Engineering Report: ER-11 SONP Rev. 1 BOUNDING UNCERTAINTY ANALYSIS … · 2019. 11. 20. ·...

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Caldon® Ultrasonics

Engineering Report: ER-11 SONP Rev. 1

BOUNDING UNCERTAINTY ANALYSIS FOR THERMAL POWER DETERMINATION AT FARLEY UNIT 1 USING THE LEFM,r+ SYSTEM

Prepared by: Jonathan Lent ,\ Reviewed by: Ryan Hannas~~

May 2019

ER-l 180NP Rev. 1 Prepared by: J JL

Schlumberger-Private

Reviewed by: (la:


eron International Corporation ("Cameron") All information c -.: publication is con ,aen ,a a ny reproduction or use of . c , . ., these instructions, dr ,· 'ltteA-f)eunissjon of an . ~'l.1-'

ameron is forbidden.

All Rights Reserved. Printed in the United States of America.

Engineering Report No. ER-1180NP Rev. 1 May 2019 \

ER-l l 80NP Rev. 1 Prepared by: JJL


Reviewed by: fl.Y


Engineering Report: ER-1180NP Rev. 1

BOUNDING UNCERTAINTY ANALYSIS FOR THERMAL POWER DETERMINATION AT FARLEY UNIT 1 USING THE LEFM./+ SYSTEM

Table of Contents

1.0 INTRODUCTION 2.0 SUMMARY 3.0 APPROACH 4.0 OVERVIEW 5.0 REFERENCES 6.0 APPENDICES

A Information Supporting Uncertainty in LEFMY"+ Flow and Temperature Measurements A.1 LEFM v" + Inputs A.2 LEFMY"+ Uncertainty Items/Calculations A.3 LEFM v" + Meter Factor Calculation and Accuracy Assessment AA [ ] A.5 [ ]

B Total Thermal Power and Mass Flow Uncertainties using the LEFMv'+ System

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1.0 INTRODUCTION The LEFM ./ and LEFM ./ +1 are advanced ultrasonic systems that accurately determine the volume flow and temperature of feedwater in nuclear power plants. Using a feedwater pressure signai input to the LEFM ./ and LEFM ./ +: mass flow can be determined and, along with the temperature output are used along with plant data to compute reactor core thermal power. The technology underlying the LEFM ./ ultrasonic instruments and the factors affecting their performance are described in a topical report, Reference 1, and a supplement to this topical report, Reference 2.

The LEFM ./ +, which is made of two LEFM ./ subsystems, is described in another supplement to the topical report, Reference 3. The exact amount of the uprate allowable under a revision to 10CFR50 Appendix K depends not only on the accuracy of the LEFM./ + instrument, but also on the uncertainties in other inputs to the thermal power calculation.

It is the purpose of this document to provide an analysis of the uncertainty contribution of the LEFM ./ + System [ ] to the overall mass flow and thermal power uncertainty of Farley Unit 1 (Appendix B).

The uncertainties in mass flow and feed water temperature are also used in the calculation of the overall thermal power uncertainty (Appendix 8). [

] A detailed discussion of the methodology for combining these terms is described in Reference 3.

This analysis is a bounding analysis for Farley Unit 1. [

['

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2.0 SUMMARY For Farley Unit 1, Revision I results are as follows:

1. The mass flow uncertainty approach is documented in Reference 3. The uncertainty in the LEFM'li"' +'s mass flow offeedwater is as follows:

o Fully Functional LEFM ./ + system mass flow uncertainty is [ ]

o Maintenance Mode LEFM ./ + system mass flow uncertainty is [ ]

2. The uncertainty in the LEFM ./+feed water temperature is as follows:

o Fully Functional LEFM ./+system temperature uncertainty is [

o Maintenance Mode LEFM ./ + system the uncertainty is [ ]

3. The total thermal power uncertainty approach is documented in Reference 3 and Appendix B of this document. The total uncertainty in the determination of thermal power uses the LEFM ./ + system parameters and plant specific parameters, i.e., heat gain/losses, etc. and is as follows:

o Thermal power uncertainty using a Fully Functional LEFM ./ + system is [ ]

o Thermal power uncertainty using a Maintenance Mode LEFM ./ + system is [

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3.0 APPROACH

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All errors and biases are calculated and combined according to the procedures defined in Reference 4 in order to determine the 95% confidence and probability value. The approach to determine the uncertainty, consistent with determining set points, is to combine the random and bias terms by the means of the RSS approach provided that all the terms are independent; zerocentered and normally distributed.

