Orifice plate meter wet gas flow performance

Flow Measurement and Instrumentation 20 (2009) 141–151

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Flow Measurement and Instrumentation

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Orifice plate meter wet gas flow performanceRichard Steven a,∗, Andrew Hall b,1aMultiphase and Wet Gas Flow Research, Colorado Engineering Experiment Station, Inc., 54043 WCR 37-Nunn, CO 80648, USAb BP Exploration Operating Team, Aberdeen, UK

a r t i c l e i n f o

Article history:Received 25 March 2008Received in revised form22 May 2009Accepted 1 July 2009

Keywords:Two phaseWet gasFlowVenturiOrifice plateMeter

a b s t r a c t

Orifice plate meters are often used to measure wet gas flows. Research into the wet gas response of thehorizontally installed orifice platemeter is discussed in this paper. Consideration is given to the significantinfluence of the wet gas flow pattern, as this has previously been found to be relevant to the wet gasresponse of other differential pressure type flow meters. A wet gas flow correlation for 2′′ to 4′′ orificeplatemeters has beendeveloped frommultiple data sets from fourwet gas flow test facilities. This correctsthe liquid induced gas flow rate error for a known liquid flow rate to±2% at a 95% confidence level.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Orifice meters have been studied for many years and theirperformance in single phase flows is well documented in thestandards [1]. Between 1967 and 1977, Chisholm [2,3] researchedthe response of orifice meters to two phase flow. No furtherresearch on the behaviour of orifice meters in wet gas flows wasreleased until 2007, when Hall et al. [4] and Steven et al. [5–7]showed data from CEESI that indicated Chisholm’s equation [3]was appropriate for predicting the over-reading (i.e. the positivebias on the gas flow prediction induced by the liquids presence)of an orifice meter in wet gas flow conditions, across a significantrange of the flow conditions tested. Only at very low or high gasvelocities (or gas densimetric Froude numbers) did Chisholm’sequation become inaccurate.This paper reports the results of analysing a large combineddata

set from various studies of orifice meters in wet gas flow. Orificedata (2′′, 3′′ and 4′′) was supplied by ConocoPhillips, Chevron, BP,Emerson and CEESI. Furthermore, the CEESI wet gas flowmeteringJoint Industry Project released wet gas orifice data in July 2007,and the members of a wet gas flow metering JIP run by TÜV NELalso agreed to release wet gas orifice data to this combined database. This paper describes the development of the Chisholm wet

∗ Corresponding author. Tel.: +1 970 897 2711; fax: +1 970 897 2710.E-mail addresses: [email protected] (R. Steven), [email protected]

(A. Hall).1 Tel.: +44 1224 833507.

0955-5986/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2009.07.001

gas correlation for orificemeters to take appropriate account of theeffect of the common industrial practice of extrapolating their useto higher gas velocities.

2. Definition of wet gas flow

Wet gas flow is defined here as any gas and liquid flow thathas a Lockhart–Martinelli parameter, XLM , less than 0.3 [8]. TheLockhart–Martinelli parameter is defined as:

XLM =

√Superficial Liquid InertiaSuperficial Gas Inertia

=m`mg

√ρg

ρ`(1)

wheremg andml are the gas and liquid mass flow rates and ρg andρl are the gas and liquid densities respectively.Many gas meters have responses in wet gas flow that are

dependent on the gas to liquid density ratio (effectively adimensionless representation of the pressure). Often, the gas toliquid density ratio is indicated by DR,

DR = ρg/ρ`. (2)

The gas densimetric Froude number (3) is defined as the squareroot of the ratio of the gas phases inertia if it flowed alone inthe pipe to the weight of the liquid phase. The liquid densimetricFroude number (5) is defined as the square root of the ratio of theliquid phases inertia if it flowed alone in the pipe to the weight ofthe liquid phase. In these equations, g is the gravitational constant(9.81 m/s2 or 32.2 ft/s2), D is the pipe internal diameter and Usg

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142 R. Steven, A. Hall / Flow Measurement and Instrumentation 20 (2009) 141–151

Fig. 1. The shell flow pattern map with sketches of flow patterns.

and Usl are the superficial gas and liquid velocities calculated byEqs. (4) and (6) respectively.

Frg =Usg√gD

√ρg

ρ` − ρg(3)

Usg =mgρgA

(4)

Fr` =Us`√gD

√ρ`

ρ` − ρg(5)

Us` =m`ρ`A

. (6)

Finally, DP meters in wet gas flows tend to have a positive biasor over-reading on their gas flow rate prediction. The uncorrectedgas mass flow rate prediction is often called the apparent gas massflow, mg,apparent . The over-reading is the ratio of the apparent toactual gas flow rate. Eqs. (7) and (8) show the over-reading andpercentage over-reading (where1Ptp and1Pg are the actual two-phase differential pressure and the differential pressure if the gasflowed alone respectively).

OR =mg,apparentmg

∼=

√1Ptp1Pg

(7)

OR(%) =(mg,apparentmg

− 1)× 100% ∼=

(√1Ptp1Pg− 1

)× 100%. (8)

3. Horizontal wet gas flow patterns and flow pattern maps

Horizontal wet gas flows have the liquid phase dispersed inthe pipe dependent on the flow conditions. The description of thisliquid dispersion is called a flow pattern (or flow regime). A visualaid that predicts the particular flow pattern at set flow conditionsis called a flow pattern map. Fig. 1 shows a flow pattern map fornatural gas and hydrocarbon liquid flow in a 4 inch pipe, developedby Shell Exploration and Production. It is therefore relevant forpredicting wet natural gas flow patterns in 4 inch pipes.At low gas dynamic pressures, the gravitational force will

dominate and the liquid will flow at the base of the pipe drivenby interfacial shear stress applied by the gas flow. This is calledstratified or separated flow. If there is a relatively large ratio ofliquid to gas flow rate for a set gas to liquid density ratio, stratifiedflow can be unstable and resultingwaves can periodically block thepipe. This is called slug flow. For any given gas to liquid flow rateratio and density ratio combination (i.e. set Lockhart–Martinelliparameter), if the gas flow rate is high enough, the liquid phase

