the americas flow measurement workshop - geometry of differential pressure flow meters

8/3/2019 The Americas Flow Measurement Workshop - Geometry of Differential Pressure Flow Meters.

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The Americas Workshop26-28 April 2011

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The Effect of Geometry on Differential Pressure MeterPerformance

Klaus J Zanker, Letton-Hall Group USAPhilip A Lawrence, Cameron Valve & Measurement USA

1 Introduction

Recently there have been various independent studies regarding the effect of unprocessedhydrocarbon fluids on the geometric stability and application of various types of differentialpressure (dP) meters used in upstream flow measurement, particularly in the field of erosion, akey parameter in the operation of meters that obstruct the flow (dP devices).

Most of the technical work for this type of erosion testing has been performed in a laboratoryusing techniques to accelerate years of wear into a short period spanning a few months.

This paper discusses and focuses on the relative differences in operation and applicationbetween the main dP meter types that have been subject to erosion testing based on this

accelerated wear methodology. Techniques together with information showing methods to reducethe wear, particularly in the newer cone meter family, are discussed.

2 The Differential Pressure (dP) Meters

Daniel Bernoulli 1700 1783 and Giovanni Battista Venturi 1746-1822 established the basictheory:

Figure 1. Venturi Meter Theory

Conservation of energy in a perfect fluid (incompressible and frictionless) gives:

By continuity the flow Q is the same at sections 1 & 2, hence


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The Venturi has CD = 0.99, only 1% deviation from the Bernoulli theory. This is because theacceleration from the upstream pipe to the throat tends to produces a uniform velocity profile, witha thin boundary layer blocking just 1% of the throat area. The high throat velocity produces thedP, but it also makes the throat taping sensitive to imperfections and liable to erosion.

The standardized un-calibrated Venturi is available with from 0.4 to 0.75 to meet the 1.0%uncertainty of C

D.

The downstream cone acts as a diffuser to recover some of the kinetic energy at the throat. Thismakes the Venturi a relatively low loss device, but at the expense of size, weight andmanufacturing cost.

2.2 The Orifice Plate

The orifice is a much smaller and lighter device, consisting of a thin plate (1/4 in) held betweenflanges. The pressure taps are in the flanges and do notexperience a high velocity. The main feature of the orificeplate is the sharp edged concentric hole, which makes theflow separate and contract downstream to the Vena

Contactor. This is like the Venturi throat, but formed by fluidstreamlines and not solid surfaces. The orifice CD = 0.6, whichreflects the Vena Contactor area being less that the orificebore area. The orifice does not have a diffuser and suffers asudden expansion loss, but despite this it almost displacedthe Venturi because of its simplicity in single phase flow. Thesharp edge is sensitive to damage and this led to the

introduction of a fitting (Daniel 1930) that allows the orifice to be taken out of the line underpressure to examine the sharp edge. The sharp edge is not good with erosion making the orificeless desirable for multiphase flow, but it is used with wet gas.

The standardized un-calibrated orifice plates are available with from 0.2 to 0.6 to meet the 0.5%uncertainty of CD.

2.3 The Cone Meter

The cone meter is an annular Venturi without a diffuser and the low pressure tap is in the base ofthe cone, where it does not experience a high velocity or erosion.

Figure 3 - Horizontal Cone Meter

With multiphase flow in a horizontalpipe the meter is self cleaning. Liquidand solids will not be trapped at thebottom of the pipe and gas will not betrapped at the top of the pipe. Thethroat is formed by the annular area

between the pipe wall and conemaximum diameter. This physicalthroat is not the highest velocitylocation because the angle of the conedirects the flow to contract furtherdownstream, giving CD = 0.82 to 0.85


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Figure 4 - Vertical Cone Meter

The cone meter is available with from 0.45 to 0.85, but it has not been standardized yet, apartfrom the API chapter 22.2 D.P test protocol, which details a method for performance typeapproval.

2.4 The Wedge Meter

Figure 5- Wedge Meter Cross Section

The wedge meter was designed as part of the Dual-Stream wet gas meter, which consists of aVenturi in series with the wedge. It was chosen to have a very different response to wet gas (overreading) than the Venturi, so that both the gas and liquid flow could be measured.

