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--Development of a mechanistic model for theprediction of slug
length in horizontalmulti phase flowMGOPALCorrosion in Multiphase
Systems Center, Ohio University, Athens, USA
Synopsis
A mechanistic model for the prediction of slug length in multi
phase flow is presented based ona unique concept involving the
Froude number. It is shown that the Froude number in the liquidfilm
ahead of the slug is greater than unity. It decreases to values
less than unity inside themixing zone of the slug and then
gradually increases within the body of the slug. The slug
tailoccurs as the Froude number tends to unity once more. Agreement
with experimental data isgood. The model also closely predicts the
data of other researchers in large diameters pipes.
Notation
lloF
aLFSLSGSjtWL,tWG =tj
PL> PG6fjfGv,VLFhEF
area occupied by the gas above the stratified layer of
liquidarea occupied by the stratified layer of liquidperimeter of
liquid contact with wall over which shear stress acts.perimeter of
gas contact with wall over which gas phase shear stress acts.width
of gas-liquid interface.wall shear stress for liquid and gas
respectivelyshear stress at gas-liquid interface.density of liquid
and gas respectivelypipe inclination (small values, close to
horizontal).interfacial friction factorgas phase friction
factortranslational velocity of the slug.liquid film
velocityeffective film height ahead of the slug
@BHRGroup 1998 Multiphase Technology 359
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ULPu-, psau, aLS>Co, XI
PL
8
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Several flow regimes occur in multiphase flows, including,
stratified, slug, and annular flows.The production rates from the
wells are such that these multiphase flow pipelines are expectedto
be in slug flow at some time in their lives. This is a highly
turbulent flow regime, leading toincreased pipe damage from
internal corrosion and mechanical impacts. This is related to
theslug length. It is therefore, important to obtain a detailed,
mechanistic understanding of slug flowcharacteristics, and to
determine the overall slug length.
Mathematical models have been developed that describe the
relationship between differentvariables as knowledge of slug flow
features have increased over the last decade. However, adetailed
understanding of the motion of gas within the slug, and the
distribution of phases in thedifferent zones of the slug is not
known. This is essential information that may be used todevelop a
complete mathematical model to predict slug length.
This paper describes a mathematical model that has been
developed to predict slug lengthutilizing the phase distribution
and velocity profiles within the slug. The experimental
techniqueshave been described elsewhere (Gopal and Jepson, 1997,
1998a,b).
2BACKGROUND
Figure I shows the profile of a slug. Waves form on the liquid
film, that grow to bridge the pipe.This causes the liquid to be
accelerated by the gas. As the slug front moves through the pipe,it
overruns the slow moving liquid film ahead of it and accelerates it
to the velocity of the slug.A mixing vortex is created in this
process. This leads to a scouring mechanism on the pipe wallwith
high rates of shear. Also, as the liquid is assimilated by the
slug, a considerable amount ofgas is entrained (Jepson, 1987). This
leads to the creation of a highly frothy, turbulent regionbehind
the slug front called the mixing zone.
Beyond the mixing region of the slug, the level of turbulence is
reduced, and buoyancy forcesmove the gas towards the top of the
pipe. The cross sectional area available for liquid flowincreases,
a boundary layer develops, and the liquid velocity decreases. This
is the slug body.Eventually a point is reached where the liquid
velocity is no longer sufficient to sustain thebridging of the
pipe, and the slug body is curtailed. This is called the slug tail.
The liquidvelocity decreases in the liquid film, its height
rebuilds with waves forming on its surface, andthe next slug is
initiated.
Dukler and Hubbard (1975) published the first realistic
mechanistic model for slug flowcharacteristics. They established
fundamental equations that could predict several slug
flowcharacteristics. The agreement with experimental data was good
and a better understanding ofthe mechanisms was achieved. However,
many parameters, such as slug frequency and the voidfraction within
the slug, were required to complete the calculation. Also, their
definition of themixing zone is not adequate (Gopal and Jepson,
1998b). The slug lengths in their studies variedfrom 12 to 25 pipe
diameters.
Nicholson et al. (1978) found a non-zero gravity induced drift
velocity, even for horizontalpipes, and determined that this
velocity needed to be incorporated in the calculation of the
slugtranslational velocity. They modified and extended the model of
Dukler and Hubbard to apply
@BHR Group 1998 Multiphase Technology 361
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to the entire intermittent flow regime. The slug lengths in
their case varied from 10 to 60 pipdiameters. It is to be noted
that the model ignores any slip between gas and liquid within
thslug. It has been found (Jepson, 1987) that for large diameter
pipes, this is not true for hightslug velocities.
