Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 8.6.2 - Measurements of gas entrainment in 2- and 3-phase high pressure stratified flow
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00210
 Material Information
Title: 8.6.2 - Measurements of gas entrainment in 2- and 3-phase high pressure stratified flow Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Johnson, G.W.
Hoffmann, R.
Lawrence, C.
Nossen, J.
Hu, B.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: 2-phase
3-phase
stratified flow
gas entrainment
 Notes
Abstract: Phase fraction and pressure drop measurements for 2- and 3-phase flows were made for horizontal stratified flows using a North Sea hydrocarbon crude, natural gas and brine at 100bar and 80C. A traversing dual-energy gamma densitometer oriented horizontally, parallel to the pipe cross section allowed the determination of phase distribution in the liquid layer. Large waves were observed for low gas rates while stratified wavy flow with a fully dispersed liquid layer was observed for some of the gas-oil experiments, in agreement with Hu et al. (2009). The transition region between these types of stratified flows was investigated for different fluid combinations. It was determined in this investigation that for gas-brine flows, waves were observed at the gas liquid interface at large gas flowrates. In contrast, for gas-oil flows the gas volume fraction in the liquid layer was observed to be as large as 75% for high gas flowrates. In three-phase flow, the continuous liquid phase dictated whether wavy or stratified wavy flows with a fully dispersed liquid layer were observed. A model for gas dispersion in the stratified liquid layer gave reasonable estimates of gas dispersion levels for the different types of fluids.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00210
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Holding Location: University of Florida
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Resource Identifier: 862-Johnson-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Measurements of gas entrainment in 2- and 3-phase high pressure stratified flow


George W. Johnson* and Rainer Hoffmann*

Statoil ASA, Research Centre Porsgrunn, NO-3908 Norway


Chris Lawrencet Jan Nossent and


Bin Hut


t Institute for Energy Technology, PO Box 40, NO-2027 Kjeller, Norway



geoj@statoil.com
Keywords: 2-phase, 3-phase, stratified flow, gas entrainment




Abstract

Phase fraction and pressure drop measurements for 2- and 3-phase flows were made for horizontal stratified flows
using a North Sea hydrocarbon crude, natural gas and brine at 100bar and 80C. A traversing dual-energy gamma
densitometer oriented horizontally, parallel to the pipe cross section allowed the determination of phase distribution
in the liquid layer. Large waves were observed for low gas rates while stratified wavy flow with a fully dispersed
liquid layer was observed for some of the gas-oil experiments, in agreement with Hu et al. (2009). The transition
region between these types of stratified flows was investigated for different fluid combinations. It was determined
in this investigation that for gas-brine flows, waves were observed at the gas liquid interface at large gas flowrates.
In contrast, for gas-oil flows the gas volume fraction in the liquid layer was observed to be as large as 7 .'. for high
gas flowrates. In three-phase flow, the continuous liquid phase dictated whether wavy or stratified wavy flows with a
fully dispersed liquid layer were observed. A model for gas dispersion in the stratified liquid layer gave reasonable
estimates of gas dispersion levels for the different types of fluids.


Nomenclature


Roman symbols
a empirical constant (-)
b empirical constant (-)
g gravitational constant (ms 2)
h height (m)
t point in time (s)
w weighting fraction (-)
y coordinate (m)
A area (m2)
C wave speed (nms1)
D pipe diameter (m)
Fr Froude number (-)
H equivalent height (m)
L length (m)
N integer (-)
P pressure (mPa)
S perimeter (m)


T integer (-)
U velocity (nms1)
WC water cut (-)
Greek symbols
a mean phase fraction (-)
7 surface tension (Nm 1)
6 difference per meter (m 1)
e hydraulic surface roughness (m)
cross correlation function (-)
p mass density (kgmn3)
p dynamic viscosity (kgmi1s 1)
a standard deviation (-)
T time lag (s)
Subscripts
c critical value
i integer associated with sample time
k fluid phase
n integer associated with instrument position














