linearity of coriolis mass flowmeters - vsl · 3! march 26, 2014 5 mass flow w/coriolis flowmeters...

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Linearity of Coriolis Mass Flowmeters Dean Standiford Director Global Calibration Quality

March 26, 2014 2

Overview !! Purpose:

–! To answer the customer’s question, “How do I know the output from my Coriolis flow meter is valid beyond the calibrated mass flow range?”

!! Scope: –! High Capacity Coriolis flow meters

•! 6”, 8”, 10” •! >25% of maximum flow range •! Based on water calibration

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March 26, 2014 3

Summary Coriolis flowmeters are inherently linear devices. Each Coriolis flowmeter has a unique mass flow calibration constant (flow calibration factor, FCF), that when determined correctly, is valid for the entire operating mass flow range.

March 26, 2014 4

Agenda !! Coriolis mass flow equation

!! Calibration processes

!! Mass Flow Linearity Results

!! Validating the Calibration

!! Conclusion

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March 26, 2014 5

Mass Flow w/Coriolis Flowmeters !! Basic Measurement Measuring tubes are forced to oscillate producing a sine wave. At zero flow, the two tubes vibrate in phase with each other. When flow is introduced, the Coriolis forces cause the tubes to twist resulting in a phase shift. The time difference between the sine waves is measured and is directly proportional to mass flow rate.

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March 26, 2014 6

Coriolis Mass Flow Equation !! Mathematical Derivation Force:

(1) Coriolis Force, named for Gustav Coriolis

(2)

Because the direction of the flow changes between the inlet and outlet tube, the direction of the force changes.

As the tube vibrates about axis “o”, an oscillation moment develops:

(3)

Since: , combine equations (2) & (3)

or (4)

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March 26, 2014 7

Coriolis Mass Flow Equation !! Mathematical Derivation cont’d. Making the substitution into:

(5) Equation (4) becomes:

(6)

The moment “M” is being resisted by the mechanical properties of the sensor tube. The torque on the tube is given by:

(7) Where: is the stiffness of the tube & is the amount of twist (in degrees). By definition: so: (8)

(9)

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March 26, 2014 8

Coriolis Mass Flow Equation !! Mathematical Derivation cont’d. By definition:

(10) Substituting (10) into (9):

(11) All of the values (except ) are constants that when lumped together MMI calls the flow calibration factor:

(12)

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Coriolis Mass Flow, kg/min

Coriolis Mass Flowmeter

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March 26, 2014 9

Calibration Processes !! Calibration operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication.

NOTE 1 A calibration may be expressed by a statement, calibration function, calibration diagram, calibration curve, or calibration table. In some cases, it may consist of an additive or multiplicative correction of the indication with associated measurement uncertainty.

NOTE 2 Calibration should not be confused with adjustment of a measuring system, often

mistakenly called “self-calibration”, nor with verification of calibration VIM – International vocabulary of metrology, Basic and general concepts and terms (JCGM 200:2008)

March 26, 2014 10

Calibration Processes !! calibration - The comparison of measuring

equipment of unknown measurement uncertainty to a reference standard of known measurement uncertainty to determine an estimate of the error. –! Such as: comparing the reading of a flow meter to a calibrated

reference to determine the estimate of error (step 1), which can then be used to adjust the flow meter output if required (step 2).

!! verification - Evidence by calibration that specified requirements have been met. –! A decision made by analyzing the calibration data.

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March 26, 2014 11

Calibration Processes !! Micro Motion mass flow calibration process for a

Coriolis Mass Flowmeter –! Ensure stable process conditions –! Determine Coriolis zero offset

•! Intercept

–! Determine mass flow error at the best flowrate for adjusting FCF

–! Make an adjustment to the FCF •! Slope

–! Verify the adjustment is valid

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March 26, 2014 12

Calibration Processes !! What is the “best flowrate” for adjusting the FCF?

