7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
GasWater TwoPhase Flow Measurement with A Vcone meter and Conductivity Rings
Chao Tan and Feng Dong
Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering & Automation,
Tianjin University, Tianjin,300072, China,
Email: fdoni,' lju CLdu en
Keywords: Gaswater twophase flow, flow meter, flow measurement
Abstract
Twophase flow is commonly encountered and of paramount significance in both natural and industrial processes, and yet its
theological complexity makes the accurate measurement on its process parameters difficult to achieve and hence presents an
urgent issue to scientific researchers and industrial engineers. In this work, a series of experiments on gaswater twophase
flow were conducted in a 50mm diameter horizontal pipe, the flow parameters were measured with a conductivity ringsensor
and a Vcone meter. The mass fraction of gas is determined by combining the static pressure to obtain the inline gas density
with ideal gas law and the gas volumetric fraction deprived from holdup measurement by conductivity rings. A velocity ratio
based measuring correlation for gaswater twophase flow mass flow rate measurement is presented by introducing the
velocity ratio and water holdup with conductivity rings. The average relative error of mass flow rate measurement with this
correlation is 2.9%. The average relative error of water holdup measurement is 10%.
Introduction
Gaswater twophase flows are of paramount significance in
both industrial and scientific researches and applications,
and yet the measurement always brings difficulties to the
researchers and engineers. They are encountered in a variety
of different transportation pipelines, fluidized bed, power
plants and chemical reactors, and also involved in safety and
fiscal issues (Thorn and Johansen et al., 1997). Most of the
problems encountered in multiphase flow measurements
arise from the increased number of the characteristic flow
parameters as compared to those in singlephase flows.
Because multiphase flow always involves the interactions
between phases, like mass transfer, momentum transfer and
heat transfer. In addition, all the changes and interactions
are simultaneous and transient, which make the flow
process more complicated.
Many methods have been proposed to solve this issue, such
as, capacitance probes, ultrasonic techniques, tomographies
and singlephase flow meters and etc (Skea and Hall, 1999;
Falcone and Hewitt et al., 2001). Among them the
differential pressure (DP) meters play a significant role. At
present, the application of differential pressure flow meters
in multiphase flow measurements are of increasing research
interests, like Venturi and Orifice meters, and a number of
correlations have also been developed for multiphase flow
measurements with DP meters (Reimann and John et al.,
1982; Steven, 2002). As a newly developed DP meter,
Vcone meters have attracted wide research interests on
their applications in twophase flow measurement (Stewart
and Hodges et al., 2002).
The measuring model that adopted by the DP meters in flow
measurement is the pressure drop model which in twophase
flow measurement is mainly classified into homogeneous
model and separated model based on the assumptions on the
flow conditions. Usually, a phase concentration
measurement is needed to jointly determine the flowrate of
each individual phase.
In this work, a series of experiments on gaswater twophase
flow were conducted in a 50mm diameter horizontal pipe,
the flow parameters were measured with a conductivity
ringsensor and a Vcone meter. The diameter ratio of the
adopted Vcone meter is 0.65, and the acquisition rate of the
conductivity rings is 1000Hz. A velocity ratio based
measuring correlation for gaswater twophase flow mass
flow rate measurement is presented by introducing the
velocity ratio and water holdup with conductivity rings. The
velocity ratio based Chisholm correlation in conjunction
with de Leeuw's selection on Blasius parameter evidently
improves the measuring accuracy of the mass flowrate
measurement by using the Vcone meter, the average
relative error of mass flow rate measurement is 2.9%, and
error of mass flow rate measurement with this correlation is
2.9%..
Nomenclature
volumetric flowrate (m3/s)
flow velocity (m/s)
pressure (Nmn2)
area (m2)
mass flowrate (kg/s)
mass fraction
discharge coefficient
adjust coefficient
pipe diameter (m)
cone diameter
dimensionless conductivity
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
S slip ratio
w droplet entrainment rate
Fr Froude number
n tuning factor
Greek letters
a volumetric fraction
0 diameter ratio
X LockhartMartinelli
qp twophase flow multiplier
e expansion factor
1 realtime void fraction
p density
jy correction coefficient
( contraction coefficient
Subsripts
w continuous phase, water
g discrete phase, gas
tp twophase
ave Average
m mixture
LE liquid entrained
H homogeneous
Vcone flow meter
From the momentum equation, and the continuity equation,
the flow rate of a fluid flowing through a throttling set is:
q =u2A0 = Ao Ap
Si P
where Ao is the throat area of the Vcone,
Ao = D(2 d2), is diameter ratio, fl= D2
4 D
Ap is the differential pressure, correction coefficient Vy to
different tapping method, the expansion factor e and the
contraction coefficient j .
