Mm029139. in Situ Verification Technology for Coriolis Flow Meters

8/8/2019 Mm029139. in Situ Verification Technology for Coriolis Flow Meters

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An In Situ Verification Technology 1/5for Coriolis Flowmeters

Timothy J. Cunningham

Micro Motion, Inc7070 Winchester CircleBoulder, CO 80301

(303) 530-8590 (303) 530-8596 (fax) [email protected]

Abstract: Structural Integrity Meter Verification is a robust new Coriolis verification technology which usesthe onboard electronics to very accurately measure the stiffness of the flowtubes. The flow tube stiffness isdirectly related to the flow calibration factor and is uninfluenced by process conditions. Meter Verificationcompares the measured stiffness to the factory baseline stiffness to confirm that the flow calibration factor isunchanged from the factory value. Structural Integrity Meter Verification also performs additional electronicsand software checks to ensure accurate measurement. This new technology allows users to save moneyand reduce downtime by verifying Coriolis meters in situ.

Sometimes Coriolis meters are used with corrosive fluids that can etch away the tube or with erosive fluids

that can cause localized thinning of the tubes. In these applications the precision and accuracy of the Cori-olis flowmeter outweighs the replacement costs. A Coriolis meter has been deliberately corroded whiletracking the flow calibration factor and the stiffness. Finite element analysis was used to analyze the rela-tionship between stiffness and flow calibration factor for erosive applications. Meter Verification results forthese cases are compared to the experimental and analytical data.

1. INTRODUCTION

Flowmeters are commonly validatedby comparingthe indicated flow measurement to a reference flowmeasurement. Flowmeters are also commonly veri-fiedby tracking a secondary variable that is highlycorrelated to the flow measurement. For example,

orifice plates can be measured to verify accuracy.Other verification techniques include spindown testsfor turbine meters and speed of sound and trans-ducer gain checks for ultrasonic meters.

Coriolis meters have historically used secondaryvariables to verify performance, e.g. drive gain.Unfortunately drive gain is only loosely correlatedwith the flow measurement. A method of verifica-tion using a known density fluid has been used suc-cessfully, but this approach is prone to user error.

In response to customer demand for an easy to usemeter verification methodology for Coriolis flowme-

ters, Micro Motion has developed Structural Integri-ty Meter Verification that uses the onboard electron-ics to verify the integrity of the flow tube as well asthe electromechanical components, the transmitterelectronics, and the transmitter software.

2. CORIOLIS FLOWMETER BACKGROUND

Structural Integrity Meter Verification uses the stiff-ness of the flow tubes as the secondary variable to

verify the correctness of the Flow Calibration Factor(FCF). The FCF is the proportionality constant that

relates the time delay, t, to the mass flow rate, m.

= m FCF t (1)

Equation (1) can be derived from first principles, forexample starting with the Housner differential equa-

tion describing a fluid-conveying beam [1, 2]. Thesederivations result in a term corresponding to theFCF as shown in Equation (2).

3

EIm C t

L= (2)

where C is a dimensionless geometric constant re-lated to the boundary conditions and beam proper-ties. The

3EI

Lterm, corresponding to the FCF, has

units of force/length, the units of stiffness.

Going through these derivations in detail to showthis relationship between stiffness and flow calibra-

tion factor is beyond the scope of this paper. How-ever a much simpler dimensional analysis of Equa-tion (1) shows that the FCF has units of stiffness.

Rearranging equation (1)

=

mFCF

t(3)

shows that the units of the FCF are mass flowrate/time delay. This is shown dimensionally as

AN IN-SITUVERIFICATION TECHNOLOGYFOR CORIOLIS FLOWMETERS


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Mass

Time

Time

(4)

For example, FCF is commonly expressed in units

of (gm/sec)/sec. In a consistent system of units,mass can be represented by force/(acceleration ofgravity), taking advantage of Newtons Second Law.Plugging this into equation (4)

2* /Force Time Length Mass

Time ForceTime

Time Time Length

= = (5)

shows very simply that the flow calibration factorhas units of stiffness (Force/Length).