The wedge is very different to the Venturi, orifice and cone meters, which are axi-symmetric andby varying the area ratio (2) produce a series of meters. The wedge meter is three dimensionaland with the wedges reaching the centreline it only has one area ratio 2 = 0.5 or = 0.707. Thewedge meter has a CD = 0.79 and has not been standardized.

With multiphase flow it is common toinstall the cone meter on a blind Tee,turning the horizontal flow to verticallyupward flow to improve mixing andreduce gravity effects.

Liquids and solids will tend to fill the lowpressure cone base tap, giving a falsedifferential pressure.The solution is to use a wall tap a littledownstream of the cone. This wall tapexperiences the highest velocity making itsensitive to imperfections and liable toerosion, loosing the advantage of thecone base tap.Slug flow could bend the support strut.The cantilever strut can be replaced by adiametric strut and/or three welded websupports between the downstream cone

and pipe wall can give additionalstructural strength to the meter.


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The Venturi, orifice and cone meters have a throat with a low pressure tapping at the maximumvelocity. The wedge does not have an obvious throat and the low pressure tapping is not at athroat, but in the pipe wall. The wedge meter is closer to a total loss device than a classicalBernoulli device.

3. Meter Comparisons

The Venturi, orifice, cone and wedge meters are different and it is not obvious how to comparethem. The discharge coefficients are different as seen in Fig 6.

Figure 6 - Meter Discharge Coefficient (per beta)

Another way of comparing the meters is by the differential pressure they produce for the sameflow in the same pipe size (same V1).

and

With J = CD Y E a / A = CD Y E 2 Then we get

1/J2

is a multiplier that expresses dP in terms of the upstream dynamic pressure (velocity head).

Taking an example from Fig 7: a = 0.55 Venturi, a = 0.6 cone and a = 0.68 orifice allproduce the same dP (10 V1

2/ 2).

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Beta

Cd

Cone Orifice

Venturi Wedge


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Figure 7- Meter Differential Pressure

If the overall energy loss is important the loss/differential is relevant because it is the loss incurredfor the desired differential pressure.

Figure 8 - Meter Pressure Loss

The low loss of the Venturi is due to the diffuser downstream of the throat, but it increases thesize, weight and cost of the meter.

1

10

100

1000

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Beta

dp

/V^2/2

Cone Orifice Venturi wedge

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Beta

Loss/Differential

Cone orifice Venturi Wedge


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Figure 10. = 0.8 Cone and Orifice

5. Meter Erosion

There has been experimental and Computational Fluid Dynamic (CFD) work on flow meter

erosion. The CFD gives a good insight into the process [Ref 1 & 2].

Figure 11 - Venturi - Predicted Velocity Contours (m/s)

0.6

0.2

0.8

0.1

CONE ORIFICE


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Figure 12 - Venturi - Predicted Erosion Depth Contours (mm)

Figure 13 - Cone - Velocity Contours (m/s)


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Figure 14 - Cone - Predicted Erosion Depth Contours (mm)

Figure 15 - Wedge-Predicted Erosion in Water-Sand (kg/m2-s)

There is also experimental data using high sand concentration and high velocity to accelerate theerosion process to yield lab results in a few months instead of many years in the field.


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Figure 17- Photographs of the Cone Meter

Figure 18 - Photograph Showing Erosion of the Venturi Throat Taps.

Table 2. Summary of the Erosion Test Results.

The Venturi is least affected, because the tap and bore erosion counteract each other.

The Wedge with the highest and lowest dP has the worst erosion scar (0.343), but the changein CD (1.72%) is modest. This is because the scar is in the pipe wall and not on the wedges.

The cone scar is modest (0.14) but it affects the narrow annular gap of the cone throat, causinga large (10.77%) change in CD.

The effect of erosion on meter performance is complex. It depends upon , the meter design, thelocation of the scar, the size of the scar and the sensitivity of the meter to the scar.

Meter Beta % Cd Max Scar in LocationVenturi 0.5 -0.63 0.014 bore tapWedge 0.7 1.72 0.343 wall

Cone 0.5 10.77 0.14 wall/tap


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Probably the best way to compare erosion in different meters is on the basis of equal dP,because dP is the driving force that produces the erosion.

