Contoh Kalkulasi Uncertainty.pdf

8/13/2019 Contoh Kalkulasi Uncertainty.pdf

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PE IKO FIELD DEVELOPMENT PROJE T

VENDORS DOCUMENT FRONT SHEET

VENDORJKMS PROJECT NOCONTR CT NOP CK GE DESCRIPTION

DOCUMENT TITLEDOCUMENT NUMBERDOCUMENT REVISION

NO. OF P GES Inc. Front Sht.)

JORDAN KENT METERING SYSTEMS LTD971JK11545C 084/97/001PECIKO FIELD GAS METERING P CK GE

Uncertainty Calculations15451151B

21

02 11.3.98 JSL General Update1 02.12.97 JCM Fist Issue For Approval JSL

ISSUE D TE BY PURPOSE OF REVISION CHECKED PPROVEDCLIENTPPPLIER DOCUMENT NO. 084-?112

I COMP NY DOCUMENT NO.PPA-70-X1-241-F


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I JORD N KENT METERING SYSTEMS LIMITED JKMS Reference: 97/JKl1545j Client Reference: C 084/97/001

PROJECT: PECIKO DEVELOPMENT PROJECT UNCERT INTY C LCUL TIONSONSHORE CUSTODY TRANSFERGAS METERING SYSTEM

B 09 03 98 Revised In Line With Document PPA 70 X1 243 F.02/12/97 First Issue For Approval

JKMS DOCUMENT REF: 154511510REVISION: B


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Section

1

3

45

6

7

8

9

10

12

Main

ONTENTS

escription

Environmental and Process ConditionsSymbolsIntroduction and Summary of ResultsOverall Calculated System UncertaintyEmpirical Coefficient of discharge UncertaintyAGA3 section 1.12.4.1)

Empirical Expansion Factor UncertaintyAGA3 sect 1.12.4.2 )

Orifice Plate Bore Diameter UncertaintyAGA3 sect 1.12.4.4)

LMeter Tube Internal Diameter UncertaintyAGA3 sect 1.12.4.5)

Temperature Transmitter UncertaintyUncertainty in DP due to differential pressure deviceAGA section 1.12.4.6)

Uncertainty in Pf due to Absolue Pressuremeasurement devices

Fluid Density uncertainty

\

JKMS DOCUMENT REF: 1545 1510REVISION: B


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1.0 Environmental and Process Conditions

**

*

*

Ambient temperaturevariation

DescriptionSupply Voltage VariationCalibration IntervalOperating TemperatureOperating PressureTotal operating flowrate

qm(t)No. of streams in serviceStream flowrate

qm(s)Orifice DP DPMolecular WeightDensity at std. condoDensity at flow cond .Viscosity

0.000001Meter Tube Dia. @ 20COrifice Dia. @ 20CBeta @ 20CPipe expo coeff. 0.00001Orifice expo coeff. 0.00001Meter Tube Dia. @ TfOrifice Dia @ TfBeta @ Tf

=

UnitsVolts

Monthsco

BarAMMSCFD

m3skg Ism3skg/s

mBarkg m3kg m3

cPkg m s

mmf cf cmm

Main

19.5 C to67.1 F to

35 C95 F

Case No.1 2 3 4

0.72 0.72 0 72 0.726 6 6 6

17.7 40.4 40.4 40.4290.9 313.6 313.6 313.6

55.516 78.316 78.316 78.316200 650 650 1300

65.549 213.033 213.033 426.06656.375 183.922 183.922 367.8441 1 2 265.549 213.033 106.516 213.03356.375 183.922 91.961 183.922

60.4124 490.1914 121.9426 490.191420.3 20.3 20.3 20.3

0.8600 0.8634 0.8634 0.863455.362 72.961 72.961 72.961

0.01 0.01 0.01 0.0110.00 10.00 10.00 10.00

0.5477 0.5477 0.5477 0.54770.3622 0.3622 0.3622 0.3622

0.661 0.661 0.661 0.6611.116 1.116 1.116 1.1161.665 1.665 1.665 1.665

0.5477 0.5478 0.5478 0.54780.3622 0.3623 0.3623 0.36230.6613 0.6614 0.6614 0.6614

* At standard conditions 15.56 c (60 F , 1.01560 BarA (14.73 psia)

JKMS DOCUMENT REF: 1545/1510REVISION: B

Buat 5 case untuk melihat sebaran akurasi meter.

