Wet gas metering with a horizontally mounted Venturi meter

Flow Measurement and Instrumentation 12 (2002) 361–372www.elsevier.com/locate/flowmeasinst

Wet gas metering with a horizontally mounted Venturi meter

R.N. Stevena,b,∗

a Flow Centre, NEL, East Kilbride, Glasgow, G75 0QU, UKb Department of Mechanical Engineering, University of Strathclyde, Glasgow, UK

Received 15 May 2001; received in revised form 9 January 2002; accepted 9 January 2002

Abstract

Wet gas metering is becoming an increasingly important problem to the Oil and Gas Industry. The Venturi meter is a favoureddevice for the metering of the unprocessed wet natural gas production flows. Wet gas is defined here as a two-phase flow with upto 50% of the mass flowing being in the liquid phase. Metering the gas flowrate in a wet gas flow with use of a Venturi meterrequires a correction of the meter reading to account for the liquids effect. Currently, most correlations in existence were createdfor Orifice Plate Meters and are for general two-phase flow. However, due to no Venturi meter correlation being published before1997 industry was traditionally forced to use these Orifice Plate Meter correlations when faced with a Venturi metering wet gasflows. This paper lists seven correlations, two recent wet gas Venturi correlations and five older Orifice Plate general two-phaseflow correlations and compares their performance with new independent data from the NEL Wet Gas Loop with an ISA ControlsLtd. Standard specification six inch Venturi meter of 0.55 beta ratio installed. Finally, a new correlation is offered. 2002 ElsevierScience Ltd. All rights reserved.

Keywords: Wet gas metering; Two-phase flow metering; Venturi meter; Flow measurement

1. Introduction

Wet natural gas metering is becoming an increasinglyimportant technology to the operators of natural gas pro-ducing fields. With many gas fields coming to the latterstages of their production lives their previously dry gasflows are becoming “wet” when the heavier hydrocarboncomponents condense due to the reducing pressure in theproduction lines and changing conditions in the wellitself can also cause water to be present in the flow. Also,when some wells produced wet gas flows from the pro-duction outset the separator on the off-shore platformwas sized accordingly, so with an increasing amount ofliquid present in the wells later life these separators areundersized and the result is a wet gas leaving the separ-ators “dry” gas outlet to the dry gas meters. These oper-ators are also encountering wet gas flows when, due totheir desire to utilize the existing off-shore infrastruc-tures to the maximum, they open “marginal” fields.

∗ Present address: McCrometer Inc., 3255 Weat Stetson Avenue,Hemet, CA 92545-7799, USA. Tel.:+1-909-765-5344; fax:+1-909-652-3078.

E-mail address: [email protected] (R.N. Steven).

0955-5986/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0955-5986 (02)00003-1

These are relatively small fields that produce wet gasflows in the vicinity of these older larger wells and thetwo wells flows are combined upstream of the nowcommunal off-shore platform. That is, small fields thatproduce wet gas flows from the outset and would not beprofitable if they required their own infrastructures (i.e.off-shore platforms with a separator) are being tappedby running this wet gas flow to the neighbouring mainwell’s production pipeline upstream of the separator.There is therefore a necessity to meter this wet gas flowprior to the mixing point as traditionally the platformsare designed to have gas flow metered after the separ-ator.

“Wet Gas” is a term commonly used in the industrybut as yet no one definition has been agreed upon. As aresult every operator, meter manufacturer and academictends to have his own definition. These can vary con-siderably but there is general agreement that the termdenotes a relatively small amount of liquid in a flow thatis predominantly of gas. This research decided to adoptthe Shell Expro definition of the wet gas range, whichis a flow with a Gas Volume Fraction greater than 95%.That is, the gas phase occupies in excess of 95% of thepipe volume. At the flow conditions typical in the North

362 R.N. Steven / Flow Measurement and Instrumentation 12 (2002) 361–372

Nomenclature

D the pipe diameterAt the area of the Venturi throatKg,l the gas and liquid flow coefficients (i.e. for each phase, the respective product of the velocity of

approach, the discharge coefficient and the expansibility factor)

m. g,l,tp the gas, liquid and two-phase flowrates respectively�Pg,l the superficial gas and liquid differential pressures between the upstream and throat tappings

respectively�Ptp the actual two-phase differential pressures between the upstream and throat tappingsrg,l the gas and liquid densities respectivelyx the “quality” of a two-phase flow, i.e. the ratio of the gas to total mass flowrateX the modified Lockhart–Maretinelli parameter, defined as the square root of the ratio of �P1 & �Pg

Frg the gas densiometric Froude numberUsg the superficial gas velocityg the gravitational constant (9.812 m/s2)

Sea natural gas production this loosely translates to themaximum liquid content for wet gas being when theliquid phase has equal mass to the gas phase. Beyondthis limit is considered to be general two-phase/multi-phase flow.

Currently, wet gas metering is a technology in itsinfancy. No meter design has yet to prove itself to becapable of metering wet gas flows to the accuracydesired by industry. However, one of the favoured met-ers for wet natural gas production flow metering is theVenturi meter. Like all Differential Pressure (DP) metersthe Venturi meter readings of the wet gas flow areadversely affected by the liquid presence. That is, theliquid presence directly affects the pressure differentialread by the Venturi between the upstream and throatpressure tappings. Therefore, in order to derive the cor-rect gas flowrate a correlation needs to be applied. Thereare only two wet gas Venturi correlations known to thegeneral industry and these have only been available forthe last few years. As Venturis have been used longbefore this for metering wet gas flows traditionallyindustry used general two-phase flow Orifice Plate metercorrelations due to a lack of any alternatives. The currentproblem facing operators is that nobody knows which ofthe existing correlations is the most accurate whenapplied to wet gas Venturi meters. There is a distinctlack of independent data to check the performance ofeach correlation. All existing data has been used in thecreation of the existing correlations.

