Paper 3.2 An Update on V-Cone Meter Wet Gas Flow Metering ... · Flomeko 2005 6–9 June 2005 1 AN...

Paper 3.2

An Update on V-Cone Meter Wet Gas Flow Metering Research

Richard Steven McCrometer Inc

Tom Kegel and Charles Britton

CEESI

Flomeko 2005 6–9 June 2005

1

AN UPDATE ON V-CONE METER WET GAS FLOW METERING RESEARCH

Richard Steven, McCrometer Inc

Tom Kegel, CEESI Charles Britton, CEESI

1 INTRODUCTION With the increasing importance of wet gas flow metering to industry, the Differential Pressure (DP) meter wet gas flow correlations are being increasingly utilised. Currently little information exists regarding the applicability of such correlations beyond the limits of the data sets used to create them. In particular little is known about the repeatability of a DP meter with wet gas flows, meter size and liquid property effects on the validity of the DP wet gas correction factors. In 2001 NEL tested a 6” schedule 80, 0.75 Beta Ratio V-Cone meter with a N2 / kerosene wet gas flow as part of the UK governments Department of Trade and Industry (DTI) funded Flow Programme. In 2002 McCrometer and NEL jointly presented analysis of this data at the North Sea Flow Measurement Workshop (NSFMW) [1]. The parameters that affected the “over-reading” (i.e. the positive error induced by the presence of liquid with the gas flow) were shown and a wet gas flow correlation was offered. For a known liquid mass flow rate or liquid to gas flow rate ratio the meters gas prediction was to ±2% with a few outliers. In 2003 McCrometer presented results of repeat tests at NEL and a single wet gas data set from a 4” schedule 80, 0.75 Beta Ratio V-Cone meter tested with natural gas (NG)/ decane at CEESI [2]. The V-Cone meter was shown to be repeatable and the results from CEESI were similar to those of NEL. However, in general, the question of what effect meter size and liquid phase properties have on DP meter wet gas over- readings is largely unanswered, even though the applicability of published correlations in different applications is a very relevant industrial issue. This paper shows several V-Cone meter wet gas data sets from four wet gas test loops and compares them, to investigate repeatability, meter size and liquid property effects. The two NEL 6” schedule 80, 0.75 beta ratio N2/kerosene data sets are shown, along with four CEESI 4” schedule 80, 0.75 beta ratio natural gas (NG) / decane data sets, one K-Lab 6” schedule 160, 0.75 beta ratio NG/condensate data set and one CEESI 2” schedule 80, 0.70 beta ratio NG/Stoddard (a hydrocarbon liquid) / water data set. Results show repeatability of the V-Cone meter with wet gas flows, and also allow an examination of the effects of extrapolating the published V-Cone meter wet gas flow correlation for gas to liquid density ratios above and below the limits of the NEL data set used to form the published correlation. (This exercise results in a modification of the originally published V-Cone meter 0.75 beta ratio wet gas correlation at low gas to liquid density ratios.) By comparing the CEESI 2” and 4” meter hydrocarbon liquid data, some initial scaling information can be found; and comparing the water and Stoddard liquid data sets on the 2” meter, some initial liquid property effects can be determined. 2 THE V-CONE METER In order to discuss the V-Cone meter performance with wet gas flows, a brief discussion of the meter in dry gas is first given. The V-Cone meter is a Differential Pressure (DP) type flow meter with a centrally mounted cone pointing upstream, supported by a strut. The upstream pressure is read from a wall tapping and the downstream pressure is read from the centre of the back face of the cone. Figure 1 shows a sketch of a V-Cone meter with a wall section cut away to expose the primary element.


2

The shape and position of the primary element is the only difference between a V-Cone and other DP meters. The V-Cone meter is in every way a DP meter (with advantages gained from the choice of a cone as the primary element). Therefore with single phase flow the generic DP meter equation form is used (with unique V-Cone meter constants) and all secondary instrumentation is similar to any other DP meter.

Fig. 1 – The V-Cone Meter. The advantages of using a cone as a DP producing element with single phase flows are

well reported and documented in the Southwest Research Institute (SWRI) report to McCrometer [2] on V-Cone flow meter testing complying to “API 22 -Testing Protocol, Section 2 Differential Pressure Flow Measurement Devices” [3]. This report is publicly available by request to McCrometer. A summary of this SWRI report was given at Flomeko 2004 [4]. For single phase flows with calibration the V-Cone meter will give an uncertainty of 0.5%. 3 WET GAS FLOW DEFINITIONS Although no standards organisation has yet published guidelines on wet gas flow definitions, in the last few years researchers have begun to standardise the methods of defining wet gas flow conditions. These common methods are used in this paper and are described below. 3.1 The Wet Gas Flow Definition Wet gas flow is commonly considered to be a two-phase flow where the liquid can be one or multiple components flowing in a gas such that the Lockhart-Martinelli parameter (denoted by the symbol “XLM” here).XLM ≤ 0.3. (See part 3.3 for the Lockhart Martinelli definition.) 3.2 The Gas to Liquid Density Ratio It is common practice to non-dimensionalise the line pressure of a wet gas flow by describing it in terms of the gas to liquid density (i.e. lg ρρ , denoted here in the text as “DR”). The gas density is

directly proportional to pressure and liquid density is essentially incompressible (i.e. constant density regardless of the flow pressure). 3.3 The Lockhart Martinelli Parameter, XLM The Lockhart Martinelli parameter indicates the relative amount of liquid entrained in the gas flow. It has a complex history and the current definition used by most wet gas flow meter researchers is not the same as the original parameter defined by Lockhart and Martinelli. In this paper the definition of the Lockhart Martinelli parameter is the square root of the ratio of the liquid phase inertia (if the liquid was flowing alone in the pipe) to the gas phase inertia (if the gas was flowing alone in the pipe). That is:

l

g

g

l

LM

m

mXρρ

.

