Cc, Distribute constant of velocity
E ray energy
f Pulse feuency
I ray reaiin intensity
IE, ray intensity
Kc, Flow rate constant
L, Linear fractions of water
Lc, Linear fraction of oil
qVolume flow rate
o, Oil flow rate
Qw Water flow rate
QTotal Total flow rate
R Radius of the pp
Vo Oil velocity
Vw Water velocity
Vm Oil water mixture velocity
Vwo Velocitysi between oilwater
Z Atom number
a Oil fraction
SWater fraction
S Absorpin coefficient
SAttenuation coefficient
density
so Oil area fraction
Sw Water area fraction
Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The Flow Rate Mleasurement of OilWater Two Phase Flow Using Turbine Flow Mleter
and y Ray Densitometry
Donghui Li, Jingyu Xu, Feifei Feng and Yingxiang Wu
Institute of Mechanics, Chinese Academy of Sciences
Beijing 100190, China
Donghui li@1~26.com and xujinevuiiaimech.ac.cn
Key words: oilwater two phase flow, turbine flow meter, flowpattemn, homogenized model, driftflux model
Abstract
This paper describes the principle of a model for an oilwater two phase flow meter. Its hardware is composed of a turbine
flow meter and y ray densitometry. In the system, the mixture velocity measurement of oilwater two phase flow was
investigated by a turbine flow meter. The Influences of viscosity variations to turbine flowmeter were experimentally studied
in the range of 50 to 1500mPas. It is shown that the linear work area of the turbine flowmeter is reduced when the oil
viscosity goes up; meanwhile, the measurement results are not sensitive to the flow pattern of the oilwater two phase flow.
The oilwater fraction was measured by using single beam y ray densitometry. The measurement error is mainly caused by the
geometry distribution of oil and water in the cross section, the slip between oil and water is another cause of measurement
error, the two kinds of error are both flow pattern dependent. In order to improve the flow pattern dependency in the fraction
measurement, an oilwater two phase flow conditioner was employed in the pipe to transform the segregated flow into
dispersed flow for most of the considered flow rates. The experimental data show that the oilwater two phase fraction
measurement errors are less than 10%. Further progress was made in the study of slip between the two phases using the
driftflux model, according to the theory, an empirical revised formula is given to modify the measurement result, and finally
the error is confined within 15%.
1. Introduction
2. Nomenclature
With the development of the ocean oil industry, the
need of multiphase flow meter becomes more and more
urgent. This is because of significantly reduced space
demands on the platform when using multiphase
flowmeter instead of the conventional test separator.
Meanwhile, there are also many economic benefits in the
using multiphase flowmeter on platforms. Due to these
facts, considerable researches have started from the early
1980s, as at now, there are several types of flow meters
that have been commercially used in oil industry. Thev
work on different principles and have different ways to
meter the gasoilwater multiphase flow. One of them
works on partial separation based measurement, as their
name suggests partial separation based measurement
systems partially separate the flow, usually into
predominantly liquid and predominantly gas stream before
measurement. As a result, each flow stream then only
needs to be measured over a limited range of component
fractions [1]. In this work style, liquid phase includes oil
and water. How to metering the oilwater mixed flow is the
most important part of work in the three phase metering.
This paper describes a type of oil water two phase
flow meter with its hardware composed of a turbine flow
meter and y ray densitometry. In the system, the oilwater
mixture velocity measurement was investigated by a
turbine flow meter. The oilwater component fraction was
measured by using single beam y ray densitometry.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Fluid passes through the pipe and drives the turbine
rotation. The flow equation is as below:
S=' (6)
Where the q is volume flow rate; f is turbine's output
pulse frequency and kO is a flow rate constant which may
be influenced by the fluid viscosity.
As we know, the viscosity of crude oil usually ranges
from 50 to 3000mPas. In order to avoid that the turbine
flow meter works in a nonlinear work area, an
experimental study was conducted to reveal the linear
work area of the turbine flow meter and the influence of
the flow pattern.
4.1 Experimental setup
Turbine flowmeter
The turbine flow meter used in this project is made by
Tianjin Sure Instrument Science and Teclmology Co.,LTD.
The model is LWGY50. Its pipe diameter is 50mm, flow
rate ranges from 4 to 40 cubic metres per hour.
Flow loop
The flow loop is located in the Multiphase Flow
Laboratory, Institute of Mechanics. It is used to simulate
oilwatergas three phase flow. The flow loop is shown in
Fig.2. The experimental section is comprised of a 20
metres long horizontal pipe, including a 3m up steam pipe
and 3m down steam vertical pipe: the pipe diameter is
50mm and made by transparent Plexiglass in order to
observe the flow regime conveniently.
