Chinese Journal of Chemical Engineering, 16(2) 320—324 (2008)
RESEARCH NOTES
Performance of a Horizontally Mounted Venturi in Low-pressure
Wet Gas Flow*
FANG Lide (方立德)** and ZHANG Tao (张涛)
Key Laboratory for Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin
University, Tianjin 300072, China
Abstract The performance of a Venturi tube used in wet gas flow have been explored mainly under higher-pressure
condition, but very often, low-pressure test exists in some oil and gas fields in Tianjin Dagang Oil and Gas Field in
China. In this study, the performance of horizontally mounted Venturi meters in low-pressure wet gas flow is discussed. Three 50 mm Venturi meters were tested systematically, with β values of 0.4048, 0.55 and 0.70, the operation pressure of 0.15 MPa, 0.20 MPa, 0.25 MPa, the gas densiometric Froude number from 0.6 to 2.0, the modified
Lockhart-Maretinelli parameter from 0.0022 to 0.06, and the ratio of the gas liquid mass flow rate from 0.5 to 0.99.
The effects of modified Lockhart-Maretinelli parameter, pressure, gas densiometric Froude number, diameter ratio,
and gas-liquid mass flow rate ratio to the Venturi tube are analyzed with new independent data. Furthermore,
low-pressure performance was compared with that under high pressure.
Keywords gas-liquid two phase flow, wet gas metering, Venturi meter, over-reading
1
INTRODUCTION
Wet gas has been defined as 90% gas, 95% gas
and even 98% gas by different technical papers [1].
Normally, two ways are employed to meter wet gas,
one is to use a multiphase flow meter in wet gas,
while the other is to use a standard dry gas meter and
apply corrections to the measurements [2].
As a mature single-phase flow measurement device, the Venturi meter (or tube) is easily to be considered for two-phase flow measurement [3]. Some
tests have been done under high-pressure wet gas loop
with high Lockhart-Maretinelli (LM) parameter to
study the over-reading of Venturi meters in wet gas
condition. In Steven’s paper [4], a 6˝ Venturi meter
with diameter ratio (β) of 0.55 was installed in NEL
(National Engineering Laboratory，UK) with pressure
2 to 6 MPa and Lockhart-Martinelli parameter 0 to 0.3.
After that, NEL engineers Stewart and Boam presented two reports and a paper [5-7], three 4˝ meters
were chosen with different β values (0.4, 0.60, 0.75)
and tested over a range of pressure (1.5-6.0 MPa), gas
velocity [gas densiometric Froude number (Frg)
0.5-5.5] and liquid fraction (Lockhart-Martinelli parameter X＝0-0.4). Furthermore, Britton et al. [8],
Kegel [9] did some tests in Colorado Engineering Experiment Station with pressure under 1.4-7.6 MPa,
and Lockhart-Martinelli parameter between 0 and 0.25.
However, very few full tests were done under
low-pressure wet gas condition, so the authors implemented a full test program at Tianjin University (TJU)
multiphase flow loop to cover this range. The results
add to the experimental database, and provide necessary reference for the application of Venturi meters in
low-pressure wet gas metering.
2
OVER-READING THEORY
Defined over-reading as Eq. (1):
OR =
mg =
m'g =
m'g
mg
=
ΔPtp
ΔPg
Cε AT 2 ρg ΔPg
1− β 4
Cε AT 2 ρg ΔPtp
1− β 4
the real gas mass flow rate can be corrected to
m'g
mg =
OR
(1)
(2)
(3)
(4)
Generally, the over-reading caused by two factors:
one is the liquid presence in gas, which caused a
blockage effect; the other is gas-accelerating effect to
liquid, which caused a drag pressure drop.
