6'*^ South East Asia Hydrocarbon Flow Measurement Workshop
Venturi-Tube Performance in Wet Gas: Computation and Experiment
Michael Reader-Harris, David Hodges & Jeff Gibson
TUV NEL
7'^-9'^ March 2007
6** South East Asia Hydrocart)on Flow Measurement Workshop
7'^ - 9*^ March 2007
Venturi-Tube Performance In Wet Gas: Computation
and Experiment
Michael Reader-Harris, TUV NEL
Jeff Gibson, TUV NEL
David Hodges, TUV NEL
1
INTRODUCTION
Various one-off tests performed on wet-gas flowmeters appeared to show that changing the
test fluids could affect the meter performance. It was believed that fluid properties, such as
liquid surface tension and viscosity could play a major role; however, no data existed that
quantified the effects in a systematic manner. Quantifying the effect is important given the
increasing use of wet-gas meters for gas and liquid allocation measurementKnowledge of the extent of any change in meter perfonmance is significant because current
wet-gas correlations which correct for the liquid presence are not able to account for large
changes in fluid properties. Many correlations in existence were developed on test facilities
that utilize only a single pair of test fluids. Consequentiy, the use of such correlations on
meters exposed to different fluids from those of the original test facility may well introduce
systematic errors in the estimates of the individual-phase flowrates.
In order to investigate this, NEL canried out wet-gas testing of diameter ratio, /?, 0.6 and 0.75
Venturi tubes using three gas-liquid combinations (nitrogen-kerosene, argon-kerosene and
nitrogen-water) and at two gas-liquid density ratios. These data were presented in [1] and [2].
The results showed that changing the gas type had little measurable effect on the Venturitube performance with the largest deviations in over-reading relative to the nitrogen-kerosene
data not exceeding a range of -0.023 to 0.02, suggesting no effect of argon compared with
nitrogen.
Changing the liquid type had a more significant impact on the Venturi-tube performance.
With the exception of the smallest gas densimetiic Froude number used, all Venturi tubes
produced over-readings that were smaller for the nitrogen-water tests than for the nitrogenkerosene tests. Deviations in over-reading varied from -0.012 to -0.095 (at the maximum
value of the Lockhart-Martinelli parameter value used).
In addition to the testing. Computational Fluid Dynamics (CFD) analysis of wet-gas flow
through Venturi tubes was undertaken in order to help understand the results of the tests.
The wet-gas analysis was earned out using the Eulerian multiphase model within Fluent 6.3.
These results are discussed at length in this paper.
The fluid conditions and Venturi-tube dimensions were chosen so as to match tests
undertaken on 4-inch (100 mm) NB Venturi tubes manufactijred in accordance with ISO
5167-4:2003, with diameter ratios of 0.4, 0.6 and 0.75. The effect of changing the fluid
combinations was also examined using the CFD. The experimental data were previously
reported either in NEL report 2002/100 [3] or in [1] and [2].
2
DEFINING WET-GAS PARAMETERS
Several recognised dimensionless parameters are used in order to facilitate the comparison
with experimental data. These include the gas densimetric Froude number, the LockhartMartinelli parameter and the Venturi-tube over-reading. These are stated here for clarity.
The gas densimetric Froude number, Frgas, is the ratio of the inertial force to the force of
gravity for a given fluid flow and is defined as:
6** South East Asia Hydrocarbon Fiow Measurement Workshop
7*^ - 9*^ March 2007
Fr,.s=^J^^
g D \Pliquid ~ Pgas
(1)
where Vs.gas is the superficial gas velocity (i.e. the velocity of the gas if it were it to flow alone
in the pipe), g the acceleration due to gravity and D the pipe diameter.
The Modified Lockhart-Martinelli parameter, X, can be defined as;
^^
miqmd
Pgas
^2)
"^gas "^Pliquid
where m is the mass flowrate.
The Venturi-tube over-reading is defined as the ratio between the indicated mass flowrate In
wet gas, based on the measured two-phase differential pressure, Apiwo..phase. and that which
would have been indicated if the gas phase flowed alone in the pipe, with a differential
pressure of Apgas^
Over - reading = \
(3)
Whereas parameters such as flow rate, gas superiicial velocity and density are known, or can
be easily calculated from line temperature and pressure, the droplet size and flow pattern are
generally unknown for a given application. The analysis is further complicated by the fact that
the flow pattern rarely confomns to one single regime (e.g. mist or annular), but is rather a
combination of several flow patterns. For example, if an annular-mist flow is present, it is not
possible to know how much liquid is attached to the walls, and how much is suspended in the
gas stream as a mist, without carrying out techniques such as tomography; the size of the
droplets in the mist phase is also unknown. All of these factors will have an impact on the
Venturi-tube over-reading to some degree.
The following CFD analyses, therefore, assume a simplistic, homogenous flow pattem
entering the Venturi tubes and have been carried out in order to determine whether such a
simple approach will give adequate results for wet-gas flow. More information on the flow
pattern is required to extend the applicability of the model.
The experimental data showed that the test-meter over-reading reduces with increasing
pressure, but increases with increased gas densimetric Froude number. The influence of
Froude number is more marked at lower values, except for the Venturi tube of diameter ratio
0.4, which showed an altogether different trend with gas densimetric Froude number and
Lockhart-Martinelli parameter. In annular-mist flow, as the flow velocity increases, so the
droplet size decreases, thereby ensuring that the droplets are more likely to remain
completely suspended within the gas phase whilst being carried along at close to the gas
velocity.