will be forced to flow along a layer around the periphery of thepipe with the gas flow in a central core entrained with smallliquid droplets. This is called annular or annular mist flow. Asthe gas dynamic pressure increases for all other conditions heldconstant, the amount of entrainment of the liquid increases, theaverage entrained droplet size reduces and the thickness of theliquid annular ring reduces due to the faster flow rate and theconservation of mass and also the loss of liquid mass from theannular ring flow as it transfers to droplet flow. Eventually, at alarge enough gas dynamic pressure, the ring is no more than awetted wall and all the liquid flows as entrained droplets. This iscalledmist flow. If the gas dynamic pressure continues to increase,the droplets continue to be broken up into ever more numerousbut smaller diameter droplets. Finally, the droplets are so small,the liquid phase is effectively atomized. This is called homogeneousflow, since the liquid phase is evenly distributed throughout theflow in such away as thewet gas flow can bemodelled as a pseudo-single phase flow. Steven [9] describes this phenomenon in moredetail.In Fig. 1 at high gas densiometric Froude numbers, the

prediction is an annular-mist flow pattern. There is no preciseboundary for where annular mist flow can be considered tobecome a mist flow or when a mist flow is effectively ahomogeneous flow. This is because flow pattern maps are madeby experimental observation and it is often not possible to visuallydistinguish between these flow patterns. In reality (for relativelylow liquid loading so as we don’t need to discuss slug flow here) asthe gas dynamic pressure increases, horizontal wet gas pipe flowswill tend from stratified flow, to a transitional flow, to annularmist, tomist flow and finally to homogeneous flow. Note, however,that Fig. 1 does show boundaries drawn between stratified, slugand annular mist flow. It is easier to visually distinguish betweenthese flow patterns. However, these boundaries are not meantto be taken as precise, but rather the approximate centre of thetransition zones. An unspecified large zone of transition straddleseach flow pattern map’s boundary. In reality, except for the verylow gas dynamic pressure stratified flow, observers find thatgeneral two-phase and wet gas flows look unsteady and transient,and particular flow patterns can be difficult to categorize as theyseem to the observer to be continuously changing.Due to flow pattern maps being created by experimental

observations, often there are little theoretical considerationstaken into account. This means that flow pattern maps are onlyapplicable to the precise flow conditions that were created tocreate the map. They cannot be extrapolated. A rare exceptionto this is the semi-empirical flow pattern work of Taitel andDuckler [10]. This work shows that the flow pattern is dependenton many variables (e.g. pipe diameter) and therefore flow patternmaps should not be applied to predict the flowpattern outwith theflow conditions for which they were created. This may seem to thereader rather obvious, but the author has repeat evidence that thisgeneral rule is repeatedly violated by engineers in industry. A verycommon error is the assumption that the Shell Exploration andProduction wet gas flow pattern map (for 4′′) is applicable to otherdiameter pipes. It is not. Set wet gas flow parameters (i.e. gas andliquid densiometric Froude numbers) that produce an annularmistflow in a 4′′ pipemay produce a stratified flow pattern in a 2′′ pipe.Thankfully for all flow pattern map prominence in two-phase/wetgas flow metering technical papers, they are not often used todirectly aid any wet gas flow metering calculations. Typically theyare used to teach engineers that the liquid dispersion in the gasflow can and will change with flow conditions, and for researchersto predict flow patterns as an aid to their flow modelling efforts.Beyond this flow pattern, maps are of limited practical use.Nevertheless the particular flow pattern through an orifice

plate meter has been found to strongly influence the response of

R. Steven, A. Hall / Flow Measurement and Instrumentation 20 (2009) 141–151 143

Fig. 2. NEL nitrogen/kerosene, 4′′ , 0.66 beta ratio, orifice meter data showingpressure/density ratio effect.

the meter to the presence of liquid, and hence the flow patterninfluence cannot be ignored.

4. A brief history of DP meters wet gas flow research

Chisholm [3] modelled a separated flow pattern only. From thismodel, Chisholm concluded that the response of orifice metersto many different two-phase/wet gas flow conditions was suchthat the over-reading was a function of the Lockhart–Martinelliparameter and gas to liquid density ratio. Fig. 2 shows a sampleof test results from NEL that confirm this. Chisholm stated that, forthe 2.5 to 4 inch pipe diameter range of his test data, the orificeplate meter wet gas correlation was:

mg =mg,apparent√1+ CXLM + X2LM

(9)

where C =(ρg

ρ`

)n+

(ρ`

ρg

)n(10)

with n = 0.25. (11)

In 1997, de Leeuw [11] tested a 4 inch, 0.4 beta Venturi meter ina test facility (SINTEF) and in the field (Coevorden). At SINTEF thetest conditions with nitrogen and diesel oil were:

15 ≤ P(bar) ≤ 90, 0.02 ≤ DR ≤ 0.13, 0 ≤ XLM ≤ 0.3and 1.5 ≤ Frg ≤ 4.8.

At Coevorden, the field conditionswith natural gas and condensatewere approximately:

P = 90 bar, DR = 0.15(estimated),0 ≤ XLM ≤ 0.15(estimated) and 0.5 ≤ Frg ≤ 1.

De Leeuw reported that the Venturi, like the orifice plate, hadan over-reading that was a function of the Lockhart–Martinelliparameter and gas to liquid density. However, de Leeuw showedthat, for the Venturi meter, the over-reading was also dependenton the gas densiometric Froude number. For all other parametersheld constant, he showed that, at low gas densiometric Froudenumbers, where the flow pattern was stratified, the over-readingwas insensitive to the gas densiometric Froude number, assuggested by Chisholm for orifice meters. However, he alsoshowed that, at higher gas Froude numbers where the flowpattern was annular mist flow, the over-reading was sensitive tothe gas densiometric Froude number. Fig. 3 shows subsequentlyrecorded Venturi meter wet gas data indicating this. The de Leeuwcorrelation was a modification to Chisholm’s correlation defined

Fig. 3. NEL 6 inch, 0.55 beta Venturi meter nitrogen/kerosene wet gas data at DR0.059.