Reference 4 defines the contributions of individual error elements through the use of sensitivity coefficients defined as follows:

A calculated variable Pis determined by algorithm f, from measured variables X, Y, and Z.

P = f(X, Y, Z)

The error, or uncertainty in P, dP, is given by:

dP=![_I dX + qi dY + qi dZ 8){ l'Z of XZ oZ XY

As noted above, P is the determined variable--in this case, reactor power or mass flow-- which is calculated via measured variables X, Y, and Z using an algorithm f (X, Y, Z). The uncertainty or error in P, dP, is determined on a per unit basis as follows:

dP ={x o/1 }dX +{Y_ql }dY +{z o/1 }dz P PoXrz X PoYxz Y PoZxr Z

where the terms in brackets are referred to as the sensitivity coefficients.

If the errors or biases in individual elements (dXIX, dYIY, and dZIZ in the above equation) are all caused by a common (systematic) boundary condition (for example ambient temperature) the total error dP/ P is found by summing the three terms in the above equation. If, as is more often the case, the errors in X, Y, and Z are independent of each other, then Reference 4 recommends and probability theory requires that the total uncertainty be determined by the root sum square as follows (for 95% confidence and probability):

Obviously, if some errors in individual elements are caused by a combination of boundary conditions, some independent and some related (i.e., systematic) then a combination of the two procedures is appropriate.

ER-1180NP Rev. I Prepared by: J JL


Reviewed by: RL~


4.0 OVERVIEW The analyses that support the calculation of LEFM ./+uncertainties are contained in the appendices to this document. The function of each appendix is outlined below.

Appendix A.1, LEFM,I + Inputs

This appendix tabulates dimensional and other inputs to the LEFM ./ +. The spreadsheet calculates other key dimensions and factors from these inputs (e.g., the face-to-face distance between pairs of transducer assemblies), which is used by the LEFM./ + for the computation of mass flow and temperature.

Appendix A.2, LEFM,I + Uncertainty Items Calculations

This appendix calculates the uncertainties in mass flow and temperature as computed by the LEFM ./ + using the methodology described in Appendix E of Reference l and Appendix A of Reference 33

, with uncertainties in the elements of these measurements bounded as described in both references4. The spreadsheet calculations draw on the data of Appendix A.1 for dimensional information. It draws from Appendix A.4 [

]. It draws from Appendix A.5 [ ].

These uncertainties are an important factor in establishing the overall uncertainty of the LEFM./+.

This appendix utilizes the results of the calibration testing for the plant spool piece(s) for the uncertainty in the profile factor ( calibration coefficient). The engineering reports for the spool piece calibration tests are referenced in Appendix A.3 to this report.

3 Reference 3 (ER l 57P-A) develops the uncertainties for the LEFM ,/ + system. Because this system uses two measurement planes, the structure of its uncertainties differs somewhat that of an LEFM3. 4 Reference 3 (ER l57P-A) revised some of the time measurement uncertainty bounds. The revised bounds are a conservative projection of actual performance of the LEFM hardware. ER 80P used bounds that were based on a conservative projection of theoretical performance.

ER-1180NP Rev. l Prepared by: JJL


Reviewed by: {ll~



Appendix A.3, Meter Factor (Calibration) Uncertainties

Included with Revision 1 only - N/ A for Revision 0 As noted above, the calibration test report for the spool piece(s) establishes the overall uncertainty in the meter factor of the LEFM., +. [

]

[

].

