

measured flowrate. The % error for each point was then calculated as follows:-


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% error = ((Fcalc- Fmeas)/Fmeas) x 100%

The mean and standard deviation of this %error were calculated for each data set and the

correlations were rated in accordance with the following table:-

Designation Error Range (%) Maximum Standard Deviation (%)

Very Good -5.0 to +5.0 5.0Good -10.0 to +10.0 10.0

Moderate -20.0 to +20.0 10.0

Poor Outside of the above error ranges

Failed For at least one data point, the correlation fails to

converge.

1.3.3. Overall Performance of Correlations

Values were assigned to each correlation in each dataset as follows:-

Very Good 3 pointsGood 2 points

Moderate 0 points

Poor or Failed -3 points

The maximum score attainable is therefore 3 x (number of datasets) and this was awarded

100%. The minimum score attainable is -3 x (number of datasets) and this was awarded

0%. Otherwise, linear interpolation was used. The overall scores for dP prediction and

flowrate prediction were then averaged for each correlation, and the correlations sorted in

descending order of performance as shown below.

Vertical and Predominantly Vertical Oil Wells

Number of datasets = 33

Correlation Score %

Hagedorn & Brown 84

OLGAS-89 83

Ansari 81

OLGAS-92 81

Duns & Ros 80

NoSlip 80

Orkiszewski 76

Beggs & Brill Revised 73

Beggs & Brill Original 71

Mukherjee & Brill 70

Govier, Aziz & Fogarasi 59


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Highly Deviated Oil Wells


Correlation Score %

Duns & Ros 96

OLGAS-89 96OLGAS-92 96



NoSlip 79



Gas/Condensate Wells


Correlation Score %

Hagedorn & Brown 47

NoSlip 47

OLGAS-89 47

Gray 42

OLGAS-92 42



Duns & Ros 17

Ansari 14

BJA for Condensates 8


Orkiszewski 8


Oil Pipelines


Correlation Score %

Oliemans 46

NoSlip 38



Duns & Ros 25OLGAS-89 23

OLGAS-92 21

Xiao 21



AGA & Flanigan 0

BJA for Condensates 0


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Gas/Condensate Pipelines


Correlation Score %

BJA for Condensates 67AGA & Flanigan 64

OLGAS-89 64

OLGAS-92 64

Xiao 64


Oliemans 61



NoSlip 56


Duns & Ros 33

2. SINGLE PHASE FLOW CORRELATIONS

2.1. Applicability

Single phase flow correlations can be used as follows:-

Vertical Oil

Flow

Horizontal

Oil Flow

Vertical Gas

Flow

Horizontal

Gas Flow

Moody

AGA

Panhandle A

Panhandle B

Hazen Williams

Weymouth

2.2. Recommendation

Moody is the recommended correlation for all single phase applications.

3.

SLUG CORRELATIONS

The slug sizing correlation of Scott, Shohan & Brill is available through the PIPESIM

Windows interface. Further slug options can be accessed via expert mode as follows:

Main-code: SLUG

Sub-codes: PISS,SIZE


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The SLUG main-code allows the selection of slug behaviour correlations. At present

three slug correlations are available: the severe-slugging group PI-SS, and the slug

sizing correlations of Norris and of Scott, Shohan & Brill (SSB).

PISS = ON Start calculation of PI-SS

= OFF End calculation of PI-SS

SIZE = SSB Switch on Scott, Shohan & Brill slug size correlation.

= NORRISSwitch on Norris slug size correlation.

= OFF Switch off slug size correlation.

Note:The SIZE and PISS sub-codesare not related, and can be set independently of one another.

The PI-SS routine is based upon a correlation developed at Koninklijke Shell

Laboratorium. PI-SS is a dimensionless number which is a means of quantifying the

likelihood of severe riser-slugging. Normally one would turn the PI-SS calculation on

after the first node of the flowline and switch it off at the downstream riser base. If the

value of PI-SS is less than one at the riser base and the flow regime (as predicted by the

Taitel-Dukler correlation) is stratified, then severe riser slugging is possible. Conversely,

PI-SS values significantly greater than one indicate that severe riser slugging is not likely.

The PI-SS number can also be used to estimate slug size. As a rule of thumb the slug

length will be approximately equal to the riser height divided by PI-SS, i.e. PI-SS values

less than unity imply slug lengths greater than the riser height. PI-SS is calculated at each

node in the flowline (while PISS=ON) using averaged holdup data, etc., but it is only the

value recorded at the downstream riser base which is of any real significance. PI-SS is

printed as part of the PRIMARY output (see the PRINT main code).

The SIZE sub-code enables the user to specify a slug sizing correlation. At present two

correlations are available, namely, the Norris correlation and the SSB correlation. The

Norris correlation was developed from Prudhoe Bay operational data and gives slug

size as a function of pipe diameter. The SSB correlation was developed by Scott, Shohan

and Brill and published in SPE paper 15103 in April 1986. The correlation takes account

of slug growth. Normally one would switch the SIZE option on at the start of the profile

and slug sizes will be automatically estimated whenever slug (or intermittent) flow is

predicted by the flow map correlation. It should be noted that the slug size data output is

only printed if SLUG is specified on the PRINT main code, or in the Windows menu

option define output.