.

= (1)

where g.

m is the actual gas mass flow rate, l.

m is the actual liquid mass flow rate, ρg is the gas density and ρl is the liquid density.

High Pressure Port

Low Pressure Port


3

3.3 The Gas Densiometric Froude Number, Frg The gas densiometric Froude number is a non-dimensional way of describing gas flow rate effects and is defined as the square root of the inertial force of the gas phase (if it flowed alone) to the buoyancy force on the liquid. That is:

gl

gsgg gD

UFr

ρ−ρ

ρ= (2)

where

AmU

g

g.

sg ρ= (3)

and sgU is the superficial gas velocity, g is the gravitational constant, D is the meter inlet diameter, and A is the meter inlet area. 3.4 Reporting a Positive Gas Flow Rate Error The positive error (usually called the “over-reading”) induced on any DP meter by the presence of liquids in a gas flow is commonly presented in the form of the square root of the ratio of the actual read differential pressure (DP) from the wet gas flow ( tpP∆ (where “tp” indicates “two-phase”)) and the DP that would be expected to be read from that DP meter, if the gas phase flowed alone through the meter ( gP∆ ). Therefore the over-reading is usually expressed by the term gtp PP ∆∆ .

For example a DP meter with an over-reading of gtp P/P ∆∆ = 1.15 indicates an over-reading of

the actual gas mass flow rate by 15%. Alternatively, the absolute percentage over-reading for any DP meter can be approximated to ( ) %100*1PP gtp −∆∆ .

Dimensionless groups are a problem to engineers working with wet gas, two-phase and multiphase flows. Derivations of appropriate dimensionless groups usually require unknown factors, in particular the actual averaged phase velocities. The lack of knowledge leads to compromises being made in the definition of dimensionless groups used. The appendix discusses this in more detail. 4 THE ORIGINAL NEL V-CONE WET GAS TESTS AND ANALYSIS The 6” schedule 80, 0.75 beta ratio V-Cone meter tests at NEL have previously been reported. Details of the NEL wet gas flow loop system and test procedures can be found in reference [1]. Table 1 shows the test matrix range for these tests.

Table 1 - Envelope for NEL 2001 Wet Gas Flow 0.75 Beta Ratio V-Cone Meter Tests Nominal Pressure (g) Density Ratio Frg XLM range

15 0.0239 0.57 – 1.91 0 < XLM< 0.3 30 0.0456 0.54 – 2.75 0 < XLM< 0.3 60 0.0889 0.92 – 3.53 0 < XLM< 0.3

It is conventional to plot the wet gas results as Over-Reading vs. XLM. It was found [1] that the V-Cone meter acts similar to other DP meters with respect to the fact that increasing liquid loading (i.e. increasing XLM) produces a greater over-reading. With all other parameters held constant, an increase in the gas to liquid density ratio produces a reduction in over-reading. For all other parameters held constant, an increase in the gas densiometeric Froude produces an increase in


4

over-reading. Graphs of these findings are given in Reference [1] and samples are shown below as Figures 2 and 3.

NEL DTI 2001 6" Schedule 80 0.75 Beta Ratio V-Cone Meter Wet Gas Test Results

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% O

ver-

Rea

ding

DR 0.0239DR 0.0456DR 0.0889

Fig. 2 All NEL DTI 6” 0.75 Beta Ratio V-Cone Meter Data.

NEL DTI 6" Schedule 80 0.75 Beta Ratio V-Cone Meter Wet Gas Test Results

Average Gas to Liquid Density Ratio 0.0456

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% O

ver-

Rea

ding Frg 0.54

Frg 0.91Frg 1.46Frg 1.83Frg 2.20Frg 2.75

Fig. 3 The 30 Bar NEL DTI 6” 0.75 Beta Ratio V-Cone Meter Data with the Separated Frg Values. A correction factor was produced from the NEL DTI 6” 0.75 beta ratio data that for a known liquid mass flow rate or liquid to gas flow rate ratio will correct the gas flow rate to within ±2% with a few outliers [1]. This is reproduced below; V-Cone Meter Wet Gas Correlation:

( )

++++

=

gLM

gLM

tpgg

BFrCXBFrAX

mm

11

.

.

(4)


5

where

l

g

3997.00013.0A

ρ

ρ+−= --- (4a),

l

g

0317.00420.0B

ρ

ρ−= ---(4b),

l

g

2819.07157.0C

ρ

ρ+−= ---(4c)

and gm.

is the gas mass flow rate predicted by the correction method, and ( )tpgm.

is the apparent (and erroneous) gas mass flow prediction that the single phase calculation produces when the wet gas differential pressure ( tpP∆ ) is applied to the meter. That is the value found by iterating equation

5 for the ( )tpgm.

value.

( ) 02.

=∆− tpgdtptg PCYEAmtptp ρ (5)

where E is the velocity of approach, tA is the throat (or minimum cross sectional area) while

tpY and tpd

C are the expansibility factor and the discharge coefficient predicted if the wet gas

differential pressure is used in the calculation, i.e. tpP∆ . That is:

( )( )

∆+−=

kPP

Y tptp **696.0649.01 4β (6)

( )

( ) ( )

==

DmffCg

g

gdtp

tptp πµ

.

