7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Measurement of Gasliquid Twophase flow using Ringshaped Conductance Sensor
Yanyan Shi, Chao Tan and Feng Dong
Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation
Tianjin University. Tianjin 300072, China
Email: fdlon~ Iju iedu enI
Keywords: gasliquid twophase flow, conductance sensor, ringshaped electrode, liquid fraction, velocity, calibration
Abstract
A ringshaped conductance sensor for measuring liquid fraction and velocity in gasliquid horizontal flow is presented in this
paper. Measurement system consists of six electrodes flushed on the internal wall of the cylindrical working section. The
conductance sensor is calibrated with reference to stratified, annular and bubble phase distributions and the values are
compared with available theoretical results. Experiments are carried out on multiphase flow loop and analysis is conducted to
investigate the characteristics of gasliquid twophase flow.
Introduction
Twophase flow is of great importance in an increasing
number of applications and industries. It occurs in various
geometries, petroleum plants, chemical processes, and heat
transfer equipment. To describe and analyze the twophase
flow properties, reliable measurements of liquid fraction and
velocity are always necessary. In literature, the liquid
fraction can be measured by several techniques, including
quickclosing valves, radiation attenuation, ultrasonic and
impedance method. However, the quickclosing method can
not measure the liquid fraction in real time, the radiation
method requires the construction of complicated, dedicated
facilities, and the ultrasonic method can not easily be
applied to a variety of flow patterns. Compared with the
above techniques, the impedance method is a real time
technique and has simple equipment requirements. A review
of electrical impedance technique for flow measurement has
been presented by Ceccio and George (1996). Impedance
method is successfully applied when the electrical
properties of mixture components are sufficiently different
and can be classified as either conductance or capacitance
sensors according to the applied a.c. excitation frequency (F
Devia and Fossa 2003). In the situation where water is the
continuous phase, conductance sensor is preferred. As to the
measurement of velocity profile, crosscorrelation technique
is commonly used, which was comprehensively described
by Beck and Plaskowski (1987).
As to the conductance method, a pair of flush mounted
parallel ringshaped electrodes was first employed by Asali
et al. (1985) to measure average liquid film thickness in
vertical annular flow. While Andreussi et al. (1988) and
Tsochatzidis et al. (1992) developed Coney s (1973) flat
electrode theory to the response of this ringshaped
electrode configuration. Liu (1996) analyzed the electric
field behavior of a fourelectrode conductance sensor and
measure the volume fraction of oilwater twophase flow in
a production oil well. Fossa (1998) investigated and
compared the performance of the plate and ring electrodes,
showing that the ring electrode was more suitable for
practical application. Lucas et al. (2000)embedded six ring
electrodes on the surface of an insulating plastic body to
measure solid volume fraction and axial velocity of
liquidsolid flow. Jin (2008) presented an eight ring
electrodes conductance sensor to obtain volume fraction and
velocity in vertical gaswater flow based on software
measurement technique. Kim (2009) used three ring
electrodes conductance probe to obtain void fraction and
bubble speed of slug flow.
In the present work, a ringshaped conductance sensor and
related electronic circuit are applied to investigate the liquid
fraction and velocity profile in gaswater flow. Calibration
of the sensor is performed with reference to stratified,
annular and bubble flow regimes. Static experimental points
are compared with theoretical value. Experiments are
conducted on the multiphase flow loop to characterize
twophase flow.
Measurement Principles
Application of flush mounted sensors immersed in
twophase flow is based on the theory of electrical potential
field. As the inner diameter of pipe is much smaller than the
wavelength of electric field, the electric field can be
modeled as time invariant. This problem is described by
Laplace equation of static field:
V2u = 0
Depending on the geometry of the sensor and the interface
between phases, this equation can be solved either
analytically or numerically.
