Horizontally installed cone differential pressure meter wet gas flow performance

Flow Measurement and Instrumentation 20 (2009) 152–167

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Horizontally installed cone differential pressure meter wet gas flow performance Richard Steven ∗ Director of Multiphase and Wet Gas Flow Research Colorado Engineering Experiment Station, Inc. 54043 WCR 37-Nunn, CO 80648, USA

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Article history: Received 24 April 2008 Accepted 10 June 2008 Keywords: Two phase Multiphase Wet gas flow Cone differential pressure Venturi meter

abstract Differential pressure (DP) meters which utilise a cone as the system’s primary element are increasingly being used to measure wet natural gas flows (i.e. mixtures of natural gas, light hydrocarbon liquids and water). It is therefore important to understand this meter’s response to wet natural gas flows. Research into the wet gas response of the horizontally installed cone DP meter is discussed in this paper. Consideration is given to the significant influence of the liquid properties on wet gas flow patterns and the corresponding influence of the flow pattern on the cone DP meter’s liquid phase induced gas flow rate prediction error. A wet natural gas flow correlation for 4 in. 0.75 beta ratio cone DP meters with natural gas, hydrocarbon liquid and water flow has been developed from multiple data sets from three different wet gas flow test facilities. This corrects the liquid induced gas flow rate prediction error of a wet gas flow up to a Lockhart–Martinelli parameter of 0.3, for a known liquid flow rate of any hydrocarbon liquid/water ratio, to ±4% at a 95% confidence level. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Orifice plate meters are common flow meters for dry and wet natural gas production flows. However, they can be considered too fragile for some extremely adverse wet natural gas flow conditions. For this reason metering engineers can prefer to utilise sturdier primary element designs when using a DP meter with wet gas flow conditions. The cone DP meter is widely regarded as a sturdy primary element and its use with wet gas flow applications is increasing. It is therefore important then that industry understands the response of the cone DP meter to exposure to wet gas flows. In particular, it is important to understand the wet gas performance of cone DP meters with relatively small quantities of water and light1 hydrocarbon liquid mixtures. This is because one method of metering the natural gas flow rate of a wet natural gas flow is to estimate the liquid flow rate (usually a mixture of hydrocarbon liquid and water) from an independent source (such as tracer dilution techniques or test separator histories) and then use a ‘‘wet gas correlation’’ to correct for the liquid induced gas flow rate error of a DP meter.

∗

Tel.: +1 970 897 2711; fax: +1 970 897 2710. E-mail address: [email protected].

1 This paper discusses data from wet gas flow tests that used kerosene (actually kerosene substitute Exxsol D80), decane, diesel oil, Stoddard solvent or condensate. No heavier oil data is discussed. Consequently all hydrocarbon liquid discussions in this paper refer to this range of oils only. 0955-5986/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2008.06.002

2. The Cone DP Meter Fig. 1 shows a sketch of the generic cone DP meter geometry. The axis of symmetry of the cone is aligned with the meter body’s centre line. The cone is positioned with the apex of the cone pointing upstream. The cone is supported at the apex by a hollow support bar. The precise geometry of the cone/support bar connection varies in many cone DP meter designs. However, the cone angle is always 26◦ from the pipe/meter body centre line (see Fig. 1). The back ‘‘face’’ of the cone is not flush to the cross sectional area of the pipe/meter body (i.e. it is not at right angles to the pipe/meter body centre line) but rather at an angle of 112.5◦ from the pipe centre line. That is, the ‘‘cone’’ DP meter is actually two dissimilar cones back to back (see Fig. 1). The upstream pressure port is (usually but not always) located 2 1/8th upstream and in line with the support bar. There may or may not be gussets attached to the cone (not shown in Fig. 1 but typically two flat plates 120◦ either side of the centre line of the circular support bar). These gussets serve to make the cone more resistant to shock loadings such as liquid slug strikes in wet gas flow applications. They also increase the stiffness of the design and therefore increase the natural frequency of the cone assembly. This significantly reduces the likelihood of fatigue failure at the supporting bar due to cone vibration. No significant single phase or wet gas flow performance effect has been reported due to changes in the support bar/cone connection, upstream pressure port orientation relative to the support bar or the inclusion of gussets. A cone DP meter is a generic DP meter. That is, a cone DP meter operates in the same way as any DP meter such as an orifice plate, nozzle, Venturi meters etc. These meters all operate by using the

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

153

Fig. 1. Generic sketch of a cone DP meter assembly.

principles of conservation of mass and energy and the generic single phase flow DP meter equation (which the cone DP meter uses) is: For mass flow rates:

˙ = EAt ε Cd m

2ρ 1P .

p

(1)

For volume flow rates:

s Q˙ = EAt ε Cd

Wet gas flow is defined here as any gas and liquid flow that has a Lockhart–Martinelli parameter, XLM , less than 0.3 [1]. The Lockhart–Martinelli parameter is defined as:

Superficial Gas Inertia

=

˙l m ˙g m

r

ρg ρ`

(3)

˙ g and m ˙ l are the gas and liquid mass flow rates and ρg and where m ρl are the gas and liquid densities, respectively. Many gas meters have responses in wet gas flow that are dependent on the gasto-liquid density ratio (effectively a dimensionless representation of the pressure for set liquid properties). Often, the gas-to-liquid density ratio is indicated by DR, DR = ρg /ρl .

(6)

r

m`

ρ` A

(4)

The gas densimetric Froude number (5) is defined as the square root of the ratio of the gas inertia (if it flowed alone) to the gravitational force on the liquid phase. The liquid densimetric Froude number (7) is defined as the square root of the ratio of the liquid inertia (if it flowed alone) to the gravitational force on

ρ` ρ` − ρg

(7)

.

(8)

Note that the equations above assume one liquid density. For wet natural gas flows, where there is often hydrocarbon liquid and water present with the natural gas, there is a question as to what liquid density should be used. It is commonly assumed that at moderate to high gas flow rates, typical of hydrocarbon production, the liquids are well mixed and the liquid can be assumed to be a homogenous mix of water and hydrocarbon liquid. In this case an averaged liquid density can be used ρ l hom ogenous . This can be calculated by use of Eqs. (9) and (10). These equations are derived in Appendix A. xl =

˙ water m

(9)

˙ water + m ˙ hydrocarbon m

ρ l hom ogenous =

3. Definition of wet gas flow

(5)

mg

Fr` = √ gD Usl =

ρg ρ` − ρg

ρg A Usl

Note that the cone DP meter design being discussed in this paper is the particular design where the low pressure port is located at the centre of the back face of the cone with the pressure port extending upstream through the cone and up then through the cylindrical support bar. This paper’s technical discussion does not extend to the case of cone DP meter designs where the low pressure port is located on the wall of the meter body immediately downstream of the primary element.