Water from the water tank is pumped to the experiment
pipe with a water pump, and passes through an
electromagnetic flow meter to measure the flow rate. Oil
in the oil tank is pumped and metered by an oil pump and
an oil flow rate meter. Gas comes from air compressor and
is metered by a gas mass flow meter. The three kinds of
media are mixed in the 'Y' type inlet of the experiment
pipe. At the end of the experiment pipe, the fluid passes
through a 'T' junction pipe in order to preseparate part of
gas and oil, then the remaining liquid passes into a two
class gravity separation tank. After a period of stabling
time, the oil and water are well separated and pumped back
to the water tank and the oil tank respectively for
recycling.
Airompressorpump Ele I ram malevawe
Fig 2 Gasoilwater three phase flow loop
Paper No
3. Principle of the measurement
The flow rate of the oilwater two phase flow can be
simply calculated by using the fonnulas below:
o, o aVo (1)
Q,, = PV,, (2)
~Total = 0o + 0w (3)
a + J1 (4)
Where~, Q is oil and water flow rate: y, V
is oil and water velocities; a / is oil and water
fractions and the Q~ota is the total flow rate of oil and
water. If the flow is homogenized before being measured
then it can be assumed that the two component phase
velocities are equal, and then:
V, = V,, (5)
It is shown that in order to obtain each component flow
rate, the mixture velocity must be measured and the
component fraction must also be measured accurately.
4. The mixture velocity measurement
In this work, the oilwater mixture velocity is measured
by using a turbine flow meter. The turbine flow meter is a
popular flow meter which is conunonly used in single
phase flow metering. It is a kind of very stable and high
accuracy flowmeter which can work in high temperature
and high pressure enviromnent; it also has wide
measurement range and a fast response to dynamic fluid.
In recent years, researchers have begun to apply the turbine
flowmeter to multiphase metering. Turbine flow meter
used in gasliquid two phase flow was investigated
(Johnson et al 1995), obtained the error curves between
flow rate and gas fraction, the result showed that the error
can be less than 12.5% when the gas fraction is below 25%
[2]. The low viscosity oilwater two phase flow was
experimentally studied (Skea and Hall et al 1999) and it
was shown that measurement error can be controlled
within 1% in low viscosity oilwater two phase flow [3].
However when it is actually applied in oil industry, the
viscosity of crude oil from a well has wide variational
range and the oilwater fraction also have a wide
variational range, therefore it needs further research on the
valid linear work area of the turbine flowmeter and the
influences of the flow pattern.
The turbine flow meter is composed of a rotatable
turbine and two fixed axes; an electricmagnetic sensor
inspects the rotation of the turbine and outputs a serial
electric pulse, the pulse frequency represents the flow
velocity. Its schematic is shown in Fig1.
Fig.1 Turbine flowmeter
10
0 Invalid nonlinear area
0
0 Valid linear area
0
10
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
During the high viscosity oil condition, the
unacceptable turbine flowmeter error appears early where
the oil fraction is only 40% but the oil viscosity is already
above 1000 mPas. The experiment result reveals that the
turbine flowmeter linear working area is influenced by oil
viscosity and the oil fraction of the mixture. For this work,
the turbine flowmeter valid work area is drawn inFig.4.
Paper No
4.2 Experimental arrangement
The experimental water comes from the nonnal city
water supply and the oil is a kind of limpidity mineral oil,
its viscosity can range from 50 to 1800mPas. The above
two components can be mixed at the entry of the flow loop
and the oil phase fraction can be adjusted from 0 to 100%.
In order to study the viscosity character of the turbine
flow meter, an experimental arrangement was designed as
shown in Table 1, including a total of 7 groups of
measurements in the experiment. The entire flow rate data
are superficial flow rates obtained from flow meters of
each phase.
Table 1:
2 0 4 0 6 0 8 0 1000 1200
Oil viscosity ( mP s )
1400 1600
4.3 Results and discuss
Fig.4 Valid work area of turbine flowmeter
The influences of the viscosity
According to the table 1, there are seven different
viscosities of oil were studied in the experiment, the oil
was mixed with water to obtain different water cuts in the
oilwater mixture. It is obvious that the viscosity of the
mixture is in direct proportion to the oil fraction; however
the rule of mixed viscosity values in a certain oil fraction is
still not clear. It is necessary to do further research on the
mixed viscosity problem.