g Gas
1 Liquid
m Fluid mixture
o Oil
w Water/Brine



Introduction

Gas entrainment levels in stratified and intermittent
flows are difficult or impossible to determine using stan-
dard instrumentation such as a stationary gamma den-
sitometer, conductance probes and other conventional
methods for phase fraction measurements for multiphase
flows in pipes. For example, temporal variations in liq-
uid phase fractions as measured by gamma densitometer
can be attributed to varying levels of entrained gas, sur-
face waves or some combination of both.
Stratified flow is one of the common flow patterns in
oil and gas transport lines. Under high pressure condi-
tions, typically found in gas condensate and light crude
pipelines, large amounts of gas can be entrained in the
liquid layer in stratified flow. A knowledge of the distri-
bution of the fluid phases is essential for the theoretical
prediction of pressure drop, phase fractions and transi-
tion between different flow patterns.
For predicting pressure drop, flow pattern and phase
distribution in design and operation of multiphase
pipelines, transient multiphase simulators are used.
The simulations may typically cover several pipelines
over hundreds of km. To attain practical computa-
tional speeds, the multiphase simulators rely on one-
dimensional models or quasi-multi-dimensional models,
which all rely on empirical closure relations. Measure-
ments are needed for the further development of these
closures, which may include wall and interfacial friction
factors, slip ratios, entrained fractions, mixture viscosi-
ties and so on. A limited amount of data exist from mul-
tiphase experiments performed under high pressure con-
ditions using real live crude oil or gas condensate sys-
tems. This paper investigates gas entrainment levels in
stratified two- and three-phase pipe flow at high pressure
using a real crude oil and brine. Unique measurements
are presented which give insight into gas dispersion lev-
els in stratified liquid layers and the mechanisms for gas
entrainment.
Video recording of the flow has been used when
studying the entrainment of bubbles in the liquid layer in
annular and stratified two-phase flows. Through the use
of high speed film, Hewitt et al. (1990) documented the
gas entrainment process at the leading edge of waves in
annular flow. Lunde (1997), Lunde and Nuland (1997),
and Lunde and Nossen (1998) determined gas entrain-
ment in stratified wavy flow by comparing gamma den-


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


sitometer measurements of the liquid fraction with vi-
sual evaluations of the apparent interface level deter-
mined from video recordings of the flow. The video
images provided a time series of apparent levels that
could be used to calculate the fraction of liquid plus bub-
bles, which constituted the apparent liquid layer. Their
results indicated that the entrained bubbles can affect
the frictional pressure drop of the flow through the wet-
ted perimeter and the average densities. Rodriguez and
Shedd (2004) applied a backlit digital imaging technique
to obtain information on bubble entrainment and sizes
within the liquid film of an air-water horizontal annular
flow. Their images indicated that gas entrainment in the
film was primarily controlled by air flow rate and wave
behaviour. Despite the many applications of the visual
imaging technique, it has a vital bottleneck that is the
requirement of the flow visibility, permeable to visual
light. It can hardly be used for opaque or high gassy
fluids, which occur widely in industrial processes.
Spindler and Hahne (1999) measured void fraction
distribution using an optical fibre probe. The probe tip
reflects light if it is immersed in gas, while if the tip is
covered with liquid, light is transmitted. Thus the sepa-
ration of the signals leads to the determination of the lo-
cal gas fraction in the flow. By traversing the probe over
the pipe cross section, they obtained the cross-sectional
phase distribution. Roitberg et al. (2007) studied gas
entrainment using wire mesh probes combined with a
determination of liquid level position from a laser.
Recently, the development of tomographic instru-
ments such as X-ray and traversing gamma densitome-
ters allows detailed analysis of the distribution of the
fluid phases in multiphase flows. Hu et al. (2009) inves-
tigated high pressure gas and water stratified flows us-
ing an X-ray tomograph. Their results showed that the
entrained fraction, defined as the fraction of gas in the
layer, increases with increase of either superficial gas or
liquid velocities, but is less affected by the pressure. The
wave behaviour on the liquid surface is regarded as the
main mechanism in entrapping the gas in the liquid.
Generally, there are several mechanisms of gas en-
trainment in the liquid layer in two-phase gas-liquid
flows (Wood, 1991; (C i.ini, n 1996; Mali and Patward-
han, 2009). (1) Surface aeration, entrainment takes place
all along the gas-liquid surface due to the gas-liquid in-
terfacial shear and the tangential liquid vortices. The
main entraining mechanisms are the overturning surface
waves and the fall-back of liquid droplets that penetrate
the liquid surface dragging gas into the liquid. The mix-
ing zone of the gas and liquid grows with the intensity
of the shear and vortices and may reach to the channel
bottom. (2) Local aeration, entrainment occurs locally
at a surface discontinuity, such as due to plunging jet,
hydraulic jump and turbulent wake. Both mechanisms










7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


are likely to occur in transient multiphase pipeline flow.
Depending on the flow conditions, the dominant mecha-
nism may be different.
Although a large number of experimental investiga-
tions of stratified flows in pipes have been performed,
most were carried out at atmospheric conditions using
air and water which are hardly representative for the flow
conditions encountered in real oil pipelines.