For the ranges of gas densimetric Froude number arid Lockhart-Martinelli parameter tested,
the wet-gas field will be within the stratified or annular dispersed (mist) regions (see Figure 1).
The NEL data straddle the stratified and annular dispersed regions, depending on the values
of the gas densimetric Froude number and Lockhart-Martinelli parameter. However, such
flow maps are by no means comprehensive and the demarcation between the regimes is not
as precise as shown (i.e. there will be "buffer zones" around the solid lines on Figure 1).
Transition between regimes can also be occun^ing in the axial direction at the inlet to the test
device. There will also be variations in the flow pattern ft-om facility to facility and in the field;
equally, there will be limits on the values of Lockhart-Martinelli parameter and gas
densimetric Froude numbers that can be achieved.
6 South East Asia Hydrocarbon Flow Measurement Workshop
7*^ - 9*^ March 2007
Flow Pattem Map based on Shell Data
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Figure 1 . Flow map s h o w i n g conditions for wet-gas Venturi tests at NEL
3
THE HOMOGENOUS MODEL
A simple way of analysing the wet-gas flow pattem is to assume that the fluid is a
homogenous mixture of liquid and gas. The homogenous model can be applied to determine
the over-reading under such assumed conditions without the need for using CFD or testing.
In this case, the mixture is treated as though it were a denser, single phase gas. The density
of the homogenous gas can be determined using the volume fraction and gas and liquid
densities thus
Pho^ = A « , ^ / d V ^ + n - v j p^ s
(4)
where v, is the liquid volume fraction, v , - gi^^^a ^[Qnquid "*" *?gas) where q is the volume flow
rate. The homogenous density can be input to the CFD models to obtain profiles of pressure,
velocity and liquid volume fraction In order to allow comparison with the wet-gas solutions.
It can be shown that the Venturi over-reading can be expressed as a function of LockhartMartinelli parameter, X, and gas-to-liquld density ratio thus:
Over
reading ^
1'^'"°-^^^^- = V l + C X + X ^
(5)
where, the coefficient C is given by
.0.5
c=
gas
Pliquid
,0.5
Pliquid
i^ f^gas
(6)
)
In theory, the Venturi-tube over-reading will tend towards the homogenous curve at high gasFroude number where the flow pattern will become mist fiow. However, the test data
presented in this paper will show that, in some cases, the over-reading curve can actually
6 * South East Asia Hydrocarbon Flow Measurement Workshop
7"" - g'^ March 2007
exceed the homogenous solution. In reality the flow pattem may never attain homogenous
mist throughout the Venturi tube and may be, at some conditions, unstable and in a state of
transition.
4
CFD ANALYSIS METHOD
The wet-gas analysis was carried out using the Eulerian multiphase model within Fluent 6.3.
The standard default settings for the model were used, with mass transfer between phases
set to zero and lift forces assumed negligible. More information on tiie Eulerian multiphase
model can be found in the Fluent Users' Guide [4].
The CFD models were meshed in 2-dimensional, axisymmetric co-ordinates in order to save
on computational time. In this case, gravity Is (by deflnition) set to zero and it is inferred that
the droplets are small and moving fast enough that the effects of gravity can be duly Ignored.
The assumption that the flow was steady and incompressible was also applied.
The test data were generated using NEL's high-pressure wet-gas test facility. The wet-gas
tests reported in NEL report 2002/100 were undertaken at nominal line pressures, p, of 15, 30
and 60 bar gauge (actually closer to 16, 31 and 61 bar g and labelled such henceforth in this
paper for clarity) and ambient temperature, with volumetric flow rates up to 1000 m ^ r ,
depending on the diameter ratio and line pressure.
The physical property data for nitrogen used for the CFD tests are given in Table 1 for the two
pressures analysed, where p is the density and /^ the dynamic viscosity. The density of the
kerosene substitute, Exxsol D80, was taken as 805.5 kg/m^ while the viscosity was taken as
0.0024 Pa s. The small effect of line pressure on the liquid viscosity was ignored.
p
(bar gauge)
16.0
61.0
{kg/m')
19.5
72.0
(Pas)
1.791x10-^
1.880x10"^
Table 1. Physical property data for nitrogen
The Eulerian multiphase model within Fluent allows the user to specify the droplet diameter
and velocity at the inlet; a homogenous mist flow is thus assumed at this boundary. In all
cases the slip velocity between the gas and liquid phases (i.e. V^up ' Vgas - liquid) was
assumed to be negligible. In reality, it is very possible that the velocity of the gas will be
higher than that of the liquid droplets at the inlet to the Venturi tube, especially for larger
droplet sizes.
The CFD analysis was carried out for Froude numbers of 1.5, 2.5, 3 and 3.5 and LockhartMartinelli parameter values of 0.01, 0.075, 0.15 and 0.3, to match the test data. In some
instances the range of Froude number and Lockhart-Martinelli parameter was truncated
owing to limitations of the test facility. Three values of Venturi-tube diameter ratio were thus
modelled; 0.4, 0.6 and 0.75.
In the absence of any data on average droplet size for the liquid in NEL's high-pressure wetgas test facility, and given that the flow pattern was not accurately known, an attempt was
made to "tune" the CFD model by determining a droplet size that gave good correlation with
the test data at a given pressure (i.e. gas-to-liquid density ratio) and flow rate. This was done
by changing the droplet size until the over-reading at the maximum experimental LockhartMartinelli parameter value of 0.3 (giving the maximum over-reading value at a particular gas
densimetric Froude number) matched the test data to within 0.2% or better.