Define the discharge coefficient as the combination of the
above coefficients as Co = /ei the mass flow rate W
of the fluid flowing through a Vcone is calculated with:
W = A2App (2)
The homogeneous model treats twophase flows as if they
were singlephase flows by introducing a homogeneous
density defined as:
1 x 1x
= + (3)
PH Pg Pw
where PH is density of the twophase mixture, x is the
mass fraction of the gas phase, pg and P, are the
density of the gas and water respectively. Assumptions on
homogeneous model are that the two phases well mix with
each other, and no relative velocity and mass transfer
involved.
Combine (2) and (3), the mass flowrate of the homogeneous
flow is:
C ..1 I
S x+(1x) 2
p1
where Wf is the mass flowrate of gaswater mixture, Ape,
is the differential pressure. The homogeneous model is a
theoretical model that can be used particularly for a well
mixed flow, such as one phase evenly dispersed into the
other.
The basic idea of the separated model is to treat the two
phases separately each as a single fluid flowing alone in the
pipeline with its own flow parameters and properties but
with identical discharge coefficient and differential pressure.
Based on these assumptions, the flow rate of each phase
when it flows alone in the pipeline is:
CO AApp
lC
W, = A
where W and W are the mass flow rate of water and
gas respectively, Ap and Apg are the pressure
difference when each phase flows independently in the
pipeline with the same mass flow rate as in the twophase
flow. When the two fluids flow together:
W, = A, 2Ap,p,
COP
W2 = Ag 2Ap pg
where A. and A are the respective crosssection areas
that the two individual fluid flows through, they have the
relationship as:
A = A + Ag (9)
Combining equation (5) (9), the pressure relationship is:
Ap, Ap +1 (10)
Ap Ap
S
So the mass flow rate of the twophase flow is detained:
W C0A 2APp g
J1 /V[x+(1 x) ]
FpgP
A theoretical correlation as well, the separated model
therefore is hard to represent the practical flows. However, a
number of correlations were developed from this model
with certain modifications to acquire a better performance.
TwoPhase Multipliers are usually adopted in the pressure
drop analysis, defined as:
2 A (12)
Apw
A general correlation is obtained from the separated model
by combining (5)(8) and (12):
W C o A V
1P /4 q(I X)
The analyses on the twophase flow multipliers usually
focus on homogeneous model based gaswater twophase
flow, and mainly are in the wet gas measurement. Therefore
several ad hoc correlations were developed, such as
Murdock (1962) correlation, Lin (1982) correlation, de
Leeuw (1997) correlation and Chisholm (1967) correlation.
Conductivity Ring
Many measuring methods are based on the electrical
sensitivity, such as capacitance and conductance; they
generally measure the specially averaged conductivity of
fluid with one or a set of electrodes, and derive the flow
process parameters such void fraction (Jin and Xin et al.,
2008). The operating requirement of applying conductance
method is the continuous phase of the interest fluid must be
conductive. The conductance probes or electrodes can be
arranged into various structures and combinations. The
prototype of conductance probe adopted in this work
consists of six parallel mounted conductivity rings, as
shown in Figure 1 (Shi and Dong et al., 2009).
The conductivity rings obtain the flow information by
injecting electric current into the pipelines through the outer
pair of electrodes and measuring the corresponding electric
potential drop in between each successive electrode.
According to Fossa (1998), the fluid responses the
conductivity information to the 10100 kHz electric current,
i.e. the amplitude is in proportion to fluid conductance.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
respectively, connected by a horizontal Ubend tube with
the length of 2.1m. The conductivity ringsensor is located
at 15m downstream from the pipe inlet. The gas and water
is pumped into the entrance nozzle separately and mixed at
the beginning of the pipeline. At the end point of the
pipeline, the gaswater mixture is fed into a separation tank
for stagnant separation. Then the separated gas and water
will be pumped back into the gas and water tank separately.
Six groups of experiments were conducted by fixing water
flow rate and increasing gas flow rate at each group to
obtain different combination of flow conditions.
Figure 2: Twophase flow experimental loop
A Vcone flow meter of 0.65 diameter ratio was
implemented at 15.5 m, and the conductivity rings were
located 15m away down from the inlet. The flow regime
observed is mainly slug flow.
Results and Discussion
The relationship of dimensionless conductivity V*
(defined as the ratio of the voltage measured when the pipe
is full of water to that measured in experiments) and the
inlet water fraction is plotted in Figure 3, it shows that the
data trend slightly bends at 0.4 of V *, piecewise fitted as:
S= V 0.08 V* < 0.4
a=1.47V*0.23 V*>0.4
The above equation is validated with a second data set, and
the result is displayed in Figure 4. It shows that the data
points are in a linear trend with the average relative error
Cae 10%.