Experimental setup and data analysis

The experiments were performed at the Statoil Multi-
phase Flow Loop in Porsgrunn, Norway in 2005. The
200 m long horizontal 7.78cm i.d. pipe had a hydraulic
surface roughness of 2 10 6m. The system was pres-
surized at 100 bar at 80C and the experiments were per-
formed under steady state conditions. Six gas-oil and
six gas-water experiments were performed at constant
superficial liquid velocity. Six three-phase experiments
with a water cut of 0.33 and six three-phase experiments
with a water cut of 0.74 were performed. The flow pat-
tern was determined to be stratified wavy in each of the
24 experiments. For each set of experiments the super-
ficial liquid velocity was kept constant at z 0.5 m/s
and the superficial gas velocity varied in the range of
0.5 < Us, < 4.0 m/s.
The fluids chosen for the experiments were brine, a
North Sea crude oil and natural gas. The fluids were
recirculated and separated in a three-phase gravity sepa-
rator. Fig. 1 illustrates the shape of the flow loop. The
volume of the separator was 2.2m3.
The gas was circulated by means of a Bertin pe-
ripheral gas compressor, Type CP 310.1.008. The oil
pump is of the type Borneman twin-screw pump, Type
W6.5ZX1-30/324008. The water pump is an APV
canned glandless leakage proof centrifugal pump of type
HMD Type HP 2E SMRES-125 fitted with a magnetic
drive coupling.
The physical properties of the fluids are given in the
following table.


Table 1: The physical properties of the fluids


Parameter value
pg 65
Po 785
Pu 1028
P[ 1.00
Po 5.10
/w 1.74
70O 10.0 *
V... 47.7 .


units
kg mT-
kg m-3
kg m-3
kg m s 1
kg m si 1
kg m ls 1
Nm 1
Nm 1


From separator L TestSection

To separator
Horzontal section (60m) Inclinable section (40m)


Figure 1: Plan view of the experiment flow loop.


Figure 2: Orientation of the traversing gamma densito-
meter


Measurement Instrumentation

A narrow beam dual-energy traversing gamma densito-
mer and two separate broad beam single energy station-
ary gamma densitometers where used to measure fluid
phase fractions. The traversing gamma densitometer
was positioned at 40 vertical positions for each exper-
iment. The path of the gamma photons was parallel to
the pipe cross section as shown in Fig. 2. This instru-
ment has a 30mCi Ba133 source with beam collimation
of 5x10 mm and a CnZnTd detector. The segment of
pipe in the location of the measurements was made of
carbon fibre. Phase fraction measurements were made
at 7Hz at each position over a time span of > 20s.
The measurements from the two stationary single-
energy broad beam gamma densitometers encompassed
the entire cross section of the pipe. These identical in-
struments were Type (S-Tec DT-9300) mounted at a dis-
tance of 3.2m between them along the pipe axis. The
radioactive source was Cs137. Sample frequency was
100Hz and the length of time for each measurement was
approximately 60s.
Pressure drop was measured using two Rosemount
3051 pressure transducers at 1Hz. The pressure taps are
top mounted and the tubes gas filled. The distance be-
tween the pressure taps was 28 m.