For flat electrodes geometry, Coney (1973) provided
theoretical solution of electrical behavior of a liquid layer
with thickness h and electrical conductivity 7. If I is the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
length of electrodes, s their width and De their spacing, the
medium conductance Ge is then given by:
Ge = Ge xlx y
k(m)
Gre =
k (1 m)
k(ml)=~lj (1min o)SdO
sinh (miP/ 2h)
m=sinh [Fr(s + De) / 2h)
Figure 1: Cross correlation technique
The crosscorrelation velocity U,, used to predict the axial
velocity of the mixture is given as:
where k represents the complete elliptic integral of the first
kind and m is a function of geometrical parameters.
Andreussi et al. (1988) showed that the Coney's solution can
also be used in ringshaped electrodes geometry. For annular
and stratified flow, the above equation is still valid if the
length I is replaced by the wetted length of the electrodes p
and the film height h by hl, defined as:
hi = 4*HI(3)
where 4 is the cross section area of the pipe and HI is the
liquid fraction.
Ring electrodes have also been considered by Tsochatzidis et
al. (1992), who theoretically solved Laplace equation in
cylindrical coordinates for ring probe response to a
conducting annulus of thickness h.
In order to eliminate the effect of liquid conductivity,
normalized conductance Ge* is proposed as the ratio of
conductance between medium at a given liquid fraction and
liquidonly.
When ringshaped electrodes are employed under uniformly
dispersed flow condition (bubble flow), the normalized
conductance Ge is given by the models of Maxwell (1982):
L
max
where r,,, is the maximum of Rx,(r) corresponding to time
delay of the mixture flowing from sensor A to sensor B.
Experimental apparatus
Much previous study in to the development of conductance
sensor has been performed for measuring volume fraction
and very little attention has been put on the velocity. This
paper proposes a conductance sensor with six ringshaped
electrodes to measure both the liquid fraction and axial
velocity in twophase flow. Electric circuit along with the
conductance sensor is shown in Figure 2. As can be seen
from the figure, it mainly consists of four parts: current
generating unit, six ringshaped conductance sensor, signal
processing unit and signal acquisition unit.
Sensor A
seosor c
S2HI
G~e=
3 H
Sensor B ~ SL43 Signal Processing Unit
Figure 2: Ringshaped conductance measuring system
The six ringshaped electrodes are axially separated and
mounted on the inner wall of a pipe with diameter D. El
and E2 are exciting electrodes with distance Ll: M1 and M2
together with M3 and M4 are two pairs of upstream and
downstream correlation electrodes denoted as sensor A and
sensor B separately with distance L2: M2 and M3 are
volume fraction electrodes denoted as sensor C with
distance L3. The electrode width is S. An optimum
geometry of the electrodes is obtained based on the
numerical study of electric field and sensitivity to allow
sensor C optimized for liquid fraction measurement while
sensors A and B optimized for cross correlation velocity
measurement. A simple analysis of electrical field shows
that the distribution of voltage is very peak and
approximately equal to the supplied voltage in the region
adjacent to El and E2 while in the region far from these two
As reported in the literature, relationship between calculated
value of Ge* and the value of liquid fraction HI is dependent
on the separation distance De between electrodes for the case
of stratified and annular flow, with Ge very close to HI when
De is larger than the diameter of the tube. However, for
bubble flow, Ge is predicted to be independent of De and
Maxwell equation can be used to obtain HI.
Apart from the liquid fraction measurement, axial velocity of
twophase flow is commonly measured by crosscorrelation
technique with its basic principle shown in Figure 1.
When gasliquid twophase flow passes the pipe, the similar
signals from upstream sensor A and downstream sensor B
can be correlated. Suppose x(t) and v(tiare signals
respectively from sensor A and sensor B, L is the separation
between two sensors, the crosscorrelation function R,,(r)
can be calculated bv:
Rp.=~l(r) =li (tz) yt+rf ta
S00
O
ssoSensorA
.o Sensor I x i
I 25 x Sensors
B 20
4 soO
1 0 2 4 6 0 1 4 1
Condu:ctivity 1
Figure 4: Sixring electrode conductance sensor
The change in the electrical property of measured fluid has
great effect on measurements. As a result of this, the
changes of voltage on the measured electrodes under fluid
with different conductivity are firstly investigated in the
static experiment. The result is shown in Figure 4. It can be
seen that there exists a good relationship between reciprocal
of measured voltage and conductivity of the fluid measured
on the liquid fraction electrodes while the linearity is not
very well on the cross correlation velocity measuring
electrodes. However, changes are consistent with each other.