During the experiment, the mixture passes through the
turbine flowmeter and then obtains the experiment data
shown in Fig.3.
In Fig.3, the X axis is the oil fraction and the Y axis is
the relative error. With the increase of the oil fraction, the
mixed viscosity goes up and then the turbine flowmeter
measure error also increases rapidly. According to the
experimental points distribution in Fig.3, the errors were
always negative, this means that the measurement value is
always less than the actual value. If +5% accuracy is an
acceptable accuracy in industrial applications, low
viscosity oil can meet with the turbine flowmeter
application requirement when the oil viscosity is between
50 and 160 mPas in a 0 to 100% oil fraction.
In Fig.4, the X axis is the oil viscosity and the Y axis is
the oil fraction. It is obvious that the area below the curve
is the valid linear work area and the area above the curve is
the invalid nonlinear area, the turbine flowmeter used in
oilwater flow two phase flow metering must be working
in the valid linear working area.
The influence of flow pattern
The experiment studied the influence of flow pattern to
the turbine flowmeter in the oil viscosity 50mPas and
obtained the flow pattern diagram (Fig.5) after comparison
with other researcher's results. In the experiment, the flow
pattern was observed from the video which was
35 O Dwo
a ,
20 a
S20 40 60 80 100
Oilfractioninentrv( oo), Viscositv=50mP s
Fig.5. The flow pattern diagram from experiment results
recorded in the experiment. The way to define the flow
pattern according to Laflin and Oglesby [4]. There are four
kinds of flow pattern that were observed in the pipe of the
flow loop, they are respectively segregated flow, dual
COntinuous flow, water in oil emulsion and oil in water.
Fig.4 is the flow pattern diagram from experiment results,
the flow pattern data points accord well with the real line
flow pattern (Lovick and Angeli et al 2001)[5] irrespective
of the oil fraction variation, hence the turbine flowmeter is
S 225mPa r; 400mPa s
~~Y~J9 I 7
+ 4
10 20
30 40 50 60 70 80 90 100
oi fraction p. (%
Fig.3. Relative error in different viscosity
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
measurement. The oilwater two phase mixture has
different densities, influenced by gravity: they stay in
different layers in the horizontal pipe, and also have
different dynamic distributions in the pipe. In other hand,
because there are very complicated flow regimes in the
oilwater multiphase horizontal pipe flow, and the single
beam y ray could not cover the whole pipe cross section
and it only pass through the centre of the pipe, the
measured results must be flow regime dependent, and need
a geometry correction.
The correction is based on a layered distribution of two
phases in horizontal pipe, with water in the bottom layer
and oil in the top layer. Let Lo Lw to be the linear fractions
of oil and water, respectively, as shown in Fig.6.
RLw
Fig.6. Oil and water fraction in pipe
If R is the radius of the pipe and the flow pattern is
segregated flow, the oil area fraction can be shown by the
formula as below:
Paper No
flow pattern independent, the measurement accuracy is
only influenced by mixture viscosity.
5. The fraction measurement
The oilwater fraction was measured by using single
beam y ray densitometry in this work. The measurement of
component ratios in multiphase flows using y ray
attenuation was first suggested by Abouelwafa and Kendall
(1980) [6], and the technique has been used in many
current commercial multiphase metering systems. It is
proved to be a very promising technique for the purpose of
simple and fast estimating the volumetric fractions of
oilwatergas multiphase flow, and becomes the constituent
part of radial based multiphase meter or tomography [7].
5.1 Principles
The following absorption law describes the
mathematical connection between the y ray intensity I,
radiated by the y ray source and the remaining intensity I
after the transmission through a massive object with a
given length L and a density p (Minder and Liechti
1955 [8]; Momneburg 1995 [9]):
I = Io exp(r(ZE) p L)
E = (2xr*arccos()60(RL ) L ~1,l~(2RL )) (rR2)
R
Then the water area fraction will be:
(13)
The absorption coefficient rl is a function of the y ray
energy E and the atom number Z. Under the y ray energy E,
then:
I(E) = Io (E) exp( p(E)L) (s)
For oilwater twophase flow, the attenuation
coefficient of the mixture pL(E) is represented by
E, = 1 so
(14)
When the flow is dispersed flow:
E, = Lw /L And so = Lo / L
pu (E) = ap (E), + Sp (E),
(15)
Where pu(E)o and pu(E),. are the linear attenuation
coefficients of the oil and water and a , are the
respective volumetric fractions. The transmitted intensity I
through a thickness L of an oil/water mixture is therefore:
I = I, exp[ (ap (E), + Sp (E) )L ] (10)
5.3 Experimental setup
y ray source
In this project, the y ray system is comprised of two
radioactive isotopes of 241A and '3Cs which have
emission energies at 59.5keV and 662keV. Both
radioactive isotopes were assembled and shielded in a
thick lead pot to prevent the harmful high energy emission
of "7Cs The radiation intensities of both isotopes are
100mCi and 20mCi. The reason for choosing a greater
radiation intensity of 2'41Am than of '37Cs is that
2I41Am has lower photon energy and therefore weakens in
penetration of the measurement pipe. A collimated single y
ray beam of 20mm in diameter comes out from the bottom
of the source pot and can be turned on/off by a mechanism
switch to ensure the operational safety.