Data analysis

The traversing gamma densitometer was used to mea-
sure mean phase fractions in two- and three-phase flows
at 7Hz for z 20s at each position. This allowed low fre-
quency transients (ie. < 7Hz) such as waves and varying
levels of gas entrainment to be resolved.
Large variations in the time traces of phase fraction
values indicated surface waves and/or variations in the
gas entrainment levels. These variations were quantified










7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Figure 3: Picture illustrating the separation between the
stratified layer (below y,) and gas layer with wave crests
(above yj)


using the standard deviation of the time traces at each
position. The standard deviation is defined as

1 T
S- (o 1)2 (1)


where T z 140 represents the number of measurements
and a represents the time average over T for a given
position of the traversing gamma densitometer. Gamma
sources randomly emit gamma photons which contribute
to a "base standard deviation". Therefore the magnitude
of the standard deviation must be considered in relation
to the inherent deviations produced by these particular
types of instruments. Maximum and minumum values
from the time traces were recorded at each position of
the traversing gamma densitometer.
Minimum wave trough levels were defined as the min-
imum height, measured from the bottom inner wall of
the pipe, where a pure gas fraction was measured from
a single measurement during an z 0.14s time interval.
Below this critical level yc only gas-liquid mixtures were
measured. Wave crests were identified based on the
shape of the standard deviation and will be described in
the next section. An illustration of the different regions
of the stratified flow which are used for the analysis is
given in Fig. 3 where the white line at y = y, marks the
division between these regions.
The mean total liquid phase fraction was calculated
using
N
a I = 1 al(yn) w(yn) (2)
n-l
where N 40 is the total number of measurement
positions for the traversing gamma densitometer which
spanned the pipe cross section and w(y,) is the width of
the cross section at height y, normalised so that

1 N
N w(yWn) (3)
n=l
The mean mixture density p, in the stratified liquid
layer was determined by locating the minimum wave
trough level using the approach described above and av-
eraging the liquid phase fraction then dividing by the
number of positions ie.


N,
P.m A 5{^pic (yn)w(yn+)p(l-0l(Y")]W(Y"))}

(4)
where 1 < Nc < 40 is the critical position of the travers-
ing gamma densitometer coinciding with the minimum
trough level and A, is the normalized area of the liquid
layer below y,
N,
A, w(y,) (5)
n=l
The phase fraction of gas in the liquid layer was de-
termined using


1 N,

n-1


a1(Yn)]W(Yn)


The stationary gamma densitometers were used to
determine mean wave speed by calculating the cross-
correlation of the time trace measurements. The formula
for the cross-correlation is

- Ei[(1(ti) 1- )(a2( T) d2)]
-i t) a) 2VE(( ) a)2
(7)
The time lag T which gave the largest value for < was
termed Td and used to find the mean wave speed

C L(8)
Td

The length L between the stationary gamma densito-
meters was 3.2m. The stationary gamma densitometers
were not used for any other purpose.
Pressure gradient measurements were averaged over
80s to give a mean value for each experiment.

Experimental results and comparisons

Interfacial waves were present in all of the experiments
and the waves are believed to be an important mecha-
nism for gas entrainment in liquid layers. The traversing
gamma densitometer measurements gave detailed infor-
mation about the levels of gas entrainment in the strati-
fied liquid layer, distribution of the phases and variations
of these quantities in time. Tables 2-5 provide a sum-
mary of the mean liquid holdup, wave speed and level
of entrained gas for the experiments. Figs. 4-7 illus-
trate the measured mean distribution of the phases over
the cross section for gas-oil, gas-water and three-phase
flows at the lowest superficial gas velocity investigated
ie. Us, 0.50. The mean liquid phase fractions and
wave trough limit y, are represented by vertical lines in
the figures. The standard deviation of the time traces



















Gas -.--....
Oil -
Yc-
a .............


0 0.2 0.4 0.6 0.8
Vertical Position [y/D]


Figure 4: Phase fractions for gas-oil flows at Us,
0.50 and Ui 0.42


and distribution of the gas and liquid phases are rep-
resented by curves which span the pipe cross section
0 < y/D < 1.
The region where the standard deviation is relatively
large represents the wavy region above the wave trough
limit y > yc and the region of the stratified liquid layer
having entrained gas for y < yc. A large standard de-
viation represents large temporal changes in the phase
fractions at a specific point of measurement. An estima-
tion for wave height was made based on the shape of the
curve for standard deviation. An estimation for the ex-
tent of the wave crests was made by determining where
a large standard deviation in the region of y, tapered off
to some constant value for y > yc. Droplets torn from
the wave crests also contributed to temporal variations
in the phase fractions and thus contributed to variations
in the phase fraction measurements. Therefore some un-
certainty exists about estimations the wave height.
As can be seen in Figs. 4-7, the standard deviation
was also large below the wave trough level y, ie. in
the stratified liquid layer. The standard deviation of
the time traces was relatively large in the stratified liq-
uid layer near the gas-liquid interface because surface
waves, above the liquid film, periodically entrained gas
into the stratified liquid layer. In turn, the gas bubbles in
the liquid film periodically returned to the gas phase due
to buoyancy.
The largest superficial velocity is seen in Figs. 8-11
which present the phase fraction distributions, mean liq-
uid phase fractions, and wave trough limit at Us, 4.0.
Much larger levels of gas entrainment in the stratified
liquid layer are seen in these figures. It can be seen
that gas-oil (Fig. 8) and gas-water (Fig. 9) flows dif-
fer significantly for large gas superficial velocities, with