Maron et al. (1982) derived a model for slug flow based on
periodic distortion of thhydrodynamic boundary layer followed by a
recovery process. As the slug front overruns thliquid film, the
boundary layer is destroyed by the mixing eddy. At the end of the
mixing zon,this boundary layer begins to redevelop. The model
considered two separate types of slug, onwith aeration and the
other without. In the first case, the entrained gas bubbles in the
slug lea"the boundary layer region due to buoyancy effects and tend
to agglomerate in the upper portioof the pipe. The slug length is
the distance required for complete separation of the gas from
thliquid. In the second case, the slug length is given by the
distance required for the boundarlayer to fully develop and reach
the center of the pipe. They developed their boundary laytanalysis
in a coordinate system moving with the slug front and introduced a
one-seventh POWIlaw model to describe the velocity profile within
the boundary layer. They showed that thmodel could be applied to
predict pressure drop for a wide quasi-steady frequency range
(slugs. However, stability analysis indicated that the slug pattern
stabilized over a narro'frequency range corresponding to a minimum
pressure drop. It is to be noted that no informatioabout the pipe
diameter or working fluids were given.
Dukler et.al. (1985) applied the concepts developed by Maron et
al. (1982) and formulatea generalized model for the prediction of
the minimum stable slug length for horizontal anvertical slug flow.
The model utilized the velocity profile developed by Maron et al.
(1982) ithe boundary layer, and combined this with an inviscid
potential core. An assumption was madthat a flat velocity profile
resulted at the end of the mixing zone. The velocity at the center
WIallowed to decrease due to frictional effects predicted by a
Blasius-type equation. The slulength was predicted by the distance
required for the complete development of the boundarlayer. The
results of the model were applied to 5 cm I.D. vertical and
horizontal, and 3.8 CIhorizontal pipes, with air and water as the
working fluids. It was found that the experiment..,- ...~ ~~..; ./
./ ;>:1 .:.-_------ --:--/// -'
/JII/1/111/////I//I//JV////////I//////////////4Ft 4.5-9.0 Sleady
jump
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.... - --/// -
--""'J/////I///I/////I//I//l/I////I////I//////////M
Ft >9.0 SIron; jump
Figure 3: Various types of hydraulic junps
@ BHR Group 1998 Multiphase Technology 377
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v vSL, so D
378
Figure 4: Schanatic flow chart of slug length mcdel
@ BHR Group 1998 Multiphase Techno/~
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20
CDCD00
~5:-g:
15
:>-IIIen
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w'"o
@OJ::J:::0G>ac:o
cOz.; 1.0o..""
Film Slug
Distance
81.1/0".
". eOOl'd''''.'e! ."'.'e",i Film
~cococo
~::>-~.,;;tg.
~Figure 6: Schanatic diagran of Frolrle nunber variation with
distance into the slug
-
0.8
~JS 0.6-!.cEisIii 0.4::g
0.2
0
I-----Modell
-------------------------(11'-0----:-- C'> 0o
1.5 2 2.5Mixture Velocity, mls
3 3.5
Figure 7a; Variation of meanliquid film thickness for
water-carbon dioxide ssystans. Canparison with lOCdel.
1.5 2 2.5 3 . 3.5Mixture Velocity, mIs
Figure 7b: Variation of mean liquid film thickness for
ARmPAK90lM-caroon dimsystem. Canparison with lOCde1.
@BHR Group 1998 Multiohase Techn%nv "'Ri
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1008020
_#1
--e .#2- #3
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......--::::
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1.5
~ 1.30;
'is.I:it 1.1Jl
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@BHR Group 1998 Multiphase Technology 385
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~(J)
)
8
60 I I I i I I I I I I i I I I i j j I iii I I I i I I j I j /1
ARCOPAC900 Water
Nicholson et.al. (2.58 em)SO t- I 0 Nicholson et.a!. (5.18
em)
Crowley etal. (17 em)EB Jepson and Taylor (30 em)40 t- o J Kouba
(7.6 em)
]
Q r- ...30~ .. t 0 0 20 ~ 0
00 EB EB0
.c90 #10 t-~~ ~ EBEB
0
o 1 2 3 4 5 6 7SlUR velocity, mls
Figure 1..: Canparisonof total slug length frQlldifferent
systems.
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~.g
fa;t~o
-
2
r-r~-"'"..,..,..l""'~""'r"'I""'''''''''''II""7'''''''''''P'"T"",,...,...,...,...,..,,1""7''''''''''''
- /--/-7- -Q~~~//~ V
E 1.5
0.5
o
.
. , .-e--- Experiment
--- - Model
.
.
1.5 2 2.5 3Slug velocity, mIs
3.5 4
Figure 12a: canparison of slug length model with average slug
length for water-cdioxide system.
2
...E 1.5 -......-oS ......-llIl
........co ~ ......-oJIlII.e
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References
Agarawal, S.S., G.A Gregory, and G.W. Govier, " An Analysis of
Horizontal Two-PhaseFlow in Pipes", Can. 1. Chern. Eng., 51, 280,
(1973).
Andritsos, N., and Hanratty, T. J., "Influence of Interfacial
Waves in Stratified Gas-LiquidFlows", AIChE Journal, 33, 3, 444,
(1987).