Fig. 4. Flow programme 4 inch Venturi data for 31 bar, Frg = 1.5 showing a betaeffect (NEL).

in Eqs. (9) and (10), but with the exponent n a function of the gasFroude number:

for 0.5 ≤ Frg < 1.5 n = 0.41 (12)

and for Frg > 1.5 n = 0.606(1− exp(−0.746Frg)). (13)

That is, de Leeuw accounted for the flow patterns influence on theVenturi meters gas flow rate prediction liquid induced error byadding a gas densiometric Froude number variable to Chisholm’swet gas flow orifice meter correlation.Since publication of de Leeuw’s work, there has been further

research into the response of Venturi meters to wet gas flow. In2003, Stewart [12] showed that a Venturi meter has a wet gasresponse that is sensitive to the beta ratio of the meter. The higherthe beta ratio, for all other parameters held constant, the lower theover-reading. Fig. 4 shows a sample graph from this Venturi meterstudy. Chisholm did not report this beta ratio response for orificeplate meters. However, this has since been shown for orifice platemeters by Steven et al. [5]. A sample graph is produced as Fig. 5.In 2006, Steven [9,13] and Reader-Harris et al. [14,15] showed

that the Venturi meter has a wet gas response that can be sensitiveto the liquid properties of the flow. Fig. 6 shows a sample graphof Reader-Harris’s findings. Chisholm did not report this liquidproperty response for orifice plate meters. However, Steven [9]suggested that the liquid property effect seen with Venturi meterswas caused by the relationship between the liquid properties andthe gas dynamic pressure. Gas dynamic pressure indicates theamount of energy in the gas available to drive the liquid phase.Note here, that for a setmeter inlet diameter and set fluid densities,


Fig. 5. CEESI natural gas/kerosene, 4′′ , orifice meter data showing beta ratio effect.

1.7

1.6

1.5

1.4

1.3

1.2

1.1

0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3Lockhart-Martinelli Parameter (-)

0 0.325

1.8

Ven

turi

Met

er O

verr

eadi

ng (

-)

1

Fig. 6. Flow programme 4 inch, 0.75 beta Venturi data at DR 0.046 and Frg2.5,showing a liquid property effect (NEL).

the terms gas dynamic pressure and gas densiometric Froudenumber are directly linked. That is, an increasing or reducinggas dynamic pressure has a corresponding increasing or reducinggas densiometric Froude number. Hence, effectively we can saythat the liquid property effect seen with Venturi meters wascaused by the relationship between the liquid properties and thegas densiometric Froude number. This relationship sets the flowpattern and hence the DP meter response to wet gas flow. Theconclusion was that, for all other parameters held constant, asthe gas densiometric Froude number increased (i.e. as the gasdynamic pressure increased), the flow patternwould tend towardshomogeneous flow. Therefore, all wet gas correlations for gas flowmeters should, by theory, tend towards the homogeneous modelcorrection.The wet gas homogeneous model for DP meters can be shown,

Steven [9], to be described by Eqs. (9) and (10) with the exponentn = 0.5. This derivation is reproduced here as Appendix A. Stevenclaimed that all DP meters that utilize the Chisholm style wet gascorrelation, Eqs. (9) and (10), should have the Chisholm exponentn as a function of gas densimetric Froude number where, as thegas Froude number tends to infinity, the Chisholm exponent ntends to 0.5. For orifice meters, Chisholm simply used the constantn = 0.25, Eq. (11).In 2007, Hall et al. [4] and Steven et al. [5] showed that orifice

meters had a gas densiometric Froude number effect, aswas shownby de Leeuw for a Venturi meter. Fig. 7 shows a graph of data firstshown by Hall. This graph concentrates on a Lockhart–Martinelliparameter rangewhere there was a concentration of data allowingfor a clear gas Froude number effect to be visible.

Fig. 7. 4 inch 0.68 beta orifice meter wet gas data at DR 0.0648 from CEESI (BPdata).

The well documented phenomenon of an orifice meter under-reading at very low Lockhart–Martinelli parameters, as for ex-ample shown by Ting [16], is evident in Fig. 7. Chisholm’scorrelation does not account for this. Wet gas orifice meter cor-relations typically do not account for any under-reading. Thisunder-reading is evident for XLM < 0.02 and is less than −2%.Therefore, as the Chisholm correlation is said to have a perfor-mance of±2% there is little advantage in applying the correlation.Typically, for a known liquid flow rate, if the Lockhart–Martinelliparameter is less than 0.02, no correction method is applied.Fig. 7 shows the gas flow rate from the orifice meter, uncor-

rected for the effect of liquid. The rising over-reading gradients co-incide with rising gas Froude numbers. Fig. 7 shows the same phe-nomenon for an orificemeter as shown in Fig. 3 for Venturi meters.Fig. 7 also shows that for set gas to liquid density ratio and Lock-hart–Martinelli parameter, as the gas densiometric Froude num-ber increases, the results tend towards the homogeneous model,as theory predicts. The effect of correcting the orifice meter gasflow rate by applying the Chisholm correlation for a known liq-uid flow rate is also shown. The result of not correcting for the gasdensiometric Froude number effect can be seen in the correctedvalues. The lower gas densiometric Froude number value data (i.e.Frg = 1.59) is being corrected towards a 0% to−2% trend, and thehigh gas densiometric Froude number value data (i.e. Frg = 5.82)is being corrected towards a 0% to+2% trend.Hall [4] showed multiple natural gas and hydrocarbon liquid

data sets from the CEESI 4 inch wet gas facility and one naturalgas, hydrocarbon liquid and water data set from the CEESI 2 inchwet gas facility. A search for any liquid property effect on the wetgas response of the orificemeter was inconclusive. The data hintedat the same trend as found for Venturi meters (i.e. see Fig. 6).However, the differences were in the same order of magnitude asthe reference meter uncertainties, and it was concluded that if aliquid effect existed, for practical purposes, it was not seen as asignificant. The comparison of the very limited 2 inch data to the4 inch data hinted that the 2 inch meter had a slightly smallerover-reading than the 4 inchmeter for similar flow conditions. Thissuggested a small diameter effect.All the Hall and Steven data sets agreed with Figs. 2 and 7

in that the lower the gas to liquid density ratio, the higher theover-reading and the higher the gas Froude number the higher theover-reading. In most cases, the gas densiometric Froude numbereffect was small enough that the Chisholm correlation (whichonly accounts for the Lockhart Martinelli parameter and gas toliquid density ratio effects) gave±2% for a known liquid flow rate,but there were cases where the gas densiometric Froude numbereffect caused Chisholm’s correlation to be in error by more than±2%, even at relatively modest values of gas densiometric Froudenumbers. At very low gas densiometric Froude numbers (where


Fig. 8. 4 inch 0.5 beta orifice meter data at DR 0.018 from CEESI showingthe Chisholm correlation & gas densimetric Froude number issue (Chevron &ConocoPhillips data).