Superficial Liquid Inertia

r

Frg = √ gD

(2)

ρ

˙ is the mass flow rate m Q˙ is the volume flow rate (at actual conditions) E is the ‘‘velocity of approach’’ (a geometric constant) At is the minimum cross sectional (or ‘‘throat’’) area Cd is the discharge coefficient ρ is the fluid density 1P is the differential pressure.

XLM =

Usg

Usg =

21P

where

s

the 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 and Usl are the superficial gas and liquid velocities calculated by Eqs. (6) and (8).

ρhydrocarbon ρwater . ρwater (1 − xl ) + xl ρhydrocarbon

(10)

Finally, DP meters with wet gas flows tend to have a positive bias or over-reading on their gas flow rate prediction. The uncorrected gas mass flow rate prediction is often called the ˙ g ,apparent . The over-reading is the ratio apparent gas mass flow, m of the apparent to actual gas flow rate. Eqs. (11) and (12) show the over-reading and percentage over-reading (where 1Ptp and 1Pg are the actual two-phase/wet gas differential pressure and the differential pressure if the gas flowed alone, respectively.) OR =

˙ g ,apparent m

OR (%) =

˙g m 

s ∼ =

˙ g ,apparent m ˙g m

1P tp 1Pg  − 1 ∗ 100% ∼ =

(11)

s

! 1P tp − 1 ∗ 100%. 1Pg (12)

4. A history of cone DP meters wet gas flow research Steven et al. [2] describes the history of the DP meter wet gas flow response research. This research was largely conducted for

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

orifice plate and Venturi meters. It has been found that all generic DP meters have the same wet gas trends. In 1962 Murdock [3] effectively stated that the orifice plate meter has a wet gas over-reading dependent on the Lockhart–Martinelli parameter. Between 1967–77 Chisholm [4,5] stated that the orifice plate meter had a wet gas over-reading dependent on the Lockhart–Martinelli parameter and the gasto-liquid density ratio. Both Murdock and Chisholm assumed separated flow when modelling the wet gas flow. In 1997 de Leeuw [6] stated that a Venturi meter had a wet gas over-reading dependent on the Lockhart–Martinelli parameter, the gas-to-liquid density ratio and the gas densiometric Froude number. De Leeuw also made an important discovery with regards to the flow pattern. That is, it was found that the Venturi meter’s wet gas over-reading was dependent on the type of flow pattern at the inlet to the meter. For otherwise set parameters, when the gas densiometric Froude number (and hence the gas dynamic pressure) was low enough for the flow pattern to be stratified, the Venturi meter was insensitive to the gas densiometric Froude number. However, as the gas densiometric Froude number increased to the point where the flow pattern began to transition into annular mist the over-reading began to increase. As the gas densiometric Froude number increased further and the flow pattern moved through the stratified/annular mist transition zone, to annular mist flow and then to mist flow, the over-reading increased. (The influence of a wet gas flow pattern on generic DP meter over-reading is discussed in some detail by Steven et al. [7]). In 2002–03 Stewart et al. [8,9] showed that Venturi and cone DP meters have wet gas over-reading dependent on the Lockhart–Martinelli parameter, the gas-to-liquid density ratio, the gas densiometric Froude number and the beta ratio. In 2006 Steven [10] suggested from limited data that there may be a DP meter diameter effect on the wet gas flow response. In 2006 ReaderHarris et al. [11,12] and Steven et al. [7,10] independently showed that liquid properties could, under some flow conditions, have an effect on a DP meter’s wet gas flow response. (As de Leeuw [6] has stated that the flow pattern affects the Venturi meter wet gas over-reading, it is of interest to note here that Taitel and Dukler’s [13] research into horizontal flow patterns states that both pipe diameter and liquid properties influence the flow pattern. The findings of Reader-Harris et al. [11,12] and Steven et al. [7,10] are therefore all directly linked to the flow pattern.) Research into the wet gas flow response of cone DP meters was started by Ifft [14] in 1997 with visual experiments on air/water flow through orifice plates and cone DP meters. Higher pressure and flow rates analytical research was started in 2002 by Stewart et al. [8]. This paper showed the cone DP meter wet gas flow response had the same trends as other DP meters. That is, when exposed to wet gas flow, the cone DP meter has an over-reading that is dependent on Lockhart–Martinelli parameter, the gas-to-liquid density ratio, the gas densiometric Froude number and beta ratio. In 2003–04 Steven [15,16] confirmed this with more data. In 2005 Steven et al. [17] produced a blind data fit cone DP meter wet gas correlation for 4 in. and 6 in., 0.75 beta ratio cone DP meters with gas/light hydrocarbon liquids:

˙g =  m

˙ g ,apparent m 1+AXLM +BFrg 1+CXLM +BFrg



(13)

where for density ratio, ρg /ρl ≥ 0.027: (14)

0.0317 B = 0.0420 − p

(15)

ρg /ρl

(16)

ρg /ρl

and for ρg /ρl < 0.027, A = +2.431, B = −0.151, C = +1.0. Note, that in order to predict the gas flow rate from this correlation, the liquid mass flow rate needs to be supplied from an external source. This is an input to Eq. (3) which in turn is substituted into Eq. (13). An iteration is then carried out on the gas mass flow rate term in equation set (13)–(16). A good iteration starting point to ensure convergence is the apparent gas mass flow rate prediction. Fig. 2 shows all wet gas flow data available to Steven [17] in 2005 plotted on a ‘‘Murdock’’ plot (i.e. Lockhart–Martinelli parameter vs. Over-Reading). The gas flow rate error result of applying this correction method for a known liquid mass flow rate is also shown scattered around the x-axis. For this data range (listed in Appendix B as Tables B.1, B.4 and B.5) the gas flow rate is predicted to ±2% to 95% confidence. However, in 2007 Evans [18] and Steven [19] independently showed that the Steven et al. [17] correlation is not suited to extrapolation to higher gas densiometric Froude numbers. Fig. 3 reproduces the graph shown by Steven [19]. Here it can be seen that for the three data sets with higher gas densiometric Froude number ranges than used by Steven et al. in 2005 (i.e. Tables B.2, B.3 and B.6), the equation set (13)–(16) gives significant errors in the gas flow rate predictions for the extrapolated gas densiometric Froude number data. Therefore, in 2008 Steven et al. [20] offered a new cone DP meter wet gas flow correlation based on the Chisholm/de Leeuw [4–6] style equation and fitted this to all the available data sets (i.e. Tables B.1–B.6 in Appendix B). De Leeuw [6] based his 4 in., 0.4 beta ratio Venturi meter wet gas correlation on the mathematical form developed by Chisholm [5,6] and then included a gas densiometric Froude number term:

˙ g ,apparent m ˙g = q m 2 1 + CXLM + XLM

(17)

where

 C =

ρg ρ`

n

 +

ρ` ρg

n (18)

for 0.5 ≤ Frg < 1.5 n =
constant value, i.e. for stratified flow and for Frg > 1.5 n = f Frg , i.e. for annular mist flow. Note Chisholm solely stated the ‘‘Chisholm’’ exponent ‘‘n’’
was a constant (n = 1/4). De Leeuw found function n = f Frg by plotting data as shown in Fig. 4. It was this same procedure (as explained in detail by Steven et al. [2] when discussing similar issues with orifice plate wet gas metering) that was utilised to develop the cone DP meter correlation. Fig. 5 shows the result of plotting the data of Table 1 in Appendix B, i.e. 6 in., schedule 80, 0.75 beta ratio cone DP meter data for gas with light hydrocarbon liquid. Using this data fit the Steven et al. [20] updated cone DP meter correlation is Eqs. (17) and (18) with Eqs. (19) and (20): for Frg ≤ 0.5 n = 0.19 for Frg > 0.5 n =

0.3997 A = −0.0013 + p

ρg /ρl

0.2819 C = −0.7157 + p

1 2

1−

(19)

!!

