Terry Cousins, Reynolds Number Correction of … · Reynolds Number Linearisation •!At the time...

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The Reynolds Number Correction of Liquid Ultrasonic Meters and Coriolis Meters

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0.1% !!!!!

•! We have to remember that in Liquid Custody Transfer Measurement we are looking for 0.1%’s –! This may be a claimed value. –! This may be an aspiration value. –! It may even be a believed value

•! After 45 years I now know that it is a notional value. –! The slightest “twitch” in procedures, installation, design, change

in fluid properties etc. will destroy that notion.

•! It is therefore necessary to consider all the aspects of a meter that go into the final performance of a meter – this presentation considers one of them REYNOLDS NUMBER.

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Some History of Reynolds Number Correction

•! Whatever the belief to the contrary, all meters involved in measuring fluids are influenced to a greater or lesser extent by Reynolds number. –! Even PD meters have a small Reynolds number effect, although

it is generally seen as a only a viscosity effect. –! Reynolds number correction, or linearisation has been endemic

in flow meters from the earliest days.

•! The early BS 1042 (1964)1, shows clearly the non-linearity of the square edge orifice plate.

Some History of Reynolds Number Correction

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Reynolds Number Linearisation

•! At the time of BS 10420 (1964) the correction calculations were done by hand.

•! There was no shame in a meter having a Reynolds number Characteristic

•! Nowadays, in ISO 5167, for orifices, of course there is an equation, and the flow computer does the correction.

•! It is, however, a linearisation based on knowledge of the Reynolds number, and as a consequence requires an associated extra uncertainty based on the knowledge of the flowing Reynolds number, and confidence in the shape of the curve.

Linearisation and (LCP)

•! Linearisation of a meter, for whatever reason, will introduce extra uncertainty, both in the statistical meaning and the concept that there is now doubt about the performance.

•! The following quote(2) is worthy of noting: –! “One note of caution! Clever electronics can take

any signal, however nonlinear, and straighten the characteristic before the signal is output !.. (Referring to the steep part of a turbine meter curve) The characteristic is probably very sensitive to minor variations in this region, and any attempt to use the characteristic could lead to disguised, but serious, errors.”

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Linearisation and (LCP)

•! This tells us that when we linearise the base parameter ( I call LCP, Linearisation Correlation Parameter) must be: –!Well understood. –!Stable. –!Easy and consistent to determine.

•! The relationship between the meter calibration and the LCP must also be: –!Well understood. –!Stable. –!Easy and consistent to determine. –!And should have the minimum of variation.

Reynolds Number as a LCP

•! Going back to basics:

•! To obtain Reynolds number ,we need to know:

–!Flowrate, velocity, mass or volume. –!Characteristic dimension, usually diameter. –!Kinematic viscosity, or Density & Absolute

Viscosity.

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Reynolds Number as a LCP

•! Essentially we know: –!Flowrate (Although if not corrected for the

Reynolds number curve will not be correct). –!We know the characteristic dimension.

•! We often do not know, with any degree of certainty: –!Kinematic viscosity. –!Density. –!Absolute Viscosity.

•! If we are unsure of the viscosity or the density then our LCP is going to be fragile, and the correction will be almost certainly be wrong!!

Reynolds Number

•! BS 1042 acknowledged that there was an increase in uncertainty (Tolerance in BS1042 speak) associated with the correction. They recommended the following calculation procedure: –!BS 1042 advised an iterative process to get a

better answer. •! From the flowrate ,viscosity and density (usually estimated)

calculate the Reynolds number. •! From the Reynolds number get the new correction factor. •! Correct the flowrate and repeat the process.

•! This was a nightmare to do by hand!!!

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USM Reynolds Number

•! Concentrating only on Multi-path USMs •! It is convenient to divide the Reynolds Number

effect on USMs into 4 Sections: –! High Reynolds numbers-above 1,000,000–Gas, LNG possibly

Butanes etc. –! Medium Reynolds numbers-10,000 to 1,000,000- Kerosenes, jet

fuels, light and medium crudes, diesels. –! Low Reynolds numbers (Transition)-2000 to 10,000-Heavy oils,

Bunker oils –! Low Reynolds numbers (Laminar)

•! Each of these regions has a different effect depending on the design and installation

USM High Reynolds Number

•! Generally fluid machines become more consistent as the Reynolds number increases.

•! With LNG, high Reynolds numbers, USMs they generally exhibit on the smallest of non-linearity “out of the box”

•! Below is the calibration of 11 eight path meters within the Reynolds number range of 700,000 to 3,000,0000. All within 0.08% out of the box6

0.9980

0.9984

0.9988

0.9992

0.9996

1.0000

1.0004

1.0008

1.0012

1.0016

1.0020

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Flow rate (m3/hr)

Met

er fa

ctor

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USM Medium Reynolds Number

•! This is the area where a majority of liquid meters operate.

•! This is also where the non-linearity starts to show. •! If Non-linearised the curves against flowrate, what the

user is interested in, appear to be non-repeatable.


•! The scatter is due to the fact that the meter is non-linear with Reynolds number.

•! The level of non-linearity depends on the design, in particular the transducer path positions.

•! For example the curves shown next are typical for two different solutions to the Gaussian quadrature equation: –! Most common is the Gauss-Jacobi. –! The Legendre solution can and is used. –! The major physical difference is that the outer transducers

of the Legendre are further out from the centre than the gauss-Jacobi.

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•! As can be seen both curves need linearising to bring them into normal specified linearity of a Custody Transfer USM.

•! It is clear that the Gauss-Jacobi requires more linearising.