Fig. 9. Magnified Chisholm correlation data from Fig. 6.

video of the flow pattern shows a rather unstable wavy stratifiedflow) the over-reading is less than predicted by Chisholm; thecorrection is too great, causing an under-predicted gas flow rate.At large gas densiometric Froude numbers (where video of the flowpattern shows annular mist flow) the over-reading is greater thanpredicted by Chisholm; the correction is too small, causing an over-predicted gas flow rate. This phenomenon is shown in Fig. 8 for a4 inch 0.5 beta orificemeter with natural gas and Stoddard solvent.Fig. 9 magnifies the Chisholm corrected data shown in Fig. 8.It should be noted that Chisholm fitted his correlation to data

from orifice plate meters with beta ratios at or below 0.5, and withgas densiometric Froude numbers below values of 3.6 (and themajority below values of 2). A small wet gas flow beta ratio effectdoes exist for orifice plate meters (as shown by Steven et al. [5])where higher beta ratios do have lower over-readings. Chisholmdoes not account for this. Therefore, the 0.68 beta ratio platebeing discussed with Fig. 7 would have a lower over-reading thanChisholm’s data at the samewet gas flow conditions. Also, as highergas densiometric Froude numbers cause higher over-readings, atgas densiometric Froude numbers greater than approximately 2(i.e. higher than the majority of Chisholms data) we would expectany orifice plate to have a greater over-reading than Chisholm’scorrelation suggests. Here, in Fig. 7 we see that Chisholm’scorrelation gave the correct gas flow rate to within the stated 2%uncertainty. Therefore, here the beta ratio and gas densiometricFroude number effects appear to have cancelled each other out.This is by coincidence rather than by design. Due to the fact that theChisholm correlation result is influenced by the opposing trends

Fig. 10. All orifice meter wet gas data available by March 2007 uncorrected, andcorrected by Chisholm’s equation.

of the beta ratio and gas densiometric Froude number, it is notpossible to directly state the gas densiometric Froude numberrange in which Chisholm’s correlation is applicable, as this is alsobeta ratio related. However, a good rule of thumb is to assumeChisholm’s correlation may be inaccurate at beta ratios greaterthan 0.5 and/or at gas densiometric Froude numbers greater than2. Chisholm’s correlation is therefore not perfect and a modifiedChisholm correlation for the over-reading of an orifice meter inwet gas conditions that is sensitive to the gas densiometric Froudenumber (as de Leeuw created for a Venturi meter) and shown towork across all beta ratios, could be of significant benefit.

5. The existing orifice meter wet gas flow data sets and theChisholm correlation performance

Six recent orifice meter wet gas data sets recorded by CEESIwere shown by Hall [4] and Steven [5]. These were a 3 inch meterdata set obtained for ConocoPhillips (COP), a 4 inch meter data setobtained for Chevron (CVX), two 4 inchmeter data sets from a jointCOP, CVX and CEESI test series, and 2 inch and 4 inch meter datasets from tests for BP. The ranges of these data sets are reproducedin Tables B.1–B.6 in Appendix B.Fig. 10 shows these data sets together on one graph. Fig. 10

shows the uncorrected gas flow rate measurements and the gasmeasurement for the orifice meters after the Chisholm correlationhas been applied for a known liquid flow rate. There is a clearscatter greater than ±2%. This was shown by Hall and by Stevento be due to the gas Froude number effect for the 3 inch and 4 inchdata. The BP 2 inch data scatter was attributed to the possibility ofa joint effect of gas densiometric Froude number and diameter. Itcan be seen from Fig. 10 that Chisholm’s correlation gave a ±4%performance for the available data sets.

6. New orifice meter wet gas data sets

Two large and one small orifice meter wet gas data sets havenow become available for further analysis. The large data sets weregathered by wet gas flowmetering joint industry projects at CEESIand NEL. The small data set is an independent 4 inch, 0.65 betaratio, nitrogen/kerosene test at NEL funded by Emerson Process.Tables B.7–B.9 in Appendix B show the ranges of these data sets.Fig. 11 shows the uncorrected gas measurement of the orifice

meters, and the Chisholm correlation performance for a knownliquid flow rate, for the CEESI JIP data. Here, as with all CEESIwet gas differential pressure (DP) meter data, each data point isthe average DP of 50 instantaneous readings. That is, every sixseconds for five minutes, CEESI reads a DP and then averages the


Fig. 11. Orifice meter data uncorrected and corrected by Chisholm (CEESI JIP data).

Fig. 12. Orifice data uncorrected and corrected by Chisholm for DR 0.024 (NEL JIPdata).

DP’s after the fiftieth reading. (This was found by CEESI to give agood result for a steady wet gas flow. No significant difference inresultswas found taking data over longer periods. The details of theNEL DP sample rate of the data used in this paper is not availableto the authors. However, the NEL data discussed in this paper wassupplied by reputable third parties who independently checkedand confirmed the NEL data was trustworthy.)The Chisholm correlation fits the data to ±2%. The CEESI JIP

tested four 4′′ orifice meter beta ratios, i.e. 0.34, 0.40, 0.50 and0.68. The gas densiometric Froude number ranges of these testswere modest, ranging from 0.36 to 3.78. That is, three out offour beta ratios and most of the gas densiometric Froude numberranges were within Chisholm’s data range. It is therefore notsurprising then that Chisholm’s correlation fits this data set verywell. However, it is also noteworthy that the greatest errors (i.e.+1.5% to+2%) are for both the 0.68 beta ratiometer and for the 0.5beta ratiometerwith the higher gas densiometric Froude numbers.Here then, the 0.68 beta ratio data suggests that the beta ratio andgas densiometric Froude numbers counter effects do not cancelout completely, the large beta ratios lower over-reading is notcompletely compensating for the higher gas densiometric Froudenumbers effect (Frg > 2). The 0.5 beta ratio meters gas flow rateprediction errors greater than +1% all have Frg > 2, i.e. abovethe majority of Chisholm’s wet gas flow gas densiometric Froudenumber values.Figs. 12–17 show the uncorrected gas flow measurement of