3
EXPERIMENTAL APPARATUS
Each Venturi meter was calibrated in dry gas at
each test pressure prior to the respective wet gas tests,
to establish a dry gas baseline performance against
which the wet gas results could be compared. Both the
Venturi calibrated test and wet gas test were conducted
on TJU multiphase flow loop at pressure from 0.15
MPa to 0.25 MPa across a range of gas velocity. TJU’s
low-pressure wet gas test facility is a complete system
with full automatic control and multiple functions,
which is not only a multiphase flow experiment system, but also a multiphase flow meter calibration system. As an experiment system, the test can be conducted in horizontal pipe, vertical pipe and 0-90° inclined pipe. As a calibration system, the test meter can
be calibrated in standard meter method. Fig. 1 shows
schematic of TJU multiphase flow loop.
Received 2007-05-08, accepted 2008-02-12.
* Supported by the National High Technology Research and Development Program of China (2006AA04Z167, 2007AA04Z180).
** To whom correspondence should be addressed. E-mail: leed_amy@yahoo.com.cn
321
Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
According to ISO5167-1, 4 (2003), a classical
Venturi tube with a machined convergent section must
have its straight length and diameter ratio according
with Table 1.
In this test, three Venturi tubes with β value equal
to 0.4048, 0.55 and 0.70 were fabricated, the length of
Venturi tubes is 388 mm, diameter is 50 mm, the
length of cylindrical throat is 20 mm, conical convergent angle is a constant of 21°, conical divergent angle
is 12°, the pipe wall roughness is 0.06 mm, and
stainless steel flanges used in connection [10, 11]. Type
1151 differential pressure transducers from Rosemont
were used, and the uncertainty of pressure transducers
is 2.5‰。
The experimental parameters are listed in Table 1.
Table 1
Diameter
ratio β
Pressure/
MPa
0.4048
Figure 1 Schematic of TJU multiphase flow loop
1—liquid tank; 2—air inlet; 3—compressor; 4—cooler system;
5—gas tank; 6—liquid pump; 7-9—Alicat mass flow controllers;
10—vortex flow meter; 11,13—roots flow meter; 12,15,16—
turbine flow meter; 14—electrical flow meter; 17—horizontal
experimental pipe; 18—vertical experimental pipe; 19—water
tower; 20—gas liquid separator; 21—gas liquid mixer
The facility makes up of six components, which
are medium source, single phase flow pipe and standard meters, horizontal pipe, vertical pipe, 0-90° inclined pipe and computer control system. Gas is compressed air provided by two compressors, and it passes
through cooling and drying units to access to two 12
m3 tanks. With these tanks, the pressure-regulating
valve can hold a stable pressure 0-0.5 MPa for the test.
The liquid used is water (oil or oil and water mixture
also can be used) and a water pump pushes the water
to a 30 m high water tower, which can hold a stable
pressure for driving liquid flow. The uncertainty of the
liquid standard meters is 5‰, and the gas standard
meters is 1%.
Gas and liquid whose flow rates have been measured through standard meters enter the mixer which
makes the liquid become 100-1000 μm mist, and then
go through the 50 mm experimental pipe (Fig. 2). The
ball valve installed 14D upstream of the meter is used
when maintaining the metering system. Generally, the
valve remains full open not to perturb the flow. An ball
valve which adjusts the test pressure is installed at the
outlet of the experimental pipe. The ball valve has a hole
on the ball with the same diameter as upstream pipe.
Figure 2
0.55
0.7
4
4.1
Experimental parameters
Lockhart-Martinelli
parameter
Frg
0.15
0.8-1.5
0.0022-0.0338
0.20
1.0-1.88
0.0022-0.0472
0.25
0.67-1.81
0.0022-0.0495
0.15
1.04-1.78
0.0022-0.0572
0.20
1.09-1.85
0.0022-0.0431
0.25
0.92-1.73
0.0022-0.0514
0.15
1.04-2.0
0.0024-0.0480
0.20
1.08-2.0
0.0025-0.0525
0.25
0.87-1.66
0.0027-0.0576
RESULTS AND ANALYSIS
Effect of influencing parameters
It has been showed that under high-pressure the
over-reading of a Venturi was dependent on the gas
Froude number Frg, Lockhart-Martinelli parameter X,
gas density ρg (or pressure P) and the Venturi β value.