4Re (7)

Where ( )tpg

Re is the Reynolds number calculated by the uncorrected gas flow rate, gµ is gas

viscosity and D is the meter’s inlet diameter. Figure 4 shows the performance of Equation 4 with the NEL data that was used to create it.


6

NEL DTI 2001 6", Schedule 80, 0.75 Beta Ratio V-Cone MeterWet Gas Test Data

Corrected by Equation 4 and Uncorrected Results

+2%

-2%-10

0

10

20

30

40

50

0 0.05 0.1 0.15 0.2 0.25 0.3

X

% G

as E

rror

Uncorrected DR 0.0239Corrected DR 0.0239Uncorrected DR 0.0456Corrected DR 0.0456Uncorrected DR 0.0889Corrected DR 0.0889

Fig. 4 NEL DTI 2001 Uncorrected and Corrected by Equation 4 Data for a Known Liquid Flow Rate.

5 REPEATABILITY OF THE 6” SCHEDULE 80 0.75 BETA RATIO V-CONE METER Repeat tests at 15 and 60 Bar(g) for the same V-Cone meter were carried out by NEL in May 2003 and these results have been presented at the NSFMW in 2003 [5]. Figure 5 shows the uncorrected and corrected by Equation 4 data for a known liquid flow rate.

NEL McCrometer 6", Schedule 80, 0.75 Beta Ratio V-Cone MeterWet Gas Test Data

Corrected by Equation 4 and Uncorrected Results

+2%

-2%

-10

-5

0

5

10

15

20

25

30

35

40

45

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% G

as E

rror Uncorrected DR 0.022

Corrected DR 0.022Uncorrected DR 0.088Corrected DR 0.088

Fig.5 NEL McCrometer 2003 Uncorrected and Corrected by Equation 5 Data for a Known Liquid Flow Rate. Figure 5 shows data corrected by Equation 4, that was not used in the development of the equation, but was from the same meter at the same test conditions and in the same laboratory. Again it is seen that for a known liquid flow rate the over-reading of the V-Cone meter was corrected to give a final gas flow rate prediction of ±2%. The NEL results are therefore considered repeatable.


7

6 EXTRAPOLATION OF THE 6” SCHEDULE 80, 0.75 BETA RATIO V-CONE METER WET GAS CORRELATION BEYOND THE PARAMETER LIMITS OF THE NEL TEST MATRIX

With V-Cone meter wet gas flow repeatability shown in 2003 there was still little evidence that this correlation (or any DP meter wet gas correlation) could be used outside of the limits of the wet gas test matrix that was used to create it. However, since 2001 McCrometer has tested a 4” Schedule 80, 0.75 beta ratio V-Cone meter at the CEESI wet gas test loop five separate times. The initial tests were done as part of a sponsored Joint Industry Project (JIP) and McCrometer does not have permission to show that data set but the following four tests were funded by McCrometer and they cover the full test matrix available at CEESI. CEESI operates a 4” wet gas loop with natural gas (NG) and decane (a hydrocarbon liquid) being the flowing fluids. The range of the V-Cone meter tests encompassed the available ranges of the parameters at the CEESI test rig. A description of the CEESI wet gas test system is given in Reference [6]. The test matrix covered by the four tests are shown in Table 2.

Table 2. Envelope for CEESI Wet Gas Flow 0.75 Beta Ratio V-Cone Meter Tests

Nominal Pressure (g) Density Ratio Frg XLM range 15 0.014 0.48 - 1.45 0 < XLM< 0.25 45 0.054 0.91 – 2.80 0 < XLM< 0.25 75 0.094 1.25 – 3.75 0 < XLM< 0.25

The CEESI test loop therefore tested a different sized meter with different fluids than NEL. The maximum density ratio was slightly higher than at NEL and the minimum density ratio was significantly less than at NEL. The gas densiometeric Froude number ranges were similar for NEL and CEESI. The NEL and CEESI test meters were both schedule 80, 0.75 beta ratio V-Cone meters. The CEESI tests are shown along with the NEL DTI 2001 tests in Figure 6. The legend indicates uncorrected data (i.e. the gas prediction percentage error to the test rigs reference meter) and corrected data (i.e. the gas prediction after the application of Equation 4 [by use of the test rigs liquid reference meters] to the test rigs reference meter).

Schedule 80 0.75 Beta Ratio V-Cone MeterNEL 6" DTI 2001 Wet Gas Data and the Collected CEESI 4" Wet Gas Data

Corrected by Equation 4

+2%

-2%-10

0

10

20

30

40

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% G

as E

rror

NEL DTI 2001 Uncorrected DR 0.0239NEL DTI 2001 Corrected DR 0.0239NEL DTI 2001 Uncorrected DR 0.0456NEL DTI 2001 Corrected DR 0.0456NEL DTI 2001 Uncorrected DR 0.0889NEL DTI 2001 Corrected DR 0.0889CEESI McC 2002 Uncorrected DR 0.0533CEESI McC 2002 Corrected DR 0.0533CEESI McC July 2004 Uncorrected DR 0.0570CEESI McC July 2004 Corrected DR 0.0570 CEESI McC Aug 2004 Uncorrected DR 0.0157CEESI McC Aug 2004 Corrected DR 0.0157CEESI McC Aug 2004 Uncorrected DR 0.0542CEESI McC Aug 2004 Corrected DR 0.0542CEESI McC Aug 2004 Uncorrected DR 0.093CEESI McC Aug 2004 Corrected DR 0.093CEESI McC Dec 2004 Uncorrected DR 0.0144CEESI McC Dec 2004 Corrected DR 0.0144CEESI McC Dec 2004 Uncorrected DR 0.0474CEESI McC Dec 2004 Corrected DR 0.0474CEESI McC Dec 2004 Uncorrected DR 0.0840CEESI McC Dec 2004 Corrected DR 0.0840

Fig. 6 NEL and CEESI Wet Gas Data Comparisons.