the 4′′, 0.66 beta ratio orifice meter tested by the NEL JIP, andthe Chisholm correlation performance for a known liquid flowrate. The Chisholm correlation fits the data to−5%/+4%. Here, theChisholm correlation over predicts the over-reading for low gasdensiometric Froude numbers and therefore under predicts the gas




flow rate, and under predicts the over-reading for high gas Froudenumbers and therefore over predicts the gas flow rate. The low gasdensiometric Froude numbers are within Chisholm’s range, so it islikely that it is the 0.66 beta ratio causing the difference, as this cantend to have a smaller over-reading than the beta ratios to whichChisholm fitted wet gas data. The high gas densiometric Froudenumbers are well above Chisholm’s range and hence cause a largerover-reading (above what the high beta ratio can compensate for).There is a subsequent over prediction of gas flow rate after theChisholm correction is applied for a known liquid flow rate.These two new large data sets therefore agreewith the previous

findings. Chisholm’s correlation is generally applicable but itcan give errors greater than ±2% for high gas Froude numbers(Frg > 2) and/or larger beta ratio (β > 0.5) orifice plate


Fig. 16. All density ratio Orifice data uncorrected and corrected by Chisholm (NELJIP data).

Fig. 17. All NEL wet gas JIP Orifice data corrected by Chisholm.

meters. The authors therefore decided to investigate whether itwas possible to improve Chisholm’s correlation. De Leeuw hadchanged the Chisholm exponent n from a constant value to afunction of the gas Froude number for his Venturi meter. It wastherefore considered necessary to update the Chisholm exponent nfor the orificemeter to be a function of the gas densiometric Froudenumber. This would be done usingwet gas flow data across the fullrange of beta ratios available (i.e. 0.34 ≤ β ≤ 0.68) to absorb thesmall beta ratio effect into the correlation uncertainty.Data sets from the NEL JIP, a portion of the CEESI JIP, the Emer-

sonProcessNELdata andhigher beta Chevron/ConocoPhillips/CEESItests were used to fit the new Chisholm exponent n to the gas den-siometric Froude number. With a new correlation, the remainingindependent data sets could be used to validate the performanceof the data fit. It took a number of iterations of possible equationsand their constants before all the NEL and CEESI data sets fitted thenew correlation to a satisfactory performance.

7. Modifications of the Chisholm orifice meter wet gascorrelation

The first step was to replicate de Leeuw’s Venturi meter plotof Chisholm’s exponent n vs. gas Froude number, Fig. 18. Thiswas done by isolating each combination of gas to liquid densityratio and gas densiometric Froude number from the selected data,and plotting the data as Lockhart–Martinelli parameter vs. over-reading.The individual data sets were then fitted to the Chisholm/de

Leeuw equation set (9) and (10). Fig. 19 shows a sample ofthis procedure. Table C.1 in Appendix C show the results of thisexercise. Plotting Chisholm’s exponent n vs. gas Froude numberfor the selected orifice wet gas data gave Fig. 20. Although there

0.5

0.4

0.3

0.2

0.1

0.6

Coevorden data set

Var

iabl

e n

00.5 1 1.5 2 2.5 3 3.5 4 4.50

Gas Froude Number

5

Fig. 18. Plot of Chisholm exponent n vs. gas densimetric Froude number (DeLeeuw [14]).

Fig. 19. 4 inch, 0.66 beta orifice meter data DR 0.046 and Frg2.97 (NEL JIP data).

Fig. 20. 4 inch, 0.66 beta orifice meter Chisholm exponent n vs. Frg (NEL JIP data).

was some scatter, it was immediately apparent that the orificemeter had a very similar response to de Leeuw’s Venturi meter.The low gas Froude number (Frg) flows were stratified flows andthe Chisholm exponent was a constant below a Froude number ofapproximately 1.5. In Fig. 1 this is shown to be the approximatetransition value between stratified and annular mist.Whereas de Leeuw had claimed his 4 inch, 0.4 beta Venturi

meter had a constant Chisholm exponent of 0.41 for Frg ≤ 1.5,Chisholm had claimed that orifice meters (with diameter between2.5 and 4 inch, and beta less than 0.5) had a constant Chisholmexponent of 0.25 for all his data. The analysis of the combineddata sets suggested that the Chisholm exponent was 0.214 forFrg ≤ 1.5. Therefore at Frg > 1.5, where the flow patternbecomes annularmist, a data fit is required that links the Chisholmexponent to the gas densiometric Froude number. The boundaryconditions of this data fit were required to be that at Frg = 1.5 the


Fig. 21. All orifice meter data uncorrected & corrected by Chisholm’s equation forknown liquid rate.

Fig. 22. All orifice meter data corrected by Chisholm’s correlation for known liquidflow rate.

Chisholm exponent shall be (approximately) 0.214 and as statedearlier, as the gas densiometric Froude number tends to infinity,the exponent n should approach homogeneous flow, i.e. n→ 0.5.The data fit was:

for Frg ≤ 1.5 n = 0.214 (14)

and for Frg > 1.5 n =

{(1√2

)−

(0.3√Frg

)}2. (15)

In fact, the data sets suggest that the orificemeter is rather resistantto the homogeneous model (n = 0.5). As the gas densiometricFroude number rises, the over reading of the orifice meter doestend towards the homogeneous model (as theory predicts) butthe approach is slow. This data suggests that gas densiometricFroude number values well in excess of any industrial applicationwould be required before the orifice meter acted as if it was seeinghomogeneous wet gas flow. Nevertheless, Eq. (15) is designed toconverge on the homogeneous model as theory requires.

8. Comparison of Chisholm and the new orifice meter wet gascorrelation

Figs. 21–24 show the comparison between Chisholm’s corre-lation, defined by Eqs. (9)–(11) and the new correlation, definedby Eqs. (9), (10), (14) and (15). Fig. 21 shows all the uncorrectedreadings and Chisholm correlation corrected gas flow rate predic-tions. Fig. 22 shows the corrected gas flow rate predictions for

Fig. 23. All wet gas orificemeter data uncorrected & corrected by new equation forknown liquid rate.