The equivalence of FCF and stiffness shows whystiffness is the secondary variable that is highly cor-

related to the FCF. The problem now becomes oneof how to determine the stiffness of the flow tubes.

2.1 Meter Verification Theory

Coriolis Structural Integrity Meter Verification usestechniques from Experimental Modal Analysis andStructural Dynamics theory to very accuratelymeasure the stiffness of the flow tubes using theembedded electronics and onboard pickoff anddrive coil and magnets.

Figure 1 shows a typical Coriolis mass flow meter.The drive coil and magnet at the top center in-

between the tubes is used to drive the Coriolisflowmeter at resonance. A feedback control systemin the flowmeter electronics applies a sinusoidalcurrent to the drive coil to maintain resonance at aspecific amplitude. The two pickoff coils and mag-nets produce a voltage in response to the reson-ance motion. The pickoffs are used as the feedbacksignal to control amplitude. The transmitters digitalsignal processing uses the pickoff responses to es-timate the frequency of vibration, used in the densi-ty measurement, as well as the time delay between

the two pickoff sinusoids, t, needed for the massflow measurement. Further details discussing the

operation of a Coriolis flowmeter are given in Ref-erence [3].

Meter Verification runs on top of the standard Cori-olis signal processing and drive control. A series oftones are added to the drive signal. These tonesexcite off-resonance responses in the two pickoffs.The embedded flowmeter electronics measuresthese tonal inputs and responses to produce a fre-quency response function (FRF).

Figure 1. Typical Coriolis Flowmeter

A structural dynamics FRF can be modeled as a

second order system with the parameters of stiff-ness (K), mass (M), and damping (C). Applyingelectromagnetic theory to the problem, the FRF canbe defined by pickoff voltage/input current.

( )( )( ) 2

X jFRF H

F M jC K

= = =

+ +

(6)

The Meter Verification results are based on fittingthe measured FRF to the second order model toindependently estimate K, M, and C. Figure 2shows this graphically. The lower frequency portionof the FRF is dominated by the stiffness. The high-er frequency portion is dominated by the mass.

These mass and stiffness lines, as they are called,are shown in the plot, and are actually reciprocalsof the mass and stiffness.

Figure 2. Nominal Frequency Response Function

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Frequency Response Function

Frequency (Hz)

FRF

Magnitude

Nominal KNominal M

Freq=sqrt(K/M) Peak ~1/


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The resonant frequency is determined by thesquare root of ratio of the mass and stiffness. Theheight of the resonant peak is determined by the

non-dimensional damping coefficient , which isrelated to the damping, C, by Equation (7).

2C

KM = (7)

The embedded core processor performs the signalprocessing necessary to generate the FRF; curvefits the FRF to generate estimates for K, M, and C;and handles all of the bookkeeping to keep track ofthe results generated by Meter Verification.

3. RESULTS

Meter Verification distills all of its results down totwo simple numbers that it presents to the custom-er. Meter Verification starts with the factory baseline

verifications during the standard meter calibrationprocess, which Micro Motion performs on both airand water as part of its comprehensive diagnosticprogram. However since the process fluid does notchange the stiffness of the meter, the factory base-line stiffnesses on air and water are statistically thesame. Each meter verification measurement isnormalized by the average of these stiffnesses andconverted into a stiffness uncertainty, which is thepercentage change in the measured stiffness fromthe factory baselines.

( ), ,1 %

2

( )

uncertainty

measured

factory air factory water

stiffness

stiffnessstiffness stiffness

=

+

(8)

Normalizing the stiffness uncertainty in this waymakes it easy to track any changes in the flowmeterby using a format that is convenient to view. (Thisstiffness uncertainty should not be confused withthe term measurement uncertaintyas it is used inmetrological terms.)