I* Holdup
Figure 1: Conductivity ring array
Experimental Facility
The gaswater twophase flow experiments were conducted
at the threephase flow test loop of Tianjin University in
China, as Figure 2 illustrates. The horizontal pipeline is
manufactured of steel tubing with internal diameter of 50
mm. The total length of this pipeline between entrance
nozzle and the outlet is approximately 16.6m, consists of
two horizontal legs with the length of 7.2m and 7.30m
I.
1
.**
02 04 06
V*
08 10
Figure 3: Dimensionless conductivity V*
referenced water volumetric fraction
versus
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
analysis on gasliquid twophase flow.
2) Correlation with density ratio:
Z<1
00 02 04 06 08 10
3) Other Correlation
Figure 4: Predicted and reference water holdup
In gaswater twophase flow, due to the low viscosity of
each phase, the flow velocity is not identical and therefore
the slip ratio between the two phases is usually taken into
consideration. Wallis (Wallis, 1969), Dukler and Hubbard
(Dukler and Hubbard, 1975) believe that the slip ratio only
takes effect in vertical gaswater flow, while in horizontal
pipe, the perpendicular act direction of gravity and
buoyancy against flow velocity direction makes the slip
velocity neglectable. As experimentally demonstrated by
Nicholson (Stanislav and Kokal et al., 1986) and Bendiksen
(Bendiksen, 1984), however, that the phase slip indeed
exists in horizontal flow, especially within slug flow, the
typical intermittent flow, gas and water each flows in its
own velocity, and therefore the slip effect must be taken into
analysis.
(A) Slip ratio prediction correlations
The slip ratio has been investigated widely but still no well
accepted correlation presented as the physical velocity of
each phase is involved. A definition based correlation is:(Xu
and Wu et al., 2008)
s Ug la g ag (is)
S ___u ag/aw (15)
u u, A A, /L
Where ag = qg /q is the volumetric fraction, r is the
realtime void fraction measured by conductivity rings.
The calibration under typical flow distribution shows that,
the dimensionless conductivity V* has a direct relationship
with water volumetric fraction, with a slope of unity. As
such, V* is used as the prediction of void fraction in
segregated flow regimes.
Several correlations of slip ratio S are listed below to dig
its physical meaning and further build regression model:
1) Correlation considering liquid drop entrainment:
Smith introduced "equal velocity head" into gaswater
twophase flow, and defined entrainment rate as
w= WL/W, i.e. the ratio of mass flowrate of entrained
liquid drop to that of the whole liquid phase (Smith, 1969).
Then the slip ratio is presented:
+( 11 + w[(i x)x]p /pl 1/2F 2
S[ l+w(1 x)x J pJ
Chisholm suggested that w is 0.4 based on a series of
1
S=
1 /1 /
I p.
From the above correlations, the slip ratio is related to the
wetness x and density ratio of gasliquid twophase flow.
As the LM coefficient X contains both the two
parameters, therefore X is adopted to analyze the slip ratio
in this work. The relationship of and slip ratio is:
* .
Figure 5: Relationship of slip ratio and X
An exponential relationship is observed between S and
w which is regressed into the following correlation
according to Figure 5 and :
S 0.023fLa P
1 a p9
(B) Slip ratio based homogeneous model
The assumption of homogenous model is the two phases
have identical flow rate, however in actual flow the slip
exists. The mix density of twophase flow considering slip
ratio is:
x x+S(1 x)
PH S (1x)
Pg Pw
In view of the momentum change Wu, and Wu and
introducing effective average velocity u then the
momentum of homogeneous flow is:
I Holdupl
1+x 1
S = P \
(p v4
Pw
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
W, = Wuw, + Wu
xWUg + ( x)Wun
(21) by Murdock and Lin, and the other is by Chisholm and de
Leeuw. The former form by Murdock and Lin (1982)
introduces a factor 0 to describe the crosssectional void
fraction == Ag/A as:
u, = xu + (1 x)u,
where pe is the effective density, and we have:
W = puA = pA[xug + (1 x)u
1 _A[X +(1x)u]
p, W
Knowing that xW= pgu Aa, then:
1 xug+(1x)u
p a
Pu _
1
p=
From the definition of void fraction a, we have:
a=1 (27)
I Sp( x )]
Lin believes that 0 is a function of slip ratio S, density
ratio and pressures, and from calibration with wet gas,
S= f(pg /p,) as a constant. While the twophase flow
meets the assumption of separated model, then from) and
(26) a simple relationship is drawn:
lx
x+
S
ap
X/Pg
r x S(1x) 1x
P, P s )f
Comparing (25) and (20), we can see that the effective
density is different from slip ratio based mixture density, but
they become the same as the ideal mixture density when slip
ratio is unity. The measurement error of correlation (3), (20)
and (25) in gaswater twophase flow measurement by a
Vcone meter is shown in Figure 6. It shows that the error is
reduced in (20) and (25) by introducing slip ratio, and the
average relative error is 15.4% and 15.5% respectively.