0.83 1.14 ∗ exp 0.31 ∗ Frg




.

(20)

This new correlation is better suited to gas densiometric Froude number extrapolation. It includes the boundary condition that for a set gas-to-liquid density ratio, as the gas densiometric Froude number increases (i.e. the gas dynamic pressure increases) the

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 2. All cone meter data sets within original correlation range, and correlation performance.

Fig. 3. All available 4 in. and 6 in., 0.75 beta cone meter wet gas data uncorrected, and corrected by the existing cone wet gas correlation.

Fig. 4. Scan of de Leeuw’s [6] Chisholm Exponent ‘‘n’’ vs. Gas Densiometric Froude Number.

155

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 5. NEL 2001 Flow Programme 4 in. 0.75 beta cone meter data, Chisholm’s exponent ‘‘n’’ vs. Frg .

Fig. 6. All known available gas/light hydrocarbon liquid 4 in. and 6 in., 0.75 beta cone DP meter wet gas data available prior to 2007 uncorrected, and corrected by the equation set (17)–(20).

wet gas flow pattern tends to the homogenous flow pattern2 asymptotically and therefore the over-reading also tends to that of the homogenous model (as described by Steven [7]). Fig. 6 shows all cone DP meter data available to Steven et al. [20] (i.e. Tables B.1– B.6 in Appendix B). For a known hydrocarbon liquid mass flow rate equation set (17)–(20) corrected the liquid induced gas flow rate prediction error (i.e. the over-reading) to ±2.6% to 95% confidence. That is, within the limited data set originally used to data fit equation set (13)–(16) (Steven 2005 [17], i.e. Tables B.1–B.4 in Appendix B) a lower uncertainty correlation was possible than when additional data sets with wider ranges of flow conditions were added (i.e. Tables B.1–B.6 in Appendix B). However, although the uncertainty of this new correlation is higher than the old correlation it is assured not to diverge on extrapolation of gas densiometric Froude number. This is the limit to the publicly released cone DP meter wet gas response knowledge.

2 Note homogenous flow is defined as when the liquid and gas phases are perfectly mixed making a pseudo-single phase flow. Wet gas flows tend to this condition at high pressure and/or high gas velocities.

However, it is very important to note from Tables B.1–B.6 in Appendix B that all the data sets have light hydrocarbon liquids as the liquid component. That is, as yet no cone DP meter wet gas data has been presented which has water or a water/hydrocarbon liquid mixture as the liquid component of a wet gas flow. However, it was shown in 2005–06 by Reader-Harris et al. [11,12] that for Venturi meters at least, where as gas type had no effect on the meters’ wet gas response, there was a significant liquid property effect on the meters’ wet gas flow performance. It therefore stood to reason then that there could also be a liquid property effect on the wet gas flow performance of the cone DP meters as they are members of the same generic DP meter family – that is, they operate on the same physical principles. For this reason it should be understood the cone DP meter wet gas correlation shown above for 4 in. and 6 in., 0.75 beta ratio meters (i.e. equation set (17)– (20)) is only applicable for the case of light hydrocarbon liquids if an uncertainty of ±2.6% is expected. This paper will now discuss new CEESI wet gas flow data from a 4 in., schedule 80, 0.75 beta ratio cone DP meter where the data has natural gas and kerosene flows, or natural gas and water flows, or a natural gas and mixture of kerosene and water flows. However, it is first necessary to review what de Leeuw [6], Reader-Harris

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 7. The Shell gas/light hydrocarbon liquid horizontal flow pattern map.

[11,12] and Steven [7] said about Venturi meters with wet gas, the flow pattern influence on the Venturi wet gas over-reading and the liquid property influence on the flow pattern. From this we can then go on to extend the discussion to the case of the cone DP meter. 5. The known horizontal Venturi meter wet gas flow response and the relationship with flow patterns and liquid properties In 1997 de Leeuw [6] showed that flow patterns have an affect on a Venturi meters’ wet gas over-reading. It was shown that if the flow pattern was stratified flow the over-reading was dependent on the Lockhart–Martinelli parameter and the gasto-liquid density ratio but independent of the gas densiometric Froude number. However, if the gas densiometric Froude number was greater than some critical value for that pipe size and fluid properties, the flow pattern was annular mist and then the overreading was dependent on the Lockhart–Martinelli parameter, the gas-to-liquid density ratio and the gas densiometric Froude number. This was the first direct statement that flow patterns dictate the over-reading of DP meters with wet gas flows. In 2006 Reader-Harris et al. [11,12] presented wet gas flow data for Venturi meters where the wet gas flow test matrix had, for otherwise similar flow conditions, nitrogen/kerosene and nitrogen/water data. A difference in the meters over-reading was found at certain set flow conditions. Steven [7] then combined the work of de Leeuw [6], Taitel and Dukler [13] (which is a discussion on horizontal and near horizontal flow pattern influences) and Reader Harris [11,12] to produce a description of how liquid properties could affect flow patterns and therefore DP meter wet gas over-readings. De Leeuw [6] had implied that the more stratified a wet gas flow pattern was, the lower the over-reading. Taitel and Dukler [13] asserted that liquid properties affect flow patterns for all other conditions held constant. Reader-Harris [11, 12] found that for some wet gas flow conditions a Venturi meter gave different over-readings for varying liquid properties when all other wet gas flow condition parameters were set. In particular Reader Harris showed that whereas gas type did not have any effect on wet gas over-readings, for some flow conditions (moderate to high flow rates only) nitrogen/water gave a lower over-reading than nitrogen/kerosene flows. For other flow conditions (low and extremely high flow rates) nitrogen/water and nitrogen/kerosene wet gas flows gave the same Venturi meter wet gas over-reading. Steven [7] combined this information to postulate that the ReaderHarris Venturi meter data set could be explained by considering the wet gas flow pattern relationships with liquid properties. A thought experiment can explain the postulation. Imagine there are two identical pipes with two identical Venturi meters, one pipe with gas and light hydrocarbon liquid, the other pipe with