Appendix A.4, [

This appendix calculates the [ ]

Appendix A.5, [

This appendix calculates the [

Appendix B, Total Thermal Power Uncertainty due to the LEFM ~ + The total thermal power uncertainty due to the LEFM "+ is calculated in this appendix, using the results of Appendix A.2, A.4 and A.5. Plant supplied steam conditions (which enter into the computation of errors due to feedwater temperature) are used for this computation. This appendix also computes the fraction of the uncertainty in feed water temperature that is systematically related to the mass flow uncertainty.

ER-1 l 80NP Rev. 1 Prepared by: JJL


Reviewed by: {N




~CAMERON

5.0 REFERENCES


1) Cameron Topical Report ER-80P, "Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM Check System", Rev. 0

2) Cameron Engineering Report ER-I60P, "Supplement to Topical Report ER 80P: Basis for a Power Uprate with the LEFM System", May 2000

3) Cameron Engineering Report ER-I57(P-A), "Supplement to Cameron Topical Report ER-80P: Basis for Power Uprates with an LEFM Check or an LEFM CheckPlus", dated May 2008, Revision 8 and Revision 8 Errata

4) ASME PTC 19.1-1985, Measurement Uncertainty

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~CAMERON

Appendix A

Appendix A.I, LEFM~+ Inputs

Appendix A.2, LEFM~+ Uncertainty Items/Calculations

Appendix A.3, Meter Factor Calculation and Accuracy Assessment

Appendix A.4, [

Appendix A.5, [



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Appendix A.1

LEFM,/ + Inputs

No attachment to follow, as Appendix is Proprietary in its Entirety


Appendix A.2

LEFM ~ + Uncertainty Items/Calculations



Appendix A.3

LEFM,I + Meter Factor Calculation and Accuracy Assessment

Reference Caldon Engineering Reports

ER-1182 Rev 0, "Meter Factor Calculation and Accuracy Assessment for Farley Unit l ", June 2019


Appendix A.4



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Appendix A.5



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AppendixB

Total Thermal Power and Mass Flow Uncertainty using the LEFM ../ + System



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Attachment $, cqntain;,, prc:,prietary and nori,:-proprietary versl9i:is ,of 'i:ew<lirt E::i~-1181. .Under 10 CFR 2.3£'!Q, wit~hpld frpm p,ublic di;;,qlosure ,ER-1181 P Rev. 1.

IJpon r~moval of ER,.,1ta1p Rev.1. ~ttachment s is:unaontreHed.

Attachment 6

Engineering Report: ER-1181 P/NP Rev. 1, "Bounding Uncertainty Analysis for Thermal Power· Determination at Farley Unit 2 Using the LEFM./+ System" & Caldon Application

for Withholding Proprietary Information from Public Di.sclosure CAW-19-02, accompanying Affidavit, Proprietary Information Notice, and Copyright Notice



Engineering Report: ER-1181 NP Rev. 1

BOUNDING UNCERTAINTY ANALYSIS FOR THERMAL POWER DETERMINATION AT FARLEY UNIT 2 USING THE LEFM,/+ SYSTEM

Prepared by: Jonathan Lent \\_ Reviewed by: Ryan Hannas~\"

May 2019



Reviewed by: {d:

~CAMERON

ER-1181NP Rev. I


Engineering Report No. ER-1181 NP Rev. 1 May 2019

Prepared by: J JL


Measurement Systems

Reviewed by: QH

ft CAMERON Measurement Systems

WITHHOLD FROM PUBLIC DISCLOSURE UNDER CFR 2.390 Proprietary to Cameron - Partial


BOUNDING UNCERTAINTY ANALYSIS FOR THERMAL POWER DETERMINATION AT FARLEY UNIT 2 USING THE LEFM,1+ SYSTEM

Table of Contents

1.0 2.0 3.0 4.0 5.0 6.0

A

INTRODUCTION SUMMARY APPROACH OVERVIEW REFERENCES APPENDICES Information Supporting Uncertainty in LEFM ./ + Flow and Temperature Measurements A.I LEFM./+ Inputs A.2 LEFM./+ Uncertainty Items/Calculations A.3 LEFM ./ + Meter Factor Calculation and Accuracy Assessment A.4 [ ) A.5 [ ]