The tuning
process was carried out for the 0 = 0.6 Venturi tube, with the droplet diameters determined
then used to compute tiie over-reading, as a function of the Lockhart-Martinelli parameter, for
all three diameter ratios.
6 * South East Asia Hydrocarbon Flow Measurement Workshop
7'^ - 9 " March 2007
Figure 2 below shows the grid used to model the diameter ratio 0.75 Venturi tube in 2dimensional, axisymmetric co-ordinates; ttie grids for diameter ratios 0.6 and 0.75 are similar.
A total of about 5,500 cells were used, with square cells being employed in the throat to
improve the definition in this region. The cell spacing was relaxed upstream and downstream
of the throat to reduce the cell count; a total of 30 cells were used across the radius.
r^ 111 i i i^^^^Btemnni
"T
Figure 2. Grid used t o model wet-gas flow through the 0 - 0.75 Venturi tube
(cross-hairs s h o w the location of ttie inlet and throat tappings).
The velocity vras set as constant across the inlet boundary and equal to the value determined
by the following equation
V = V.s.gas 1 + X
{\
'gas
(7)
Pliquid
Vyhere the gas superficial velocity, Vsg^s, is calculated by Equation 1 for a given gas
densimetric Froude number and gas-liquid density ratio.
The turbulence was specified as applicable for the gas-liquid mixture (i.e. only one set of
turbulence equations was solved). The turbulence intensity was set to 5%, w^th hydraulic
diameter set to that of the pipe at 0.1 m. The outlet of the model was set as a pressure
boundary. The standard k-s model was used to compute the turbulent flow, with the walls
modelled as smooth using the standard vrall function approach More information on the k-e
turbulence model can be found in standard texts such as Versteeg and Malalasekera[5].
ANALYSIS OF RESULTS AT 16 BAR GAUGE
Figure 3 shows the contours of liquid volume fraction for the diameter ratio 0.6 Venturi tube at
X = 0.3 and Fr^as = 1.5 for three droplet sizes: 10, 100 and 400 pm at a pressure of 16 bar
gauge (i.e density ratio = 0.024); the three plots are to the same scale as the 400 jim case
(i.e. a range of liquid volume fraction, Vf = 0 to 0.8). The highest concentration of liquid occurs
just upstream of the corner between the convergent and throat sections. This effect is due to
the droplets impacting on the wall of the convergent section forming a liquid layer that is most
prevalent for the 400 ^m case (Fig Sc). This liquid layer can be seen to separate from the
wall to form an annular jet that enters the throat, after vi^ich it continues through the diffuser
without reattaching to the wall. The jet is still present at 100 fim, although clearly smaller in
size and intensity (Fig 3b), whilst it has all but disappeared at 10 pm droplet size (Fig 3a).
>•?•
6*^ South East Asia Hydrocarbon Flow Measurement Workshop
7^^ - 9'^ March 2007
V/=0.05
a) 10|im
Vf=0.37
Liquid jet
b) 100 ^m
W = 0.87
Liquid jet
c) 400 jam
Figure 3. Contours of liquid volume fraction in the convergent and throat of the
diameter ratio 0.6 Venturi tube for Fr^^s^LS and X=0.3 at 16 bar gauge
(scaled as per 400 ^m case).
Figure 4 shows a plot of liquid volume fraction, Vf, along the Venturi-tube wall. It can be seen
that there is a sharp build-up of liquid along the convergent section which becomes more
intense as the droplet size increases. At damp > 100 pm, Vf increases rapidly, reaching a
maximum just before the throat, within which it quickly falls back to zero and remains so
through the diffuser and outlet pipe. In these cases there is a buffer zone close to the wall
virfiereby the liquid in the core region of the flow is kept off the wall by the separated liquid jet.
As the droplet size reduces, so too does the amount of liquid build-up along the convergent
section (i.e. the liquid remains suspended in the gas) and the intensity of the jet reduces.
The liquid build-up on the convergent wall is more gradual for smaller droplet sizes, tending to
flatten-off once a maximum value is reached. At 10 f.tm, v, is small, but non-zero, along the
extent of the Venturi-tube vrall because the small amount of liquid ttiat is attached to it is able
to turn the corner and follow the wall more easily. At 1 pm, Vf is constant throughout the
Venturi tube as none of the liquid attaches to the convergent wall. Thus, the assumption that
6
South East Asia Hydrocarbon Flow Measurement Workshop
7 ' ^ - 9 March 2007
the fiuid can be treated as a homogenous mixture becomes more physically realistic as the
droplet size reduces towards 1 ^ m .
Convergent Throat
Diffuser and Outlet pipe
X 400 microns
* 200 microns
o 100 microns
c 50 microns
+ 25 microns
A 10 microns
X 1 micron
• x x x x x ' x i * m * X X t 1 I x X I f X •* z 1
0.1
0.2
0.3
0.4
0.5
0-6
0.7
0.8
0.9
x(m)
Figure 4. Liquid volume fraction, Vf, along the Venturi-tube wall for the case of the
Venturi tube of ^ = 0.6 at 16 bar gauge (Fr^as = 1.5, X = 0.3).
Figure 5 shows profiles of static pressure along the vrall vMh various droplet sizes for the 0 =
0.6 Venturi tube (as predicted for the case of Fr^as - 1.5, X = 0,3 and at 16 bar gauge). The
profiles for the dry-gas, and equivalent homogenous solutions, are also plotted for
comparison (the latter being run using an equivalent density determined by Equation 4 and
an inlet gas velocity as determined by Equation 7).