–! Because Coriolis flowmeters are linear devices: •! Any flowrate where errors are minimized

–! Zero stability –! Process repeatability –! System Limitations

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March 26, 2014 13

Calibration Processes

254cm (10”)+ line sizes 186kw (250hp) + pumps

30t (66,139lb) weigh systems Multiple reference meters

March 26, 2014 14

Calibration Process – FCF Adjustment

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rror,

%

Flow Rate, % Maximum

Coriolis Mass Flowmeter

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50% of Maximum Flow Rate = Nominal Flow Rate (~1 bar dp)

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March 26, 2014 15

Mass Flow Linearity Results

0.0

0.5

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Pres

sure

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Mas

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r, %

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ng

Flow Rate, % Maximum

CMF300 S/N: 11005156

Test #1 Test #2 Test #3

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50% of Maximum Flow Rate = Nominal Flow Rate (~1bar dp)

March 26, 2014 16


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Mas

s Erro

r, %

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ng

Flow Rate, kg/min

CMFHC2 S/N: 13053120

Test #1 Test #2

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March 26, 2014 17


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Mas

s Erro

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ng

Mass Flow Rate, kg/min

CMFHC3 S/N: 12074130

USA Netherlands China

Typical FCF adjustment flowrate = 12,000 kg/min

March 26, 2014 18


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Mas

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eadi

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Flow Rate, kg/min

CMFHC4 S/N: 12074922

USA China Test #1 China Test #2

Typical FCF adjustment flowrate = 12,000 kg/min

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March 26, 2014 19

Validating the Calibration Coriolis mass flow meters are linear, but how does MMI provide confidence to its customers about the data? !! Gather Historical Data

–! 30+ production meter calibration samples –! FCF calibrated at a flow rate less than maximum

!! Analyze data to a 95% confidence level for conclusions

March 26, 2014 20

Validating the Calibration

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Batch

Erro

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Flow Rate, kg/min

CMFHC3FCF Calibration at Boulder and then Verified at Higher Flowrate at Ede or AFTC

USA- FCF Calibration Netherlands- FCF Verify China- FCF Verify

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March 26, 2014 21


0.080.040.00-0.04

Median

Mean

0.0250.0200.0150.0100.0050.000

1st Q uartile -0.007925Median 0.0096003rd Q uartile 0.024375Maximum 0.083300

-0.003065 0.020598

0.003675 0.021654

0.025234 0.042594

A -Squared 0.46P-V alue 0.240

Mean 0.008767StDev 0.031685V ariance 0.001004Skewness -0.154286Kurtosis 0.245871N 30

Minimum -0.061000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary CMFHC3 FCF Verify Error %

RSS of lab uncertainties = 0.042%

March 26, 2014 22


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Batc

h Erro

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Flow Rate, kg/min

CMFHC4FCF Calibration at Boulder and then Verified at Higher Flowrate at Ede or AFTC

USA- FCF Calibration Netherlands- FCF Verify China- FCF Verify

12!

March 26, 2014 23


0.050.00-0.05-0.10

Median

Mean

-0.010-0.015-0.020-0.025-0.030-0.035-0.040

1st Q uartile -0.047830Median -0.0197803rd Q uartile -0.001220Maximum 0.076900

-0.036600 -0.008089

-0.037828 -0.009015

0.032331 0.053177

A -Squared 0.27P-V alue 0.659

Mean -0.022345StDev 0.040204V ariance 0.001616Skewness 0.404551Kurtosis 0.565730N 33

Minimum -0.100360

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary CMFHC4 FCF Verify Error %

RSS of lab uncertainties = 0.042%

March 26, 2014 24

Validating the Calibration - Conclusions !! Gather Historical Data

–! 30+ production meter calibration samples –! FCF calibrated at a flow rate less than maximum

!! Analyze data to a 95% confidence level for conclusions –! Sample data is normally distributed –! Mean Error for Both meters is less than 0.042%

•! (RSS of flow stand uncertainty)

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March 26, 2014 25

Conclusion Coriolis flowmeters are inherently linear devices. Each Coriolis flowmeter has a unique mass flow calibration constant (flow calibration factor, FCF), that when determined correctly, is valid for the entire operating mass flow range.

Mass Flow Error is within the meter specification when FCF is calibrated at less than maximum flow rate.

linearity of coriolis mass flowmeters - vsl · 3! march 26, 2014 5 mass flow w/coriolis flowmeters...

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