B Total Thermal Power and Mass Flow Uncertainties using the LEFM,1+ System

ER-1181NP Rev. 1 Prepared by: J JL


Reviewed by: . JetJ


{C CAMERON Measurement Systems WITHHOLD FROM PUBLIC DISCLOSURE UNDER CFR 2.390 Page 4

Proprietary to Cameron - Partial 1.0 INTRODUCTION The LEFM./ and"LEFM./ +1 are advanced ultrasonic systems that accurately determine the volume flow and temperature of feedwater in nuclear power plants. Using a feedwater pressure signal input to the LEFM ./ and LEFM ./ +: mass flow can be determined and, along with the temperature output are used along with plant data to compute reactor core thermal power. The technology underlying the LEFM,r ultrasonic instruments and the factors affecting their performance are described in a topical report, Reference 1, and a supplement to this topical report, Reference 2.

The LEFM ./ +, which is made of two LEFM ./ subsystems, is described in another supplement to the topical report, Reference 3. The exact amount of the uprate allowable under a revision to 1 OCFR50 Appendix K depends not only on the accuracy of the LEFM ./ + instrument, but also on the uncertainties in other inputs to the thermal power calculation.

It is the purpose of this document to provide an analysis of the uncertainty contribution of the LEFM ./ + System [ ] to the overall mass flow and thermal power uncertainty of Farley Unit 2 (Appendix B}.

The uncertainties in mass flow and feed water temperature are also used in the calculation of the overall thermal power uncertainty (Appendix B). [

] A detailed discussion of the methodology for combining these terms is described in Reference 3.

This analysis is a bounding analysis for Farley Unit 2. [

ER-118INP Rev. 1

1

Prepared by: J JL


Reviewed by: {tH





ft CAMERON Measurement Systems WITHHOLD FROM PUBLIC DISCLOSURE UNDER CFR 2.390 Page 5

Proprietary to Cameron - Partial 2.0 SUMMARY For Farley Unit 2, Revision 1 results are as follows:

1. The mass flow uncertainty approach is documented in Reference 3. The uncertainty in the LEFM v" +'s mass flow of feed water is as follows:

o Fully Functional LEFM ./ + system mass flow uncertainty is [ ]

o Maintenance Mode LEFM ./ + system mass flow uncertainty is [

]

2. The uncertainty in the LEFM./ + feedwater temperature is as follows:

o Fully Functional LEFM ./ + system temperature uncertainty is [

o Maintenance Mode LEFM ./ + system the uncertainty is [ ]



3. The total thennal power uncertainty approach is documented in Reference 3 and Appendix B of this document. The total uncertainty in the determi11ation ofthennal power uses the LEFMv"+ system parameters and plant specific parameters, i.e., heat gain/losses, etc. and is as follows:

o Thennal power uncertainty using a Fully Functional LEFM ./ + system is [ ]

o Thennal power uncertainty using a Maintenance Mode LEFM ./+ system is [

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Trade ] Secret &

Confidential Commercial Information

~CAMERON

3.0 APPROACH


All errors and biases are calculated and combined according to the procedures defined in Reference 4 in order to determine the 95% confidence and probability value. The approach to determine the uncertainty, consistent with determining set points, is to combine the random and bias terms by the means of the RSS approach provided that all the terms are independent, zerocentered and normally distributed.

Reference 4 defines the contributions of individual error elements through the use of sensitivity coefficients defined as follows:

A calculated variable Pis determined by algorithm f, from measured variables X, Y, and Z.