8

Figure 6 shows that there was generally a good comparison between the NEL and CEESI results. The higher CEESI gas to liquid density ratios (greater than the max NEL value of 0.0889) over-readings were corrected to with 2% of the CEESI reference meter. Within the same Lockhart-Martinelli range, the same gas to liquid density ratio range, and the same gas densiometric Froude number test range; the two test rigs gave the same over-readings, and Equation 4 corrected the gas flow rate to within 2%. However, a problem was seen at the gas to liquid density ratios less than the minimum NEL value of 0.024. All CEESI data points, with gas to liquid density ratios greater than 0.024, are in agreement with the NEL data. However, for the CEESI data where the gas to liquid density ratio is lower than the NEL limit, Equation 4 over estimates the Over-Reading and therefore over corrects. The predicted gas flow rates are therefore less than the actual values. Figure 7 highlights this result.

Schedule 80 0.75 Beta Ratio V-Cone MeterNEL 6" DTI 2001 Wet Gas Data and the Collected CEESI 4" Wet Gas Data

Corrected by Equation 4

+2%

-2%

-10

-5

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3

XLM

% G

as E

rror

CEESI McC Aug 2004 Uncorrected DR 0.0157

CEESI McC Aug 2004 Corrected DR 0.0157

CEESI McC Dec 2004 Uncorrected DR 0.0144

CEESI McC Dec 2004 Corrected DR 0.0144

Fig 7. Low Gas to Liquid Density Ratio Data from CEESI Corrected by Equation 4. The minimum NEL and a minimum CEESI gas to liquid density ratio set were plotted together (Figure 8) to investigate this result. It was found that there was little difference in the two data sets.

Schedule 80, 0.75 Beta Ratio V-Cone MeterNEL 6" and CEESI 4" Low Gas to Liquid Density Ratio Comparison

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% G

as E

rror

NEL DR 0.024 Frg 0.57NEL DR 0.024 Frg 0.94NEL DR 0.024 Frg 1.52NEL DR 0.024 Frg 1.91CEESI DR 0.016 Frg 0.49CEESI DR 0.016 Frg 0.98CEESI DR 0.016 Frg 1.45

Fig 8. Comparing NEL and CEESI Low Gas to Liquid Density Ratio Data Sets. Although there was a clear gas to liquid density ratio effect seen at both NEL and CEESI, it was found that at the low gas to liquid density ratio, the published correction did not perform well. Further analysis of all the published and unpublished data sets indicated that by capping the


9

equations 4a to 4c at a minimum value of 0.027 (i.e. assuming the gas to liquid density ratio effect to disappear below this value) a better over all performance of the correlation was achieved. That is the following amendment to the existing correlation has been made:

For 027.0≥l

g

ρρ

, then:

l

g

3997.00013.0A

ρ

ρ+−= --- (4a),

l

g

0317.00420.0B

ρ

ρ−= ---(4b),

l

g

2819.07157.0C

ρ

ρ+−= ---(4c)

For 027.0<l

g

ρρ

, then A=2.431 , B=-0.151 , C=-0.669

Note that at the gas to liquid density ratio value of 0.027 equations 4a to 4c gives the constants A=2.431 , B=-0.151 and C=-0.669. Figure 9 shows all the available data from NEL and CEESI corrected with this update. Clearly the correlation’s performance is now ± 2% with a few slight outliers.

Schedule 80 0.75 Beta V-Cone MeterAll NEL 6" Wet Gas Data and the Collected CEESI 4" Wet Gas Data

Corrected by Equation 4 with Minimum Gas to Liquid Density Ratio Cap Applied

+2%

-2%

-10

0

10

20

30

40

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% G

as E

rror

2001 6" NEL DR 0.024 Uncorrected2001 6" NEL DR 0.024 Corrected2001 6" NEL DR 0.046 Uncorrected2001 6" NEL DR 0.046 Corrected2001 6" NEL DR 0.089 Uncorrected2001 6" NEL DR 0.089 Corrected2002 4" CEESI DR 0.053 Uncorrected2002 4" CEESI DR 0.053 Corrected2003 6" NEL DR 0.022 Uncorrected2003 6" NEL DR 0.022 Corrected2003 6" NEL DR 0.088 Uncorrected 2003 6" NEL DR 0.088 CorrectedJuly 2004 4" CEESI DR 0.057 Uncorrected July 2004 4" CEESI DR 0.057 CorrectedAug 2004 4" CEESI DR 0.016 UncorrectedAug 2004 4" CEESI DR 0.016 CorrectedAug 2004 4" CEESI DR 0.054 UncorrectedAug 2004 4" CEESI DR 0.054 CorrectedAug 2004 4" CEESI DR 0.093 UncorrectedAug 2004 4" CEESI DR 0.093 CorrectedDec 2004 4" CEESI DR 0.014 UncorrectedDec 2004 4" CEESI DR 0.014 CorrectedDec 2004 4" CEESI DR 0.047 UncorrectedDec 2004 4" CEESI DR 0.047 CorrectedDec 2004 4" CEESI DR 0.084 UncorrectedDec 2004 4" CEESI DR 0.084 Corrected

Fig. 9 All the Publishable NEL and CEESI 0.75 Beta Ratio V-Cone Meter Wet Gas Test Data Corrected with the Amendment for the Low Gas to Liquid Density Ratio Minimum Case. It is not yet understood why the gas to liquid density ratio effect disappears. It is possible that at a certain minimum value, the buoyancy force on the liquid has reduced to an extent that the wet gas flow becomes largely stratified for all the gas flow rates tested. It may be the case that the flow pattern has a direct relationship with the over reading of a DP meter.