157

Fig. 8. The Shell flow pattern map with postulated approximate water boundaries superimposed.

gas and water. The flow conditions (i.e. the Lockhart–Martinelli parameter, the gas-to-liquid density ratio and the gas densiometric Froude number) are all identical. It was suggested that the gas/water based wet gas flows requires a larger gas dynamic pressure than the gas/hydrocarbon liquid flow to cause transition between the stratified and annular mist flow patterns. In terms of the Shell flow pattern map (Fig. 7) this means the boundary between stratified and annular mist would shift to the right if the liquid is water instead of light hydrocarbon liquid. This is sketched as Fig. 8. If the gas dynamic pressure is low enough to cause the liquid’s weight to be the dominant force on a gas/hydrocarbon liquid flow, the flow pattern will be stratified. If the same gas dynamic pressure is applied to the gas/water flow the flow pattern will also be stratified, as water apparently requires a larger gas dynamic force to induce a flow pattern transition from stratified to annular mist flow than light hydrocarbon liquid. However, as the gas dynamic pressure is continually increased, at some gas dynamic pressure value the gas/hydrocarbon liquid flow pattern will start transition to annular mist whilst the gas/water flow pattern remains stratified. As the gas dynamic pressure increases further the gas/hydrocarbon liquid flow pattern develops towards annular mist flow. Then at some particular gas dynamic pressure the gas/water flow pattern will begin the transition to annular mist flow. That is, the gas/water flow pattern is lagging the gas/hydrocarbon liquid flow in its transition to annular mist. As the gas dynamic pressure continues to increase the gas/hydrocarbon liquid flow becomes fully annular mist whilst the gas/water flow pattern lags it by still being in transition between stratified and annular mist. As gas dynamic pressure increases further still the gas/hydrocarbon liquid annular mist flow tends towards mist flow as the annular ring reduces in size, more liquid mass becomes entrained in the gas core and the average droplet size reduces. At some higher value of gas dynamic pressure still the gas/water flow pattern will become fully annular mist. As the gas dynamic pressure increases yet further both the gas/hydrocarbon liquid and gas/water annular mist flows continue to tend towards mist flow. Note that, unlike stratified flow where the two flow patterns were very similar, now they are now both labelled annular mist flow but the flow patterns are not now similar, as for one gas dynamic pressure value they are both at different stages of transition from annular mist to mist flow and then to homogenous flow. The gas/hydrocarbon liquid flow will reach mist flow (i.e. the annular ring will disappear) at a lower gas dynamic pressure than the gas/water flow. As the gas dynamic pressure continues to increase beyond the value where the gas/water flow reaches mist flow, both the gas/hydrocarbon liquid and gas/water mist flows tend towards homogenous flow as droplets get shattered to ever smaller diameters by the gas dynamic forces.

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 9. NEL 4 in., 0.6 Venturi wet gas data, density ratio 0.046, gas densiometric Froude number 1.5.

However, in theory, the gas/hydrocarbon liquid flow will become asymptotic to the homogenous flow condition at a lower gas dynamic pressure than the gas/water flow. Only when the gas dynamic pressure reaches a high enough value to homogenise the gas/water flow will the two cases have the same flow pattern for the first time since the gas/hydrocarbon liquid flow started its transition from stratified flow into annular mist flow. Therefore, as flow patterns affect DP meter wet gas flow over-readings, only when the gas/hydrocarbon liquid and the gas/water flows both have the same precise flow pattern, i.e. fully stratified flow or homogenous flow, would the DP meter over-readings match. In the flow patterns in between these two extremes the gas/water flow is always more stratified than the gas/hydrocarbon liquid flow. As de Leeuw effectively stated, the more a flow pattern tends to stratified flow the lower the DP meter’s over-reading, this means that the gas/water flow over-reading always trails the gas/hydrocarbon liquid flow over-reading because the gas/water flow pattern is more stratified than the gas/hydrocarbon liquid flow for any given gas dynamic pressure. The above description of flow patterns is wholly dependent on the unproven assumption that water is more resistant to flow pattern change than light hydrocarbon liquids. Kerosene is more viscous than water but has a lower surface/interfacial tension. For example, Reader-Harris et al. [21] state that for NEL experiments the fluid properties (at 21 barg and 20 ◦ C at least) were a viscosity of water of 0.001 Pa. S while that of kerosene was 0.0024 Pa. S, and the surface tension of water was 0.06 N/m2 while that of kerosene was 0.0265 N/m2 . Therefore here, kerosene is 140% more viscous than water but has 55% less surface tension. There is very limited information available on the combined effects of liquid viscosity and surface/interfacial tension parameters on wet gas flow patterns. It is implied from Reader-Harris’s [11,12] results that kerosene requires less energy from the gas flow than water to become annular mist. CEESI has video footage of natural gas/water and natural gas/kerosene wet gas flows confirming that for set wet gas flow parameters the gas/water flows are slightly more stratified than gas/kerosene. It is intuitive (but not scientifically proven) that the greater a liquids’ viscosity and surface/interfacial tension the more resistance it will have to being dispersed in the wet gas pipe flow. What is not so intuitive is what the relative effects are of the two physical parameters. In the case of water vs. kerosene wet gas flows it appears from the NEL Venturi data [11, 12], and from video footage at CEESI, that the wet gas flow pattern may be considerably more sensitive to surface/interfacial tension values than viscosity. Reader-Harris et al. [21] discuss surface tension affecting average droplet size in mist flow models and

therefore the Venturi meters over-reading. The higher the surface tension the larger the average droplet size for otherwise set flow conditions. Reader-Harris et al. [21] then stated from CFD modeling that the larger the average droplet size in a mist flow the lower a Venturi meter’s over-reading. A larger average droplet size is synonymous with a flow pattern being closer to stratified flow than a wet gas flow with smaller average droplet size. The CFD result of the larger droplet size giving smaller over-readings therefore matches all experimental evidence. However, not enough research has been done to confirm precise relationships. Reader-Harris et al. [11,12] showed three different geometry 4 in. Venturi meter wet gas flow test data sets. Each had gas/kerosene and gas/water data. For a constant gas-to-liquid density ratio and gas densiometric Froude number the Venturi over-reading across a range of Lockhart-Martinelli parameters were recorded for gas/kerosene and gas/water flows. This test series was repeated for the same set of gas-to-liquid density ratios but a different set of gas densiometric Froude numbers. A sample of the results ReaderHarris [11,12] presented from a 4 in., 0.6 beta ratio Venturi meter at a constant gas-to-liquid density ratio of 0.046 are reproduced in Figs. 9–12. Fig. 10 shows the gas densiometric value set at 1.5. For a gas/hydrocarbon liquid wet gas flow the Shell flow pattern map (see Fig. 7) suggests that this is in the early stages of transition between stratified and annular mist flow patterns. The suggested flow pattern map for gas/water flows (see Fig. 8 — although it must be understood that this is a sketch and not to be taken as precise) shows the gas/water flow pattern is fully stratified. The flow patterns for each of the water/kerosene wet gas flows are therefore very similar and Fig. 9 shows the corresponding over-readings are very similar. As the gas densiometric Froude number is increased to 2.5 Fig. 8 shows the gas/hydrocarbon liquid wet gas flow in the annular mist flow region. However, Fig. 8 also suggests that the gas/water flow will be in early transition between stratified and annular mist flow. Fig. 10 shows the gas/hydrocarbon liquid flow has a significantly higher over-reading than the gas/water flow. Fig. 11 shows the flows at a gas densiometric Froude number of 3.5. Here Fig. 8 shows the gas/hydrocarbon liquid flow well into the annular mist region – possibly deep enough for the annular ring to have effectively disappeared making it mist flow, whilst the gas/water flow is still lagging in the early stages of annular mist flow. That is, the gas/water flow has a thicker annular ring and a larger average droplet size. The two different flows are however both annular mist flows,if not identical, due to annular ring and drop diameter dimensions. However, these differences are less than the difference between stratified and annular mist flow patterns. In Fig. 11 it can be seen that the gas/water over-reading