This paper uses independent data obtained from theNEL wet gas loop with an installed standard North Seaspecification Venturi supplied by ISA Controls Ltd tocheck the performance of these two existing wet gasVenturi meter correlations. (It should be noted that theVenturi had two non-standard specifications which werethat the pressure tappings were positioned at the top of

the meter only to stop flooding and there were two extratappings downstream of the diffuser.) Selected OrificePlate meter correlations known to have been used oravailable for use by operators prior to these wet gas Ven-turi meter correlations existence were also included inthis comparison. After this comparison trends in the dataare discussed and a new correlation is offered that moreaccurately fits the ISA Controls Venturi meter geometry.Unfortunately, due to the lack of both new independentdata and the unavailability of the small quantity of exist-ing data used to create the two existing wet gas Venturicorrelations it has not been possible to compare this newcorrelation with other data sets.

2. Differential pressure meter correlations

Before the existence of the two wet gas Venturi corre-lations industry was forced to choose between existinggeneral two-phase flow Orifice Plate meter correlations.Of the many that exist (a good summary is given by Lin[1]) this research judged five to be suitable for use withactual production wet natural gas flows. The others weredisregarded as the data used to create them was judgedunsuitable, e.g. the liquid to gas flow ratio, the fluid typecombination, the pipe diameter, the pressure, theflowrates, etc. not being within reasonable agreementwith actual gas production flows. It should be noted thatthe following five Orifice Plate meter correlations didnot have perfect matches of test to actual conditionseither but were judged to be closer than the others. (Thechoice was therefore subjective.) These correlations allwork on the same principle of using the DP meter singlephase equation (Eq. 1) and then applying a correctionfactor based on the liquid quantity to correct for the factthat in wet gas flows a two-phase differential pressure

363R.N. Steven / Flow Measurement and Instrumentation 12 (2002) 361–372

(�Ptp) is read instead of the single phase pressure differ-ential (�Pg).

m. g � KgAt�2rg�Pg (1)

These five Orifice Plate meter correlations and the twoVenturi meter correlations all assume that the flows areincompressible, that there are no appreciable thermodyn-amic effects and the liquid flowrate is initially known.Also, the authors of these correlations assume that thedifference between the actual gas mass flow and the indi-cated gas mass flow is due to the effect of the liquidpresence alone. That is, any dry gas metering errors wereignored. The five Orifice Plate correlations here are.

2.1. The homogeneous flow model

The homogeneous flow model treats the two-phaseflow as if it were a single-phase flow by using a homo-geneous density expression (Eq. 2) which averages thephase densities so that the single-phase Orifice Platemeter equation can be used (i.e. Eq. 1).

1rh

�xrg

�1�xrl

(2)

where x is the mass quality, rh is the homogeneous den-sity and subscripts ‘ l’ and ‘g’ are for liquid and gasrespectively. Therefore substituting this homogeneousvalue for density into Eq. (1) and replacing �Pgwith�Ptp and rearranging gives Eq. (3).

m. g � x.� KgAt�2rg�Ptp

��rg

rl� x�1�

rg

rl�� (3)

(Note: In dry gas (i.e. x � 1) Eq. (3) reduces to Eq. (1)as �Ptp � �Pg).

Note that unlike the other correlations discussed inthis paper the homogeneous model is not actually a cor-relation as no data was used in its creation. Also unlikethe other correlations it takes no account of the flow pat-tern. Many researchers now considered it important totake account of the flow pattern when correcting theerror in a DP meter caused by the presence of liquid.This is because although the physical mechanismsinvolved in the phase interaction during two-phase flowthrough a Venturi are not well understood it is clear thatthe flow pattern affects the pressure loss in the flow andtherefore directly effects the pressures read by the meter.The most recent flow pattern map (see the Shell ExproFlow Pattern Map [2]) and the semi-empirical flow pat-tern prediction method (see the Taitel and Duckler [3])predict that typical wet natural gas production flows willhave annular dispersed (or “mist” ) flows. That is, the

liquid is likely to be entrained in droplet form in the gasflow. (It should be noted here that horizontal and verticalflows of otherwise similar conditions have different flowpatterns and hence wet gas DP meter correlations arerestricted to the orientation of the meter used to collectthe data sets used in their creation. This paper discusseshorizontal flow only.)