Fig. 24. All wet gas orifice meter data corrected by new correlation for knownliquid flow rate.

the Chisholm correlation (for known liquid flow rates). There are1010 wet gas test points with 0 < XLM ≤ 0.35, with Chisholm’scorrelation correcting 92.7% of the data to within ±2%. Exclud-ing data at XLM ≤ 0.02, where the error induced on the gas pre-diction is of similar uncertainty to the wet gas corrections, thereare 699 points. Chisholm still has a performance of−5% to+4.3%,but corrects only 90.1% of the data to within ±2%. Therefore, theChisholm correlation corrects all known orifice meter wet gas datafor a known liquid flow rate to±2% within a 90% confidence level.The data that does not lie within the ±2% band is not consideredto be randomly spread but a direct consequence of the correlationnot taking account of the gas densiometric Froude number effect.The Chisholm correlation corrects all known orifice meter wet gasdata for a known liquid flow rate to±2.8%within a 95% confidencelevel.Fig. 23 shows the uncorrected readings and and new modified

Chisholm correlation corrected gas flow rate predictions. Fig. 24shows the corrected gas flow rate predictions for the newmodifiedChisholm correlation (for known liquid flow rates). Taking the1010 points in the range of 0 < XLM ≤ 0.35 the new correlationcorrects 98.3% of the data to within ±2%. The spread is −2.4% to+2.9%. Again, excluding data at XLM ≤ 0.02 the new equation stillcorrects 98.0% of the 699 points to within±2%with the spread stillbeing −2.4% to +2.9%. Therefore, the new correlation corrects allknown orifice meter wet gas data for a known liquid flow rate to±2% within a 95% confidence level.


9. Conclusions

Orifice meters can be used to meter wet gas flow, as the orificemeter gives a predictable responsewithwet gas flow. Data from anorifice plate meter operating with wet gas flow is repeatable andreproducible. The orifice meter does not continually dam up anddoes not give unsteady erratic readings when used with wet gasflow (as is often suggested). Instead, the wet gas flow immediatelyfinds some equilibrium condition with the plate, with some smallconstant quantity of liquid held up in the vicinity of the plateand, from then on, the oncoming liquid flow of the wet gas flowsthrough with the gas flow. The resulting steady wet gas flowthrough the orifice produces DP’s that give good averaged values,hence the repeatable and reproducible test results.The orifice meter wet gas response appears to be less sensitive

to changes in parameters such as beta ratio, liquid properties andgas densiometric Froude numbers than other DP meter designs,such as Venturi meters and cone meters. However, there arestill small but significant beta ratio and gas densiometric Froudenumber effects. Chisholm’s correlation does not account for these.When accounting for the gas densiometric Froude number with asimple modification to Chisholm’s equation, and using data from awider beta ratio range to fit the correlation, the performance of thecorrelation significantly improved. The new correlation correctsthe gas flow rate to within ±2% at 95% confidence level across allthe available data sets.In 2007, Hall and Steven [4] suggested that wet gas data

collected for a 2 inch orifice, had a lower over-reading than wetgas data for a 4 inch orifice, and postulated that the differencecould be due to a diameter effect. Here, the new orifice meterwet gas correlation taking account of the gas densiometric Froudenumber effect fits most of this 2 inch data set to 0 to −2%. Thereare a few outliers for the 2 inch data. It is therefore concludedfrom this evidence that some of the relatively poor fits found forthe Chisholm correlation on the 2 inch data was due to the gasdensiometric Froude number effect and not diameter. However,the data still suggests that there could be a diameter effect. Thereis not enough data for different diameter orifice meters for anyconclusive statement to be made on this matter.

Acknowledgments

The authors acknowledge the contributions of BP, CEESI,Chevron, ConocoPhillips, Emerson Process, and the sponsors of theTÜV NEL and CEESI wet gas JIP’s in making data sets available foranalysis.

Appendix A

The homogeneous flow model assumes the gas and liquidphases flow at the same velocity and are perfectly mixed togetherso as they flow as a single phase flow with an averaged fluiddensity. This then allows the application of the single phase DPmeter equation. The algebraic steps to develop the homogeneousmodel are as follows. Let ν be the specific volume, and ρ thedensity. Subscripts denote the phases. Let Mtotal be the total massof a homogeneous mix held in a volume Vtotal.

νhomogenous =1

ρhomogenous(A.1)

then νhomogenous =VtotalMtotal

=Vliquid + VgasMtotal

=VliquidMtotal

+VgasMtotal

. (A.2)

The flow quality/dryness fraction (x) definition is:

x =mgas

mgas + mliquid=mgasmtotal

(A.3)

Table B.1Orifice meter, CEESI, 3 inch, various beta (ConocoPhillips).

Parameter Range

Pressure 6.7 to 78.9 barDifferential pressure 13.4 to 568 mbarApprox max gas flow rate at 6.7 bar — 1.8 MMscf/d (330 m3/h)

at 42 bar — 13.9 MMscf/d (382 m3/h)at 79 bar — 18.3 MMscf/d (253 m3/h)

Gas to liquid density ratio 0.0066 to 0.089Frg range 0.22 to 5.31XLM <0.080Inside full bore diameter 0.0783 m (3.083 inch)Beta 0.2433, 0.3649, 0.4865, 0.7298Gas phase Natural gas (94 mol% CH4)Liquid phase Decane

Table B.2Orifice meter, CEESI, 4 inch, 0.680 beta (Chevron).

Parameter Range

Pressure 32 to 57 barDifferential pressure 9.95 to 1620 mbarApprox max gas flow rate 32 bar — 18.5 MMscf/d (680 m3/h)

57 bar — 33.5 MMscf/d (663 m3/h)Gas to liquid density ratio 0.044 to 0.081Frg range 0.67 to 7.25XLM <0.250Inside full bore diameter 0.10226 m (4.026 inch)Beta 0.6800Gas phase Natural gas (94 mol% CH4)Liquid phase Stoddard solvent

1− x =mliquid

mgas + mliquid=mliquidmtotal

. (A.4)

For a unit time a set mass of liquid and gas flows so the flow ratesymbol is dropped here. Substitution of Eqs. (A.3) and (A.4) intoEq. (A.2) for a unit of time therefore gives:

νhomogenous =Vl(Ml1−x

) + Vg(Mgx

) = 1ρhomogenous

= xVgMg+ (1− x)

VlMl, i.e.: (A.5)

1ρhomogenous

=xρg+1− xρl

(A.6)

ρhomogenous =ρgρl

ρlx+ ρg(1− x). (A.7)

For a homogenized flow this density value is applied to the singlephase DPmeter equation alongwith the actual two-phase DP read.That is:

mtotal = EAtK√2ρhomogenous1Ptp (A.8)

and so: mg = xmtotal = xEAtK√2ρhomogenous1Ptp. (A.9)

Or substituting Eq. (A.7) into Eq. (A.9) and re-arranging gives:

mg = x

EAtK√2ρg1Ptp√

ρgρl+ x

(1− ρg

ρl

) = x

mg,apparent√ρgρl+ x

(1− ρg

ρl

) . (A.10)

Note that when the gas is dry (i.e. the quality (x) is unity) thehomogeneous equations reduce to the single phase equations.Due to the assumption of fully mixed flow, it is usually

considered only appropriate when the gas to liquid density ratiois high, flow rates are very high and the flow pattern is mist flow.