There are cleariy two generic pressure profiles: the first occurs at a small droplet size and is
very similar to that obtained in dry gas, except that the pressure drop is much larger. The
pressure profiles can be seen to collapse onto the homogenous solution as the droplet size
tends towards zero, which is as would be expected (see inset of Fig. 5). At this point there is
no liquid attached to the Venturi tube-wall, all of the liquid being carried through the Venturi
tube in droplet form wflthin the gas. However, it is clear that the pressure drop in a Venturi
tube can exceed the homogenous solution.
The second pressure profile emerges once the droplets have reached a certain critical size
and is related to the behaviour of the liquid layer that forms on the wall once the droplets
reach 25 fjm or larger.
Referring t)ack to Figs 3 and 4, the change in pressure profile
corresponds to the point at which the liquid separates from the Venturi tube-wall, This
causes a progressive drop in pressure along the throat that persists up to the inlet to the
diffljser. In addition, the spike in pressure at the intersection of the throat with the convergent
section is not as intense in this case owing to the separation of the liquid layer from the wall at
this point.
Figure 6 shows the difference between the velocity contours for the 1 fam and 100 |jm cases
v»4ierein the core flow is cleariy reduced for the 100 |im case compared with that for 1 ^m.
However, this increase in velocity (which would increase the Ap) is not enough to counter the
reduced drag force imparted by the droplets suspended in the gas as they get larger in size
(tending to reduce Ap). This explains w/hy the Venhjri tube over-reading firstly increases
then decreases as the liquid droplets get larger.
t
6 South East Asia Hydrocarbon Flow Measurement Workshop
7 * - 9 " March 2007
-5000 '
« -10000
CL
- r «
*
c
2
+
*
X
-15000
Homogenous
1 micron
10 microns
25 microns
50 microns
100 microns
200 microns
400 microns
-20000
-25000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x(m)
Figure 5. Wall pressure profiles (referred t o the inlet tapping pressure) for the case of
the Venturi tube of y9= 0.6 at 16 bar gauge (Frggj = 1.5, X = 0.3)
a) 1 (jm droplet size
b) 100 |im droplet size
Figure 6. Contours of gas velocity for case of the Venturi tube of ^ = 0.6 at 16 bar
gauge for t w o droplet sizes (Ffgas = 1.5, X = 0.3).
6
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South East Asia Hydrocartxin Flow Measurement Workshop
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EFFECT OF DROPLET SIZE ON VENTURI TUBE OVER-READING
Figure 7 shows how the predicted over-reading varies vwth droplet size and gas densimetric
Froude numt>er, for a /? = 0.6 Venturi tube at X = 0.3 and 16 bar gauge. The shape of the
curve of over-reading vs droplet size is not strongly dependent on Fr^gs over the range
analysed. The over-reading initially increases, then decreases with droplet size. The peak in
over-reading occurs at a droplet size of about 25 |.im, for Frga^ equal to 2.5 and 3.0, whilst it
looks to be a bit larger for the Frgas = 1 5 case. At the smallest size computed (1 |jm), the
over-reading is very close to that obtained using the homogenous model, as previously
discussed.
Also plotted on the graph for comparison is the over-reading obtained experimentally at each
value of gas densimetric Froude number. It can he seen that, in the case of the 16 bar gauge
data, the over-reading predicted by the CFD can be optimised so that it reproduces the
values given by the tests. For example, 380 jim viras chosen as the droplet size for the model
for the case where the Frgas = 1 5 and X = 0.3 by interpolation of the curve.
For all gas densimetric Froude numbers, the chosen droplet sizes were above 25 |.im and,
thus, lay on the dovwivrard curve to the right of the peak; however, for Frgas = 3,0 it is noted
that there could be two solutions for droplet size: one at 65 [am, the other at about 5 ^ m .
The reason for the increase in over-reading above the homogenous solution at low droplet
diameter appears to be related to the difference in pressure profile that occurs when liquid
starts to build-up on the convergent wall, forming a separated jet in the throat. The
homogenous case is an idealised solution in which all the liquid is suspended in the gas
stream and, therefore, does not take this mechanism into account.
*-Frg=r5
•-Frg-2,5
^Frg=.3.0
TestFrg=1.5
- TestFrg^2.5
— TestFrg=3.0
— Homogenous
0
50
100
150
200
250
300
350
400
Droplet diameter (microns)
Figure 7. CFD results for over-reading vs particle size and gas densimetric Froude
number for the Venturi tube of ^ = 0.6 at X = 0.3 at 16 bar gauge.
RESULTS OF OVER-READING FOR ALL VENTURI-TUBE DIAMETER RATIOS
AT 16 BAR GAUGE
Figures 8, 9 and 10 detail the results of the CFD analyses for all of the Venturi-tube diameter
ratios in wet-gas flow compared with the NEL experimental data. The general trend obsenk/ed
by experiment is that, for a given value of gas densimetric Froude number and LockhartMartinelli parameter, the over-reading increases as the diameter ratio reduces, and reduces
as line pressure increases. It should be noted that, as the diameter ratio reduces, the
maximum gas densimetric Froude number (i.e. gas velocity at fixed line pressure and pipe
-tft
6 South East Asia Hydrocarbon Flow Measurement Workshop
7"^ - 9*^ March 2007
diameter) achievable in the tests reduces ovwng to the increased system resistance (for
example, there are no data for Frgas = 3 for y? = 0.4).