5.4 The dynamic measurement Results
A group of experiments were performed using dynamic
y ray dynamic measurement to study the measurement
[ap~ (E) o + pu (E),. ]L (11)
(12)
The linear attenuation coefficients of water and mineral
oil over the same energy range reveals the differences in
the photon absorption may be used to distinguish the two
materials. The photon attenuation is greater in water than
in oil. This is because oxygen has a higher atomic number
than carbon, and also because water (p=1.00 gent ) has a
higher density than most mineral oils (typically p=
0.80~0.90 gent ).
5.2 Geometry correction
A single beam y ray was used as a densimeter in this
In = 1
n pi
90j m W
eo *DC
A Dolw
so.1 .. r Dw/o
40
30
20
30
40
90
S10 20 30 40 50 60 70 80 90 100
oil action inentry <" )
2 Indinitfluxmodel
20
14
02
04
'
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
the distribution constant of velocity and the Vwo is velocity
slip between the oil and water. The driftflux model usually
is applied to dispersed flows in vertical pipe: however
Franca and Lahey et al[12] found that it still has good
accuracy in segregated flows in horizontal pipe. Through
the analysis of the experimental data in this work, two
empirical formulas of segregated flow and dispersed flow
respectively were obtained:
Paper No
accuracy of fraction measurements. The data of total liquid
flow rate at 4.5m /h is shown in Fig.7. The experiment
result reveals that the error in segregated flow is much
bigger than in dispersed flow and the error even reaches a
maximal 50%, this is probably because the measured
results are flow regime dependent and there is obviously
velocity slip between oil and water in the segregated flow.
V, = 1.031 V,, + 0.079
V, = 1.035 V,, 0.017
(18)
The two empirical formulas can be used to modify the
flow rate measurement result.
6.3 The comparison of the measurement results
In the experiment, the oil and water component flow
rate were measured on the flow loop with total flow rates
of Q=3.5 m /h, 5 m /h, 6.5 m /h, 8 m /h and 12 m /h. The
experimental results were calculated by using
homogenized model and driftflux model respectively. The
comparison of the result is shown in below diagram (Fig.8,
Fig.9, Fig.10, Fig.11, Fig.12). In the diagrams, Fig.a was
calculated by using homogenized model and Fig.b was
calculated by using driftflux model. It is obvious that the
results of the driftflux model have better accuracy than the
homogenized model in all the 5 groups of data.
Fig.7. The relative error in oil fraction measurement
In a dispersed flow, the measurement accuracy is
obviously better than in segregated flow. The way to
resolve this problem is not only necessary to perform a
geometry correction in the measurement but also necessary
to homogenize the fluid before the measurement to reduce
the slip. A kind of flow conditioner can be used to
homogenize the oilwater mixture; normally a nozzle
placed on the pipe before the entry of the turbine flow
meter should be an ideal device to transform the segregated
flow into dispersed flow for most values of flow rate. In
order to obtain a further improvement, an empirical
formula deduced from the driftflux model[10] can be used
to modify the measurement result.
6. Flow rate measurement
6.1 In homogenized model
If the oil water two phase flow is homogenized before
being measured then it can be assumed that the two
component phase velocities are equal:
Oil flow rate m entrance (m /h)
V, = V = F,,
Therefore the two phase flow can be looked as single
phase flow.