5.1. Meter Erosion Parameters

It has been found that erosion depends on the following factors [Ref 3]:

n

throat

metal

sand

ccVk

mcE ...

Where:

Ec is the maximum increase in the scar depth over the time period (mm)

cc is a constant to account for the meter design and the units

msand is the total mass of sand that has passed through the meter in the time period (kg)

Vthroat is the mean fluid velocity in the cone throat (m/s)

metal is the density of the material from which the meter throat is constructed (kg/m3)

(metal = 7850 kg/m3

for steel grade materials)

k is a material constant (k = 2 x 10-9

for steel grade materials)

n is a material constant (n = 2.6 for steel grade materials)

The main factors to reducing erosion are to reduce the amount of sand and V throat.

Reducing the mass of sand has a direct linear effect on the erosion scar.

Reducing Vthroat has the largest effect (V2.6

), so halving the velocity reduces the scar depth (by 22.6

= 6.06) six fold. Vthroat can be reduces by increasing the meter size or by increasing the meter .

This information can be used to reduce an accelerated erosion test to more normal conditions.

5.2 Erosion Resistance (Cone Meter Types)

One method to negate the effect of erosion is to fit a sleeve in the rear of the meter body madefrom a hard-facing material or cobalt based alloy. The hard facing can also be applied to the mainparts of the cone differential producer element. This will help to protect and allow the device to beused without worrying about a change in geometry when sand content in the fluid is high becauseof the hardness of the sleeve (Fig 19a).

The hard faced sleeve shown as #132 in the sectional drawing (Fig 19b) is interchangeable fromthe rear end of the meter body. The cone # 18 and the support cantilever #19 can also be hard-faced to enable a longer life under extreme sand erosion conditions.

Hard-facing materials can be applied to any other dP devices when it is known where the erosionoccurs.

6. Area Ratio Change.

The use of the anti-erosion sleeve idea can be used to change the beta ratio of an existing meterwithout changing the diameter of the cone. It is an option that can be used in extreme


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circumstances where the meter range ability has been affected by a drop in the field flow rates(Fig 20). Some form of calibration to determine the new CD would be needed [Ref 4].

Field calibration of the sleeve system with a test separator is also possible when using the meterson gas dominant full-well stream measurement applications.

Fig 20- Area or Beta-Ratio Changer Using a Sleeve

7. Conclusions

The effect of erosion on meter performance is complex. It depends upon the application, the ,the meter design, the location of the scar, the size of the scar and the sensitivity of the meter tothe scar.

It is not obvious how to compare the erosion performance for different meter designs, but thesame dP for the same flow (1/J

2) seems reasonable.

Erosion can be reduced by using lower flow velocity, higher beta and avoiding pressure taps in

high velocity regions.

The relation between erosion, sand mass and velocity allows accelerated erosion testing to berelated to practical cases.

CFD is a useful tool for predicting where erosion occurs and to estimate its effect on meterperformance.

Knowledge of the scar location allows the application of hard faced erosion resistant materials.


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The newer geometry devices that are now available enhance the dP device family, are useful inthe more unusual areas of measurement (Upstream, wet gas, sub sea, etc.) and make newdevelopments possible.

Recent work with the cone meter using a hard-faced sleeve system to combat sand erosion andthe bonus of being able to change the beta ratio, without changing out the meter, is a usefuladdition.

7. References

1) BARTON, N.A., ZANKER, K.J. & STOBIE, G. Erosion Effects On Venturi and ConeMeters, ThAW 2010

2) BARTON, N.A., et al. Erosion in Subsea Multiphase Flow Meters, ThAW 2011

3) HAUGEN, K., KVERNVOLD, O., RONOLD, A. & SANDBERG, R. Sand erosion of wear-resistant materials: erosion in choke valves. Wear 186-187, pp 179-188, 1995.

4) LAWRENCE/BRAID Cameron Inc (USA & Canada), Cone Equations for Flow Computersa Technical Document - 2006

the americas flow measurement workshop - geometry of differential pressure flow meters

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