Lockhart-Martinelli parameter is defined as
X=
ρl
ρg
ΔPl
m
= l
ΔPg mg
(5)
The gas densiometric Froude number (Frg) is:
Frg =
υg
gD
ρg
ρl − ρ g
(6)
Besides these parameters, the slip ratio also has
significant effect to the over-reading. Based on the
momentum balance and separated flow theory [12-14],
the over-reading can be expressed theoretically as
Horizontal experiment pipe
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Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
⎛1
ρg ⎞
ρl
⎟X + X2
OR = 1 + ⎜ ⋅
(7)
+S⋅
⎜ S ρg
⎟
ρ
l ⎠
⎝
Equation (7) shows that slip ratio S is also a factor influencing OR, but the slip ratio is hard to be determined accurately, so it needs to find another parameter to substitute it. de Leeuw used the gas densiometric Froude number to reflect gas liquid velocity
ratio [15], but Eq. (6) can only reflect superficial gas
velocity, not including liquid velocity. The parameter
reflecting gas liquid velocity ratio is gas-liquid mass
flow rate ratio, which can be shown as
mg
ml
=
ρg α
x
=
⋅
⋅S
1 − x ρl 1 − α
(8)
Equation (8) shows that gas-liquid mass flow rate
ratio are related with gas-liquid density ratio, gas
cross-section fraction and slip ratio, and it can be acquired with the ratio of the gas to total mass flow rate.
Next, the effects of the gas Froude number Frg,
Lockhart-Martinelli parameter X, pressure P, the Venturi β value and gas-liquid mass flow rate ratio
x /(1 − x) to over-reading will be analyzed.
4.2
Effect of Lockhart-Maretinelli parameter
As expected, over-reading increases with increasing Lockhart-Martinelli parameter X, in agreement with almost all previous work under middle and
high-pressure on this subject (Fig. 3). It is mostly due
to the liquid, which reduces the gas passing area and
brings about a blockage effect to the gas and an accelerating effect to the liquid.
high-pressure, so over-reading is affected obviously
by the gas Froude number.
Figure 4 show the over-reading is less than 1 under low gas Froude number and low LM parameter as
observed in many investigations. The over-reading
less than 1 means that the differential pressure under
two phase flow is less than it under signal gas phase
flow when the gas velocity is small. The presence of a
small amount of liquid may block the gas flow channel, increasing the friction pressure drop, but, liquid
has a lubrication action at the pipe wall, which decreases the friction pressure drop. Under low gas Froude
number and low LM parameter The over-reading less
than 1 suggests simply that the blockage effect is
weaker than the lubrication action.
Figure 4 Venturi over-reading in different Frg for β＝0.55
at 0.15 MPa
Frg: ● 0.7; ■ 1.1; ▲ 2.0
4.4
Pressure effect
Pressure also affects over-reading under lowpressure and low Lockhart- Martinelli parameter by
affecting the gas liquid density ratio directly as shown
in Fig. 5. It suggests clearly that the over-reading decreases with increasing pressure. make the gas density
decreasing, From Eq. (6), under the same gas Froude
number, the low gas density under lower pressure
means higher gas superficial velocity and thus the
larger friction. So the over-reading under low pressure
is higher than that under high pressure.
Figure 3 Venturi over-reading for all diameter ratio and
pressure
β value: ○ 0.4048; ■ 0.55; ▲ 0.7
4.3 Gas Froude number
NEL (National Engineering Laboratory, UK) reported that some of the data seemed to tend to a value
slightly above unity particularly at low X values [5-7].