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

159

Fig. 10. NEL 4 in., 0.6 Venturi wet gas data, density ratio 0.046, gas densiometric Froude number 2.5.

Fig. 11. NEL 4 in., 0.6 Venturi wet gas data, density ratio 0.046, gas densiometric Froude number 3.5.

Fig. 12. NEL 4 in., 0.6 Venturi wet gas data, density ratio 0.046, gas densiometric Froude number 4.5.

lags the gas/hydrocarbon over-reading but the gap has closed compared to Fig. 10. In Fig. 12 the gas densiometric Froude number is 4.5 and both wet gas flows are well inside the annular mist flow

boundaries sketched in Fig. 8. The gas/hydrocarbon liquid flow is clearly deep in the annular mist flow prediction meaning it is likely to be mist flow tending to homogenous flow. The gas/water flow is

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 13. Sample of CEESI wet gas data showing gas-to-liquid density ratio effect on DP meter over-reading with gas/hydrocarbon liquid ‘‘HCL’’ data only.

clearly not as close to homogenous flow but still likely to be mist flow. Fig. 12 shows that the gas/water flow over-reading has nearly caught up with the gas/hydrocarbon liquid flow. All Reader-Harris [11,12] data showed these same trends. It can be shown (Steven [2,7]) that the over-reading of an idealised homogenous wet gas flow through any DP meter is given by equation set (17) and (18) where n = 1/2. That is:

˙g = s m

˙ g ,apparent m .   1   1   ρg 2 ρl 2 2 1+ + ρg XLM + XLM ρl

(21)

Note that in Figs. 9–12 the gas-to-liquid density is 0.046 and the homogenous model has been superimposed on the graph. At a gas densiometric Froude number of 1.5 the homogenous model over-reading is larger than all the data. As the gas densiometric Froude number increases to 2.5 Fig. 10 shows that the gas/kerosene data matches the homogenous flow model overreading while the gas/water data has a slightly lower over-reading. By a gas densiometric Froude number of 3.5 Fig. 11 shows that the gas/kerosene data has an over-reading slightly in excess of the homogenous flow model while the gas/water data has an over-reading that matches the homogenous model. At a gas densiometric Froude number of 4.5, both the gas/kerosene and gas/water flows have over-readings in excess of the homogenous model. It is important to note here that, by theory, as the gas dynamic pressure continually increases, a wet gas flow will tend towards homogenous flow and a DP meter’s over-reading will therefore tend towards the homogenous model over-reading. However, there is nothing in this statement that suggests a DP meter wet gas over-reading can not be larger than the homogenous flows over-reading at some condition. That is, as a wet gas flow has the gas densiometric Froude number increased and a flow pattern changes from stratified towards homogenous flow, there is no reason why the over-reading at the stratified flow condition (which is less than homogenous flow model over-reading prediction according to multiple experiments) can not increase beyond (or ‘‘over-shoot’’) the homogenous model over-reading before then tending to it. This is what is seen here in the NEL data shown in Figs. 9–12. This statement was initially made by Steven [7] but later elaborated and expanded on by Reader-Harris [21] when discussing CFD analysis: ‘‘. . . the reason for the increase in over-reading above the homogenous solution at low droplet diameter appears to be related to the difference in pressure profile that occurs when liquid starts

to build-up on the converging wall, forming a separated jet in the throat. The homogenous case is an idealised solution in which all the liquid is suspended in the gas stream and, therefore, does not take this mechanism into account.’’ It is as yet unknown to the author if increasing the gas densiometric Froude number further finally flushes away any liquid built up at the Venturi meters converging section thus making the over-reading tend to the homogenous model or, if at the maximum gas flow rates seen in industry, this does not occur. So far, of the standard DP meter designs tested with wet gas flows only the Venturi meter has been reported to show wet gas over-readings larger than homogenous flow under some flow conditions. For example the cone DP meter has not behaved like the Venturi meter in this respect. The cone meter has a significantly different geometry to a Venturi and there is no converging wall for liquid to build up at. All existing cone DP meter wet gas data sets show over-readings starting with the stratified flow having an over-reading less than that of the homogenous flow model and then approaching the homogenous flow model over-reading as the flow pattern tends to the homogenous flow. That is, there is no over shoot. (Incidentally, this is also true of the orifice plate meter.) Note, therefore, that Eq. (20) is asymptotic to the homogenous value of 1/2 as the gas densiometric Froude number increases, with no over shoot. 6. Cone DP meter natural gas, kerosene and water data and analysis In September 2007 CEESI commissioned a natural gas/kerosene/ water wet gas flow test facility. A 4 in., schedule 80, 0.75 beta ratio cone DP meter was included in the commissioning runs. The test matrix is described in Appendix B, Table B.7. The tests were split between natural gas and kerosene flows, then natural gas and water flows and finally natural gas with a mixture of kerosene and water flows. The first analysis was to check that this new natural gas and kerosene 4 in., 0.75 beta ratio cone DP meter data behaved the same as all previous data sets – i.e. plot sample data sets to show the expected gas-to-liquid density and gas densiometric Froude number wet gas response sensitivities. These were duly found as expected (e.g. Stewart [8]), see Figs. 13 and 14. All the natural gas and kerosene data was then fitted to the equation set (17)–(20) to prove the results are the same as before, i.e. were corrected within the band of ±2.6% (see Fig. 15). The second analysis was to review the new natural gas and water 4 in., 0.75 beta ratio cone DP meter data and check that

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

161

Fig. 14. Sample of CEESI wet gas data showing Frg effect on DP meter over-reading with gas/hydrocarbon liquid ‘‘HCL’’ data only.