Besides, the error increases in higher gas void fraction, but
the errors of (20) and (25) stays around 20% when gas
void fraction is greater than 80%. It indicates that the
mixture density based correlation has flaws in describing
gaswater twophase flows, and the introduction of slip ratio
can improve the measurement precision in high gas void
fraction.
I Normal Homogeneous Model
o Homogeneous Model with Slp Ratio
A Homogeneous Model with Effective Density
 
00 02 04 06 08 10
Volumetrc Gas Fraction
Figure 6: Measurement error of homogeneous model with
different mixture density correlation
(C) Slip ratio based separated model
Two main forms of modified correlation were developed
based on the separated model assumption, one is presented
O =s Pg
SPW
Then the mass flow rate can be determined through 0. p
is fitted with LM coefficient v by piecewise of S:
qp =1.17+ 6.7/, S <1
qp = 1.5 +0.55/1 S >1
5
*
S. ......... .. .. .. . . . . . ..... ........... ...
2 m
, , .
000 001 002 003 004 005 006
1/X
S<1
*
S. ...
2 : : : . . . . . .: :
1/X
S>1
Relationship of X and q( at different range
Figure 7:
of S
Thus:
As seen from Figure 7, the linearity of the trend of p, and
1/z is not high, and as such the prediction precision by the
model modified with 0 is not high. To further investigate
the effect of slip ratio to separated model, the Chisholm
correlation is studied with its coefficient C as:
/2 f(l/z)= + c/z+ 1/z2
Combining the form suggested by Chisholm and de Leeuw,
coefficient C with slip ratio is:
c _
P S '
where n is a tuning factor. When n equals 0.5,
comparing coefficient C determined by (31) and by (30)
with experimental data in Figure 8, a linear relationship is
observed. Substituting n=0.4 and 0.5 into (31), the
corresponding slope of data trend in Figure 8 is 0.72 and 1.3
respectively. Besides, for a given slip ratio and density ratio,
the relationship of n and C is plotted in Figure 9. It
shows that n has a monologue relationship with C, and
thus the value of n makes the slope of Figure 8 unity lies
between 0.4 and 0.5. de Leeuw believes that n is affected
by gas Froude number Fr In this work, Frg lies
between 0.003 and 1.556 which, according to de Leeuw's
analysis, makes n equal to 0.41. This is in line with the
above analysis.
A5c
C from Expenments
Figure 8: prediction on coefficient C
6m
4 .
04 02 00 02 04 06 08
Figure 9: relationship of n and C
Substituting (31) into (30), a modified correlation of
calculating the mass flow rate of gaswater twophase flow
is:
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
CA C 2p1p
I S Pr \" + \" .
S + 1 p+
/p) S p 1
(1 x +
When n = 0.41, the measurement results of (32) is listed
in Figure 10, average relative error Eae is around 2.9%.
MassFlo wate
30
25
20
S15
10 15 20 25 30 35
Reference Mass Flowrate (kg/s)
Figure 10: Prediction of mass flow rate with (32)
Conclusions
A method of combining a Vcone flow meter with
conductivity rings is presented to measure the process
parameters, such as gas void fraction and total mass flow
rate, of gaswater twophase flow in a horizontal pipe. The
measurement results are validated in correlations based on
homogeneous model and separated model respectively.
The slip ratio is considered and introduced into the
correlations based on the flow feature of gaswater
twophase flow. An experimental data based slip ratio
correlation is presented based on the conductivity rings and
on the existing slip ratio correlations. The slip ratio is also
introduced into the homogeneous model and separated
model respectively to test the measurement precision of
those models. The Chisholm form based correlation is then
modified with the slip ratio and de Leeuw's analysis to
achieve higher measurement precision. The average relative
error of mass flow rate measurement with this correlation is
2.9%. The average relative error of water holdup
measurement is 10%. This work provides a theoretically and
experientially integrated model for the differential pressure
meters in twophase flow measurement in conjunction with
secondary sensors to provide phase concentration and static
pressure compensation.
Acknowledgements
The author appreciates the support from National Natural
Science Foundation of China (No. 50776063) and Natural
Science Foundation of Tianjin (No. 08JCZDJC17700).
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