P = f(X, Y, Z)

The error, or uncertainty in P, dP, is given by:

dP = of I dX + of I dY + ofl dZ 8X yz oY xz az xr

As noted above, P is the determined variable--in this case, reactor power or mass flow-- which is calculated via measured variables X, Y, and Z using an algorithm f (X, Y, Z). The uncertainty or error in P, dP, is determined on a per unit basis as follows:

dP = { X iJJ I } dX + { y iJJ I } dY + { z of I } dZ P PoXrz X PoYxz Y PoZxr Z

where the terms in brackets are referred to as the sensitivity coefficients.

If the errors or biases in individual elements (dX/X, dYIY, and dZIZ in the above equation) are all caused by a common (systematic) boundary condition (for example ambient temperature) the total error dP/ P is found by summing the three terms in the above equation. If, as is more often the case, the errors in X, Y, and Z are independent of each other, then Reference 4 recommends and probability theory requires that the total uncertainty be determined by the root sum square as follows (for 95% confidence and probability):

Obviously, if some errors in individual elements are caused by a combination of boundary conditions, some independent and some related (i.e., systematic) then a combination of the two procedures is appropriate.

ER-l l81NP Rev. 1 Prepared by: JJL


Reviewed by: {2tJ

{e CAMERON Measurement Systems WITHHOLD FROM PUBLIC DISCLOSURE UNDER CFR 2.390 Page 7

Proprietary to Cameron - Partial 4.0 OVERVIEW The analyses that support the calculation of LEFM v' + uncertainties are contained in the appendices to this document. The function of each appendix is outlined below.

Appendix A.1, LEFM,I + Inputs

This appendix tabulates dimensional and other inputs to the LEFM v' +. The spreadsheet calculates other key dimensions and factors from these inputs (e.g., the face-to-face distance between pairs of transducer assemblies)~ which is used by the LEFM v' + for the computation of mass flow and temperature.

Appendix A.2, LEFM,I + Uncertainty Items Calculations

This appendix calculates the uncertainties in mass flow and temperature as computed by the LEFMv'+ using the methodology described in Appendix E of Reference land. Appendix A of Reference 33, with uncertainties in the elements of these ,measurements bounded as described in both references4• The spreadsheet calculations draw on the data of · Appendix A. l for dimensional information. It draws from Appendix A.4 [

]. These uncertainties are an important factor in establishing the overall uncertainty of the LEFMv'+.

This appendix utilizes the results of the calibration testing for the plant spool piece(s) for the uncertainty in the profile factor ( calibration coefficient). The engineering reports for the spool piece calibration tests are referenced in Appendix A.3 to this report.

3 Reference 3 (ER l 57P-A) develops the uncertainties for the LEFM ./ + system. Because this system uses two measurement planes, the structure of its uncertainties differs somewhat that of an LEFM3. 4 Reference 3 (ER l57P-A) revised some of the time measurement uncertainty bounds. The revised bounds are a conservative projection of actual performance of the LEFM hardware. ER SOP used bounds that were based on a conservative projection of theoretical performance.



Reviewed by: RH


ft CAMERON Measurement Systems WITHHOLD FROM PUBLIC DISCLOSURE UNDER CFR 2.390 Page 8

Proprietary to Cameron - Partial

Appendix A.3, Meter Factor (Calibration) Uncertainties

Included with Revision 1 only - N/ A for Revision 0 As noted above, the calibration test report for the spool piece(s) establishes the overall uncertainty in the meter factor of the LEFM v" +. [

]

[

l

Appendix A.4, [

This appendix calculates the [

Appendix A.5, [

This appendix calculates the [ ]

Appendix B, Total Thermal Power Uncertainty due to the LEFM ./ + The total thermal power uncertainty due to the LEFM v" + is calculated in this appendix, using the results of Appendix A.2,A.4 and A.5. Plant supplied steam conditions (which enter into the computation of errors due to feedwater temperature) are used for this computation. This appendix also computes the fraction of the uncertainty in feed water temperature that is systematically related to the mass flow uncertainty.