Fig. 15. Appendix B, Table B.7 CEESI gas/HCL only wet gas data corrected with equation set (17)–(20).

Fig. 16. Sample of CEESI gas/water only, wet gas data showing gas-to-liquid density ratio effect on DP meter over-reading, corrected with equation set (17)–(20).

it had the same gas-to-liquid density ratio and gas densiometric Froude number wet gas response trends as the gas/hydrocarbon liquid flows. These were duly found as expected, see Figs. 16 and 17. All the natural gas and water data was then fitted to the

equation set (17)–(20) to investigate if this equation set (based on gas/light hydrocarbon liquid data) is suitable as a correction factor for the gas/water wet gas data. The result is shown in Figs. 16–18. Clearly this is not the case. The gas/water data is over corrected

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Fig. 17. Sample of CEESI wet gas data showing Frg effect on DP meter over-reading, with gas/water, corrected with equation set (17)–(20).

Fig. 18. Appendix B, Table B.7 CEESI gas/water only wet gas data corrected with equation set (17)–(20).

by this gas/light hydrocarbon liquid wet gas flow correction. This indicates the gas/water data has generally a smaller wet gas overreading than the gas/light hydrocarbon liquid data. An example of this is shown by comparison of gas/kerosene and gas/water data at similar flow conditions (see Fig. 19). Therefore, this cone DP meter’s wet gas data3 is indicating the same general liquid property wet gas response as reported by Reader-Harris et al. [11,12] for the Venturi meter. The gas/light hydrocarbon liquid derived wet gas equation (set (17)–(20)) corrects the gas/light hydrocarbon liquid data to within the prescribed ±2.6% as expected. However, this correction factor over-corrects the gas/water data. In this random example (Fig. 19) the error can be greater than −6%. Fig. 20 shows all the CEESI wet gas multiphase facility commissioning data for the 4 in., 0.75 beta ratio cone DP meter. This includes many data points where the liquid is a mixture of kerosene and water. Two significant points are noticeable from the data with the liquid mixtures. The first is the fact that the combination of liquids has not led to a radical change in the meter’s response to the wet gas. This suggests that the mixing of hydrocarbon liquid and water did not

3 Due to the cone DP meter data being taken during a facility commissioning exercise, the test matrix is not designed to facilitate the direct comparison of the cone DP meter liquid property wet gas response sensitivities with that of the Venturi, but even so, substantial information can be extracted from this data.

cause very significant foaming or very significant liquid property changes due to any chemical interactions between the natural gas, water and hydrocarbon liquid. The second is that taking average liquid properties for a water/hydrocarbon liquid mixture, gives a tendency for the existing hydrocarbon liquid based 4 in., 0.75 beta ratio cone DP meter wet gas correlation to over predict that liquid induced gas flow rate prediction error. It is therefore advisable to be cautious in applying to any DP meter any wet gas correlation that is not derived from data gathered from wet gas flow tests on that meter’s geometry with similar liquid properties. Much of the wet natural gas production flows are flows of natural gas, water and hydrocarbon liquids. It would therefore be greatly beneficial if the available DP meter wet gas correction factors did not have a bias if water is present in the wet gas flow. Ideally, this would mean a ‘‘water cut4 ’’ term would be added to the correction factor to account for the liquid properties. However, there is not as yet a good enough understanding of the effect a water cut has on any DP meters wet gas response for such a correlation to be produced. For example, on close examination of this water cut data it was found that while the kerosene/water

4 Water Cut is defined here as the water volume to total liquid volume flow rate at standard conditions.

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

163

Fig. 19. Sample of CEESI wet gas data showing Liquid property effect.

Fig. 20. All Appendix B, Table B.7 CEESI wet gas data corrected with equation set (17)–(20).

mix wet gas flow data generally showed the over-reading to be between that of the two pure liquid cases of gas/kerosene and gas/water, as would be expected if the liquid properties were truly homogenised, it did not behave entirely as expected. Applying the existing hydrocarbon liquid data based 4 in., 0.75 beta ratio cone DP meter correlation to the water cut wet gas data showed some points with even greater correction errors than the pure water wet gas flow data. Further examination showed that the relationship between water cut and over-reading was more complex than the simple assumption of homogenous liquid mixes. Detailed research on this particular issue was hampered by the fact that the data came from a commissioning run of the facility and therefore the test matrix was not designed for this particular research. In particular the changing of liquid properties between kerosene and water at a constant pressure, constant gas flow rate and constant Lockhart Martinelli parameter meant that the gas to liquid density ratio and the gas densiometric Froude number varied along with the water cut. That is, it was not possible to align every parameter except one during the tests. As DP meters have wet gas responses sensitive to both the gas-to-liquid density ratio and the gas densiometric Froude number any third effect of water cut is therefore not clear from this data set. Research is on-going.

However, currently the natural gas production industry is utilising the 4 in., 0.75 beta ratio cone DP meter to measure wet natural gas flows with hydrocarbon liquid/water mixes. Whereas the gas/hydrocarbon liquid data can be corrected to ±2.6% for a known hydrocarbon liquid flow rate this is not currently the case if the flow contains water. Fig. 20 shows errors well in excess of −5% are possible in such a case. In-lieu of a sophisticated wet gas flow metering correlation that accounts for water/hydrocarbon liquid interaction (which is as yet beyond the state of the art) a practical compromise for a stop gap solution is to fit all available data (i.e. Appendix B, Tables B.1–B.7) in order to encompass all liquid property possibilities (i.e. a water cut range of 0% to 100%). This increases the uncertainty of the gas mass flow rate prediction from the case of hydrocarbon liquid alone, but also avoids the bias possibly in excess of −5%, as earlier discussed, if water is present. The gas/hydrocarbon liquid cone DP meter wet gas correlation (equation set (17)–(20)) was formed by fitting the 6 in., 0.75 beta ratio cone DP meter nitrogen/kerosene data according to de Leeuw’s [6] technique. A plot of Chisholm’s exponent ‘‘n’’ vs. gas densiometric Froude number was made which was data fitted with an equation chosen to be asymptotic with the homogenous model as the gas densiometric Froude number increases (see Fig. 5 and the associated data fit, Eq. (20)). Therefore, to develop the new correlation for natural gas/water/hydrocarbon liquid wet gas flow

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Fig. 21. De Leeuw Style Data Fit to Appendix B, Tables B.1 and B.7 data.

Fig. 22. All Appendix B data uncorrected and corrected by new wet gas equation set (17), (18), (22) and (23).

metering applications, the water cut data is also now fitted. For set gas densities, gas flow rates and Lockhart Martinelli parameters, the average gas-to-liquid density and gas densiometric Froude number values were set and the Chisholm exponent ‘‘n’’ estimated. The original NEL data (Appendix B Table B.1) and the new CEESI water cut data (Appendix B Table B.7) are plotted together in Fig. 21. The new 4 in., 0.75 beta ratio cone DP meter correlation for use with water cut wet gas flows is equation set (17), (18), (22) and (23): for Frg ≤ 0.5 n = 0.143 for Frg > 0.5 n =

1 2

1−

(22)

!!