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010






0.8


0.2 0.4 0.6 0.8
Vertical Position [y/D]


Figure 5: Phase fractions for gas-water flows at Us,
0.50 and Ui 0.50


the former having much larger levels of entrained gas.
Figure 8 represents a stratified gas-oil flow having the
largest level of gas entrainment in the stratified liquid
layer in this investigation. For even larger superficial gas
velocities annular flow would eventually develop. In this
experiment the magnitude of the maximum value of the
normalized cross correlation (Eq. (7)) was small indi-
cating that the correlation between the time traces from
the stationary gamma densitometers was weak. There-
fore periodic waves were not identified for this experi-
ment. However a critical value y, was found which sug-
gests that non-periodic random waves could have been
present at the interface between the gas-liquid mixture
region and the gas region.
Several factors may lead to relatively large gas en-
trainment levels in the stratified oil layer compared with
gas-water flows. 1. Gas bubbles were smaller due to a
smaller surface tension between the gas and oil relative
to gas and brine. 2. More powerful waves were ob-
served in gas-oil flows compared with gas-water flows.
3. Buoyancy forces were smaller between gas and oil
compared with gas and brine.
Fig. 12 shows the mean wave speeds for two- and
three-phase experiments and Fig. 13 shows the gas en-
trainment levels in the stratified liquid layer. Both wave
speeds and gas entrainment levels in the stratified layer
increased monotonically with increasing superficial gas
velocities. Gas entrainment levels and wave speeds were
quantitatively similar for all of the experiments with gas
superficial velocities Us, < 2.0 m/s. At larger super-
ficial gas velocities wave speeds and gas entrainment
levels in the stratified liquid layer increased for gas-oil
and the oil dominated three phase case relative to the
gas-water two-phase experiments and water dominated





























0 0.2 0.4 0.6
Vertical Position [y/D]


Figure 6: Phase fractions for gas-oil-water flows at
Us, 0.50 and U1 0.50 with WC 0.33


three-phase experiments. Johnson (2009) reported close
agreement of theoretical shallow water wave speed with
measured wave speed in high pressure gas-water exper-
iments in a 10cm id pipe as well as with data by An-
dritsos (1986) which was obtained at atmospheric con-
ditions. Shallow water wave speed for two-phase flow in
a horizontal pipe is given by


C Ui + VgH cos O


where U1 is the local phase velocity for the liquid, g the
acceleration of gravity, H = A1/Si and 0 is the angle
of pipe inclination from the horizontal plane. For these
experiments 0 0.0.
Figure 15 compares the measured and theoretical
wave speed using Eq. (9) for all of the experiments. As
seen in Fig. 15, Eq. (9) agrees within +-2'' for gas su-
perficial velocities Us, < 2.0. For larger gas flowrates
the increased level of gas entrainment in the liquid layer
might influence wave speeds.


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010






0.8


Vertical Position [y/D]


Figure 7: Phase fractions for gas-oil-water flows at
Us, 0.50 and U~ 0.50 with WC 0.74


Table 3: Results for gas-water flows


0o
0.69
0.49
0.39
0.34
0.26
0.21


Table 4: Results for gas-oil-water flows for WC=0.33


Usg Usl
0.5 0.5
1.0 0.5
1.5 0.5
2.0 0.5
3.0 0.5
4.0 0.5


O-w
0.29
0.22
0.20
0.20
0.11
0.08


C9gl
0.04
0.01
0.10
0.11
0.31
0.60


Table 2: Results for gas-oil flows


agl Fr
0.06 1.0
0.09 1.7
0.09 2.5
0.14 3.5
0.50 8.4
0.75 23.1


Table 5: Results for gas-oil-water flows for WC=0.74


0o0
0.19
0.13
0.11
0.08
0.06
0.03


Ow
0.55
0.44
0.35
0.32
0.32
0.18


Us0
0.42
0.42
0.42
0.42
0.42
0.42


Oo
0.64
0.47
0.39
0.33
0.21
0.12











7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


0 0.2 0.4 0.6
Vertical Position [y/D]