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· Commercial Information



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5.0 REFERENCES


1) Cameron Topical Report ER-80P, "Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM Check System", Rev. 0

2) Cameron Engineering Report ER-160P, "Supplement to Topical Report ER 80P: Basis for a Power Uprate with the LEFM System", May 2000

3) Cameron Engineering Report ER-157(P-A), "Supplement to Cameron Topical Report ER-80P: Basis for Power Uprates with an LEFM Check or an LEFM CheckPlus", dated May 2008, Revision 8 and Revision 8 Errata

4) ASME PTC 19.1-1985, Measurement Uncertainty



Reviewed by: aH

ft CAMERON Measurement Systems


Appendix A

Appendix A.1, LEFM ,/ + Inputs

Appendix A.2, LEFM ,/ + Uncertainty Items/Calculations

Appendix A.3, Meter Factor Calculation and Accuracy Assessment

Appendix A.4, [

Appendix A.5, [



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Appendix A.1

LEFMy""+ Inputs



Appendix A.2

LEFM,/+ Uncertainty Items/Calculations



Appendix A.3

LEFM ./ + Meter Factor Calculation and Accuracy Assessment

Reference Caldon Engineering Reports

ER-1183 Rev 0, "Meter Factor Calculation and Accuracy Assessment for Farley Unit 2", June 2019



Appendix A.4



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Appendix A.5



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Appendix B

Total Thermal Power and Mass Flow Uncertainty using the LEFMv"+ System



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Attachment 7 contains proprietary ana rion'"proprietary versions of report ER-1182. Und.er 1 Q CFR 2..39Q, withhol<;I fr9m pub,li9 <;lis<;:19$1,irE;! E:R-1t~2P R~v. 1.

UPPl1 n.=m1oval of l;R-11 B?P Rev. 1, A(tacflmerit 7 is uncontrolled.

Attachment 7

Engineering Report: ER-1182P/NP Rev. 1, "Meter Factor Calculation and Accuracy Assessment for Farley Unit 1" & Caldon Application for Withholding Proprietary

Information from Public Disclosure CAW-19-03, accompanying Affidavit, Proprietary Information Notice, and Copyright Notice

Measurement Systems



METER FACTOR CALCULATION AND ACCURACY ASSESSMENT FOR FARLEY UNIT 1

Prepared by: Jonathan Lent Reviewed by: Ryan Hannas Reviewed for Proprietary Information by: Joanna Phillips~t};f .

July 2019

ER-1182NPRev.1 Prepared by: JJL


Measurement Systems

eron International Corporation ("Cameron") All information containe publication is con i en I ert of C o uction or use of these instructions, drawings, or fan officer of

ER-1182NP Rev. 1


Engineering Report No. ER-1182NP Rev. 1 July 2019

Prepared by: JJL


Reviewed b~;.: RSH '(}. ~

Measurement Systems

Table of Contents

1.0 INTRODUCTION .................................................................................................... 1

1.1 SCOPE .......................................................................................................................... l 1.2 BACKGROUND .......................................................................................................... 1 1.3 REPORT SUMMARY ................................................................................................. 2

2.0 CALIBRATION TESTS .......................................................................................... 3

2.1 METER SETUP ........................................................................................................... 3 2.2 INST ALLA TI ON SITE MODEL ................................................................................ 3 2.3 CALIBRATION DATA AND PARAMETRIC TESTS .............................................. 6

2.3.1 TEST COLLECTION PROCEDURE .......................................................................... 7

3.0 METER FACTOR CALCULATION .................................................................... 8

3 .1 METER FACTOR DEFINITION ................................................................................ 8 3.2 TESTRESULTS .......................................................................................................... 8 3.3 MEASURED VELOCITY PROFILES ...................................................................... 12

3.3.1 SWIRL RATE DEFINITION ..................................................................................... 15 3.3.2 FLATNESS RATIO DEFINITION ........................................................................... 17