0.83 exp 0.3 ∗ Frg




.

(23)

Note from Fig. 21, that the Chishom exponent ‘‘n’’ is generally lower for the wet gas flows with water content than the flows with no water. This is to be expected as a lower value of ‘‘n’’ indicates a lower over-reading (i.e. see Eqs. (17) and (18)). Therefore, Eq. (23) is fitted to give a lower Chisholm exponent than Eq. (20) for any gas densiometric Froude number. Also note that, at gas densiometric Froude numbers below 0.5, the Chisholm exponent relationship with the gas densiometric Froude number disappears. De Leeuw [6] stated for his Venturi meter data that this relationship disappeared at gas densiometric Froude numbers below 1.5 which coincides with the flow pattern transition point between annular mist flow and stratified flow. There is no discrepancy here.

Different primary element designs affect wet gas flow patterns through the meter in different ways. (This is synonymous with Reader-Harris’s comment on the Venturi meter geometry affecting a homogenous wet gas flow while here we saw that the cone meter does not seem to have this same affect. Now we are seeing experimental evidence at the opposite end of the flow pattern spectrum, that the Venturi does not perhaps affect the stratified flow pattern as much as a cone DP meter). In fact it is debatible if Eq. (22) could be ignored on the grounds that the vast majority of industrial flows have considerably higher flow rates than this. Fig. 22 shows all uncorrected and corrected (equation set (17), (18), (22) and (23)) 4 in. and 6 in., 0.75 beta ratio cone DP meter data (Appendix B Tables B.1–B.7). The CEESI ‘‘water cut’’ data is data from Appendix B Table B.7. Fig. 23 shows the corrected data only. The result is for known liquid flow rate and known average liquid properties (for example from test separator history or tracer dilution methods), the gas flow rate can be predicted to ±4% to 95% confidence.5 It is noteable, and understandable, that the data with the water content is concentrated on 0 to −4% while the data with

5 Data below a Lockhart Martinelli parameter of 0.02 was ignored as the liquid induced error was too small to distinguish from the single phase scatter. The remaining 669 points were corrected to < ± 4.1% to 95.6% or < ± 4% to 94.6%. This was rounded up to make the statement < ± 4% at 95% confidence.

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165

Fig. 23. All Appendix B data corrected by new wet gas equation set (17), (18), (22) and (23).

no water content is concentrated at 0 to +4%. Maximum spread of the data was +5.9% to −7.1%. It may be noticed the correlation is stated to be for a 4 in., 0.75 beta ratio cone DP meter only when some data is for a 6 in., 0.75 beta ratio cone DP meter. However, as this 6 in. data has no water content the author has decided to err in the side of caution and not assume that water cut data for the 6 in. meter will automatically fit this correlation. 7. Conclusions With cone DP meters being used to meter wet natural gas flows their response to wet gas flow must be well understood if low uncertainty gas flow predictions are to be made. It was previously found that the cone DP meter has the same general wet gas flow responses to changes in the Lockhart Martinelli parameter, gasto-liquid density ratio, gas densiometric Froude number and beta ratio as other DP meters. A 4 in. and 6 in., 0.75 beta ratio cone DP meter correlation was previously produced from data sets from gas/hydrocarbon liquid flows only. For a known liquid hydrocarbon flow rate (and no water present) this correlation (equation set (17)–(20)) is still the most advanced available for these conditions and it will give ±2.6% at 95% confidence. However, it has been shown that liquid properties can affect a DP meter’s response to a wet gas flow. Wet gas flows with water content generally have a lower liquid induced gas flow rate prediction positive bias than hydrocarbon liquid wet gas flows and this appears to be due to the flow pattern at the meter inlet. The precise effect of a water/hydrocarbon liquid mixture (often called ‘‘water cut’’) on wet gas flows is still not well understood. However, data analysis here shows that using this gas/hydrocarbon liquid correlation with a 4 in. or 6 in., 0.75 beta ratio cone DP meter on wet gas data, with water content, gives a gas flow rate prediction uncertainty greater than 2.6%. In fact the uncertainty could be considerably greater than 5%. A practical stop gap solution while industry continues research is to use a correlation that encompasses the full water cut range. This correlation (equation set (17), (18), (22) and (23)) will give ±4% at 95% confidence for a known liquid flow rate. Acknowledgements The author acknowledges the contributions of BG Group, BP, CEESI, Chevron, ConocoPhillips, Emerson Process, McCrometer, the UK National Measurement System Flow Programme and the sponsors of the TÜV NEL and CEESI 1999–2002 wet gas JIP’s in making data sets available for analysis.

Appendix A. Homogenous mixes of liquids with wet gas flows It is assumed here, that for cases where the wet gas flow has a liquid component consisting of water and hydrocarbon liquid, these two liquid components are perfectly mixed by the gas flow and there is one liquid component of average liquid properties related to the relative quantities of water and hydrocarbon liquid present. The following discussion shows how to average the liquid mix density. Let ν lhom ogenous be the specific volume of the homogenously mixed liquids. Let ρ l hom ogenous be the density of the homogenously mixed liquids. Therefore:

ν lhom ogenous =

1

ρ l hom ogenous

.

(A1.1)

Then if we let M ltotal and V ltotal be the total mass of the liquid mix and the total volume of the liquid mix respectively (per unit time) we get (when cancelling out the rates):

ν lhom ogenous = =

V ltotal M ltotal Vwater M ltotal

Vwater + Vhydrocarbon

= +

M ltotal Vhydrocarbon M ltotal

.

(A1.2)

Let the liquid mix flow quality (xl ) be defined by: xl =

˙ water m ˙ water + m ˙ hydrocarbon m

=

˙ water m

(9)

˙ ltotal m

and 1 − xl =

˙ hydrocarbon m ˙ water + m ˙ hydrocarbon m

=

˙ hydrocarbon m

(9a)

˙ ltotal m

˙ water , m ˙ hydrocarbon and m ˙ ltotal are the water, hydrocarbon where m liquid and total liquid mass flow rates, respectively. In unit time a set mass of water and hydrocarbon liquid flows so the flow rate symbol can be dropped here. Substitution of Eqs. (A1.3) and (A1.4) into Eq. (A1.2) for a unit of time therefore gives: ν lhom ogenous = 

Vwater Mwater xl

Vhydrocarbon

+ M

hydrocarbon

 =

1−xl

1

ρ l hom ogenous

(A1.3)

i.e.

