flow measurement uncertainty - analysis based on field grade components

8/11/2019 Flow Measurement Uncertainty - Analysis Based on Field Grade Components

1/12

INTRODUCTION

This paper provides a guide to estimating the un-

certainty of a flow measurement made with field

grade instruments. It is applicable to calibrated or

uncalibrated turbine or ultrasonic based measure-

ments. Pressure and temperature measurements con-

tribute uncertainty, the uncertainty components of

each instrument are described. A set of typical

manufacturers specifications are used as an example.

The effects of ambient temperature on both mea-

surements are described.

A flow computer acquires signals from the pres-

sure and temperature transducers and converts the

readings into engineering units. A gas chromatograph

and the equation of state contribute uncertainty tothe determination of compressibility under flowing

base conditions. The components that contribute un-

certainty are described and typical values are pro-

posed.

The process of combining uncertainty components

is illustrated based on hypothetical values. The con-

cepts of sensitivity coefficient, expanded uncertainty

and coverage factor are described. The data are or-

ganized such that the relative contributions of the

components can be readily compared. The value of

this organizational structure is illustrated by compar-

ing calibrated and uncalibrated turbine meters.

The paper concludes with a brief discussion of

advanced topics. These include topics from flow

measurement, instrument calibration and measure-

ment uncertainty.

Flow Measurement Uncertainty - Analysis Based on Field Grade Components

Thomas Kegel

Colorado Engineering Experiment Station, Inc., (CEESI)Nunn, Colorado USA

MEASUREMENT UNCERTAINTY

When a measurement is made there are two im-

portant values associated with the result of the mea-

surement process. The first is the numerical value of

the variable being measured, the second is the un-

certainty associated with that numerical value. This

section provides an introduction to measurement un-

certainty by briefly describing the paper standards

and terminology.

Paper Standards

The uncertainty analysis procedure commonly used

with flow measurement processes is described in the

standards ANSI/ASME MFC-2M1, ANSI/ASME

PTC 19.12, and ISO 51683. All three of these stan-dards are based on an uncertainty analysis method

developed for comparing results of rocket engine

tests4.

A document more recently published by ISO de-

scribes an uncertainty analysis procedure originally

developed to compare the test data of different cali-

bration laboratories5. From a practical point of view,

the newer ISO method does not differ significantly

from the older method of Ref. 1-3. It has been

adopted by the National Institute of Standards and

Technology (NIST) as well as a number of large cor-

porations as a formal policy6. In addition, the latest

revision of the standard ANSI/PTC 19.17includes

the ISO method. It is likely that future revisions of

flow measurement uncertainty standards will adopt

the ISO method. This paper therefore teaches the

application of that method.


2/12


3/12


4/12

222222 41.006.020.014.026.0 ,,,,'Vbu

results in uVb

= 0.54 % for the ultrasonic meter.

The expanded uncertainty5 is the product of stan-

dard uncertainty and a coverage factor. That prod-

uct defines the confidence level. Most measurements

are stated at 95% confidence with a coverage factor

of 2.0. In the present example the expanded uncer-

tainties are 2.00.68 % = 1.36 % for the turbine meter

and 2.00.54 % = 1.08 % for the ultrasonic meter.

Using a coverage factor of 2.0 in the present ex-

ample is a simplifying assumption. A different value

may be required in a real uncertainty analysis. The

details represent an advanced topic beyond the scope

of this paper.

PRESSURE MEASUREMENT

The hypothetical pressure transmitter is config-

ured as follows:

Upper Range Limit (URL) = 2500 psig

Span = 1400 psig (20 mA)

Zero = 500 psig (4 mA)

Measured Pressure = 1054 psig (13.85 mA)

The uncertainty in pressure measurement is made

up of six components:

1. Combined Performance Specification

2. Stability

3. Ambient Temperature Effect

4. Calibration Process

5. Barometric Pressure

6. Data Acquisition

Determining numerical values for the six compo-

nents is discussed below. The behavior of four of the

components is shown in Figure 1. The x-axis is pres-

sure, the y-axis is the uncertainty expressed as a per-

cent of reading. The uncertainty decreases as the

pressure increases, this is due to full scale effects.

Such effects are present in all measurement pro-

cesses. In some processes the relative magnitude may

be very small and the effect may not be apparent.

The components of uncertainty for pressure mea-

surement are combined using Eq. 4, the units of u

are psi. Combining the numerical values:

222222 99.012.047.018.222.1 ,,,,'Pfu

results in uPf

= 2.73 psig which is 0.26% of 1068 psia.