5 case tersebut dibuat dengan memvariasi baris untuk range dP stack.

(case 1: 5%; case 2:25%; case 3: 50%; case 4:75%; case 5: 100%)

Untuk parameter yang lain dibuat fix sesuai operating pressure.


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Main

2.0 Symbols

Symbol Descriptionp Beta0 Meter tube diameterd Orifice boreddm Difference d measurement - dm)dDm Difference 0 measurement - Om)dm Mean orifice diameterOm Mean tube diameterDP Differential pressureECd Uncertainty in CdEd Uncertainty in dED Uncertainty in 0EdPtx Uncertainty in DPEPtx Uncertainty in measured absolute pressure PfETtx Uncertainty in fEXi Uncertainty in mole fractionEY Uncertainty in empirical expansion factorEZf Uncertainty in compressibility factorm Dynamic viscosityMr Molar mass 0 9as mixtureMri Molar mass of) th gas componentN Number of gas components1t 3.141592654Pf Fluid static presureqm Mass f10wrateR Universal gas ~ o n s t n tReD Reynolds No. ;Tf Fluid t e m p e r t ~ r e-


Unit

-mmmmmmPa%%%%%%%%%kg m s

--Pakg/skg mol k-C


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Main

3.0 Introduction and Summary of ResultsAGA 3 states that the volume flowrate through an orifice plate qm is given bythe following equation,

where,Cd =Y =P =

Co-efficient of dischargeExpansion factorOrifice differential pressure

d =Ev =Pt P =

Orifice plate boreVelocity of approachfluid density at PI TI

Differentiation of the flow equation (AGA3 sect 1.12.3.1 ) gives sensitivity coefficients for thecalculation of the flowrate uncertainty from the uncertainties in each variable .

, Calculated Uncertainty, ExVariable Sensitivity

Coefficient, Sf< 1 2 3 4Cd 1 0.46329 0.46256 0.46293 0 46256Y 1 0.00435 0.02504 0.00623 0.02504

DP 0.5 0.42652 0.25182 0.29788 0 25182d 2.472951333 0.05774 0.05774 0.05774 0.05774D -0.'472980872 0.28868 0.28868 0.28868 0.28868p O q 0.15000 0.15000 0.15000 0.15000

Sx Ex)2Variable Case No.

1 2 3 4Cd 0.2146 0.2146 0.2143 0.2140y 1.9E-05 6.3E-04 3.9E-05 6.3E-04

DP 0.0455 0.0159 0.0222 0.0159d 0 02038 0.020384961 0.020385 0.020385D 0 0186 0.Oi8t? 0.0186 0.0186p 0 00563 0.005625 0.005625 0.005625

The sensitivity coefficients for d and D include sensitivities in the velocity of approach fac tor Ev that aredependant upon b (see AGA3 section 1.12.3.1)



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Main

4.0 verall System Uncertainty

To obtain a value for the overall system uncertainty, the individual uncertainties, once multiplied bytheir sensitivity coefficients, are combined using the root-sum-square method to give the overall Imass flowrate uncertainty Eqm

Sum of SquaresSquare root of sum of squares

verall System Uncertainty


t

10.30480.55210.5521

Case No2 3 4

0.2751 0.2812 0.27510.5245 0.5303 0.52450.5245 0.5303 0.5245


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Ecd

5.0 Empirical Coefficient of discharge AGA3 section 1.12.4.1)The uncertainty in Cd is a function of Re and diameter ratio p