ν lhom ogenous = (1 − xl )

Vhydrocarbon Mhydrocarbon

+ xl

Vwater Mwater

(A1.4)

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R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167

Table B.1 Cone meter, NEL, 6 in, beta 0.750 (DTI Flow Programme, 2001)

Table B.4 Cone meter, CEESI, 4 in, beta 0.751 (CEESI wet gas JIP 1999-2002)

Parameter

Range

Parameter

Range

Pressure Differential pressure Approx max gas flowrate

16.5 to 61.9 bara 5.47 Pa to 428 mbar 16 bar - 12.6 MMscf/d 31 bar - 24.6MMscf/d 61 bar - 42.6 MMscf/d 0.023 to 0.090 0.53 to 3.52 < 0.310 0.14699 m (5.787 in.) 0.7498 Nitrogen Exxsol D80

Pressure Differential pressure Approx max gas flowrate

13.6 to 77.5 bara 3.54 Pa to 92.77 mbar 13 bar - 4.1 MMscf/d 50 bar - 12.4 MMscf/d 77 bar - 14.5 MMscf/d 0.013 to 0.088 0.53 to 2.60 < 0.175 3.815 in. (0.0969 m) 0.7512 Natural gas (94 mol% CH4 ) Decane

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

Table B.2 Cone meter, K-Lab, 5 in, beta 0.750 (BG Group, 2005)

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

Table B.5 Cone meter, NEL, 6 in, beta 0.748 (McCrometer, 2005)

Parameter

Range

Pressure Differential pressure Approx max gas flowrate

35.2 to 47.7 bara 26.2 to 2030 mbar 47.7 bar - 93.3 MMscf/d 35.2 bar - 62.2 MMscf/d 0.042 to 0.060 4.28 to 8.80 0.045 to 0.279 5.187 in. (0.13175 m) 0.7500 Natural gas Sleipner condensate

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

Parameter

Range

Pressure Differential pressure Approx max gas flowrate

15.7 to 62.0 bara 12.92 to 657 mbar 16 bar - 22.4 MMscf/d 31 bar - 43.5 MMscf/d 61 bar - 84.2 MMscf/d 0.022 to 0.090 0.80 to 4.35 < 0.300 5.786 in. (0.1470 m) 0.7478 Natural gas (94 mol% CH4 ) Exxsol D80

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

Table B.3 Cone meter, CEESI, 4 in., beta 0.750 (Chevron, 2005) Table B.6 Cone meter, NEL, 4 in, beta 0.749 (Emerson Process, 2005)

Parameter

Range

Pressure Differential pressure Approx max gas flowrate

39.7–75.8 bara 9.69–750 mbar 42 bar–24.9 MMscf/d 73 bar - 42.5 MMscf/d 0.042 to 0.082 0.94 to 7.38 < 0.227 3.826 in. (0.0971 m) 0.7499 Natural gas (94 mol% CH4 ) Stoddard solvent

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

Parameter

Range

Pressure Differential pressure Approx max gas flowrate

15.6 to 60.6 bara 26.4 to 529 mbar 16 bar - 17.4 MMscf/d 60 bar - 31.5 MMscf/d 0.024 to 0.090 1.4 to 4.7 < 0.302 3.829 in. (0.09725 m) 0.7492 Nitrogen Exxsol D80

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

i.e.: 1

=

ρ l hom ogenous

xl ( 1 − xl ) + ρhydrocarbon ρwater

(A1.5)

i.e.

ρ l hom ogenous

ρhydrocarbon ρwater = . ρwater (1 − xl ) + xl ρhydrocarbon

(10)

Appendix B See Tables B.1–B.7

Table B.7 Cone meter, CEESI, 4 in, beta 0.750 (Commissioning Run, 2007) Parameter

Range

Pressure Differential pressure Approx max gas flowrate

13.5 to 69.0 bara 25 mbar to 431 mbar 13 bar - 7.4 MMscf/d 56 bar - 24.9 MMscf/d 69 bar - 32.7 MMscf/d 0.012 to 0.074 1.02 to 5.41 < 0.305 3.826 in (0.0971 m) 0.7499 Natural gas Exxsol D80 and/or water 0% to 100% water cut

Gas-to-liquid density ratio Frg range XLM Inside full bore diameter Beta Gas phase Liquid phase

References [1] Steven R. Wet gas flow definitions, In: North sea flow measurement workshop. 2007. [2] Steven R, Hall A. Orifice plate meter wet gas flow performance. Journal of Flow Measurement and Instrumentation. [3] Murdock JW. Two-phase flow measurements with orifices. Journal of Basic Engineering 1962;84(December):419–33. [4] Chisholm D. Flow of incompressible two-phase mixtures through sharp-edged orifices. Journal of Mechanical Engineering Science 1967;9(1).

[5] Chisholm D. Research note: Two-phase flow through sharp-edged orifices. Journal of Mechanical Engineering Science 1977;19(3). [6] De Leeuw R. Liquid correction of venturi meter readings in wet gas flow. In: North sea workshop, Paper 21. 1997. [7] Steven R. Horizontally installed differential pressure meter wet gas flow performance review. In: North sea flow measurement workshop. 2006. [8] Stewart D, Steven R. et al. Wet gas metering with V-cone meters. In: North sea flow measurement workshop, Paper no. 4.2. 2002.

R. Steven / Flow Measurement and Instrumentation 20 (2009) 152–167 [9] Stewart DG. Application of differential pressure meters to wet gas flow. In: 2nd international South East Asia hydrocarbon flow measurement workshop. 2003. [10] Steven R. Liquid property and diameter effects on venturi meters used with wet gas flows. In: International fluid flow measurement symposium. 2006. [11] Reader-Harris MJ, Hodges D, Gibson J. Venturi-tube performance in wet gas using different test fluids. NEL report 2005/206. 2005. [12] Reader-Harris MJ. Venturi-tube performance in wet gas using different test fluids. In: North sea flow measurement workshop. 2006. [13] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas–liquid flow. AIChE Journal 1976;22(1). [14] Ifft S. Wet gas testing with the V-cone flowmeter. In: North sea workshop, Paper 22. 1997. [15] Steven R. Research developments in wet gas metering with V-cone meters. In: North sea flow measurement workshop. 2003.

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[16] Steven R. et al. Wet gas metering with V-cones. In: 3rd International South East Asia hydrocarbon flow measurement workshop. 2004. [17] Steven R, Kegel T, Britton C. An update on V-cone meter wet gas flow metering research flomeko. 2005. [18] Evans R, Ifft S. Wet gas performance of differential pressure flow meters. In: North sea flow measurement workshop. 2007. [19] Steven R. V-cone wet gas metering. In: North sea flow measurement workshop. 2007. [20] Steven R, Hall A, Stobie G. A re-evaluation of axioms regarding orifice meter wet gas flow performance. In: 6th International South East Asia hydrocarbon flow measurement workshop. 2007. [21] Reader-Harris M, Hodges D, Gibson J. Venturi-tube performance in wet gas: Computation and experiment, Paper 11.1, In: SE Asia hydrocarbon flow measurement workshop. 2007.