The results for the ;9= 0 6 Venturi tube (Figure 9) show how the CFD follows the correct trend
in over-reading as X i s reduced from the "tuning" point of X = 0-3, being within 1 % of the test
points down to a value of 0.15. However, there is a clear departure from the test data at low
liquid loading (i.e. X < 0.15), in which the test data tend to lie about 2 - 4 % above the CFD
curves; this is especially notable at Frgas = 1 5 where there is increased curvature in the test
data. This effect would appear to intensify as y7 increases.
The results show that the method also works well when applied to the p = 0,4 Venturi tube the CFD data at F/-gas = 1 , 5 being within 1.2% of the test data for X > 0.1. It is clear that there
is not as much deviation in the curves at low X compared with the ^ = 0,6 case, the maximum
difference between the CFD and test data being about 2.5%. , From the limited test data at
Frgas = 2.5, it appears tiiat the curves would be more linear as Fr^a^ increases.
The comparison between the CFD and test data is not as good for the 0 = 0,75 Venturi tube the biggest differences this time occurring at X = 0,3 (alUiough the predicted results generally
lie vifithin 3 or 4 % of the test data over most of the range of Fr^as and X), This result is
perhaps to be expected given that the models were tuned to the 0 = 0.6 Venturi tube and that
the over-reading will be more sensitive to the inlet boundary conditions as y9 increases
Referring to the flow map in Figure 1, it is likely that, at Fr^as = 1.5 and at low values of X. the
flow entering the Venturi tube will tend to be stratified. A liquid layer along the wall of the
Venturi-tube inlet pipe may also serve to increase the over-reading further.
10
6
•
South East Asia Hydrocarbon Flow Measurement Workshop
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1.8
0.00
0,05
0,10
0,15
0,20
0.25
0,30
0,35
Lockhart Martinelli, X
Figure 8. CFD vs test results for the ^ = 0.4 Venturi tube at 16 bar gauge.
a
n
>
O
0.00
005
0.15
010
020
0.25
0,30
0,35
Lockhart Marttnelll, X
Figure 9. CFD vs test results for t h e ^ = 0.6 Venturi tube at 16 bar gauge.
1.8
j ^
—•-Frg=3.0CFD
- o- Frg=3.0Test
-•-Frg^2.5CFD
- o Frg=2.5Test
—*—Frg=1.5CFD
- i - Frg=1.5 Test
Homogenous
1.7
1.6
1,5
T3
(0
at
1,4
ID
1.3
>
o
j ^ < —^ ^ ^ ^
i-^te - *
'
A -. ^ ^ ^ 1 ^ ^
-J>-^
J ^ '
^ ^ ^ : - ^ > > ^
1.2
^ » ^ > > ^
1.1
1,0
/^^^^^^^*
^^.^f^^^' '
^ ^ ^
0.00
0,05
0.10
0.15
0,20
0.25
0.30
0.35
Lockhart Martinelli, X
Figure 10. CFD vs test results for the 0 - 0.75 Venturi tube at 16 bar gauge.
11
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South East Asia Hydrocarbon Flow Measurement Workshop
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EFFECT OF DIAMETER RATIO ON VENTURI-TUBE OVER-READING
The previous results demonstrated that the Venturi-tube over-reading decreases as diameter
ratio increases; this is primarily due to the change in effective throat area caused by the
presence of the liquid jet. Figure 11 shows the velocity contours (normalised by maximum
velocity) through the convergent to the throat for all three diameter ratios; all are at the same
included angle of 21°. As diameter ratio increases, it is clear that the effective area of the
throat also reduces (compare Figure 11a with Figure 11c); this reduction accelerates the fluid
in the throat and, in turn, leads to a higher over-reading as diameter ratio reduces. Using the
point at which the velocity reaches 95% of the maximum {V/Vmax - 0,95) as a measure of the
effective throat diameter, the ratio of effective diameter to throat diameter, d^f/d, equals 0.70,
0.81 and 0.83, for the diameter ratios 0.4, 0.6 and 0.75, respectively.
a) ^ = 0 . 4
b)A=0-6
0^=0.75
Figure 1 1 . C o n t o u r s o f normalised gas velocity (Vgas/Vgas,max) t h r o u g h the t h r o a t of the
Venturi tubes at Fr^s. = 1-5 and X = 0.3, at a droplet size of 380 ^ m
Figure 12 shows a similar contour plot for the ^ = 0,4 Venturi tube, but with much lower liquid
loading ( X = 0,01); the same particle size is used (380 pm). In this case the jet is not as thick
as at the maximum value of X (and its presence is barely visible on this plot). Comparison of
Figure 12 with Figure 11a shows how the diameter-ratio effect on over-reading reduces as X
reduces. Although this general trend is also apparent in the test data, there is another
secondary mechanism which causes the deviation from the CFD at Frgas = 1,5 and for X <
0.15, as discussed eariier
12
6 * South East Asia Hydrocarbon Flow Measurement Workshop
7*^ - 9 * March 2007
Figure 12. Contours of normalised gas velocity {VgsJVgas,max) t h r o u g h the throat of the
0 = 0.4 Venturi tube at Frga^ = 1.5 and X = 0.01, at a droplet size of 380 ^im.
Figure 13 shows the liquid volume fraction on the wall for all the Venturi tubes {Frgas = 1-5, X
= 0.3), It can be seen that the liquid volume fraction increases steadily from the start of the
convergent (at x = 0,2 m) to a maximum of 0.5, 0.86 and 0.92, for diameter ratios 0.75, 0.6
and 0.4 respectively. In all cases, the CFD predicts that the jet created at the inlet comer of
the throat persists through the Venturi tube without dispersing into the gas phase or reattaching itself to the wall (thus, Vf drops to zero at some point on the throat wall and remains
zero along the diffuser and outlet pipe walls). This is probably due to the fact that the
momentum exchange between the liquid and gas was set to the default value of zero for all
computations.