5.1 Reynolds numberThe meter tube Reynolds number is defined by AGA3 part 1section 1.7.3 as

Units Case No.1 2 3qm s) kg/s 56.375 183.922 91.961

J 1 1E-06 kg m/s 10.000 10.000 10.000OTt m 0.5477 0.5477 0.5477ReD 1.31 E+07 4.28E+07 2.14E+07

5.2 Beta RatioCase No.

1 2 3Beta t 0.6613 0.6614 0.6614

5.3 ._ Uncertainty in Cd \\The uncertainty in the ~ p i r i c a l Coefficient of discharge is givenIby AGA3 part 1 section 1.12.4.1 as the product,,i,

IJC d ( F T) IJC i F T=:: XIJ i F T C d F T

where,

oC d F T.oC i F T 1 + 1 78 9 5 4 ) 0 8. R e D

IJKMS DOCUMENT REF: 1545/1510REVISION: B

4183.92210.0000.54774.28E+07

40.6614


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Y

6.0 mpirical xpansion Factor AGA3 sect 1.12.4.2 )

Ey = 4 DP/PI) when p s 0.750

BetaDPPEy


Units

mSarSarA

10.661360.41255.5160.0044

Case No.2 3

0 66;4 0.6614490.191 121.94378.316 78.3160.0250 0.0062

40.6614

490.19178.3160.0250


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Ed orifice

f O Orifice Plate Bore Diameter (AGA3 sect 1.12.4.4)iIn the absence of physical data, the AGA3 requirements as outlined in AGA3 part 2

section 2.4.3 and table 2-2 are used. For an orifice Plate Bore of > inch thetolerance given by table 2-2 is,

Tolerance = +/- 0.0005 inch per inch of diameterMeter tube diameter = 21.563 inches = 0.5477 mBeta ratio = 0.6613Orifice diameter = 14.26 inches = 0.3622 mMax allowable d = +/- 0.0005 x 14.26

= +/- 0.0071 =+/- 0.0001811 mAGA3 states that at least four independant measurements of the orifice bore must be usedThe orifice bore is taken the mean of these four measurements.AGA 3 pt 1 section 1.6.2 defines the uncertainty in orifice plate bore as the root-mean-squareof the differences between each measurement and the mean

t3dl

'where n is the number of measurements and ddm is the difference betweena measurement and the mean. Using the calculated maximum allowablevalue of d.

= +/= +/-

,0.00823280.0002091 m

Expressed as a percentabe of the orifice mean diameter.ddm / dm = +/- 0.0082328 = +/- 0.0002091 m

14.25966246 0.362195426 m

= m = +/- 0 0577 %

Although AGA3 uses the tolerance value 0.05% directly in the example calculation ofIuncertainty. The calculation above takes the maximum allowed tolerance for eachImeasurement and uses the equation given by AGA3 to combine 4 such values. Theuncertainty obtained reflects not only the tolerance in d but also the uncertainty due to the useof only four (the minimum allowed) such measurements.

JKMS DOCUMENT REF: 1545/1510 IREVISION: B


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ED pipe

8.0 Meter Tube Internal Diameter (AGA3 sect 1.12.4.5)'In the absence of physical data for the inside diameter of the meter tube, the toleranceallowed by AGA3 part 2 is used to calculate a value for the uncertainty in diameter Om. AGA 3part 2 states that, any diameter measurement made within 1 tube diameter upstream of theorifice plate shall not differ from the mean measured tube diameter by more than 0.25i.e.