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4. REFERENCES

[1] Aziz, K., Govier, G. W. and Fogarasi, M.: "Pressure Drop in Wells Producing

Oil and Gas," J. Cdn., Pet. Tech. (July-Sept., 1972), 38-48.

[2] Beggs H . D., and Brill, J. P.: "A Study of Two Phase Flow in Inclined Pipes,"

J. Pet. Tech., (May 1973), 607-617.

[3] Dukler, E. A., et al: "Gas-Liquid Flow in Pipelines, I. Research Results," AGA-

API Project NX-28 (May 1969).

[4] Duns, H., and Ros, N. C. J.: "Vertical Flow of Gas and Liquid Mixtures in

Wells," 6th World Pet. Congress (1963), 452.

[5] Eaton, B. A.: "Prediction of Flow Patterns, Liquid Holdup and Pressure Losses

Occurring During Continuous Two-Phase Flow in Horizontal Pipelines, "Trans. AIME (1967), 815.

[6] Flanigan, O.: "Effect of Uphill Flow on Pressure Drop in Design of Two-Phase

Gathering Systems, " Oil and Gas J. (March 10, 1958), 56, 132.

.

.

PRINT SLUG $ Switch on slug output printing

SLUG SIZE=NORRIS $ Switch on Norris correlation before profile

NODE DIST=0.0 ELEV=-5000. LABEL='Bottom Hole'

NODE DIST=0.0 ELEV=-3000.NODE DIST=0.0 ELEV=-1000.

NODE DIST=0.0 ELEV=0. LABEL='Flowline'

SLUG PISS=ON SIZE=SSB $ Switch on PI-SS, change to SSB

$ correlation for slug size prediction

NODE DIST=1000. ELEV=10.




NODE DIST=5000. ELEV=10. LABEL='Riser base'

SLUG PISS=OFF $ Switch off PISS

.

.


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[7] Hagedorn, A. R. and Brown, K. E.: "Experimental Study of Pressure Gradients

Occurring During Continuous Two-Phase Flow in Small-Diameter Vertical

Conduits," J. Pet. Tech. (April 1965), 475-484.

[8] Lockhart, R. W. and Martenelli, R. C.: "Proposed Correlation of Data for

Isothermal Two-phase, Two-Component Flow in Pipes," Chem. Eng. Prog.

(January 1949), 45, 39.

[9] Manhane, J. M., Gregory, G. A. and Aziz, K.: "A Flow Pattern Map for Gas-

Liquid Flow Pattern in Horizontal Pipes, " Int. J. of Multiphase Flow.

[10] Oliemans, R. V. A.: "Two-Phase Flow in Gas-Transmission Pipeline,"

ASME paper 76-Pet-25, presented at Pet. Div. ASME meeting Mexico City,

Sept. 1976.

[11] Orkiszewski, J.: "Predicting Two-Phase Pressure Drops in Vertical Pipes,"

J. Pet. Tech. (June 1967), 829-838.

[12] Palmer, C. M.: "Evaluation of Inclined Pipe Two-Phase Liquid Holdup

Correlations Using Experimental Data", M. S. Thesis, The University of

Tulsa. (1975).

[13] Payne, G. A.: "Experimental Evaluation of Two-Phase Pressure Loss

Correlations for Inclined Pipe", M.S. Thesis, The U. of Tulsa (1975).

[14] Taitel, Y. and Dukler, A. E.: " A Model for Predicting Flow Regime

Transitions in Horizontal Gas-Liquid Flow," AICHE Jour. (Vol.22 No.1),

January 1976, 47-55.

[15] Scott, S. L., Shoham, O., and Brill, J. P.: "Prediction of Slug Length in

Horizontal Large-Diameter Pipes," SPE 15103, (April 1986).

[16] Brill, J. P. et al.: "Analysis of Two-Phase Tests in Large Diameter Flow

Lines in Prudhoe Bay Field", Society of Petroleum Engineers Journal, June

1981.

[17] Norris, L.: "Correlation of Prudhoe Bay Liquid Slug Lengths and Holdups

Including 1981 Large Diameter Flowlines Tests". Internal Report Exxon

(October 1982).


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[18] Mukherjee, H. and Brill, J. P.: "Liquid Holdup Correlations for Inclined

Two-Phase Flow", Journal of Petroleum Technology May 1983 1003-1008.

[19] Minami, K. and Brill, J. P.: "Liquid Holdup in Wet Gas Pipelines", SPE

Journal of Production Engineering, May 1987.

[20] Ansari, A., Sylvester N. D., Shoham, O., and Brill, J. P.: "A Comprehensive

Mechanistic Model for Upward Two-Phase Flow in Wellbores".

SPE 20630. SPE Annual Technical Conference, Sep 1990.

[21] Xiao, J. J., Shoham, O., and Brill, J. P.: "A Comprehensive Mechanistic

Model for Two-Phase Flow in Pipelines".

SPE 20631. SPE Annual Technical Conference, Sep 1990.

[22] Baker, A. C., Nielsen, K., and Gabb, A.: "Pressure loss, liquid-holdup

calculations developed".

Oil & Gas Journal, Mar 14, 1988.

[23] Gray, W. G.:"Vertical flow correlation - gas wells"

API Manual 14BM January 1978.

[24] Beniksen, K. H., Malnes, D., Moe, R. and Nuland, S.: "The Dynamic Two-

Fluid Model OLGA: Theory and Application".

SPE 19451 March 1990.

flow correlation selection

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