The uncertainty must be expressed as a percent of

absolute (psia) not gage (psig) units because the pres-

sure value is used to calculate compressibility.

Combined Performance Specification

In the present example the vendor claims the ac-

curacy is 0.15% of span, the term accuracy is

said to include the four components listed below.

Regardless of vendor terminology, the user should

make sure that all four components are included.

1. Repeatability

2. Reproducibility

3. Linearity

4. Hysteresis

In the present example the span is fixed and so

this uncertainty component can be calculated in units

of psig. Doing so results in:

psig1400

%100

%15.0span%15.0 -!

"

#$

%

&.'.'U

= 2.10 psig [5a]

u= 0.58(2.10)=1.22 psig [5b]

0.0

0.2

0.4

0.6

0.8

500 700 900 1100 1300 1500

Pressure [psig]

StandardUncertainty[%

] Total

Stability

Accuracy

Data Acq

Amb Temp

Figure 1: Pressure Measurement

Uncertainty Components


5/12

Repeatability and Reproducibility

Repeatabilityis the ability of the transmitter to

measure a constant pressure over a short period

of time. Reproducibility is the ability of the trans-

mitter to measure the same pressure subject to varia-

tions that occur over a long period of time. A short

period of time might be measured in minutes while a

long period of time might be months.

Linearity

The sensitivity is the ratio of pressure transmit-

ter input (psi) to output (mA). In the present example

the sensitivity is 56.25 [psi/mA]. The linearity de-

fines the consistency of the sensitivity value over the

pressure range. Stated differently, the linearity mea-

sures the degree to which the input and output arerelated by a straight line.

Hysteresis

This effect accounts for a dependence of the out-

put on the direction change of the input. An example

would be the backlash present in a gearing system. A

good machinist will eliminate backlash by first back-

ing out the tool and then moving it into the part. In a

pressure transmitter the hysteresis arises from the

mechanical properties of the sensor. Hysteresis con-tributes measurement uncertainty because the direc-

tion of change of a measureand prior to a measure-

ment is generally unknown.

Stability

The vendor claims the stability is 0.25% of

URL. Calculating uncertainty in pressure units re-

sults in:

psig2500%100

%25.0

URL%25.0 -!"

#

$%

&

.'.'U

= 3.75 psig [6a]

u= 0.58(3.75) =2.18 psig [6b]

Ambient Temperature Effect

It has been proposed that all measuring devices

are first thermometers. Every instrument exhibits

sensitivity to changes in ambient temperature. In a

pressure transmitter the ambient temperature effects

the mechanical properties of the elastic element. The

uncertainty component accounts for the magnitude

of the effect. In the present example the vendor states

an uncertainty of:

) *span%35.0URL%45.0 ,.'U [7]

for every 100F change in the ambient temperature.

In the present example the pressure transducer is

installed in an environment where the temperature

variation is controlled to within 2.5F which repre-

sents a total potential temperature change of 5F. The

uncertainty due to the ambient temperature effect

therefore becomes:

) * !!

"

#

$$

%

&-,.'

F100

F5span%35.0URL%45.0

!

!

U

= 0.81 psig [8a]

u= 0.58(0.81) = 0.47 psig [8b]

Calibration Process

In the present example the role of the calibration

process is to maintain the transmitter within the origi-

nal performance specifications. No additional uncer-tainty is assumed to be contributed by this compo-

nent.

Barometric Pressure

In the present example a fixed value of baromet-

ric pressure is assumed. This value is calculated based

on the elevation of the meter station. It is assumed

that the barometric pressure can vary by 0.2 psia

due to meteorological conditions. This variation rep-

resents an uncertainty in the fixed value

Data Acquisition

The 4-20 mA transmitter output is converted into

engineering units by a flow computer. This process

adds uncertainty in the conversion of the analog sig-

nal to digital. The vendor claims an accuracy of

0.1% of full scale. The term %full scale from


6/12

the computer vendor is assumed to mean the same

as %span from the transducer vendor. The con-

version process to pressure units is similar as that

used with Eq. 5:

psig1400%100

%15.0

span%10.0 -!"

#

$%

&

.'.'U

= 1.71 psig [9a]

u= 0.58(1.71) =0.99 psig [9b]

TEMPERATURE MEASUREMENT

The hypothetical temperature transmitter is con-

figured as follows:

Span = 100 F

Zero = 0 F

Measured Temperature = 50 F (12 mA)

The uncertainty in temperature measurement is

made up of the following components:

1. Combined Performance Specification

2. Stability

3. Ambient Temperature Effect

4. Calibration Process

5. RTD Probe

6. Self Heating

7. Heat Transfer Effects

8. Data Acquisition

The determination of numerical values is described

below. Combining the values:

) * 222222 59.001.037.003.015.02 ,,,,'Tfu

results in uTf

= 0.73 F which is 0.14% of 510 R. The

uncertainty must be expressed as a percent of abso-

lute (R) units because the temperature value is used

to calculate compressibility.