1.0
0,9 h
o.s
0.7 h
• beta=0,4
fO
u.
0.6
E
0.5
O
>
•u
3
• beta=0,6
• beta=0,75
^
0.4
0.3
0,2
0,1
0.0
0,1
04
0.5
06
0,7
0.8
09
x(m)
Figure 13. Effect of diameter ratio on the build-up of liquid on the convergent wall
(X = 0.3, Frgas = 1-5, ddrop = 380 pm)
9
RESULTS OF VENTURI-TUBE OVER-READING AT 61 BAR GAUGE
Figure 14 shows the relationship t>etween over-reading and droplet diameter at 61 bar gauge;
the trend is very similar to that obtained at 16 bar gauge, with an initial rise in over-reading as
droplet diameter is reduced until a maximum is reached, this time at about 50 nm, below
which the over-reading reduces again to meet the homogenous solution. The peak value in
over-reading predicted at a droplet size of at 50 pm is chosen as the solution for Frg^s = 3.5 as
it is the closest to the test data.
Figures 15 and 16 show the results of the CFD analysis for 61 bar gauge for the diameter
ratios 0.6 and 0.4 respectively (0.75 vras not modelled). Whilst an excellent level of
agreement was obtained for Fr^as = 1 5 at txDth 0 = 0.6 and 0.4 (the CFD being within 1,5%
across the entire range of X tested), it was not possible to tune the model as closely at Ffgas
= 3,5 because the peak in over-reading predicted by the CFD wras still about 0.9% below the
13
6
South East Asia Hydrocarbon Flow Measurement Workshop
7 " - 9"^ March 2007
equivalent test point at X = 0.3. It is interesting to note that all the test data lie above the
homogenous solution for Frgas > 2.5,
If. as surmised, the change to the pressure profile caused by jet formation at Inlet to the
Venturi-tube throat is responsible for increasing the over-reading above the homogenous
solution, then it is possible that the CFD under-predicts its intensity at 61 bar g.
1.550
-*-Frg=1,5
—•—Frg=3.5
Test, Frg=1,5
Test. Frg=3,5
Homogenous
1.350
1.300
100
200
300
400
500
600
700
800
goo
10OO
Droplet diameter (microns)
Figure 14. CFD results for over-reading vs particle size and gas densimetric Froude
number for the 0 = 0.6 Venturi tube at X = 0.3 and at 61 bar gauge.
• "•- Frg=5 0Test
- «- Frg^,5Test
-•-Frg=3,5CFD
• o- Frg=3.5Tesl
• o- Frg=2.5Test
-*-Frg=1.5CFD
- 1 - Frg=1,5Tesl
Homogenous
0.00
0.05
0.10
0,15
0,20
0,25
0.30
0.35
Lockhart Martinelli, X
Figure 15. CFD vs test results for the 0 = 0.6 Venturi tube at 61 bar gauge.
14
6^ South East Asia Hydrocarbon Flow Measurement Workshop
7 * - 9 * March 2007
1.6
1.5
, .
' >•
"
^ ^
•a
CO
£
-I*
.o^
1.4
1.3
-o- Frg=3.5Test
-c- Frg=2,5Test
- ^ F r g = 1 5CFD
- * - Frg= 1.5 Test ~
Homogenous
•>'^3^^*^^^
e
>
O 1.2
^.«<^/>>^
1.1
1.0
0.00
0.05
0.10
1
1
0.15
0.20
0.25
0.30
0,35
Lockhart Martinelli, X
Figure 16. CFD vs test results for the ^ = 0 . 4 Venturi tube at 61 bar gauge.
10
EFFECT OF CHANGING FLUIDS ON VENTURI-TUBE OVER-READING
One of the key objectives of the current work was to assess whether changing the gas and/or
the liquid in the high-pressure loop would affect the Venturi-tube over-reading. In order to
investigate this, two additional cases were modelled using the CFD; in both instances, only a
0 = 0.6 Venturi tube was modelled at a single line pressure. The range of Fr^^s was limited to
Frgas - 1 -5, for argon/Exxsol and Fr^as = 3.0, for nitrogen/water.
In both cases the line pressure was adjusted in order to give the same gas-to-liquid density
ratio as the baseline case of nitrogen/Exxsol at 16 bar g (i.e. 19.5 kg/m^). This meant
reducing the line pressure for the argon/Exxsol tests and increasing It for the nitrogen/water
tests as described below.
10.1
Effect of Changing The Gas From Nitrogen To A r g o n
For the CFD analysis, Uie physical properties of argon at were taken to be:
p = 19.5 kg/m^
/ i = 2.23xl0"^kg/m-s
(I.e. the same density as in the test for nitrogen at 16 bar g)
(from NEL's Physical Properties Database at 10 bar, 20*'C)
Section 7 detailed how the CFD models were "tuned" to the nitrogen/Exxsol test data at X =
0.3 for each given Fr^gj by changing the droplet diameter. For the case of argon/Exxsol it was
assumed that the droplet diameter would be the same as for nitrogen/Exxsol. Therefore, the
CFD simulations are simply modelling the effect of gas viscosity on the Venturi-tube overreading.