Figure 8: Phase fractions for gas-oil flows at U,,
4.00 and U1 0.42


0 0.2 0.4 0.6
Vertical Position [y/D]


Figure 9: Phase fractions for gas-water flows at Ug,
4.00 and U1 0.50


0.8 1


0.2 0.4 0.6 0.8
Vertical Position [y/D]


Figure 10: Phase fractions for gas-oil-water flows at
Us, 4.00 and U1 0.50 with WC 0.33


0.2 0.4 0.6 0.8
Vertical Position [y/D]


Figure 11: Phase fractions for gas-oil-water flows at
Us, 4.00 and U1 0.50 with WC 0.74


S........ Gas -----
Oil

Yc












7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Oil --
Water -
5 WC 0.33 -0--
WC 0.74 ---


4 5


Figure 12: Mean wave speed as a function of superficial
gas velocity


Figure 14: Liquid phase fractions as a function of su-
perficial gas velocity


Oil ---
Water --
WC 0.33 ---
r0.8 1 n 7A


Oil --
Water -
5WC 0.33 ---
WC 0.74 ---


U ---u --------------------------
0 1 2 3 4 5
Usg




Figure 13: Gas entrainment levels in the liquid layer as
a function of superficial gas velocity


0 1 2 3 4 5 6
Theoretical wave speed




Figure 15: Measured wave speeds compared with Eq.

(9)


Oil ---
Water -
WC 0.33 -
WC 0.74 -B-


Y










7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


A model for gas dispersion

A correlation based on the Froude number will be pre-
sented which gave reasonable comparisons with the
measured gas entrainment levels illustrated in Fig. 13.
The Froude number is given by

Fr = (10)

which gives the ratio of inertial forces to gravitational
forces. In the previous section, it was shown that Eq. (9)
gave reasonable estimates for mean wave speeds com-
pared with measurements. Reformulating Eq. (9) gives
the relative velocity between the waves and the local ve-
locity of the stratified liquid layer ie.

C, = C Ui = gH (11)


Therefore in this case, using Eq. (11),


the Froude number equivalently represents a ratio be-
tween characteristic velocities U1 and C, and is thereby
dependent on wave motion. As shown in Fig. 14 the
phase fraction of liquid decreases with increasing super-
ficial gas velocity. This results in large values for U1 and
therefore large Froude numbers in this region as indi-
cated in Tables 2-5.
The following empirical correlation is proposed

agi = 1 exp(-aFrb) (13)

where a and b are empirical constants to be determined
based on the measurements from this work. It was found
that a = 0.03 and b 1.20. The comparison with the
data is given in Fig. 16 where a reasonable match be-
tween Eq. (13) and measurements is seen. In only one
instance, gas-oil Us, 3.0, did the model predict sig-
nificantly lower gas entrainment levels than were mea-
sured.

Conclusion

The gas entrainment levels was investigated in two- and
three-phase high pressure steady-state pipe flows. It was
found that gas entrainment levels in the stratified liquid
layer increased monotonically with increasing superfi-
cial gas velocities. Similarly, wave speeds increased
with increasing superficial gas velocities. A periodic
variation in the gas entrainment levels was found based
on statistics of the time trace data which indicated that
waves entrain gas into the liquid layer. Interfacial waves
were present in all of the experiments and a correlation
was found between wave properties and gas entrainment


Entrainment Correlation -
Oil -
Water -
WC 0.33 --
WC 0.74 --


Froude Number


Figure 16: Comparison between Eq. (13) and measured
gas entrainment in the stratified layer


level in the stratified liquid layer based on the Froude
number. The effects of the different physical proper-
ties of the different fluids, although not explicitly ac-
counted for in the Froude number, influence measured
mean phase fractions on which the Froude number de-
pends. The model followed the trends of the gas entrain-
ment levels qualitatively for the different fluids and flow
rate combinations.


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