Combined Performance Specification

In the present example the vendor claims the ac-

curacy is 0.25% of span:

F100%100

%25.0span%25.0 -!

"

#$%

&.'.'U

= 0.25F [10a]

u= 0.58(0.25)=0.15F [10b]

The term accuracy is assumed to include the

same four components as discussed with the pres-

sure measurement.

Stability

In the present example the vendor claims the sta-

bility is 0.25% of span. The standard uncertainty is u

= 0.15 F.

Ambient Temperature Effect

The vendor states an uncertainty of:

0.25%span)F4.0( ,.'U [11]

for every 50F change in the ambient temperature.

In the present example the temperature transducer

is installed in an environment where the temperature

variation is controlled to within 2.5F which repre-

sents a total potential temperature change of 5F. The

uncertainty due to the ambient temperature effecttherefore becomes:

) * !!

"

#

$$

%

&-,.'

F50

F5span%25.0F4.0

!

!

U

= 0.05 F [14a]

u= 0.58(0.05) = 0.03 F [14b]

Calibration Process

In the present example the role of the calibration

process is to maintain the transmitter within the origi-nal performance specifications. No additional uncer-

tainty is assumed to be contributed by this compo-

nent.

RTD Probe

The vendor claims an uncertainty that varies with


7/12

temperature. In the current example that value is U

= 0.63 F (u= 0.37 F)

Self Heating

When current flows through a resistor heat is gen-

erated. The heat results in a potential measurement

offset that is estimated as uncertainty. In the present

example this effect is assumed to be included in the

RTD probe uncertainty.

Heat Transfer Effects

The transmitter output indicates the temperature

of the tip of the temperature sensor RTD. The de-

sired value is the temperature of the flowing gas. If

there is a temperature difference between the flow-

ing gas and the pipe wall heat transfer will result.Heat transfer is present between the RTD and pipe

wall due to conduction through the thermowell as well

as direct radiation. The result is to drive the RTD

temperature closer to the pipe wall temperature. Heat

transfer due to convection is present between the

thermowell and the flowing gas. The convection will

drive the RTD temperature toward that of the flow-

ing gas. The difference between the RTD reading

and the flowing gas temperature (Tht) is a measure-

ment error, the magnitude must be estimated as an

uncertainty component.

The numerical value of Tht

is a function of gas

density, gas velocity, and thermowell geometry as well

as the difference between flowing gas and pipe wall

(Tgw

)10. The relationship between Tht

and gas ve-

locity is shown in Figure 2 based on the following

conditions:

thermowell: 0.5 OD, 0.25 ID, 3 length withinpipe

pipe wall temperature = 60 F and 80 F

gas temperature = 50 F

gas pressure = 1068 psia

In the present example it is assumed that the gas

velocity is 20 ft/s and the pipe wall temperature is 80

F. Under such conditions Tht = 0.02 F (u= 0.01

F).

Data Acquisition

The 4-20 mA transmitter output is converted intoengineering units by the same flow computer as used

for pressure measurement. The standard uncertainty

is u = 0.59 F.

COMPRESSIBILITY

The hypothetical gas composition used in the

present example is contained in column 2 of Table 1.

The process of determining uncertainty in calculated

compressibility is made up of four components:

1. State Equation

2. Chromatograph Repeatability and Reproducibil-

ity

3. Chromatograph Calibration Standard

4. Sensitivity Coefficients

The determination of numerical values is described

below. Combining the values:

222222 002.006.0,19.006.0 ,',' ZbZf uu

result in uZf= 0.20 % and uZb= 0.06 %.

State Equation

The AGA 8 equation of state11provides a value

of compressibility given inputs of pressure, tempera-

ture and gas composition. The uncertainty in the state

equation is U= 0.1% (u= 0.06%).

Figure 2: Heat Transfer Effects in

Temperature Measurement

0.1

1

10

1 10Velocity [ft/s ]

TemperatureDifference,/

Tht

[F]

/Tgw= 30F

/Tgw= 10F


8/12


9/12

VOLUME AT FLOWING CONDITIONS

The volume flow is measured using either a tur-

bine or ultrasonic meter. The uncertainties for using

these meters are specified by the AGA 714and AGA

915standards. For operation at higher flowrates the

uncertainties are 1.0% (u= 0.58%) for the turbine

meter and 0.7% (u = 0.41%) for the ultrasonic

meter. Performance of either meter at lower flowrates

will have higher uncertainties, the low flow condi-

tions are not considered in this example.