\Any diamcter measureJ \\iUlli;::eD., OfUl orifice pJate-DlI x 5':025

Taking the mean meter tube diameter as 21.563 inches 'the allowed tolerance is,Permitted tolerance = +/- 21.563 x 0 25/100

= +/- 0.05391 = +/- 0.00136925 mThe uncertainty in the mean meter tube diameter Om is the root-sum-square of the diametermeasurements and the m ~ n diameter.

dDm is the difference between the measured diameter and the mean diameter and n is thenumber of measurements. Using the largest deviation in D permitted and the minimum numberof readings (n =

dOm = +/- 0.0622 = 1 0.001581 m

Expressing this uncertainty :as a percentage of the mean meter tube diameter,,dDm/Dm 1 0.06225 x 100 = +/- 0.001581 m

21.563 0.5477 mE = dDm/D = 1 0 2887Although AGA3 uses the to,lerance value 0.25 directly in the example calculation ofuncertainty. The c l c u l t i o ~ above takes the maximum allowed tolerance for eachmeasurement and uses the equation given by AGA3 to combine 4 such values. The uncertaintyobtained reflects not only the tolerance in d but also the uncertainty due to the use of only four(the minimum allowed) such measurements.



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ETtx

9.0 Temperature Transmitter Uncertainty9 1 Platinum Resistance Thermometer Sensor

The required accuracy for the PRT is 0.19C over the range a to 10aoCas per spec. PPA-70-2-1-B-2 7.3.3.i

Units Case No.i 1 2 3 4Tf c 17.7 40.4 40.4 40.4Tf oK 290.85 313.55 313.55 313.55Tolerance oK 0.19 0.19 0.19 0.19As the units of temperature in thermodynamic equations is Kelvin, this toleranceis therefor expressed in o K.

9.2 3144CA Temperature TransmitterThe Fisher - Rosemount Ltd. model 3144 temperature transmitteris calbrated over the range 0 to 100C it's performance is specified below:

9.2.1 AccuracyRosemount state a digi tal accuracy of 0.14C, and a D A accuracy of 0.02 of span. '.Total analogue accuracy is defined as the sum of the digital & D A accuracies.Calbration Range: 100

Ii Units Case No..t. 1 2 3 4

Tf c 17.7 40.4 40.4 40.4Tf \ oK 290.85 313.55 313.55 313.55Digital accuracy I oK 0.14 0.14 0.14 0.14D A accuracy oK 0.02 0.02 0.02 0.02Total accuracy oK 0.16 0.16 0.16 0.16

9.2.2 StabilityFisher-Rosemount state figures for stability of 0 1 of reading or 0 1 cwhichever is greater, for 24 months.Calibration every 6 months is assumed,

JKMS DOCUMENT REF: 1545 1510REVISION: 8


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ETtx

xpressed as a p e r e n t ~ g e of the operating temperatureUncertainty in measured temperature

ETtx


Units ~ 1 ~ . ~ . ~ r ~ ~0.1078


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EdPtx

10.0 Uncertainty in dp due to differential pressure device(AGA section 1.12.4.6)

10.1 Rosemount 3051CD High Range Differential Pressure TransmitterCalibrated spanTemperature variation (max.)Unit range codeDigital/AnalogueUnit URL (Upper Range Limit)Supp\y voltage variation.Calibration interval

500152

Analogue6220.72

6

mBarC

mBarVoltsmonths

Rosemount 3051CD Low Range Differential Pressure TransmitterCalibrated spanTemperature variation (max.Unit range codeDigital/Analogue IUnit URL (Upper Range Limit)Supply voltage variationCalibration interval

125

152

Analogue6220.72

6

Hi9h/LoW Range Transmitter Switch PointSwitch Point 124

?1.1 Accuracy (Edpa)

mBarC

mBarVoltsmonths

mBar

The Rosemount 3051 C02 differential pressure t r n s m i t t ~ r has a stated accuracy of 0.075%of span from 1: 1 to 10:1 6f URL, including hysteresis, terminal based linearity and repeatabiltyof the pressure sensor.

Units Case No.1 2 3 4

Accuracy mBar 0.0938 0.3750 ' 0.0938 0.375010.1.2 Stability Edpst)

Rosemount do not quote figures for transmitter drift over 1 month, drift over such a shortperiod is considered insignificant. A figure for drift over 60 months is given as 0.25% ofURL. The calibration interval shall be 6 months.