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•! However, all is not clear-cut, Engineering does not allow something for nothing!! –! The Legendre is difficult to manufacture in small sizes, because

of the port positions. –! Also it can be noisier because the outer transducers are nearer

the maximum turbulence position, this is particularly a problem if the range takes them down to the transition region.

•! Other meter designs have paths at different spacing's and even more paths: –! The positioning is usually experimentally designed to improve

base linearity. –! However, the same comments do apply in engineering terms.

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•! How do we Linearise them? •! There are three base methods of determining the

LCP: –! Direct Linearisation, using calculated Reynolds number.

•! Issues is how to obtain the Viscosity and to a lesser extent the density.

•! VOS-Viscosity, can be used •! A viscometer can be used. •! Fixed known values can be used. •! All are difficult and can be fragile.

–! Profile •! Here the assumption is made that profile changes in some in a

consistent relation to Reynolds number. •! Also that the profile is the same at calibration as on site. •! It should be noted that this method begs for some flow profile

control into the meter, to give any consistency.


–! Weighting Factors •! These are the factors that are derived from the design of the

meter to give each path the correct value in the calculation of mean velocity.

•! Described in detail in Reference 3. •! It is dangerous as it moves the meter from the design

parameters, and it requires the ability ton be able to get into the meter and modify it.

•! Because of the non-linearity the question of calibration in this region becomes important. –! Is the curve repeatable and stable enough to be derived just from a

water calibration, remembering the uncertainties we are looking for? –! The answer is that a calibration over the operating condition ranges

needs to be carried out. –! This is described well in reference 4, from NSFMWS 2013.

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•! Does Proving solve the problem? •! It may, but can also lead to proving problems:

–! Any proving correction on site must be Reynolds number based, not flowrate.

–! If the correction method is not valid then proving through the year can look like the meter drifts, and is not repeatable, because temperature changes the viscosity.

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USM Transition and Laminar Reynolds Number

•! At transition the issues are non-linearity combined with non-repeatability. –! Non- repeatability is due to the large variation in turbulence and

profile due to the flow changing from laminar to turbulent with time.

–! It can be mitigated by moving the outer paths away from the walls towards the centre’

–! It can be solved by using a reduced bore section at the transducers4.

•! Laminar flow, not only has a rapid variation in profile with Reynolds number, but has practical problems with temperature gradients4.

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Reynolds Number and Coriolis Meters

•! To Quote “Measurement, Instrumentation, and Sensors Handbook, Second Edition: edited by John G. Webster “Coriolis meters have no Reynolds number constraints and can be applied to almost any liquid or gas!. “ –! This has also appeared in most of the sales literature for Coriolis

meters over the years. •! Yet when the meters are calibrated on oil, rather than the consensus

of water, it is clear that they have, below 10,000 Reynolds number a variation dependent on the meter design, manufacture, and almost certainly have done over their entire history.

•! The first indication of this came from the NEL data presented in 2008, showing the data for two different manufacture meters. –! They exhibited shifts with viscosity. –! But Reynolds number was not plotted.


•! Subsequently the data was re-plotted and “lo” there was a strong Reynolds number effect.

•! This has now been vindicated by other data, and for other sizes of meter, two examples of which are shown below.

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Coriolis Meter Questions

•! The description of why Reynolds number causes non-linearity I leave to a subsequent presentation at the workshop, but that leaves two other important questions: –! How can over 25 years gone by without this being known? –! What are the implications?

•! There appear to be a number of reasons for missing and essential feature: –! They started as process meters, and 0.1% was not an issue. –! Lack of proper testing over all the required parameters. –! A belief that because they are “mass meters” they are not

sensitive to the vagaries of other meters. This is summed up in a cartoon by Steiner Fosse of NPD (He has give me permission to show it here):

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Sales Talks from the Early Years“New Religion”

All our worries are over.... .....just install Coriolis Meters

Implications

•! The major implication begs the question,“is a water calibration sufficient to characterize a Coriolis meter” –! It will depend on the repeatability of the curve from meter to meter. –! There will still be at Low Reynolds number an uncertainty penalty to

pay for such calibration policy. –! My view is that when dealing with 0.1’s the meters should be

calibrated over the process Reynolds numbers.

•! Another implication is, if it took us over 20years to find this issue, what other issues have not been found? –! Are we sure that water calibrations sufficient for Gas? –! How well do they work with water/ oil mixtures? –! These all require data to show the true operation.

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Conclusions

•! The conclusions are simple and short: –!No fluid machines are immune to Reynolds

number to a greater or lesser extent. –!0.1% is a difficult number to achieve in flow

measurement, and every care needs to be taken to achieve it.

–!Proper calibration of meters is required to achieve this with meters with fundamental non-linearity, even with proving.

–!Nothing substitutes for proper testing of meters.

References

1.! BS1042 Part 1 1964 2.! Liptak B.G - Editor in Chief “Instrument-Engineers-Handbook-Fourth-Edition-Volume-

One-Process-Measurement-and-Analysis” Fourth edition CRC publication for ISA 3.! Øyvind Nesse StatoilHydro “Experience with ultrasonic meters on high viscosity oil”

25TH North Sea Flow Measuremen Workshop 2007 4.! Gregor J Brown, et al “A Multipath Ultrasonic Meter with Reducing Nozzle for

Improved Performance in the Laminar/Turbulent Transition Region” 27th International North Sea Flow Measurement Workshop 20 – 23 October 2009

5.! Edited by John G. Webster “Measurement, Instrumentation, and Sensors Handbook, Second Edition” Halit Eren

6.! Gregor Brown et al, Cameron, UK “LNG Allocation Metering Using 8-Path Ultrasonic Meters”, 25th North Sea Flow Measurement Workshop 16 - 19 October 2007

Terry Cousins, Reynolds Number Correction of … · Reynolds Number Linearisation •!At the time...

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