2.2. The Murdock correlation

The Murdock correlation [4] is based on Orifice Platemeters and it was formed with a large data setencompassing general two-phase flow and it is thereforenot restricted to wet gas flows. Murdock’s method wasto consider the two-phase flow to be separated (or“stratified” ) flow. This was the first indirect indicationin a published paper that the flow pattern is importantwhen predicting a DP meters liquid induced error. How-ever, it should be noted that the modeled flow pattern isnot the flow pattern that typically exists in wet naturalgas production. The Murdock correlation is given asEq. (4).

m. g �KgAt�2rg�Ptp

1 � 1.26m. l

m. g

�Kg

Kl��rg

rl

�KgAt�2rg�Ptp

1 � MX(4)

Note that X is a modified version of the Lockhart–Marti-nelli parameter as it is the ratio of the superficial flowsmomentum pressure drops and not the friction pressuredrops as in the original definition by Lockhart and Marti-nelli. Murdocks definition is:

X � ��Pl

�Pg

� �m. l

m. g

��Kg

Kl��rg

rl

(5)

The value 1.26 represents the gradient of a best fit linethrough all Murdock’s data plotted on the graph��Ptp /�Pgvs. X. Hence Murdock’s correlation factor isa function of X alone.

2.3. The Chisholm correlation

Chisholm published a general two-phase Orifice Platemeter correlation [5] and then later improved it for thecase of higher quality two-phase flows (i.e.X�1) [6].Chisholm’s model assumes stratified flow and the shearforce at the boundary is directly considered. Thisresulted in the correlation allowing for the effect ofpressure independently of the Modified Lockhart–Marti-nelli parameter (X). The Chisholm correlation offered in[6] is given as Eq. (6).



�1 � ��rl

rg�1/4

� �rg

rl�1/4�X � X2

(6)

Note that the Chisholm correlation factor is a functionof X and pressure (through the gas density term).

2.4. The Lin equation

The Lin correlation [7] is for general stratified two-phase flows through Orifice Plate meters. Like Chish-olm, Lin includes the effect of shear between the phasesand the correlation allows for the independent effects ofpressure and liquid mass content. The Lin correlation isgiven as Eq. (7) with one of the terms θ (i.e. the “shearfunction” ) expanded in Eq. (8).

m. g �KlAt�2rl�Ptp

�m. l

m. g

�q � �rl

rg

(7)

where:

q � 1.48625�9.26541(rg /rl) � 44.6954(rg /rl)2

�60.615(rg /rl)3�5.12966(rg /rl)4 (8)� 26.5743(rg /rl)5

Note that Lin chose to use the liquid single phase equ-ation in the numerator as he was dealing with generaltwo-phase flow.

2.5. The Smith & Leang correlation

The Smith & Leang correlation [8] is formed for Ori-fice Plate and Venturi meters using the concept of a“Blockage Factor” . That is, Eq. (1) can be altered to takeaccount of the liquid presence by introducing a para-meter that accounts for the partial blockage of the pipearea by the liquid. The letters ‘BF’ denote this parameter.Eq. (9) gives the BF factor and Eq. (10) gives the Smithand Leang correlation.

BF � 0.637 � 0.4211x�0.00183

x2 (9)

and

m. g � KgAt(BF)�2rg�Pg (10)

Hence, the Smith and Leang correlation corrects for theliquid induced error by a correction factor that is a func-tion of the flow quality (x) alone.

The two more recent wet gas Venturi meter corre-lations are.

2.6. The modified Murdock correlation

In 1998 Phillips Petroleum informed this author thatthey had logged wet gas Venturi data from an actualproduction well and had then used the data to update theMurdock correlation (i.e. change the gradient M from1.26 to 1.5.) The resulting correlation was used in-houseand never published. The pressure was 45 bar but noother parameters are known. The correlation is given asEq. (11).


1 � 1.5m. l

m. g

�Kg

Kl��rg

rl

�KgAt�2rg�Ptp

1 � MX(11)

2.7. The de Leeuw correlation

The de Leeuw correlation is the only Venturi wet gascorrelation yet published. de Leeuw claims the liquidinduced error in the gas flow prediction is not onlydependent on the pressure and the Lockhart–Martinelliparameter but also the gas densiometric Froude number(Frg). Eq. (12) shows the gas densiometric Froude num-ber calculation.

Frg �Usg

�gD�rg

rl�rg

(12)

de Leeuws correlation is given in the form of Chisholmscorrelation with the constant of 1/4 replaced by a para-meter denoted as n. de Leeuw claims that n is solely afunction of the gas densiometric Froude number (Frg) asshown in Eqs. (13a) and (13b):

n � 0.41 for 0.5�Frg�1.5 (13a)

n � 0.606(1�e�0.746Frg) For Frg�1.5 (13b)

The fact that there are two values of nis of interest.According to the Shell Expro two-phase flow patternmap [2] the gas densiometric Froude number value of1.5 which divides Eqs. (13a) and (13b) is on the bound-ary of two different flow patterns. Hence, de Leeuw isclaiming the flow pattern plays an important part in themagnitude of the error induced by the gas being wet.The de Leeuw correlation is given as Eq. (14).


�1 � ��rl

rg�n

� �rg

rl�n�X � X2

(14)

It should be noted that de Leeuw used a simplified defi-nition of the Modified Lockhart–Martinelli parameter byassuming the superficial flows flow coefficients to beequal and hence they cancel in Eq. (5). Therefore, pro-


vided the meter geometry, the fluid properties, the liquidflowrate, the pressure, the single phase discharge coef-ficients and the differential pressure between theupstream and throat tappings are known an iteration pro-cedure can predict the gas mass flowrate for each of theabove correlations.