4.0 METER FACTOR ACCURACY ASSESSMENT .............................................. 19

4.1 FACILITY UNCERTAINTY .................................................................................... 20 4.2 MEASUREMENT UNCERTAINTY ........................................................................ 20 4.3 EXTRAPOLATION -PROFILE VARIATION ALLOWANCE .............................. 21 4.4 MODELING SENSITIVITY UNCERTAINTY ........................................................ 23 4.5 DATA SCATTER- MEAN METER FACTOR UNCERTAINTY ........................... 23

5.0 REFERENCES ....................................................................................................... 25

APPENDIX A-CALIBRATION DATA ..................................................................... 26

APPENDIX B - METER UNCERTAINTY .................................................................. 27

ER·1182NPRev.1 Prepared by: JJL Reviewed bY.: RSH ~ .


Measurement Systems Page 1

ER-1182NP Rev 1, M..eter Factor Calculation and Accuracy Assessment for Farley Unit 1

1.0 INTRODUCTION

1.1 Scope

This report documents calibration and uncertainty analysis of the Farley Unit 1 flow elements SIN · 4400010594-001 (Loop A), SIN 4400010594-002 (Loop B), and SIN 4400010594-003 (Loop C).

This report includes:

• Meter factor(s) ( e.g., profile factor) and meter factor uncertainty • Description of the hydraulic models • Description of the tests conducted • [ J

1.2 Background

The flow meter uses measurements of the fluid velocity projected onto acoustic paths to determine the volumetric and mass flow. The meter makes the transit time measurements of ultrasonic energy pulses that travel between transducers and combines these with the distance separating the transducers to calculate the velocity. The flow meter uses eight acoustic paths that are arranged as two crossing planes, each plane containing four chords (essentially two four path meters). The meter calculates volumetric flow by numerically integrating the fluid-velocity chord length product along the chords.

The calibration test was performed at Alden Research Laboratories (Alden), an independent hydraulic laboratory. Alden can provide flow rates up to -16,000 gpm. For these hydraulic models, the piping pressure losses and cavitation limited the maximum calibration flow rate to -14,000 gpm.

During the calibration, reference flow rates were determined by Alden using a weigh tank, fill times, fluid temperature and barometric pressure measurements. All elements of the lab measurements including weigh tank scale, time measurements, thermometers and pressure gages, are traceable to NIST standards. In order to determine the meter factor, the flow meter outputs are compared against the reference flow rates.

The Farley Unit 1 calibration test procedure was ALD-1167 Rev. 2, which provided overall guidance for the test setup and test scope.

ER-1182NP Rev. 1 Prepared by: JJL Reviewed by~


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1 .3 Report Summary


a. Table 1 provides the Farley Unit 1 meter factors and uncertainties when calibrated in the installation model. Refer to Section 4 for a detailed summary.

Table 1: Calibration Summary

b. The electronics worked within specifications [

C. [

Table 2: [

I [



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2.0 CALIBRATION TESTS The objectives for the calibration tests were to:

• Determine the meter factor in a piping configuration that models the installation site, • Determine the sensitivity of the meter factor to variations in the hydraulic model, • Determine the [ J

2.1 Meter Setup

The meter was installed in accordance with portions of Cameron Engineering Field Procedure EFP-68. Specifically, the portions of EFP-68 accomplished:

• [ • [ ] .. [ ]

[

]

2.2 Installation Site Model

The hydraulic model configuration was designed as a hydraulic duplicate of the principle hydraulic features of the installation site (see Reference 1 for plant details). The general piping arrangement is shown in Figures l ~ 3 for Loops A - C respectfully. [

Trade




ER-1182NP Rev.1 Prepared by: JJL Reviewed by: RSH ~ \\


Figure 1: Plant Hydraulic Configuration - Loop A




LOOP A

Reviewed by: RSH ~ i

LOOPS

Figure 2: Plant Hydraulic Configuration - Loop B




~BLIND FLANGE

------- ----

14" SCH 60

Figure 3: Plant Hydraulic Configuration - Loop C

2.3 Calibration Data and Parametric Tests

LOOPC


Reference I outlines the model tests and parametric tests performed. These parametric tests included variations to the model, such as changes to the upstream hydraulics. With these parametric tests, installation uncertainty is addressed.