Figure 5 shows the normalized conductance Ge as a
function of liquid fraction HI under the stratified gasliquid
flow regime which is simulated by introducing known
volumes of liquid into a horizontally positioned test pipe.
The experimental result shows that Ge is very close to HI
which is in agreement with theory.
Llquid fraction HI
Figure 5: Static calibration for stratified flow
Figure 6 illustrates the normalized conductance Ge against
liquid fraction HI for annular flow. Annular liquid film is
established by inserting plastic rods of known diameter into
the pipe. The experimental points coincide with the
theoretical deduction. It can be noted that, for the proposed
conductance sensor geometry, good linearity is attained
electrodes, a linear dependence exists. Radical current
density is equal to zero and axial current density tends to be
uniform in the region between electrodes El and E2. It is a
well known fact that the irregular variations of voltage
distribution and current density in the vicinity of the
exciting electrodes will introduce nonlinear components into
the output of the measuring sensors, resulting in great
problem in the sensor design. Some research presents that
the measuring electrodes should be mounted in the linear
dependence region (Liu 1996, Hu 2008). However, further
study is required to get an optimum sensor configuration
based on the investigation of sensitivity (Shi and Dong
2008). The optimal parameters of the ringshaped
conductance sensor are shown in Table 1.
Table 1 Parameters for the conductance sensor geometry
Prameters D/mm L1/mm L,2/mm L,3/mm S/mm
Value 50 200 77 60 5
Bidirectional current signal is employed as exciting source
in this paper which is comprised of a voltage generating and
a voltage controlled current circuit Apart from the general
advantages of traditional alternative current source such as
minimizing corrosion of electrodes, having a much higher
output impedance to maintain a constant output amplitude
over a wide range of load impedances encountered in
different process applications, the presented bidirectional
current source help the system consume less time and have
higher efficiency because filter and demodulation parts are
eliminated. The frequency of the exciting current generated
in this system is adjusted between 5 and 120 kHz, while the
amplitude can be regulated in the range between 0 mA and
10 mA. Fluctuation of the current is less than 1% which
meets the precision requirement well.
The output of sensors A, B, C is fed to identical signal
processing circuit. Each of these circuits has a high input
impedance voltage follower to ensure negligible current is
drawn from the electrodes. The output of the voltage
followers is connected to operational amplifiers with low
voltage offset.
The voltage output from the signal processing umit is
obtained by data acquisition system based on the software of
Labview, as is shown in Figure 3.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Sensor Calibration
In this work, a preliminary set of experiments is carried out
in static conditions to relate measured conductance value to
volume fraction. In order to eliminate the measuring error of
liquid conductivity, the normalized conductance Ge is used
and can be written~as:
Ge. w
G V
where G and G, are the conductance
fraction and liquidonly condition,
corresponding voltage value.
(7)
at a given liquid
V and V, are
Figure 3: Signal acquisition program
i.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
measured at the inlet and the result is shown in Figure 9.
between Ge* and HI for the case of stratified and annular
flow.
* Calibratzon data
Linearfit
DD 02 04 06
Liquid fraction HI
08 1
Figure 6: Static calibration for annular flow
Figure 7 depicts the relationship between normalized
conductance Ge and liquid fraction HI of bubble flow
condition which is achieved by a number of plastic spheres
of known diameter which are suspended at fixed positions.
The measurements almost coincide with theoretical value.