3.1 Meter Verification Stability

The signal processing used in Meter Verification

has been designed to enhance the stability of themeasurement. Each stiffness uncertainty mea-surement is the average of the stiffness estimatesfrom many FRFs. In turn, each FRF that is fit is av-eraged from many individual FRF measurements.This averaging results in a very stable stiffness un-certainty estimate. In line with standard measure-ment techniques, the variation in the meter verifica-tion uncertainty is several times better than the

base flow accuracy. Figure 3 shows a typical meterverification uncertainty plot with a standard devia-tion of less than 0.01% under laboratory conditions.Note that stiffness uncertainty is calculated for eachof the two pickoffs, further increasing the confi-

dence in the measurement.

Figure 3. Meter Verification Stability

Meter Verification uncertainty variation is of coursesubject to field effects. The specification limits forstiffness uncertainty are set such that under the full

range of field effects there is a 3 probabilityagainst giving a false alarm. Meter Verification,specification limits and field effects are discussedmore fully in References [4] and [5].

3.2 Meter Verification Corrosion Detection

Because Coriolis meters operate with no movingparts, the calibration is expected to be unchangedover the life of the meter. Most customers usingMeter Verification will expect to see stiffness uncer-tainty results around 0%, indicating that the meter isunchanged from the factory baseline. However, be-cause of their value proposition, Coriolis meters aresometimes used with incompatible, corrosive, fluidswhere the lifetime of the meter may be on the orderof 1 to 2 years. For these applications, Meter Verifi-cation can be used to detect changes due to corro-sion in the tubes.

Finite element analysis (FEA) is used extensively inthe design of Coriolis flowmeters [6]. FEA can alsomodel the effects of corrosion in flowmeters. Thedetails of this FE work are beyond the scope of thispaper, but these analyses illustrate some of thetechnology behind Meter Verification.

Figure 4 is an extension of Figure 2, where the no-minal FRF is shown in blue. The FE model wasmodified to simulate corrosion and used to generate

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Uncertainity%

Structural Integrity Normalized Stiffness

Meter Verification Counter

l spec

u spec

KLPOoutlet

KRPOinlet


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a second FRF, shown in green. Note that with thecorroded tubes the frequency has decreased. A keyfeature of the meter verification technology is thatthe test tones used to generate the FRF are dynam-ically determined, based on the instantaneous drive

frequency. These test tones are shown as blue xsfor the nominal case and as green os for the cor-roded case.

Most importantly, the independent estimations ofthe mass, stiffness, and damping are unaffected bythe actual resonant frequency. The change in stiff-ness instead is detected by the shift in the esti-mated value for K. Figure 4 shows that the cor-roded tubes have an FRF with a higher stiffnessline, corresponding to less stiffness, than the no-minal case. The curve fit correctly estimates thechange in stiffness independently from the changein resonant frequency.

Figure 4. Change in FRF with Stiffness Reduction

Figure 5. FCF vs Stiffness with Corrosion

To experimentally verify the ability of Meter Verifica-tion to detect corrosion, a flowmeter was corrodedusing a very strong, incompatible, acid. At each cor-rosion step the flowmeter was recalibrated to getthe new FCF. Figure 5 shows the change in FCF

versus the change in stiffness for each corrosionstep. Note that even with careful laboratory tech-nique, the corrosion is not uniform as indicated bythe different change in stiffness for the left and rightpickoffs (LPO, RPO). However note that the FCFchange has an approximately 1 to 1 relationshipwith the averaged change in stiffness, as expecteddue to their essential equality.

These results show that corrosion is very detectablewith Meter Verification. Another application of Cori-olis flowmeters where wear is expected is with ero-sive slurries, the subject of next section.

3.3 Meter Verification Erosion Detection

It is difficult to do a controlled experiment for ero-sive wear of a Coriolis meter. However finite ele-ment analysis can be used to investigate the detec-tability of erosion with Meter Verification. Figure 6shows a beam finite element model used to analyzeerosion. The red elements on the inlet tube bendare where most of the erosion is expected. The wallthickness of these elements was progressively de-creased with the stiffness uncertainty and FCF cal-culated at each iteration. The FE results are shownin Figure 7. Note how the LPO and RPO stiffnesseschange it opposite directions, a hallmark of nonuni-form changes to the flow tubes. These stiffness un-certainties have diverged from the baseline with atotal spread of about 1% for an FCF decrease of~1.2%