3. The NEL wet gas loop tests

The comparison of these existing correlations and thedevelopment of the new correlation presented in thispaper were achieved by the use of independent dataobtained from the new wet gas loop at NEL. An ISAControls standard North Sea specification 6” Venturimeter with a 0.55 diameter (or “beta” ) ratio of 6 mmpressure tappings was the meter installed. The upstreampressure tapping and the throat pressure tapping lengthswere approximately 1809 and 210 mm respectively. Thissystem uses nitrogen and a kerosene substitute as thefluids simulating wet natural gas flows. (Actual wet natu-ral gas could not be used due to Health and Safetyguidelines).

3.1. A description of the NEL wet gas loop

A schematic diagram of the NEL wet gas loop is givenin Fig. 1(a) (and a simplified line diagram is given inFig. 1(b)) where individual components are itemized.The wet gas separator (item 1) has a volume of approxi-mately 11.2 m3 and was rated to 77 bar. It was upstreamof the blower (item 8) and these components were separ-ated from each other by one ball valve (item 4) at theseparator outlet (item 2) and then two T-junctions. Thefirst T-junction directly downstream of this ball valvehad one line going to the second T-junction while theother line led to another ball valve (item 5) and then themain test line downstream of the test piece (item 17).The purpose of this second line was to allow the systemto operate as a dry gas facility when required. Thissecond T-junction had two butterfly valves, one in theupstream line before the junction (item 6) and one in theblower by-pass line (item 7). That is, the pipeline splitwith one pipe (with no valve) leading to the blower inletand the other pipe (with the valve) by-passing the blowerand the gas cooling system (item 9). The gas blower wasa 200 kW Howden centrifugal blower.

The gas cooling system was a bi-water high pressureair cooler positioned directly downstream of the blower.Once the gas flow left the cooling system it then passedthe next T-Junction (i.e. the blower by-pass rejoining themain pipework) and then the pressurizing/de-pressuriz-ing system (item 10) before turning up through two 900

bends taking it from the basement (the position of allcomponents so far mentioned) into the main gas hall. Astraight length of pipework 10 diameters long down-

stream from the pipe bend led the dry gas flow to aSpearman Flow Conditioner (item 11) and then to thedry gas reference meter (item 12) situated a further 10diameters downstream. This gas reference meter was anInstrumet turbine meter rated to a maximum of 1000m3/h by calibration at NMI. The pressure was read bya Yokogawa Pressure Transducer (0–70 bar). A further10 D downstream from the meter there was a PlatinumResistance PT100 standard temperature probe and 5 Dfurther down was a weir plate (not shown) followed ata further 5 D by the liquid injector position (item 15).Two injector types are used during the experiments tocheck that the injector type did not influence the flowpattern at the inlet to the test meter and hence the meterreadings. An open pipe and then a nozzle both injectingdownstream on the centerline were used, each coveringthe same test matrix. No difference in the meter readingswas found so all the data was grouped together and con-sidered valid.

From the injection point there was a distance of 50 Dto the test piece (item 17) which allowed the two-phasesto mix before the inlet to the test piece. A non-intrusive“Sea Spy” high pressure camera supplied by Tritech Ltdwas installed 10 diameters upstream of the test piece(item 16). The Venturi had the pressure and differentialpressure read by Yokogawa Pressure Tranbsducerswhich were calibrated at NEL. After the test piece thetwo-phase flow continues downstream for 20 D beforereaching a T-junction. One pipe leads to the other T-junction mentioned earlier which forms the dry gas setup (i.e. the isolating the separator) and the other leadsto a double out of plane bend that has a ball valvebetween the bends and takes the two-phase flow verti-cally down back into the wet gas separator inlet (item3) located in the basement. The liquid flowrate was sup-plied by an eleven stage Ingersoll-Dresser pump (item13) which could supply up to 60 m3/h of kerosene. Itwas necessary to use a bank of liquid reference flowmeters (item 14) as the liquid flow range required forthe full wet gas test matrix crossed the range of threedifferent meters. The 1/2” , 1” and 3” turbine meters used(supplied by Emo Ltd) were capable of metering 0.15–1.5 m3/h, 1.5–15 m3/h and 5–150 m3/h respectively andall three were calibrated by NEL. Each had a PT100Temperature Probe positioned upstream to allow a den-sity calculation. They were assembled in parallel to eachother with ball valves before and after each individualmeter. On deciding on the required liquid flowrate priorto each test the appropriate meter is selected, its valvesopened and the others closed.

Naturally, no pump could economically and safelygive the full range of liquid flowrates required so thepump was sized for the maximum required flowrate andan Automatic Re-circulation Valve supplied by Schroed-ahl Ltd (item 18) was set up downstream of the pumpexit to split the minimum practical flowrate from the


Fig. 1. (a) Schematic diagram of NEL wet gas loop. (b) Line diagram of NEL wet gas loop.

pump into two flows, one that leads the required injec-tion flowrate to the injector and one that leads the excessflow back along the return to separator pipe (item 19).The correctly set Automatic Re-circulation Valve judgedby these reference meter readings allows the desired splitbetween the two liquid flows. Therefore, with the correctAutomatic Re-circulation Valve setting the desiredflowrate is then metered and taken to the injection pointby a vertically rising high pressure flexible hose. A finalball valve is positioned directly upstream of the injectorfor extra control.

3.2. The experimental range

The experiments conducted were for three pressures(20, 40 and 60 bar) and four gas flowrates (400, 600,

800 and 1000 m3/h). The liquid flowrates achieved (Ql)are given in Table 1.