Static calibration of the ringshaped conductance sensor
indicates that the proposed system can be employed for
accurate measurements of liquid fraction under different
flow conditions. Apart from the above three flow
distributions, intermittent flow is also encountered for a
wide range of flow conditions. However, intermittent flow
in horizontal pipes can be described as the flow of liquid
regions where the liquid bridges the whole pipe separated by
stratified regions.
Figure 8: Multiphase flow loop
a s
a 
Soa
300
* Calibration data
*Maxwell equation
oio obs 090 obs 1o
Liquid fraction HI
0 2 0.4 0 6
Normalized conductance Ge'
0.8 1.0
Figure 9: Liquid fraction at inlet vs normalized
conductance
Figure 7: Static calibration for bubble flow
0.o .0 0.2 0.'s 0.6 0.8 i. o
Lhqurd cractlon measured at tise minet
Figure 10: Predictive liquid fraction vs liquid fraction at
inlet
As is shown in the figure, the trend line moves towards a
new direction when Ge is higher than 0.4, expressed by:
SHI=Ge
~H = 1.47G e
0.08 Ge < 0.4
0,23 G, > 0.4
Figure 10 compares the measured liquid fraction at the inlet
Experiment
Measurements of the distribution of liquid fraction and cross
correlation velocity are conducted on oilgaswater
threephase flow loop established at Tianjin University as
shown in Figure 8. Tap water and oil can be used as liquid
phase. The working section consists of a horizontal Perspex
tube with diameter of 50 mm. Air coming from a
compressor is mixed with tap water in this paper. After the
test section, air is released and tap water flows back to the
fluid reservoir. Flow rate is controlled in the range of
3~11m3/h for water and 0~362m3/h for gas. The average
temperature in the experiment is 28"C. Pictures from the
highspeed camera allow for better visual flow regime
determination. Sensor signals are captured using data
acquisition system.
Wavelet denoising treatment method is applied to reduce
the high frequency interference. The obtained normalized
conductance Ge is compared with liquid fraction HI
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
According to Figure 12, the relationship between
crosscorrelation velocity Uce and mixture velocity Uh can
be represented as:
to the values that are calculated from conductance
measurements with the above equation. It can be seen that
the measurement result has excellent linearity and average
relative error is 10%.
The relationship between Uce and Uh can be written by drift
flux model:
u. =1 :1% +0.07 Fr~= <3.5
llcc = 0.96uh +0.5 Frm.= h> 35
U,=COUh + V
When twophase flow passes the horizontal working section,
fluctuation of signal is caused. The cross correlation velocity
U,, of twophase flow, calculated by using the fluctuating
signals from sensor A and B, is compared with the mixture
velocity Uh measured at the inlet and plotted in Figure 11.
It is obvious that Co is smaller while Vd iS higher with a
higher Froude number, which is coincided with the result
given by AlLababidi (2006).
Conclusions
. ,W
A ringshaped conductance sensor and related electronics
are developed in this work for measuring the liquid fraction
and velocity in gasliquid mixtures. The conductance sensor
and the signal processing circuit assure a costeffective
system able to characterize twophase flow. Static
calibration is performed under simulated stratified, annular
and bubble flow regimes. Medium conductance is
normalized with respect to the conductance of the pipe full
of liquid so as to avoid monitor the electrical conductivity of
liquid during the measurements. The performance of the
ring electrodes flushed to the pipe wall is described by
theoretical solutions for different twophase distributions.
The static calibration results are in close agreement with the
theory in literature. Experiments are conducted on the
multiphase flow loop. Liquid fraction predicted by the
proposed conductance sensor is compared with the
measured liquid fraction at the inlet and average relative
error is +10%. Relationship between cross correlation
velocity and mixture velocity is obtained according to
different range of Froude number. The proposed six
ringshaped electrode conductance sensor performs well in
the investigation of liquid fraction and velocity and could be
further used to study other characteristics of twophase low.
Acknowledgements
This paper is supported by Supported by National Natural
Science Foundation of China (No.50776063) and Natural
Science Foundation of Tianjin (No. 08JCZDJC17700).
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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