But this prediction was not the case under
low-pressure and low Lockhart Martinelli parameter
with X less than 0.05. It is found that OR differs for
different gas Froude number (in Fig. 4), mainly because that the gas liquid density ratio is lower under
low-pressure. According to Eq. (6), for given Lockhart
Martinelli parameter and gas Froude number, the gas
velocity under low-pressure is higher than those under
Figure 5 Venturi over-reading in different pressure for
β＝0.55 under low-pressure (Frg＝2.0)
▲ 0.15 MPa; ● 0.20 MPa
4.5
Effect of Venturi diameter ratio
Figure 6 show over-reading data from 3 Veturis
for Frg＝1.7 at 0.20 MPa. It is clear from Fig. 6 that
the β value shows definite effect on over-reading under low-pressure. In some condition, the over-reading
decreases with increasing β value with the exception
of 0.70. The decrease of Venturi diameter ratio brings
about the decrease of gas passing area in the Venturi
Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
Figure 6 Venturi over-reading in different diameter ratio
under 0.2 MPa (Frg＝1.7)
■ 0.4; ● 0.55; ▲ 0.7
throat, the increase of gas velocity and gas liquid velocity ratio, and finally results in the increasing of
over-reading.
The over-reading of β ＝ 0.70 is higher than
0.4048 and 0.55 because of differential pressure of 0.7
lower largely than the other β, it can be acquired from
Eq. (2),
mg
⎛
ΔPg = ⎜
⎜ Cε A0 2 ρg
⎝
ΔPg = K ⋅
2
⎞ 1− β 4
⎟ ⋅
⎟
β4
⎠
1− β 4
β4
(9)
(10)
For different β, the differential pressure, which
varies curvedly only with β under the same pressure
and gas Froude number, decreases rapidly with the
increasing value of β (Fig. 7). When the liquid exists
in gas, the pressure drop is higher than gas flowing
alone, for β＝0.70, small liquid fraction will make a
large over-reading.
323
Figure 8 Over-reading plots on gas liquid quality ratio for
Frg＝1.7 at 0.20 MPa
■ 0.4; ▲ 0.55; ● 0.7
ACKNOWLEDGEMENTS
The author would like to thank National Engineering Laboratory of UK for providing the reports
and professional advice on the web.
NOMENCLATURE
OR
ΔPg
ΔPl
ΔPtp
gas occupied cross-sectional area of pipe, m2
liquid occupied cross-sectional area of pipe, m2
area of the Venturi throat, m2
discharge coefficient
inner diameter of upstream line pipe, m
gas densiometric Froude number defined by Eq. (6)
－
gravitational acceleration, 9.81 m·s 2
－1
modified gas mass flow rate, kg·s
－
apparent gas mass flow rate, kg·s 1
over-reading
superficial gas differential pressure, kPa
superficial liquid differential pressure, kPa
actual two-phase differential pressure, kPa
S
ug
ul
υg
X
x
α
β
ε
ρg
ρl
slip ratio ( S = ug / ul )
－
real gas velocity, m·s 1
－
real liquid velocity, m·s 1
－
superficial gas velocity, m·s 1
Lockhart-Martinelli parameter defined by Eq. (5)
ratio of gas to total mass flow rate [ x = mg /(mg + ml )]
void fraction [α = Ag /( Ag + Al )]
diameter ratio ( β = d / D )
expansibility factor
－
gas density, kg·m 3
－
liquid density, kg·m 3
Ag
Al
AT
C
D
Frg
g
mg
m'g
Subscripts
Figure 7 Differential pressure varied with diameter ratio
in the same pressure and gas Froude number
4.6
Effect of gas liquid quality ratio
Figure 8 shows over-reading versus gas liquid
quality ratio for Frg＝1.7 at 0.20 MPa. At the same
diameter ratio, the over-reading decreased with the
increasing gas liquid quality ratio, the curves appeared
exponential for all diameter ratio, and the over-reading
decreased with the increasing diameter ratio. It is noticed that OR at β＝0.55 was the smallest than other
diameter ratio. Fig. 6 shows the same phenomenon as
that in Fig. 8. The reason of this behavior needs further investigation.
g
l
tp
gas phase
liquid phase
gas-liquid two phase
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