Bamea, D., and Taitel, Y, "A Model for Slug Length Distribution
in Gas-Liquid SlugFlow", Int. 1. Multiphase Flow, 19, 5, pp. 829,
(1993).
Benjamin, T. B.,"Gravity Currents and Related Phenomena", 1. FI.
Mech., 31, II, pp. 209,(1968).
Brill, 1. P., Schmidt, Z., Coberly, W. A, Herring, 1. D., and
Moore, D. W., "Analysis ofTwo-Phase Tests in Large-Diameter Flow
Lines in Prudhoe Bay Filed", SPE 1.,363, (June1981).
Chow, V. Te, "Open-Channel Hydraulics", McGraw-Hili, (1959).
Crowley, C. 1., Sam, R. G., Wal1is, G. B., and Mehta, D. C.,
Slug Flow in a Large DiameterPipe: I. Effect of Fluid Properties",
AIChE Annual Meeting, San Francisco, CA, (1984).
Dukler, A E., and Hubbard, M. G., " A Model for gas-Liquid Slug
Flow in Horizontal andNear Horizontal Tubes", Ind. Eng. Chern.
Fundam., 14,4,337, (1975).
Dukler, A E., Maron, D. M., and Brauner, N., "A Physical Model
for Predicting theMinimum Stable Slug Length", Chern. Eng. Sci.,
40, 8, 1379, (1985).
Fairhurst, C. P., "Slug-Flow Behaviour Clarified in Large
Diameter Pipeline Study", 0& G1., 49, (Oct. 3, 1988).
Gopal, M., and Jepson, W. P., "The Study of Dynamic Slug Flow
Characteristics usingDigital Image Analysis", Part I & II,
JERT, Vol. 120, June 1998 (a, b, to be published).
Gopal, M., and Jepson, W. P., "Development of Digital Image
Analysis Techniques for theStudy of Velocity and Void Profiles in
Slug Flow", Int. 1. Multiphase Flow, Vol. 23, No.5,945-965,
1997.
Green, A S., Johnson, B. V., and Choi, H. 1., "Flow Related
Corrosion in Large DiameterMultiphase Flowlines", SPE paper 20685,
(Houston, TX: SPE 1989).
Jepson, W. P., " The Flow Characteristics in Horizontal Slug
Flow", 3rd Int. Conf.MultiphaseFlow, PaperF2, 187, (1987).
Jepson, W. P., "Modelling the Transition to Slug Flow in
Horizontal Conduit", Canad. J.Chern. Engg., 67,731, (1989).
@BHR Group 1998 Multiphase Technology 38!
-
Jepson, W.P. and Taylor. R.E., "Slug Flow and its Transitions in
Large Diameter, HorizontalPipes," Int. 1. Multiphase Flow, 19, 411,
(1993).
Kordyban, E. S., and Ranov, R. R., "Mechanism of Slug Formation
in Horizontal Two-PhaseFlow", 1. Basic Engg., 92, Series D, 857,
(1970) .
. Kouba, G. E., "Horizontal Slug Flow Modelling and Metering",
Ph.D. Thesis, University ofTulsa, 1986.
Kouba, G. E., and Jepson, W. P., "The Flow of Slugs in
Horizontal, Two Phase Pipelines",Pipeline Eng. Symp., 37,
(1989).
Lin, P. Y., and Hanratty, T. J., "Prediction of the Initiation
of Slugs with Linear StabilityTheory", Int. 1. Multiphase Flow, 12,
79, (1986).
Maron, D. M., Yacoub, N., and Brauner, N., "New Thoughts on the
Mechanisms of Gas-Liquid Slug Flow", Lett. Ht. Mass Transfer, 9,
333, (1982).
Nicholson, M. K., Aziz, K., and Gregory, G. A., "Intermittent
Two Phase Flow in HorizontalPipes: Predictive Models", Canad. 1.
Chern. Eng., 56, 653, (1978).
Nydal, O. J., Pintus, S., and Andreussi, P., "Statistical
Characterization of Slug Flow inHorizontal Pipes", Int. 1.
Multiphase Flow, 18, 3, pp. 439, (1992).
Scott, S. L., Shoham, 0., and Brill, J. P., "Prediction of Slug
Length in Horizontal Large-diameter Pipes", SPEPaper 15103, (1986)
.
. Taitel, Y., and Dukler, A. E., "A Model for Predicting Flow
Regime Transitions inHorizontal and Near Horizontal Gas-Liquid
Flow", AIChE 1.,22, 1,47, (1976).
Zhou, x., and Jepson, W. P., "Corrosion in Three-Phase
Oil/Water/Gas Slug Flow inHorizontal Pipes", Corrosion/94, Paper
no. 94026, (Houston, TX: NACE International,1994).
390 @ BHR Group 1998 Multiphase Technolog~
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