10

7 FURTHER WET GAS FLOW 0.75 BETA RATIO V-CONE METER RESULTS FROM K-LAB

The K-Lab test facility at the Kårstø Terminal in Norway is considered to offer flow conditions close to those that are found in real unprocessed (or “upstream”) wet natural gas production flows. This Statoil operated facility utilises the surrounding terminal facilities to offer a large test matrix. As a result, the laboratory offers unique test conditions with regards to meter size, line pressure, gas flow rate and mix of liquids. The details of the lab have been described in Reference [7]. In 2005 the BG-Group tested a 6” schedule 160, 0.75 beta ratio V-Cone meter with wet gas flow at unusually high gas velocities. The expected gas densiometeric Froude number was approximately three times greater than the existing test results. The existing correlation (Equation 4) was not designed to work with large gas densiometeric Froude number extrapolations, therefore the meter was wet gas “calibrated” at K-Lab in Feburary 2005. These high gas flow rate wet gas tests gave interesting results but this is out-with the scope of this paper and will be the subject of a separate paper. What is relevant here is that K-Lab was asked to test the meter at a relatively low gas densiometeric Froude number to allow a comparison with the existing wet gas data sets. A good match between K-Lab and the existing NEL and CEESI data sets would therefore build confidence in the validity of the higher gas densiometeric Froude number data from K-Lab. This relatively low gas flow rate data set from K-Lab is described in Table 3 and presented in Figure 10. Table 3. Relatively Low Frg Value 6” Schedule 160 0.75 Beta Ratio V-Cone Meter K-Lab Data

Nominal Pressure (g) Density Ratio Frg XLM range

51 0.059 4.37 0 < XLM< 0.25

K-Lab Wet Gas Test 6", Schedule 160, 0.75 Beta Ratio V-Cone Meter

Average Frg 4.37 , Average Gas to Liquid Density 0.059

+2%

-2%

-10

0

10

20

30

40

50

0 0.05 0.1 0.15 0.2 0.25 0.3

XLM

% G

as E

rror

Uncorrected Corrected by Equation 4

Fig 10. The K-Lab Uncorrected and Corrected by Equation 4 Data. It can be seen in Figure 10 that the data recorded at K-Lab for a 6” schedule 160, 0.75 beta ratio V-Cone meter could be corrected to within 2% of the dry gas reference meter by the NEL data based Equation 4 for a known liquid flow rate. Therefore the different fluids and inlet diameters of the three 0.75 beta ratio V-Cone meters appear to have made no noticeable difference in the performance of the V-Cone meter at the different test laboratories. That is, at similar wet gas flow conditions (where “similar” means the matching of the relevant non-dimensional parameters) all three test rigs data sets agreed with each other. It should be noted that Equation 4 did not perform well at the higher Frg value of 6.75 tested at K-Lab. The large extrapolation to these much higher gas flow rates caused the prediction to


11

diverge. Therefore a cautionary Frg cap of 5.0 is suggested for Equation 4. It should be noted that this maximum Frg value is larger than those typically found in the majority of industrial wet gas flows. McCrometer has created a different wet gas correlation for a Frg range of 5.0 to 8.75 that has a slightly higher uncertainty than Equation 4. 8 THE CEESI 2” SCHEDULE 80, 0.7 BETA RATIO V-CONE METER WET GAS TESTS In 2004 CEESI, developed a 2” schedule 80 wet gas test facility that could inject water, a hydrocarbon liquid, or a mix of water and hydrocarbon liquid, into a natural gas flow. The details of this test loop are described in reference [8]. The hydrocarbon liquid chosen by CEESI was Stoddard solvent. Stoddard is a mixture of liquid hydrocarbons which consists mainly of C9 through C13 with trace quantities of other components. For the commissioning runs, CEESI requested a V-Cone meter from McCrometer. A 2” schedule 80, 0.7 beta ratio V-Cone meter was available. It has been reported [1] that there is a V-Cone meter beta ratio effect on the size of over-readings with wet gas flows. However, since there is a relatively small difference between the 0.7 beta ratio and the 0.75 beta ratios being discussed in this paper, the new 2” schedule 80, 0.7 beta ratio V-Cone meter data set was considered directly comparable to the larger 0.75 beta ratio data sets. The tests were conducted by CEESI at the nominally chosen test pressure of approximately 13 bara (although individual test runs varied). After a dry run to calibrate the meter to be within 0.5% (by applying a discharge coefficient to Reynolds number line fit), the wet gas runs were conducted with water only, Stoddard only, and then a range of water/Stoddard mixes. The low pressure and gas flow rate tended to fluctuate slightly between runs meaning the average gas density varied somewhat. However, the gas to liquid density ratio and gas densiometric Froude number varied significantly for the mixed liquid runs (even with nearly constant Lockhart Martinelli numbers, gas mass flow rates, and gas densities) as the averaged liquid density changed depending on the ratios of water to Stoddard being injected as both these parameters are directly affected by the liquid density. Hence, it was not possible to visually compare individual points or individual runs by plotting on the normal Over-Reading versus Lockhart Martinelli graph. Most of the data points have unique combinations of the dimensionless parameters and therefore the points would not represent a group of constant density ratio or constant gas densiomtric Froude number with varying Lockhart Martinelli parameter values. For example, Figure 11 shows the plot of the NG / Stoddard data alone. At first glance it looks like the relationship between the Over-Reading to Lockhart Martinelli parameter is not linear. A closer inspection shows that the gas densiometric Froude numbers are not constant, and in fact the higher the Frg value, the bigger the over-reading gradient (as expected). Table 4 shows the individual wet gas points tested. The only direct way to compare the different 2” V-Cone meter wet gas data sets was to apply the correction factor for a known liquid flow rate and then compare how well (or how poorly) the correction factor removed the over-reading from the different data sets. By applying the correction factor (Equation 4), it was assumed that if the water produced a higher or lower over-reading than the liquid hydrocarbon, or if the 2” meter produced a higher or lower over-reading than the 4” CEESI meter, then a different magnitude of gas uncertainty would be found. It should be noted that CEESI chose a nominal test pressure where the gas to liquid density ratio was considerably below the cap discussed in section 6 of this paper. Hence the low density ratio cap applied when using the correlation. The first data set corrected with Equation 4 was the NG/Stoddard data set (with no water). With the NG being the same as that used in the 4” CEESI line and Stoddard having very similar liquid