Figure 17 compares the CFD results with test data of over-reading in argon/Exxsol relative to
nitrogen/Exxsol for a /? = 0.6 Venturi tube at Frg^s = 1 5 and a density of 19.5 kg/m^. The
graph was produced by taking the average of the results for X and over-reading (typically two
data points) for the argon/Exxsol and nitrogen/Exxsol data sets. As the values of X were
close, but not identical, for the argon/Exxsol and nitrogen/Exxsol data sets, a ^ ^ order
polynomial curve was then fitted to the nitrogen/Exxsol data to enable interpolation to
compare over-reading at the same value of X.
15
6^ South East Asia Hydrocarbon Fiow Measurement Workshop
7*^ - 9'^ March 2007
~
~
c
n
o
-0.2
•
-0.4
- A
-0.6
A
-0,8
o
o
c
o
•
A
... _ .
-£
A
A
A
a-CFD
A
A Test data
•
-1
-1.2
-
A
-1,4
-1.6
A
A
•
0.00
0.05
0.10
0,15
0.20
0.25
0,30
0,35
Lockhart-Martinelti, X
Figure 17 Comparison of percentage over-reading difference for t w o fluid
combinations: CFD results vs test data ( ^ = 0.6 Venturi tube at Frgas - 1-5)
It can be seen that the over-reading in argon/Exxsol is generally smaller than in
nitrogen/Exxsol. The CFD predicts that the shift in over-reading is negligible across the range
of X. The test data exhibits larger shifts in over-reading of between -0.5% and -1.6%,
generally increasing in magnitude with X.
10.2
Effect of Changing The Liquid From Exxsol D80 To Water
In this case the modelling was restricted to a /? = 0.6 Venturi tube at Fr^^s = 3.0 and one line
pressure. In the experiments, the line pressure of the nitrogen was adjusted to 21 bar to give
roughly the same density ratio, pga/puqwd, as for the nitrogen/Exxsol tests at 16 bar g. The
droplet diameter for the nitrogen/water computations was initially assumed to be the same as
for nitrogen/Exxsol (i.e. droplet diameter damp = 65 |im, for Fr^as = 3.0).
For modelling purposes the physical properties of nitrogen at 21 bar and ambient temperature
were taken to be:
p = 24.21 kg/m^ (from the experimental data)
/^= 1.798x10'^ Pa s (from NEL's Physical Properties Database at 21 bar, 20°C)
The fluid properties of tiie water were taken to be:
p = 1000 kg/m^ and
A = 0.001 P a s
Figures 18 and 19 compare the results of Venturi tube over-reading against X for Frgss = 3.0
for nitrogen/water and nitrogen/Exxsol, as predicted by the CFD and determined by
experiment respectively. The test data shows that the over-reading is smaller in magnitude
for nitrogen/water than for nitrogen/Exxsol; however, the CFD predicts a negligibly small
difference in over-reading between the two fluid combinations, although the shift is in the
same direction.
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6^ South East Asia Hydrocarbon Flow Measurement Workshop
7"^ - 9"^ March 2007
C
•o
a
—•—Frg^3.0. N2/Exxso)
- « - Frg=3,0, N2/H20
0.00
0.05
0.10
0,15
020
0.30
0.25
0.35
Lockhart Martinelli, X
Figure 18 Comparison of Venturi-tube over-reading obtained by CFD simulation for t w o
f l u i d combinations and at t w o values of Fr.gas
1.8
^ ^
1.7
^
^-p"""''^
•o
m
e
p
*
-
^
"
"
^
-
"
*
- '*''
1
- A ^ ^_ "» ' ^* -
^ffi*^
1
'**"
^ ^ ^ , ' , -* '
^^""^'^ '
1
—0—Frg=3,0. N2/Ex)(SOI
—
• * - Frg=3.0, N2/H20
1
1
10
0.00
"
^^'
0 05
0 10
0 15
0 20
025
0.30
0,35
Lockhart Martinelli, X
Figure 19 Comparison o f Venturi-tube over-reading obtained by experiments for t w o
f l u i d combinations and at t w o values of Fr^^
Figure 20 details the shift in over-reading between nitrogen/water and nitrogen/Exxsol for the
CFD and test cases respectively. This graph was produced in a similar manner to Figure 17
in the previous section whereby a polynomial curve fit was applied to the test data to allow
interpolation to intermediate values of X.
The CFD predicts a maximum shift In over-reading of -0.56% at X = 0.3, whilst the
experimental data shows a maximum shift in over-reading o f - 4 . 1 % , at this point.
One possible explanation for difference between the CFD and test data may be that the
droplet size (assumed to be the same for both nitrogen/Exxsol and nitrogen/water in the CFD
analyses) will, in fact, be different in the experiments. Refemng back to Figure 7, it can be
seen that, for given values of Frgas and value of X, the over-reading will reduce as the droplet
size increases. Another possible cause of the difference is that the phase boundaries are
different with different gas/liquid combinations [6]. The effect of droplet size is considered
here.
It is known that the more surface tension a liquid has, the less tendency it has to break up into
droplets; thus, an increase in surface tension gives rise to larger droplets in a gas stream,
whilst a decrease results in smaller ones.
17
6*^ South East Asia Hydrocarbon Flow Measurement Workshop
7"" - 9'^ March 2007
The dimensionless Weber Number is the ratio between the inertial and the surface tension
forces for liquid droplets and can be used to determine droplet size
We^
Pgas^
^drop
(8)
where V is the average velocity (m/s), damp the average droplet diameter (m) and <T the
suri'ace tension of the liquid (N/m).