Table B.3Orifice meter, CEESI, 4 inch, 0.497 beta (Chevron, ConocoPhillips, CEESI).

Parameter Range

Pressure 17.2 to 59 barDifferential pressure 62.2 to 1860 mbarApprox max gas flow rate 18 bar — 8.8 MMscf/d (589 m3/h)

32 bar — 10.4 MMscf/d (382 m3/h)59 bar — 14.9 MMscf/d (284 m3/h)

Gas to liquid density ratio 0.018 to 0.083Frg range 0.62 to 2.78XLM <0.264Inside full bore diameter 0.10226 m (4.026 inch)Beta 0.497 (nominal 0.5)Gas phase Natural gas (94 mol% CH4)Liquid phase Stoddard solvent

Table B.4Orifice meter, CEESI, 4 inch, 0.338 beta (Chevron, ConocoPhillips, CEESI).

Parameter Range

Pressure 17.2 to 58.5 barDifferential pressure 0.750 to 1870 mbarApprox max gas flow rate 18 bar — 8.8 MMscf/d (589 m3/h)

31.6 bar — 10.6 MMscf/d (395 m3/h)58.5 bar — 15.0 MMscf/d (288 m3/h)

Gas to liquid density ratio 0.017 to 0.084Frg range 0.6 to 1.35XLM <0.264Inside full bore diameter 0.10226 m (4.026 inch)Beta 0.338 (nominal 0.34)Gas phase Natural gas (94 mol% CH4)Liquid phase Stoddard solvent

Table B.5Orifice meter, CEESI, 4 inch, 0.683 beta (BP, 2005).

Parameter Range

Pressure 60 barDifferential pressure 82.1 Pa to 1420 mbarApprox max gas flow rate 60 bar — 37.8 MMscf/d (707 m3/h)Gas to liquid density ratio 0.0648 onlyFrg range 1.5 to 6.0XLM <0.340Inside full bore diameter 0.10226 m (4.026 inch)Beta 0.6831Gas phase Natural gas (94 mol% CH4)Liquid phase Stoddard solvent

Table B.6Orifice meter, CEESI, 2 inch, 0.516 beta (BP, 2005).

Parameter Range

Pressure 53 to 58 barDifferential pressure 54.7 to 1550 mbarApprox max gas flow rate 2.7 MMscf/d (52 m3/h)Gas to liquid density ratio 0.039 to 0.055Frg range 0.87 to 4.65XLM <0.550Inside full bore diameter 0.04928m (1.940 inch)Beta 0.5155Gas phase Natural gas (94 mol% CH4)Liquid phase Stoddard solvent and water

It is difficult to know in practical situationswhen the gas and liquidphases are in a homogeneous mix and when they are not.Note that Eq. (1) defines the Lockhart–Martinelli parameter and

by substituting Eqs. (A.3) and (A.4) into Eq. (1) gives:

XLM =mlmg

√ρg

ρl=1− xx

√ρg

ρl(A.11)

Table B.7Orifice meter, CEESI, 4 inch, various beta (CEESI wet gas JIP, 1999–2002).

Parameter Range

Pressure 15 to 76 barDifferential pressure 4.48 to 995 mbarApprox max gas flow rate 15 bar — 4.5 MMscf/d (363 m3/h)

45 bar — 15 MMscf/d (383 m3/h)75 bar — 26 MMscf/d (381 m3/h)

Gas to liquid density ratio 0.014 to 0.111Frg range 0.36 to 3.78XLM <0.180Inside full bore diameter 4.026 inchBeta 0.3414, 0.4035, 0.4965 & 0.6826.Gas phase Natural gas (94 mol% CH4)Liquid phase Decane

Table B.8Orifice meter, NEL, 4 inch, beta 0.660 (NEL wet gas JIP, 2005).

Parameter Range

Pressure 16.2 to 62.6 barDifferential pressure 49.8 to 2380 mbar

(Most data< 1200 mbar)Approx max gas flow rate 16 bar — 7.1 MMscf/d (548 m3/h)

31 bar — 13.5 MMscf/d (536 m3/h)46 bar — 20.1 MMscf/d (536 m3/h)61 bar — 26.6 MMscf/d (535 m3/h)

Gas to liquid density ratio 0.023 to 0.091Frg range 1.06 to 5.46XLM <0.300Inside full bore diameter 0.10228 m (4.027 inch)Beta 0.6598Gas phase NitrogenLiquid phase Exxsol D80

Table B.9Orifice meter, NEL, 4 inch, beta 0.650 (Emerson Process, 2005).

Parameter Range

Pressure 16.1 to 62.1 barDifferential pressure 14 to 703 mbarApprox max gas flow rate 16 bar – 7.0 MMscf/d (541 m3/h)

61 bar – 13.0 MMscf/d(261 m3/h)

Gas to liquid density ratio 0.023 < DR < 0.09Frg range 0.5 < Frg < 2.7XLM 0 ≤ Xlm < 0.35Inside full bore diameter 0.10228 m (4.028 inch)Beta 0.650Gas phase NitrogenLiquid phase Exxsol D80

i.e.

x =1

1+{XLM

√ρlρg

} . (A.11a)

Substituting (A.11a) into Eq. (A.10) gives the homogeneous modelin terms of the Lockhart–Martinelli parameter.

mg =EAtK

√2ρg1Ptp(

1+ XLM√

ρlρg

)√ρgρl+

(1−

ρgρl

)(1+XLM

√ρlρg

). (A.12)

Rearranging gives:

mg =EAtK

√2ρg1Ptp√{(

1+ XLM√

ρlρg

)2 ρgρl

}+

{(1+ XLM

√ρlρg

) (1− ρg

ρl

)} . (A.12a)


Table C.1Fitted Chisholm exponent values.