12

properties to decane, this gave some indication of the difference between a 2” and a 4” V-Cone meter.

Table 4. The CEESI 2” Schedule 80 0.75 Beta Ratio V-Cone Meter Test Point References

Gas Liquid Water

Stoddard Gas Water Stoddart Gas/Liquid Pressure Density Density Density Density Flow Flow Flow Density Frg Xlm

(Bara) (kg/m^3) (kg/m^3)

(kg/m^3)

(kg/m^3) (kg/s) (kg/s) (kg/s) Ratio

13.542 10.69 990.65 990.65 N/A 0.317 0.481 0.000 0.0108 2.478 0.1574 13.762 10.94 991.76 991.76 N/A 0.292 0.427 0.000 0.0110 2.851 0.1214 13.875 10.98 992.02 992.02 N/A 0.294 0.303 0.000 0.0111 2.706 0.0908 13.912 10.92 992.59 992.59 N/A 0.300 0.156 0.000 0.0110 2.577 0.0491

12.156 9.81 996.39 996.39 N/A 0.292 0.505 0.000 0.0098 2.373 0.1716 12.300 9.93 996.61 996.61 N/A 0.288 0.409 0.000 0.0100 2.941 0.1122 12.429 10.02 996.73 996.73 N/A 0.281 0.295 0.000 0.0101 2.692 0.0884

12.081 9.47 771.00 N/A 771.00 0.271 0.000 0.466 0.0123 2.555 0.1903 12.188 9.56 771.21 N/A 771.21 0.262 0.000 0.356 0.0124 3.112 0.1195 12.266 9.62 771.26 N/A 771.26 0.259 0.000 0.230 0.0125 2.848 0.0844 12.284 9.63 771.28 N/A 771.28 0.267 0.000 0.118 0.0125 2.707 0.0454

12.927 10.16 952.25 998.74 776.44 0.276 0.216 0.057 0.0107 2.259 0.1023 12.978 10.20 910.47 998.76 777.48 0.283 0.144 0.095 0.0112 2.365 0.0892 13.020 10.23 845.04 998.78 777.63 0.283 0.078 0.177 0.0121 2.445 0.0992 13.045 10.25 808.79 999.03 777.42 0.289 0.018 0.109 0.0127 2.555 0.0493 13.068 10.26 845.10 999.03 777.38 0.291 0.037 0.085 0.0121 2.512 0.0465 13.078 10.27 901.51 998.92 777.33 0.292 0.069 0.054 0.0114 2.437 0.0453 13.102 10.28 951.74 998.79 777.02 0.288 0.108 0.029 0.0108 2.341 0.0496

13.134 10.20 949.50 995.84 772.45 0.312 0.421 0.110 0.0107 2.550 0.1762 13.278 10.33 899.42 996.51 773.61 0.305 0.305 0.236 0.0115 2.547 0.1899 13.347 10.36 842.30 996.54 773.51 0.309 0.145 0.325 0.0123 2.664 0.1684 13.152 10.19 949.18 993.83 770.60 0.277 0.349 0.087 0.0107 2.266 0.1632 13.244 10.24 896.92 995.00 773.40 0.287 0.212 0.169 0.0114 2.407 0.1420 13.310 10.24 841.94 994.45 772.58 0.288 0.113 0.248 0.0122 2.498 0.1378 12.992 9.96 945.09 993.68 769.79 0.278 0.219 0.061 0.0105 2.303 0.1033 13.045 10.03 896.61 995.48 772.81 0.283 0.152 0.121 0.0112 2.400 0.1020 13.083 10.04 836.40 996.29 774.30 0.284 0.070 0.179 0.0120 2.494 0.0961