For each of the pressures tested it was found that theextra resistance caused by the liquids presence meantthat at a gas flowrate of 1000 m3/h the desired upperrange of the liquid flowrate could not be reached. There-fore, the maximum liquid flowrate at which the blowercould maintain the 1000 m3/h gas flowrate had to be theupper end of the experimental range. The lower liquidflowrate limits were close to zero as possible , i.e. the1/2” liquid reference meter’s minimum limits.

Previously, the lack of any independent wet gas datafor DP meters had meant that an independent compari-son of these existing correlations was not possible. Allexisting data had already been used to form these exist-ing correlations. Hence, with the new data set attained


Table 1The maximum phases flowrates for the three pressures tested

20 bar 40 bar 60 barQg max (m3/h) Ql max (m3/h) Ql max (m3/h) Ql max (m3/h)

400 10.96 22.22 36.44600 16.39 32.15 48.40800 16.36 41.13 65.111000 3.04 13.51 24.25

at the NEL an independent comparison of the existingcorrelations could now be made.

3.3. The performance comparison of the existingcorrelations for the wet gas Venturi meter case

The method of comparing the seven correlations per-formances was chosen to be by comparison of the rootmean square fractional deviation (denoted as ‘δ’ ).

d � �1n

n

i � 1

�m. g(predicted)i�m. g(experimental)i

m. g(experimental)i

�2

(15)

The independent test data from the NEL wet gas loopwas used to find d‘s for each correlation for the wholedata set taken as one and then for each of the three subdata sets created when the full data set was broken downinto three individual pressure data sets. (Note, that arith-metically δ for the whole data set does not necessarilyequal the sum of the δ’s for the three individual pressuredata sets).

The results are shown in Table 2. A secondary methodof comparison was to use the type of plot used by Lin[6], i.e. a plot of the ratio Predicted to Actual Gas Mass

Table 2The results of the root mean square fractional deviation for all pressures together and for each individual pressure

All pressures d 40 bar d

de Leeuw 0.0211 de Leeuw 0.0193Homogeneous 0.0237 Homogeneous 0.0220Lin 0.0462 Murd, M=1.5 0.0410Murd, M=1.5 0.0482 Lin 0.0448Murd, M=1.26 0.0650 Murd, M=1.26 0.0589Chisholm 0.0710 Chisholm 0.0658Smith & Leang 0.1260 Smith & Leang 0.119920 bar d 60 bar dde Leeuw 0.0279 de Leeuw 0.0140Homogeneous 0.0285 Homogeneous 0.0202Lin 0.0449 Murd, M=1.5 0.0287Murd, M=1.5 0.0677 Lin 0.0479Chisholm 0.0793 Murd, M=1.26 0.0504Murd, M=1.26 0.0823 Chisholm 0.0675Smith & Leang 0.1159 Smith & Leang 0.1401

Flowrate vs The Flow Quality for each pressure. Thesegraphs are reproduced in Figs. 2, 3 and 4.

The de Leeuw correlation has the best performance atall the tested pressures. Considering it was created fromdata that was obtained from a Venturi meter that had asimilar flow conditions to the NEL this is perhaps notsurprising. This comparison therefore confirms deLeeuw’s correlation as the best currently available toengineers requiring to meter wet gas flows with Venturimeters. However, like the new correlation developed

Fig. 2. Comparison of correlations at 20 bar.




next in this paper it is still limited to a maximum gasflowrate of 1000 m3/h which is a major problem to thenatural gas production industry as many of the pro-duction flowrates are well in excess of this limit. How-ever, with no test facilities in existence capable of cre-ating higher flowrates the only course of action open tothe operators is to extrapolate the most accurate corre-lation for these lower flowrates. Hence, of the corre-lations tested here, as de Leeuw’s has the best perform-ance it is therefore the best choice for industry whenfaced with a wet gas flow Venturi meter metering prob-lem.

A far more surprising result was the good performanceof the homogeneous model. With no modeling of thelikely flow pattern it was expected it would have one ofthe poorest performances of those tested. However, thissimple model for a pseudo-single phase flow was clearlythe second best performing method of the seven chosenfor comparison. It is possible that as the predicted flowpatterns for the NEL’s test range were all annular-dis-persed flows then much of the liquid would be entrainedin the gas and under such conditions the homogeneousmodels assumption of no slip between the phases maywell be reasonably accurate. It is interesting to note thatthe performance of the homogeneous model improveswith increasing pressure because it is generally assumed

that the greater the pressure the larger the buoyancyforce holding the droplets in suspension. Hence, it maybe the case that when metering a two-phase flow with aDifferential Pressure meter, the greater the liquidentrainment in the gas flow the less the slip between thephases and therefore the better the homogeneous modelworks. Nevertheless, the performance was still clearlyinferior to de Leeuw’s correlation.

The Venturi–Murdock correlation was expected toperform better than it did. As it was the second of thetwo Venturi meter specific correlations available for test-ing it was expected that its performance would be good.However, the Venturi–Murdock correlation was seen tobe inferior to both the de Leeuw and homogeneousmethods at all pressures and at 20 bar even the OrificePlate correlation of Lin’s has a better performance. It isnot possible to analyze why this is the case as there isa lack of information regarding the creation of this corre-lation. That is, Phillips Petroleum developed it in-houseand all that is known about the data set is that the press-ure was approximately 45 bar. No other information isavailable (e.g. line size, gas and liquid flowrates, etc.).Clearly, this correlation does not fit NEL’s data wellcompared with de Leeuw’s correlation and the homo-geneous model. The reasons are probably that the otherconditions were quite different and the Murdock math-ematical model does not account for the effects of press-ure and gas flowrate. From the good performance of deLeeuw’s correlation and from the examination of trendsin the NEL wet gas loop data it is clear that the effectof pressure and gas flowrate must be included.