DR g/l Frg Exponent ‘‘n’’

NEL JIP 0.66 Beta 0.0235 1.05 0.2NEL JIP 0.66 Beta 0.0236 1.58 0.2NEL JIP 0.66 Beta 0.0237 2.12 0.24NEL JIP 0.66 Beta 0.0239 2.67 0.27NEL JIP 0.66 Beta 0.0452 1.48 0.2NEL JIP 0.66 Beta 0.0454 2.22 0.235NEL JIP 0.66 Beta 0.0456 2.97 0.26NEL JIP 0.66 Beta 0.0459 3.73 0.29NEL JIP 0.66 Beta 0.0673 1.82 0.2NEL JIP 0.66 Beta 0.0675 2.74 0.24NEL JIP 0.66 Beta 0.0678 3.66 0.27NEL JIP 0.66 Beta 0.0683 4.60 0.31NEL JIP 0.66 Beta 0.0887 2.11 0.215NEL JIP 0.66 Beta 0.0889 3.17 0.24NEL JIP 0.66 Beta 0.0893 4.24 0.28NEL JIP 0.66 Beta 0.0900 5.34 0.33CVX/COP/CEESI 0.68 Beta 0.0459 1.37 0.21CVX/COP/CEESI 0.68 Beta 0.043 2.65 0.28CVX/COP/CEESI 0.68 Beta 0.0435 3.88 0.29CVX/COP/CEESI 0.68 Beta 0.044 4.93 0.3CVX/COP/CEESI 0.68 Beta 0.08 1.86 0.22CVX/COP/CEESI 0.68 Beta 0.08 3.65 0.28CVX/COP/CEESI 0.68 Beta 0.082 5.64 0.31CVX/COP/CEESI 0.68 Beta 0.083 7.23 0.33CVX/COP/CEESI 0.5 Beta 0.044 0.69 0.21CVX/COP/CEESI 0.5 Beta 0.085 0.725 0.22CVX/COP/CEESI 0.5 Beta 0.045 1.35 0.23CVX/COP/CEESI 0.5 Beta 0.082 1.38 0.22CVX/COP/CEESI 0.5 Beta 0.045 2.67 0.33CVX/COP/CEESI 0.5 Beta 0.082 2.67 0.33Emerson 0.65 Beta 0.023 0.52 0.21Emerson 0.65 Beta 0.023 1.57 0.23Emerson 0.65 Beta 0.024 2.648 0.29Emerson 0.65 Beta 0.089 1.06 0.2Emerson 0.65 Beta 0.089 2.65 0.25CEESI JIP 0.68 Beta 0.083 3.21 0.335CEESI JIP 0.68 Beta 0.089 1.88 0.31CEESI JIP 0.68 Beta 0.104 4.04 0.36CEESI JIP 0.68 Beta 0.0464 2.51 0.29

This in turn can be expanded out and after terms cancel the re-maining expression can be expressed as:

mg =EAtK

√2ρg1Ptp√

1+{√

ρgρl+

√ρlρg

}XLM + X2LM

=mgApparent√

1+ CXLM + X2LM(9)

where: C =√ρg

ρl+

√ρl

ρg(A.13)

i.e.: C =(ρg

ρl

)n+

(ρl

ρg

)n(10)

and n = 12 .

Chisholm derived n = 0.25 using a stratified flow model. Hereit is shown that for a homogenized wet gas flow n = 0.5.

Appendix B

List of available orifice plate wet gas flow data and their rangesgiven in Table series B.

Appendix C

Result of fitting Chisholm exponent n to the NEL JIP orifice platemeter data for set gas to liquid density ratio and gas densiometricFroude number combinations shown in Table C.1.

References

[1] International Standards Organisation. Measurement of fluid flow by meansof pressure differential devices inserted in circular cross-section conduitsrunning full. In: ISO 5167, Part 2: Orifice plates.

[2] ChisholmD. Flow of incompressible two-phasemixtures through sharp-edgedorifices. Journal of Mechanical Engineering Science 1967;9(1).

[3] Chisholm D. Research note: Two-phase flow through sharp-edged orifices.Journal of Mechanical Engineering Science 1977;19(3).

[4] Hall ARW, Steven R. Newdata for the correlation of orifice platemeasurementswith wet gas flow conditions. In: International south east Asia hydrocarbonflow measurement workshop. 2007.

[5] Steven R, Ting VC, Stobie G. A re-evaluation of axioms regarding orifice meterwet gas flow performance. In: International south east Asia hydrocarbon flowmeasurement workshop. 2007.

[6] Steven R, Britton C, Kinney J. Comparisons between horizontally installedstandard and non-standard flange tapped orifice plate meter wet gas flowresponses. In: FLOMEKO 2007. 2007.

[7] Steven R, Kinney J. Wet gas flow metering with horizontally installed simpleDP meter technologies. In: Global conference on fluid flow and control. 2007.

[8] Hall ARW, Griffin D, Steven R. A discussion on wet gas flow parameterdefinitions. In: North sea flow measurement workshop. 2007.

[9] Steven R. Horizontally installed differential pressure meter wet gas flowperformance review. In: North sea flow measurement workshop. 2006.

[10] Taitel Y, Dukler AE. A model for predicting flow regieme transitions inhorizontal and near horizontal gas — liquid flow. AIChE Journal 1976;22(1).

[11] De Leeuw R. Liquid correction of venturi meter readings in wet gas flow. In:North sea workshop. 1997.

[12] Stewart DG. Application of differential pressure meters to wet gas flow. In:2nd international south east Asia hydrocarbon flow measurement workshop.2003.

[13] Steven R. Liquid property and diameter effects on venturi meters used withwet gas flows. In: International fluid flow measurement symposium. 2006.

[14] Reader-Harris MJ, Hodges D, Gibson J. Venturi-tube performance in wet gasusing different test fluids. NEL Report 2005/206. 2005.

[15] Reader-Harris MJ. Venturi-tube performance in wet gas using different testfluids. In: North sea flow measurement workshop. 2006.

[16] Ting VC. Effects of nonstandard operating conditions on the accuracy of orificemeters, Society of Petroleum Engineers Production and Facilities. 1993.

Orifice plate meter wet gas flow performance

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