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 measurement-Knowledge 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 Venturi-tube 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 nitrogen-kerosene 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 Lockhart-Martinelli 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

F r , . s = ^ J ^ ^ (1) g D \Pliquid ~ Pgas

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 showing condit ions 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 Lockhart-Martinelli 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

Pliquid ,0.5

(6) i f^gas )

In theory, the Venturi-tube over-reading will tend towards the homogenous curve at high gas-Froude 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 Lockhart-Martinelli 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 wet-gas 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 Lockhart-Martinelli 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 2-dimensional, 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 to model wet-gas f low through the 0 - 0.75 Venturi tube (cross-hairs show 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

Pliquid

(7) >•?•

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

0.1 0.2 0.3

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

0.4 0.5 x ( m )

0-6 0.7 0.8 0.9

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

-15000

-20000

-25000 0

- r - Homogenous « 1 micron * 10 microns c 25 microns 2 50 microns + 100 microns * 200 microns X 400 microns

0.1 0.2 0.3 0.6 0.7 0.8 0.9 0.4 0.5

x ( m )

Figure 5. Wall pressure profiles (referred to 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 two droplet sizes (Ffgas = 1.5, X = 0.3).

6 South East Asia Hydrocartxin Flow Measurement Workshop 7" - 9* March 2007

6 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.

* - F r g = r 5 • - F r g - 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 Lockhart-Martinelli 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 7*^-9'" March 2007

• 1.8

0.00 0,05 0,10 0,15 0,20 0.25

Lockhart Martinelli, X

0,30 0,35

Figure 8. CFD vs test results for the ^= 0.4 Venturi tube at 16 bar gauge.

a

n

> O

0.00 005 0,30 0,35 010 0.15 020 0.25

Lockhart Marttnelll, X

Figure 9. CFD vs test results for t h e ^ = 0.6 Venturi tube at 16 bar gauge.

T3 (0 at

ID

> o

1.8

1.7

1.6

1,5

1,4

1.3

1.2

1.1

1,0

—•-Frg=3.0CFD - o- Frg=3.0Test - • - F r g ^ 2 . 5 C F D - o Frg=2.5Test —*—Frg=1.5CFD - i - Frg=1.5 Test

Homogenous

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/ ^ ^ ^ ^ ^ ^ ^ * ^ ^ . ^ f ^ ^ ^ ' '

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0.00 0,05 0.30 0.35 0.10 0.15 0,20 0.25

Lockhart Martinelli, X

Figure 10. CFD vs test results for the 0 - 0.75 Venturi tube at 16 bar gauge.

11

6 South East Asia Hydrocarbon Flow Measurement Workshop 7" - 9 " March 2007

8 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 . 7 5

Figure 11. Contoursof normalised gas velocity (Vgas/Vgas,max) through the throat 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) through 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.

fO

u.

E

O > • u 3

1.0

0,9 h

o.s

0.7 h

0.6

0.5

0.4

0.3

0,2

0,1

0.0

• beta=0,4

• beta=0,6

• beta=0,75

0,1

^

0 4 0.5 x(m)

06 0,7 0.8 0 9

Figure 13. Effect of diameter ratio on the build-up of l iquid 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

1.350

1.300

- * - F r g = 1 , 5 —•—Frg=3.5

Test, Frg=1,5 - Test. Frg=3,5

Homogenous

100 200 300 400 500 600 700

Droplet diameter (microns) 800 goo 10OO

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.

0.00

• "•- Frg=5 0Test - «- Frg^,5Test -• -Frg=3,5CFD • o- Frg=3.5Tesl • o- Frg=2.5Test -*-Frg=1.5CFD - 1 - Frg=1,5Tesl

Homogenous

0.05 0.10 0,15 0,20 0,25 0.30

Lockhart Martinelli, X

0.35

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

• a CO

£ e > O

1.6

1.5

1.4

1.3

1.2

1.1

1.0

. o ^ , . ' > • "

•> ' ^3^^*^^^ ^.«<^/>>^

1 1

-I* ^ ^

-o - Frg=3.5Test -c- Frg=2,5Test - ^F rg=1 5CFD - * - Frg= 1.5 Test

Homogenous ~

0.00 0.05 0.30 0,35 0.10 0.15 0.20 0.25

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 Argon

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 over-reading.

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

o o c o

-0.2

-0.4

-0.6

-0,8

-1

-1.2

-1,4

-1.6

•

- A

A

•

-

•

~

A

~ •

A

A ... _ .

A

- £

A

A

A

a-CFD

A Test data

A

0.00 0.05 0.10 0,15 0.20 0.25

Lockhart-Martinelti, X

0,30 0,35

Figure 17 Comparison of percentage over-reading difference for two f luid 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 Pas

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.

16

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

Lockhar t Mart inel l i , X

0.25 0.30 0.35

Figure 18 Comparison of Venturi-tube over-reading obtained by CFD simulation for two f lu id combinations and at two values of Fr. gas

1.8

1.7

•o m e

1

1

1

1

1

10

^ ^

^ p * - ^ " " ^ - " *

^ - p " " " ' ' ^ - ' * ' '

^ ^ ^ ,

- A ^ ^ " ' ^ - ' * * " ^ f f i * ^ _ » *

' , -* '

^^""^'^ '

^^'

" —0—Frg=3,0. N2/Ex)(SOI

• * - Frg=3.0, N2/H20

—

0.00 0 05 0 10 0 15 0 20

Lockhar t Mart inel l i , X

025 0.30 0,35

Figure 19 Comparison of Venturi-tube over-reading obtained by experiments for two f lu id combinations and at two 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^ P g a s ^ ^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

,2 ^drop,W _ O W Pgas .E

<^drop,E '^E Pgas,W

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 Lockhart-Martinelli, X

0.30 0.35

11

Figure 20 Effect of changing gas/liquid mixture on Venturi-tube over-reading: comparing CFD predictions wi th experimental data for 0 = 0.6

(droplet size used for nitrogen/water computations shown in brackets)

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^

mV kg/s Pa Pa m^/s m/s

Vf

Vs.aas We X

P £

f l

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'

r-

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]

[3]

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.

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

24"^ International North Sea Flow Measurement Workshop 24*" - 27" 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.

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