Of the Orifice Plate meter correlations (i.e. not includ-ing the general homogeneous model that is for all DPmeters), the Lin correlation was clearly the best. Thiscorrelation was based on a very similar model to Mur-dock’s except that it took account of the pressure effect.As the original Murdock correlation did poorly com-pared to Lin’s method this is further proof that takingaccount of the pressure is indeed important. Murdock’sOrifice Plate equations poor performance was a disap-pointing result as this correlation is well known to thenatural gas producing companies and it has often beenused by engineers to attempt to correct a Venturi meterswet gas error due to a lack of any alternatives. Unlessthere is a major effect caused by the greater gas flowratesin actual production flows then a significant error in themetering would have occurred. The Chisholm corre-lation also gave a poor result. Like the Murdock corre-lation it appears this general two-phase flow Orifice Platemeter correlation does not fit wet gas Venturi meter datawell in spite of allowing for a pressure effect. The poor-est of the seven correlations by far was the Smith &Leang correlation. It appears that the form of the Block-age Factor equation was perhaps not the best to modelwet gas flows through a Venturi meter and/or the data


used to form the Smith & Leang correlation was notsimilar to wet gas Venturi data.

Finally, it should also be noted that both the Smith &Leang and Lin correlations do not appear to predict ano error situation at the dry gas condition of 100% qual-ity (see Figs. 2, 3 and 4) as is required by the theory ifthe condition of no error in dry gas flow is assumed. Forthe Smith & Leang case it was previously stated that atthe dry gas condition the Blockage Factor (calculatedby Eq. 9) is not unity as is required by theory. This isundoubtedly due to Eq. (10)’s fit to the data not havinga fixed point declaring the Blockage Factor to be unityif the gas is dry. However, as in general the Smith &Leang correlation had a poor performance across the fulldata set and the use of this correlation is not rec-ommended for Venturi meters this problem is of aca-demic interest only here. The Lin correlation had a con-siderably better performance than the Smith & Leangcorrelation. It is due to Eq. (7)’s numerator being setto the liquid flow coefficient rather than the gas flowcoefficient which causes this error to be evident at highquality flows. However, the performance of the Lin cor-relation whilst better than the Smith & Leang correlationwas still not good enough to consider its use with Ven-turi meters so again this result is of academic interestonly.

In summary, it is clear that for wet natural gas meter-ing with Venturi meters the best correlation checked herewas de Leeuw’s correlation. It was also noted thatalthough the Murdock and the Modified Murdock corre-lations performed poorly, the Lin correlation, which wassimilar to the Murdock correlation except for the fact itincluded a pressure effect performed better. This sug-gests that the pressure does indeed effect the magnitudeof the Venturi meter wet gas error. Lastly, as the deLeeuw correlation performed so well and de Leeuw hadincluded the effects of both pressure and the gas flowrateitself it seems likely that both these parameters do indeedinfluence the Venturi meter when used in wet gas flows.As the de Leeuw correlation was based on data from a 4”Venturi with a 0.401 diameter ratio and the ISA ControlsVenturi was a 6” meter with a 0.55 diameter ratio it wasdecided to fit a correlation that would be a better fit thanthe de Leeuw correlation to this different geometry. Itwas seen as initially necessary to confirm the pressureand gas flowrate effect on the wet gas induced error byexamination of the NEL / ISA Controls Ltd data beforea suitable new correlation was formed.

3.4. Trends in the NEL / ISA controls Venturi meterdata

Murdock plotted his data set on a graph of��Ptp /�Pgvs X. This author found this type of plot use-ful in showing the effects of pressure and gas flowrateon the liquid-induced over-reading error of the Venturi

meter. Fig. 5 shows this Murdock type graph with allthe NEL/ISA Controls Ltd data from each pressuretested plotted separately. It is clear from Fig. 5 that fora given value of the Modified Lockhart–Martinelli (X)as the pressure increases from 20 to 60 bar the over-reading of the meter (i.e. the wet gas induced error)reduces. Hence pressure does indeed effect the Venturimeter error.

Figs. 6–8 show Murdock type graphs for the three setpressures of 20, 40 and 60 bar and in each the four dif-ferent gas flowrates are plotted separately. These figuresshow that there is indeed a relationship between the gasflowrate and the Venturi meter over-reading. For a setpressure and Modified Lockhart–Martinelli parameter(X), as the gas flowrate increases from 400 to 800 m3/hthen so does the Venturi meter over-reading. It appearsthat this trend continues up to the 1000 m3/h case butdue to the limitations of the NEL wet gas loop highervalues of X could not be achieved at 1000 m3/h to con-firm this.

It was therefore clear that when developing a new cor-relation to predict the over-reading of the 6” /0.55 diam-eter ratio ISA Controls Ltd Venturi in wet gas the effectsof pressure and gas flowrate had to be accounted for.