)JKMS DOCUMENT REF: 1545/1510,REVISION: B I


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EdPtx


Stability mBar 0.1555 0.1555 0.1555 0.1555

10.1.3 Static Pessure EffectZero Error

The zero error due to static pressure is correctable by re-zeroing at line pressureSpan Error (Edpsp)The span error is due to static pressure is stated as being:Range 2 0.2% of reading per 69 Bar.

Units . Case No.1 2 3 4

Operating Pressure BarA 54.502 77.302 77.302 77.302Reading mBar 60.412 490.19 121.94 490.19Span Error mBar 0.0954 1.0983 0:27323 1.0983

10.1.4 Ambient Temperature EffectThe error due to ambient' temperature effect is stated as being:Range 2 (0.0125% URL + 0.0625% span)/28C for spans from : to 10:1.Instrument will be calibrated at 20C


Reading mBar 60.412 490.19 121.94 490.19Temperature Effect Error mBar 0.1559 0.3903 0.1559 0.3903

10.1.5 Power Supply Effect Edpp)The error due to power sypply effect is stated as being 0.005% of calibrated spall perv'olt.

Power Supply Effect


Units

mBar1

0.0045

Case No2 3 4

0.018 0.0045 0.018


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EPtx

11.0 Uncertainty in Pf due to bsolute Pressure measurement device11.1 Rosemount 3051 TA bsolute Pressure Transmitter

Calibrated Span.Temperature variation (max.)Unit range codeDigital/AnalogueUnit URL (Upper Range Limit)Supply voltage variationCalibration inteNal

',1.1.1 ccuracy (Epa)

10015

4Analogue

2760 72

6

SarA

SarAVmonths

The Rosemount 3051 TA'pressure transmitter has a stated accuracy of 0.075% of spanfrom 1:1 to 10:1 of URL, including hysteresis, terminal based linearity and repeatabilty ofthe pressure sensor.


Accuracy mSar 75.0 75.0 75.0 75.0

11.1.2 Stability (Eps)Rosemount do not quote figures for transmitter drift over 1 month, drift over such a shortperiod is considered inSignificant. A figure for drift over 12 months is given as 0.1 % ofURL. The calibration inte,IVal will be ,6 months.

, Units Case No. 1 2 3 4

Stability mSar 138.0 138.0 138.0 138.0

11.1.3 mbient Temperature Effect (Ept)The error due to ambient temperature effect is stated as being (0.025% URL + 0.125%span)/28C for spans from 1:1 to 30:1.Instrument will be calibra'ted at 20C

jJTemperature Effect Error


UnitsmSar 1135.96

,Case No.2 3 4135.96 135.96 135.96


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EPtx

11.1.4 Power Supply Effect (Edpp)The error due to power sypply effect is stated s being 0.005 of calibrated span ,pervolt. Units Case No.

1 2 3 4Power Supply Effect mBar 0.0036 0.0036 0.0036 0 0036

11.1.5 Mounting Position EffectThe error due to mounting position effect will be calibrated out.

';1.2 Combined UncertaintiesThese uncetainties are combined by the root sum square method:

~ c e r t a i n t yUncertainty

i0

I


Units1

mBar 207.740.3742

Case No.2 3 4

207.74 207 74 207 740.2653 0 2653 0.2653


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Erho

12.0 ensitometer Uncertainty12.1 Solartron 7812 Gas Transducer

The Solartron 7812 gas transducer h s a stated accuracy of 0.15 of reading.(Natural Gas)

UnitsReading k m Accuracy kg/m3Uncertainty

155.362

0.0830.1500

Case No.2 3 4

72.961 72.961 72.9610.1094 0.1094 0.10940.1500 0.1500 0.1500

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Contoh Kalkulasi Uncertainty.pdf