13.431 10.30 955.37 997.23 773.41 0.2935 0.1159 0.0267 0.0108 2.379 0.0504 13.469 10.28 899.84 997.09 771.68 0.2967 0.0703 0.0533 0.0114 2.480 0.0445 13.492 10.27 832.53 997.07 771.70 0.2960 0.0325 0.0879 0.0123 2.576 0.0452 13.515 10.27 801.83 996.93 771.80 0.2958 0.0155 0.1005 0.0128 2.624 0.0444

13.147 10.07 991.97 991.97 761.70 0.2941 0.5616 0.0000 0.0102 2.365 0.1924 13.336 10.20 992.72 992.72 761.96 0.2783 0.4441 0.0000 0.0103 2.223 0.1617 13.429 10.22 992.73 992.73 761.43 0.2900 0.2900 0.0000 0.0103 2.315 0.1015

It was found that (as with the 4” 0.75 beta ratio V-Cone meter) the 2” 0.7 beta ratio V-Cone meter could also be corrected to within 2% uncertainty for a known liquid flow rate. Figure 11 shows this result. Therefore, the NEL 6” 0.75 beta ratio data based correlation, corrected the CEESI 2” 0.7 beta ratio V-Cone over reading as well as it had done for the NEL 6” and CEESI 4” 0.75 beta ratio data. Hence, no significant scaling effect was seen between 6”, 4” and 2” meter data. The second set of data sets corrected with Equation 4 was the NG/Water sets, compared with the NG/Stoddard set. This allowed an investigation into liquid properties. Figure 12 shows the result. No


13

significant effect could be seen between the two types of liquid. This result was not what was expected by McCrometer or CEESI.

CEESI 2", Schedule 80, 0.7 Beta Ratio V-Cone MeterAverage Gas to Liquid Density Ratio 0.0124

Natural Gas and Stoddard DataUncorrected and Corrected by Equation 4

Frg 2.71

Frg 2.85

Frg 3.11

Frg 2.55

+2%

-2%

-10

-5

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2

XLM

% G

as E

rror Uncorrected NG & Stoddard

Corrected NG & Stoddard

Fig 11. Example of Varying Gas Densiometric Froude Numbers in Each Data Set.

CEESI 2", Schedule 80, 0.70 Beta Ratio V-Cone MeterNatural Gas with Water Only

and Natural Gas with Stoddard OnlyData Uncorrected and Corrected by Equation 4

(with Low Gas to Liquid Density Ratio Cap)

+2%

-2%

-10

-5

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

X

% G

as E

rror

Uncorrected NG & Water

Corrected NG & Water

Uncorrected NG & Stoddard


Fig. 12 Comparison of Using Equation 4 to Correct NG Flow With Water Only And Then Stoddard Only. The final three data sets had mixed water and Stoddard liquid flows. The results of correcting these data sets with Equation 4 are shown in Figure 13. Again it is seen that there is no significant difference for different types of liquid. In fact the NEL correlation based on a 6” Schedule 80, 0.75 Beta Ratio V-Cone meter utilising Nitrogen / Kerosene corrected the 2” Schedule 80, 0.70 Beta Ratio V-Cone meter NG / Mixed liquid data set to the same uncertainty as it did to the original NEL data set. As stated earlier this was not the result anticipated. It was assumed that different liquid


14

properties and different flow areas could significantly change the flow pattern at the meter inlet and therefore possibly change the scale of the over-reading induced by the liquid. Clearly, this was not established with these tests.

CEESI 2", Schedule 80.0.70 Beta Ratio V-Cone MeterNatural Gas Flow with Water Only, Stoddard Only

or a Liquid Mix of Water and Stoddard DataUncorrected and Corrected by Equation 4

+2%

-2%

-10

-5

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2

XLM

% G

as E

rror

Uncorrected NG & Water

Corrected NG & Water

Uncorrected NG & Stoddard


Uncorrected NG & Liq Mix

Corrected NG & Liq Mix

Fig. 13 All The CEESI 2” 0.7 Beta Ratio V-Cone Wet Gas Uncorrected and Corrected By Equation 4 Results. 9 CONCLUSIONS The results show the NEL 6” Schedule 80, 0.75 Beta Ratio V-Cone Meter Nitrogen/Kerosene wet gas data was repeatable. It was shown that the CEESI 4” Schedule 80, 0.75 Beta Ratio V-Cone Meter NG/Decane wet gas data was very similar to the NEL data. Within the same test parameters (or hugher gas to liquid density ratios) the NEL based wet gas correlation predicted the meters performance well. At gas to liquid density ratios below that tested at NEL, a correction to the NEL data based correlation was required. The K-Lab 6” Schedule 120, 0.75 Beta Ratio V-Cone Meter NG/Condensate data that had a gas densiometeric Froude number close to those at NEL and CEESI, matched these other data sets well. At extreme gas densiometeric Froude number values (i.e. Frg>5 a different wet gas correlation is required). Comparisons of 2” Schedule 80, 0.70 Beta Ratio V-Cone Meter data with larger meters found no scaling (piping size) effect on the predicted meter wet gas over-reading. Comparisons of 2” Schedule 80, 0.70 Beta Ratio V-Cone Meter data with NG with water and/or liquid hydrocarbon flows found no liquid property effect on the over reading. However, this paper is reporting the latest research and the authors believe these results are initial results only and significantly more testing is required. Much wider test matrices for V-Cone meters and other DP meters are needed before a complete understanding of liquid and meter size effects can be achieved. CEESI and McCrometer plan to test this 2” V-Cone meter at higher pressures (gas to liquid density ratios) but at the time of writing this work is not complete.