4. A new correlation

The results of the correlation comparison clearlyshowed the Venturi meter correlation of de Leeuw’s wassignificantly better than the other Orifice Plate meterbased correlations. It is therefore clear that the use ofOrifice Plate meter general two-phase correlations forthe particular case of wet gas metering with Venturi met-ers is not advisable. However, the de Leeuw correlationwas created from a data set taken from a 4” Venturi witha 0.401 diameter ratio while the NEL/ISA Controls Ltddata was for a 6” Venturi with a 0.55 diameter ratio. Asit is considered probable that the meter geometry directlyaffects the error induced by the liquid presence, as thisfactor will directly effect the flow pattern and thereforethe amount the meter over-reads, it was now considerednecessary to form a new correlation with the new inde-pendent data from the NEL wet gas loop that would bet-ter fit this 6” Venturi, 0.55 diameter ratio geometry.

de Leeuw had used the Chisholm correlation as a basefor creating his correlation. As will be seen from Sec-tions 2.3 and 2.6 what was in fact done to update theChisholm Orifice Plate meter two-phase correlation to awet gas specific Venturi meter correlation was thereplacing of a Chisholm constant (the numerical value,1/4) with an empirically derived equation. This equation(Eq. (13a) or (13b)) which is a function of the densi-ometric gas Froude number (i.e. a function of gas flowr-ate, the fluid densities and the meter geometry) is purelyempirical, no mathematical model was used. Therefore,


Fig. 5. NEL wet gas data plotted on Murdock type graph for individual pressures.

Fig. 6. 20 bar wet gas data plotted on Murdock type graph for indi-vidual gas flowrates.

Fig. 7. NEL wet gas data plotted on Murdock type graph for individ-ual gas flowrates.

when it was found that the de Leeuw equation type didnot fit the NEL data particularly well at the lower liquidloads it was decided that with no mathematical modelsupporting the de Leeuw correlation there was no parti-cular requirement to continue to use the Chisholm equ-ation form for the case of the ISA Controls Ltd Venturi.

After an in-depth examination of the difficultiesinvolved in developing an accurate mathematical modelit was decide to apply the data to a surface fit softwarepackage (TableCurve 3D). The equation was based on

Fig. 8. NEL wet gas data plotted on Murdock type graph for individ-ual gas flowrates.

the form ��Ptp /�P � f(X,Frg). The particular form ofequation found to be the overall best fit for each of thethree pressures is given as Eq. (16).

��Ptp

�Pg

�1 � AX � BFrg

1 � CX � DFrg

(16)

A further fit of pressure (in terms of the density ratio tokeep the equation dimensionless) to each of these con-stants (using Excel) gives the Eqs. (17), (18), (19) and(20)

A � 2454.51�rg

rl�2

�389.568�rg

rl� � 18.146 (17)

B � 61.695�rg

rl�2

�8.349�rg

rl� � 0.223 (18)

C � 1722.917�rg

rl�2

�272.92�rg

rl� � 11.752 (19)

D � 57.387�rg

rl�2

�7.679�rg

rl� � 0.195 (20)

The limits of this correlation are of course the limits ofthe data set used to create it. That is, for pressure andgas flowrate:


20 bar � P � 60 bar 400 m3 /h � Qg � 1000 m3 /h

The largest minimum Modified Lockhart–Martinelliparameter of the three pressures was a value ofX=0.001312 and therefore for simplicity this is regardedas the minimum value for the correlation. The upper lim-its of the Modified Lockhart–Martinelli parameter (X)were more complicated to find. With the definition fora wet gas flow here being a two-phase flow where theliquid mass flowing is up to and equal to the gas massflowing, then, for different pressures there is a differentdesired maximum value of the Modified Lockhart–Mart-inelli parameter (X). To get an upper limit for the valueof X this research considered the ratio of the superficialgas to liquid flow coefficients to be approximately unityand therefore, for equal phase flowrates Eq. (6) reducesto Eq. (21).

Xmax � �rg /rl (21)

However, complicating the situation is the fact that at1000 m3/h this desired value of maximum X could notbe achieved by the NEL wet gas loop. Therefore, theNEL data set’s maximum values of X (and therefore themaximum values valid for Eq. (16) need to be expressedby a surface equation (again fitted by TableCurve 3D) ofmaximum X to density ratio and gas densiometric Froudenumber. This surface fit is the equation given here asEq. (22).

Xmax �

0.108 � 2.251�rg

rl��0.06Frg

1 � 3.552�rg

rl��0.418Frg � 0.039Frg

2

(22)

Therefore, with the liquid mass flowrate assumedknown, the Venturi throat area known, the upstreampressure read (giving the phase densities from knownfluid properties and the constants A to D from Eqs. (17)–(20) and the differential pressure read and the phasesuperficial flow coefficients known, an iteration will findthe actual value of the gas mass flowrate.

It should be noted that the value of Kl is consideredto be simply the product of the Venturi meters velocityof approach and the standard discharge coefficient forflows with Reynolds numbers less than one million, i.e.0.995. Therefore, Kl � 1.0439. Due to the higher Reyn-olds numbers for the superficial gas flowrates the Venturimeters had to be calibrated at the three test pressures.The equations for the gas flow coefficient are given inEqs. (23)–(25).