Figure 6. Beam FE Model for Erosion Study

102

10-1

100

101

102

103

Frequency Response Function

Frequency (Hz)

FRFMagnitude

Nominal K

Less Stiff K Nominal M

Freq=sqrt(K/M) Peak ~1/

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-3.5

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-2.5

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0

Percent Change in Stiffness

PercentChangeinFCF

Percent Change in FCF vs. Percent Change in Stiffness

LPO

RPO


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It is interesting to note that the RPO stiffness hasincreased even though the RPO is on the inlet sideof the tubes, where the thinning has happened.The LPO stiffness has decreased even though nochange occurred on that side of the flow tubes.

Non--intuitive results like these occur frequently instructural dynamics problems. A thought experi-ment gives insight into the increase in stiffness ofthe RPO with a decrease in tube stiffness. Imaginethat the inlet bend was completely removed, thelimiting case of stiffness reduction. In that case theRPO would not move at all with a force applied atthe driver, essentially becoming infinitely stiff. Intui-tion must be used with care when interpreting MeterVerification results.

Figure 7. Fcf vs Stiffness with Erosion

4. DISCUSSION

Meter Verification measures stiffness to ensure theintegrity of the sensing element, the flow tubes.Additionally the electronics associated with the flowmeasurement need to be verified. Structural Integr-ity Meter Verification confirms the integrity of theflowmeter electronics by verifying the stiffness withthe same transducers, analog electronics, digitalelectronics, and software used for the flow mea-surement. Any change in the electronics will causethe stiffness uncertainty to go out of specification.Therefore good stiffness uncertainty confirms boththe sensing element and the electronics.

Verification is unlike flowmeter validation methodol-ogies such as proving, in which the unit under test'sflow output is compared to a primary flow output.Verifications require several additional checks toconfirm overall flowmeter performance. Thesechecks include confirming the software configura-

tion, the flowmeter' s zero, and the proper function-ing of the analog outputs. A complete verificationmight include checking the analog output functional-ity with the built-in diagnostic/trim functions.

Structural Integrity Meter Verification includes abuilt-in check of the software configuration, compar-ing it to the previously verified values. AdditionallyMeter Verification checks the current zero againstthe factory zero and the last-verified zero. MeterVerification also provides a graphical output of theresults and the ability to print a report of the currentverification. All of these features combine to com-pletely check the performance of the entire flowme-ter.

5. CONCLUSION

Structural Integrity Meter Verification is a robust

technology for in-situverification of Coriolis flowme-ters. It can be used with confidence as a cost-effective, robust, means of verifying Coriolis flow-meter performance. For applications where Coriolisflowmeter degradation is expected, for examplewith corrosive fluids, Meter Verification is a goodtool for detecting flowmeter wear.

REFERENCES

[1] Effect of detector masses on calibration of Cori-olis flowmeters, Lange U., Levien A., PankratzT., Raszillier H., Flow Measurement Instrumen-tation, Volume 5 Number 4, 1994.

[2] A Finite Element for the Vibration Analysis of aFluid-conveying Timoshenko Beam, Stack C.,Garnett R., Pawlas G., 34th SDM conferenceproceedings, 1993, AIAA

[3] Coriolis Technology Creates Superior Meters,Stack C., Micro Motion White Paper WP-00510,www.micromotion.com, 2003.

[4] Using Structural Integrity Meter Verification,Cunningham T., Stack C., Connor C., MicroMotion White Paper WP-00948,

www.micromotion.com, 2007.

[5] Using Structural Integrity Meter Verification toTrack Corrosion in Coriolis Flowmeters, Cun-ningham T., Micro Motion White Paper WP-01196, www.micromotion.com, 2009.

[7] Using IMAT and MATLAB for Coriolis FlowmeterDesign, Cunningham T., Hensley D., IMAC XIXProceedings, February 2001, Paper #74

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Percent change in stiffness

PercentChangeinFCF

FCF change vs Stiffness change, inlet tubes eroded

LPO

RPO

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Mm029139. in Situ Verification Technology for Coriolis Flow Meters