6.2 In driftflux model
The driftflux model was first studied by Zuber et al in
1965[11], base upon the assumption of thermodynamics
balance, and build on the average velocity distribution of
two phase flow. The driftflux can be represented as
velocity slip, according to the model in oilwater two phase
flow, the velocity of oil can be written as:
oo as 1o 15 20
011 flow rate in1 entrance (m /h)
25 30
Fig.8, Q,, = 3.5m / h
V, = Cn,Ym + Vwo
(17)
Where the Vm is the velocity of oilwater mixture: the Co is
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
Oil flow rate in entrance Im]/h)
Oil flow rate mn entrance (m]/h)
00 05 10 15 20 25 30 35 40 45
Oil flow rate in entrance (m]/h)
Oil flow rate in entrance ( m]/h)
Fig.11, Qm = 8.0m3 / h
Fig.9, Qm
5.0m / h
Oil flow rate mn entrance (m]/h
Oil flow rate in entrance Im]/h)
Oil flow rate mn entrance (m]/h)
Fig.10, QM = 6.5m3 / h
Oil flow rate in entrance (m]/h)
Fig.12, Qm = 12.0m3 /h
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
on airoilwater flow in horizontal pipes [D]. B.S. thesis,
The University of Tulsa, 1976
[5]Lovick J and Angeli P. Experimental studies on the dual
continuous flow pattern in oilwater flows [J]. International
Journal of Multiphase Flow, 2004, 30, 139157
[6]Abouelwafa MSA, Kendall EJM, (1980), The
MeaSurement of Component Ratios in Multiphase System
Using yray Attenuation, J. Phy. E: Sci. Instrum. 13 341
[7]Grassler, T., Wirth, K.E., (2001), DualEnergy XRay
Tomography in Process EngineeringA NonIntrusive
Technique to Characterize Vertical Multiphase Flows. 2nd
World Congress on Industrial Process Tomography,
Hannover, Germany.
[8]Minder, W., Liechti, A., (1955), Rdntgenphysik,
Springer Verlag, Wien.
[9]Momneburg, H. (Ed.), (1995), Bildgebende Systeme
ftir die medizinische Diagnostik, Publicis MCD Verlag,
Mtinchen.
[10]Jingyu Xu, Yingxiang Wu,Feifei Feng, Ying Chang,
Donghui Li, Experimental investigation on the slip
between oil and water in horizontal pipes, Experimental
Thermal and Fluid Science 3;!_' r s15,178183
[11]Zuber, N. and Findlay, J. A. "Average Volumetric
Concentration in TwoPhase Flow Systems". Journal of
Heat Transfer, Transactions of the 4SM~E, 87: 453468,
1965.
[12]Franca, F. and Lahev Jr, R. T. "The Use of DriftFlux
Techniques for the Analysis of Horizontal TwoPhase
Flows".1Int. J. Addtiphase Flow, 18(6): 887801, 1992.
Paper No
After the comparison, the results of error statistics and
distribution are shown in Fig.13.
a Errors in homogenized model
o Errors in driftflux model
0 a 844 0 
a o c o
oilflowrate (ml/>
Fig.13, Error distribution in the two models
7. Conclusions
An experimental study of oil and water two phase flow
rate measurement has been conducted. In the system, the
oilwater mixture velocity measurement was investigated
by a turbine flow meter. Influences of viscosity variations
to turbine flowmeter were experimentally studied from 50
to 1500mPas. It is shown that the linear work area of
turbine flowmeter reduces when the oil viscosity goes up
meanwhile, the measurement results are not sensitive to the
flow pattern of the oilwater two phase flow.
The oilwater component fraction was measured by
using single beam y ray densitometry. The measurement
error is mainly caused by geometrical distribution of oil
and water in the cross section. The slip between oil and
water is another cause of measurement error, the two kinds
of error are all flow pattern dependent.
In order to improve the flow pattern dependency in the
fraction measurement, an oilwater two phase flow
conditioner was employed in the pipe to transform the
segregated flow into dispersed flow in the most flow rate
cases. After using a nozzle, the experimental data shows
that the oilwater two phase fraction measurement error is
less than 10%.
A further way to overcome the problems caused by slip
is using the driftflux model, two empirically revised
formulas are given to modify the measurement result, and
the measurement error is finally confined within 15%.
References
[1]R Thomn, G A Johansen and E A Hammer, Recent
developments in threephase flow measurement, Meas. Sci.
Technol.8(1997)691701.
[2]W. Jaewoo Shim. On the development of a twophase
flow meter for vertical upward flow in tubes. Korean J.
Chem. Eng., 1997, 14(6), 528532
[3]A.F. Skea, A.W.R. Hall. Effects of water in oil and oil in
water on singlephase flowmeters. Flow Measurement and
Instrumentation, 1999, 10, 151157
[4]Laflin G C and Oglesby K D. An experimental study on
the effects of flowrate, water fraction and gasliquid ratio