20 bar: Kg � (�0.001583806m. g) � 1.046511 (23)

40 bar: Kg � (�0.00125486m. g) � 1.051785 (24)

60 bar: Kg � (�0.0009251669m. g) � 1.05646 (25)

Once the iteration of Eq. (16) produces an estimate forthe gas mass flowrate this value must be checked toensure the result is valid by ensuring the measured press-ure, the calculated gas mass flowrate and Modified Lock-hart–Martinelli parameter are within the correlation lim-its. If so, then the method’s gas mass flowrate predictionis valid. From applying Eq. (16) to the NEL data set thevalues of the root mean fractional deviation for all data,20, 40 and 60 bar cases were found and are given inTable 3.

These values given in Table 3 are clearly the best ach-ieved by any correlation in this paper. This is not surpris-ing of course, as the correlation was checked on the samedata that created the correlation. Therefore, this simplychecks that the new correlation does indeed predict theactual results from the NEL/ISA Controls Ltd wet gastests well and is therefore suitable for use in predictingthe performance of a 6” /0.55 diameter ratio Venturi usedwith wet gas flows. The overall performance of Eq. (16)was to predict the gas mass flow to less than ±3%.

5. Conclusions

Of the previously existing correlations for horizontalwet gas flow the de Leeuw correlation performed by farthe best while the other Venturi based correlation, theModified Murdock correlation, performed poorly incomparison. The reason for this is likely to be that thede Leeuw correlation used data from a wide range ofwet gas conditions while the Modified Murdock corre-lation did not. Also, de Leeuw took account of pressureand gas flowrate effects which this research validatedas important.

All the correlations which had been formed for OrificePlate meters performed poorly in comparison with thede Leeuw correlation and it is concluded that these Ori-fice Plate meter correlations should not be applied toVenturi meters. However, although the de Leeuw corre-lation had by far the best performance when tested onthe independent NEL data it was noted that this corre-lation was formed with a data set for a 4” and 0.401diameter ratio. These parameters are suspected of affect-ing the wet gas meter reading for given pressures andphase flowrates so it was expected that a more accuratecorrelation could be formed from the NEL data whichwould better fit the 6” and 0.55 diameter ratio Venturi.This was found to be the case. Therefore, for theirrespective geometries the de Leeuw equation and Eq.(16) are currently the best wet gas Venturi meter corre-lations. More testing needs to be carried out before theeffects of pipe diameter and the meter diameter ratio canbe found and therefore suitable wet gas correlationsfound for other Venturi geometries. Naturally it wasdesirable to check Eq. (16) against an independent dataset in order to give the equation more validity but unfor-


Table 3The results of the root mean square fractional deviation of Eq. (16) for all pressures together and for individual pressures

Pressure (Barg) All 20 40 60

d (±) 0.0101 0.0076 0.0115 0.0108

tunately due to the lack of publicly available wet gasVenturi meter data this was not possible. The author hastherefore to leave this until more data becomes available.

Finally, it must be noted that all the above correlationsrequire the liquid flowrate as an initial input in the corre-lation. In actual wet natural gas metering field appli-cations the liquid flowrate is not initially known. It needsto be measured and methods like the tracer dilution test[9] are carried out. Such tests only guarantee a ±10%estimation of the liquid flowrate. Hence, in the field allthe correlations accuracies will be duly affected by theknock-on effect of this liquid flowrate uncertainty. Ameter which could meter the wet gas without the require-ment of this initial liquid flowrate knowledge is the aimof the Oil and Gas Industry in the future.

Acknowledgements

Richard Steven was an Associate of the PostgraduateTraining Partnership (PTP) between NEL and Strath-clyde University. The PTP Scheme is a joint initiativeof the UK’s Department of Trade and Industry (DTI)and Engineering Sciences Research Council (EPSRC),and is financially assisted by the DTI. Richard Stevengratefully acknowledges financial support from NEL andEPSRC. Thanks go to Dr D. Hodges of NEL for hisassistance during testing and to Dr A. Gilchrist of Strath-clyde University for technical support during this

research. Thanks also goes to ISA Controls Ltd for theirkind supply of a Venturi meter. Dr Steven is currentlythe Multiphase Development Manager at McCrometerInc.

References

[1] Z.H. Lin, Two-phase flow measurement with orifices, Chap. 29 in:Encyclopedia of Fluid Mechanics, Xian Jiao-Tong University,Xian, The People’s Republic of China, 1986.

[2] R. de Leeuw, in: North Sea Flow Measurement Workshop, Nor-way, Liquid correction of Venturi meter readings in wet gas flow,Shell Expro, The Netherlands, 1997.

[3] Y. Taitel, A.E. Duckler, A model for predicting flow regime tran-sitions in horizontal and near horizontal gas-liquid flow, AIChEJournal 22 (1) (1976).

[4] J.W. Murdock, Two-phase flow measurements with orifices, Jour-nal of Basic Engineering 84 (1962) 419–433.

[5] D. Chisholm, Flow of incompressible two-phase mixtures throughsharp-edged orifices, Journal of Mechanical Engineering Science9 (1) (1967).

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

[7] Z.H. Lin, Two-phase flow measurements with sharp-edged ori-fices, International Journal of Multi-Phase Flow 8 (6) (1982)683–693.

[8] R.V. Smith, J.T. Leang, Evaluation of correlations for two-phaseflowmeters three current–one new, Journal of Engineering forPower October (1975) 589, 594.

[9] H., deLeeuw, Wet gas flow measurement by means of a Venturimeter and a tracer technique, North Sea Flow Measurement Work-shop, Scotland, October, 1994.

Documents

Wet gas metering with a horizontally mounted Venturi meter