15

10 ACKNOWLEDGEMENTS McCrometer would like again to thank the UK’s DTI for the funding of the original V-Cone meter wet gas tests in 2001. McCrometer would also like to thank the BG-Group for their kind permission to publish K-Lab test results of a UKCNS serving meter. McCrometer would like to thank CEESI for choosing to install a V-Cone meter as one of the meters used to commission the 2” wet gas facility. 11 REFERENCES [1] Stewart. D et al., “Wet Gas Metering with V-Cone Meters”, North Sea Flow Measurement Workshop 2002, St Andrews, Scotland, UK. Paper No.4.2. [2] Southwest Research Institute, “Testing of McCrometer V-Cone Flow Meter According to the API Chapter 5.7* Test Protocol”, March 2004. Available on request from McCrometer. [3] API 22 -Testing Protocol, Section 2 Differential Pressure Flow Measurement Devices”. [4] Bob Peters et al. “Tests of the V-Cone Flow Meter at Southwest Research Institute and Utah State University in Accordance with the New API Chapter 5.7* Test Protocol”, North Sea Flow Measurement Workshop 2004, St Andrews, Scotland, UK. Paper No. 2.1. [5] Steven. R and Lawrence .P, “Research Developments in Wet Gas Metering with V-Cones”, North Sea Flow Measurement Workshop 2003, Tonsberg, Norway. Paper 11. [6] Britton. C et al. “Experimental Wet Gas Data for a Herschel Style Venturi”, Fluid Flow Measurement 5th International Symposium, April 2002, Arlington, VA, USA. [7] Wood I.M. et al. “Penguin Wet Gas Measurement”, North Sea Flow Measurement Workshop 2003, Tonsberg, Norway. Paper 5. [8] Britton. C et al. “Wet Gas Flow Measurement with Mixtures of Natural Gas, Hydrocarbon Liquids and Water”, North Sea Flow Measurement Workshop 2004, St Andrews, Scotland, UK. Paper No. 8.3. *Note that API has since re-numbered the Test Protocol to Chapter 22.2.


16

APPENDIX Dimensionless groups are a problem to engineers working with wet gas, two-phase and multiphase flows as the most relevant force ratios require unknown information, i.e. the actual averaged phase velocities. For example the ideal definitions of the Lockhart Martinelli parameter and the gas densiometric Froude number would include the actual liquid and actual gas inertias instead of the “superficial” inertias (i.e. the phase inertias if the phases were flowing alone). However, as the actual averaged phase velocities are not known, a compromise has to be made and the known superficial phase inertias are therefore used. With regards to the gas phase, as the liquid loading decreases, the inherent assumption in this compromise that the actual gas inertia and superficial gas inertia are equivalent, becomes more valid. No such approximations are valid for the liquid phase inertia of a wet gas flow. Detailed analysis of liquid effects on wet gas flow meters will have the problem of how to non-dimensionalise the analysis. The two most likely liquid forces to affect a wet gas meters performance are, the liquid viscous force and the surface (or interfacial) tension force. The driving force in wet gas flows is the gas inertia. Possible relevant dimensionless numbers will be the ratio of the gas inertia force to liquid viscous force (a type of wet gas Reynolds number – see equation A1) and the ratio of the gas inertia force to the interfacial tension force (a type of wet gas Weber number – see equation A2). That is:

DUDU

ForceViscousLiquidForceInertiaGas

ll

ggtpLiquid µ

ρ 22

Re == (A1)

DDU

ForceTensionlInterfaciaLiquidForceInertiaGas

Wel

ggtpLiquid σ

ρ 22

== (A2)

where lσ is the liquid interfacial tension and lµ is the liquid viscosity. For wet gas flows, a general approximation could be made that as long as there is not too much liquid, the actual velocity of the gas is not greatly increased by the liquid blockage of the flow area. Therefore sgg UU ≈ . However, no such approximation is available for the liquid velocity. For all

wet gas flows, with moderate or high gas flow rates, the liquid would be driven at a much higher velocity than if the liquid was flowing alone. Hence a Weber number for wet gas flow could be defined as equation A1a:

3

2.22

Dm

DDU

Wegl

g

l

sggtpLiquid ρσσ

ρ== (A1a)

where for practical reasons, lσ would need to be the surface tension of the liquid at standard atmospheric conditions, as interfacial tension information is not available for most (if not all) situations. However, defining a realistic wet gas liquid based Reynolds number is more difficult. With no liquid phase average velocity information available and the superficial liquid velocity clearly not appropriate, there is little that can be done to produce a viable dimensionless number. Only in the special case of low liquid loadings, at extremely high gas velocities, can assumptions lead to a


17

useable equation. In this special case the assumption of fully homogenised flow could be made. This means that it is assumed that the actual gas and liquid velocities are the same. Adding the low liquid loading assumption of superficial and actual average gas velocities, being approximately the same, the following dimensionless number is derived:

DmDU

DUDU

l

g

l

sgg

ll

ggtpLiquid πµµ

ρµρ

.22 4Re === (A2a)

The assumptions in this derivation are extremely restrictive. However, as yet, the authors are not aware of any published information on how to non-dimensionalise data sets, to investigate liquid property effects on wet gas flows.

Paper 3.2 An Update on V-Cone Meter Wet Gas Flow Metering ... · Flomeko 2005 6–9 June 2005 1 AN...

Documents

Transcript of Paper 3.2 An Update on V-Cone Meter Wet Gas Flow Metering ... · Flomeko 2005 6–9 June 2005 1 AN...