REDUCING THE UNCERTAINTY

The uncertainty values for all sixteen components

for turbine meter based measurement are contained

in Table 2. Column 2 shows uncertainty components

expressed as percentages of mean values. Column 3show the percent contribution to combined uncertainty

made by each component, they are calculated based

on %100

2

-!!

"

#

$$

%

&

y

xi

u

u. The summary in Table 2 is a pow-

erful tool in allocating measurement resources based

on measurement uncertainty. The turbine meter, for

example, is the largest contributor to uncertainty. It

represents the best return on an investment intended

to reduce uncertainty. The ambient temperature ef-

fects, on the other hand, contribute very little uncer-tainty. The overall uncertainty cannot be reduced by

investing in reduced uncertainty in ambient tempera-

ture effects.

The current example concludes with a hypotheti-

cal calibration of the turbine meter. The calibration

data are contained in Figure 3, the y-axis is percent

shift in K Factor from a nominal values. The data are

well within AGA 7 specifications, the uncertainty can

be reduced as a result. The fitted curve is slightly

nonlinear, the K Factor changes with flowrate. Thiswill require a more complex flow computer algorithm.

The solid lines in Fig. 3 represent the 95% confidence

interval, 95% of the data are within the interval. The

interval width is 0.2% (u = 0.1%) which accounts

for random effects present during the calibration pro-

cess. The uncertainty of the hypothetical calibration

facility flowrate measurement is 0.25% (u=0.13%)

which accounts for systematic effects associated with

the facility itself. In the current example these two

components make up the uncertainty associated with

the turbine meter measurement. The recalculated un-

certainty is uVb

= 0.39%, the details are contained in

Table 3. Having reduced the turbine meter uncer-

tainty, it can be seen that other components now domi-

nate the uncertainty. The gas chromatograph and pres-

sure transducer stability are two examples.

GENERAL DISCUSSION

It is important to emphasize that the analysis pre-

sented above is intended as an example only. Appli-

cable numerical values need to be determined for a

real uncertainty analysis. In addition, several poten-

tial uncertainty components have been neglected in

the interest of simplifying the example. These include,but are not limited to:

flowmeter installation effects

gas sampling

wet gas

pulsating flow

Considerable analysis was required to estimate

uncertainties of components that ended up contribut-

ing very little uncertainty. Two examples are the heat

transfer and the chromatographic analysis determi-nation of base compressibility. Unfortunately, the

magnitude of an uncertainty component is unknown

until the analysis is complete.

Figure 3: Turbine Meter Calibration

Data

-0.6

-0.3

0.0

0.3

0.6

20 40 60 80 100

Flowrate [%max]

KFactorShift[%

]


10/12


11/12

tnenopmoCdradnatS

]%[ytniatrecnU ]%[noitubirtnoC

erusserP

noitacificepSecnamrofrePdenibmoC 411.0 08.2

ytilibatS 402.0 59.8

tceffEerutarepmeTtneibmA 440.0 24.0

erusserPcirtemoraB 110.0 30.0

noitisiuqcAataD 390.0 58.1

erutarepmeT




eborPDTR 370.0 31.1

stceffErefsnarTtaeH 200.0 < 10.0


ytilibisserpmoCesaB

noitauqEetatS 060.0 77.0

hpargotamorhC 200.0 < 10.0

ytilibisserpmoCgniwolF


hpargotamorhC 091.0 67.7

emuloVgniwolF

eulaV7AGA 085.0 72.27

Table 2: First Summary of Uncertainty Components


12/12

tnenopmoC

dradnatS

]%[ytniatrecnU ]%[noitubirtnoC

erusserP




erusserPcirtemoraB 110.0 80.0


erutarepmeT

noitacificepSecnamrofrePdenibmoC 920.0 65.0ytilibatS 920.0 65.0


eborPDTR 370.0 04.3

stceffErefsnarTtaeH 200.0 < 10.0


ytilibisserpmoCesaB


hpargotamorhC 200.0 < 10.0

ytilibisserpmoCgniwolF


hpargotamorhC 091.0 33.32

emuloVgniwolF

yrotarobaL 521.0 01.01

ytilibicudorpeRdnaytilibataepeR 001.0 64.6

Table 3: Second Summary of Uncertainty Components

flow measurement uncertainty - analysis based on field grade components

Documents