Thus, for a given value of We, the droplet diameter ratio d^^^ w/ddmpE can be calculated using
^drop,W _ O^W
Pgas.E
<^drop,E
Pgas,W
'^E
,2
f
(7)
'W
where the subscripted E and IV refer to the Exxsol and water tests respectively.
The suri'ace tension of Exxsol D80 is given in texts as 0.0265 N/m, whilst it was determined
from laboratory tests on a sample of the water taken from the loop that its surface tension
was 0.060 N/m (a sample was taken rather than using values given in a textbook as some
foam inhibitor had been added to the water). At fixed gas-to-liquid density ratio, the gas
velocities are the same, whilst the density of the gas in each case is 19.5 and 24.2 kg/m^.
Hence, the diameter of the water droplets is calculated to be about 1.83 times larger than the
Exxsol droplets. This equates to a droplet size of 119 fim for the niti-ogen/water mixture as
opposed to 65 ^m for the case of nitrogen/Exxsol.
An additional CFD simulation was carried out for Fr^gg = 3.0 using a droplet size of 119 pm,
the results of which are also given on Figure 20. It can be seen that the trend of predicted
shift in over-reading is much closer to the test data for the larger droplet size. However, more
computations at different Frgas and gas-to-liquid density ratios would be required in order to
confirm this theory.
0,00
0.05
0.10
0,15
0.20
0.25
0.30
0.35
Lockhart-Martinelli, X
Figure 20 Effect of changing gas/liquid mixture on Venturi-tube over-reading:
comparing CFD predictions w i t h experimental data for 0 = 0.6
(droplet size used for nitrogen/water computations s h o w n in brackets)
11
CONCLUSIONS
CFD has been undertaken to examine wet-gas fiow through Venturi tubes. This analysis
indicates that it is possible to model wet-gas flow through Venturi tut)es and provide trends
that follow the experimentally obtained over-reading data well especially for 0 < 0.6, although
18
6*^ South East Asia Hydrocarbon Flow Measurement Workshop
7 * - 9*^ March 2007
limitations in the approach were evident at 61 bar g. The method described could be further
extended to examine the effect of inlet flow pattem and for other differential pressure metere,
such as nozzles, orifice plates and V-cones.
One possible cause of different over-readings with different liquids has been seen to be
droplet size. The CFD appears to show that the reduced over-reading in nitrogen-water
compared with that in nitrogen-Exxsol arises because water droplets will be larger than for
Exxsol at equivalent flowing conditions owing to their increased surface tension. However,
more computations would have to be earned out at different values of Frgas and density ratio.
The CFD does not pick up any appreciable effect from changing the gas from nitrogen to
argon; however, the experiments revealed this effect was small enough as to be largely
ignored.
Further examination of the CFD data appears to show that the build-up of a liquid layer along
the convergent section of the Venturi tubes, and its subsequent separation from the wall
within the throat region, is responsible for the increase in over-reading above the
homogenous solution which occurs in the test data at higher values of Frgas-
.. .Y
ACKNOWLEDGEMENT
This work was carried out as part of the Flow Programme, under the sponsorship of the
National Measurement System Directorate of the UK Department of Trade and Industry.
Their support is gratefully acknowledged.
This paper is published by permission of the Managing Director, NEL.
,
,"
NOTATION
D
d
ddrop
Fr
9
H
m
P
Ap
Q
V
Diameter of entrance cylinder
Throat diameter
Droplet diameter
Froude number
Acceleration due to gravity
Turbulence kinetic energy
Mass flowrate
Static pressure
Differential pressure
Volumetric flow rate
Velocity
m
m
m
m/s^
Vf
Vs.aas
We
X
P
mV
£
kg/s
Pa
Pa
m^/s
m/s
fl
p
a
Volume fraction of liquid
Gas superficial velocity
Weber number
Lockhart-Martinelli parameter
Diameter ratio (= d/D)
Dissipation rate
Dynamic viscosity
Density
Surface tension
m/s
m /s
Pas
kg/m'
REFERENCES
[1]
READER-HARRIS, M. J., HODGES, D., and GIBSON, J.
Venturi-tube
performance in wet gas using altemative test fluids. Report no 2005/206 on
Project no FEWG01. East Kilbride, Glasgow: National Engineering Laboratory,
October 2002.
[2]
READER-HARRIS, M. J., HODGES, D., and GIBSON, J.
Venturi-tube
performance in wet gas using different test fluids, in Proc. 24'^ International
North Sea Flow Measurement Workshop, St Andrews, Fife, Paper 7.1. East
Kilbride, Glasgow; National Engineering Laboratory, October 2006.
[3]
STEWART, D. G. Evaluation of dry gas meters in wet gas conditions. Report no
2002/100 on Project no FDMU07. East Kilbride, Glasgow: National Engineering
Laboratory, 2002.
n
r-
24"^ International North Sea Flow Measurement Workshop
24*" - 2 7 " October 2006
[4]
FLUENT Users" Guide Version 6.1, Febnjary 2003.
[5]
VERSTEEG, H.K., and MALAL^SEKERA, W. An Introduction to Computational
Fluid Dynamics - The Finite Volume Method. Longman Scientific and Technical
Publications, New York, l " Ed. 1995.
[6]
STEVEN, R. A discussion on horizontally installed differential pressure meter
wet gas flow performances.
In Proc. 24^' International North Sea Flow
Measurement Workshop, St Andrews, Fife, Paper 7.2. East Kilbride, Glasgow;
National Engineering Laboratory, October 2006.
20