The Farley Unit I parametric tests and calibration numbers are described in Table 3. The Farley Unit l test data is shown in Appendix A

ER-1182NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~\\--


Table 3: Test Summary (Reference ALD-1167)


Model tests consisted of 25 weigh tank runs over a range of different flow rates. Parametric tests consisted of 20 runs.

2.3.J Test Collection Procedure

Weigh tank testing at a specific flow rate began by setting the proper flow in the flow loop using a remotely operated butterfly valve located downstream of the model. The flow meter data is

ER-1182NP Rev. 1 Prepared by: JJL Reviewed by: RSH ~~




collected using a serial connection to a laptop PC. The flow data is polled by the PC from the electronics at approximately 5-second intervals. The ported information contains a time stamp and volumetric flows, as well as signal data quality, and path velocity data. Velocity data for individual acoustic paths are recorded in order to evaluate the fluid velocity profile (see Figures 7, 8, and 9).

The test procedure at any given flow rate was as follows:

• Set the flow rate and allow flow to stabilize

• Alden personnel operate weigh tank run by moving the diverter valve.

• Cameron personnel separately record a start time and a stop time along with count values from the pulse output of each transmitter. This information is used to synchronize the ported data with the weigh tank data.

3.0 METER FACTOR CALCULATION

3.1 Meter Factor Definition The meter factor accounts for (typically small) biases in the numerical integration due to the hydraulics, dimension measurements and acoustics of the application. The flow meter software multiplies the result of the multi-path numerical integration by the meter factor to obtain the flow rate. For the Alden tests, the meter factor was set at 1.000.

The meter factor is calculated by the following equation:

MF= QAlden

Qmeter

Where:

Qmeter

QAiden

= Volumetric flow rate from meter (with meter factor set to 1.000)

= Volumetric flow rate based on Alden weigh tank

3.2 Test Results Appendix A tabulates the results of the individual calibration runs for each of the different hydraulic configurations. All tables contain for each weigh tank run:

• Alden certified flow rate.

• Meter flow rate averaged over the weigh tank fill period [ ] . [ ]

Table 4 below summarizes the data [( ]

ER-1182NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~ ~




Figures 4, 5, and 6 plot the meter factors for all the tests (note: for clarity only the average meter factor at each flow rate is plotted).

Table 4: [






Reviewed bY.: RSH ~ l

\_

Figure 4: Loop A - Meter Factors vs. Flow

ER-1182NP Rev.1 Prepared by: JJL

SchlumbergersPrivate


Reviewed bY.: RSH ~~


Figure 5: Loop B - Meter Factors vs. Flow




Reviewed by~


Figure 6: Loop C - Meter Factors vs. Flow

3.3 Measured Velocity Profiles


Using the flow meter it is possible to measure and understand the actual hydraulic velocity profile. Appendix A has the velocity profiles observed during each model test. [

]

ER-1182NP Rev.1 Prepared by: JJL Reviewed bY.: RSH ~ \I-Schlumberger-Private

Trade Secret & Confidenti; Commerci. lnformatior


ER-1182NPRev.1


Figure 7: Loop A Test A-1 (Model) Velocity Profile

Prepared by: JJL Reviewed bY.: RSH ~t Schlumberger-Private

Trade Secret& Confidenlia Commercla Information

ER-1182NP Rev. 1


Figure 8: Loop B Test B-1 (Model) Velocity Profile

Prepared by: JJL Reviewed by: RSH ~Y Schlumberger-Private


Figure 9: Loop C Test C-1 (Model) Velocity Profile


3.3.1 Swirl Rate Definition

Swirl can be measured by the flow meter. Cameron quantifies swirl rate with a swirl rate calculation, as follows:

Where:

V1, V4, Vs, Vs V2, V3, V6, V1 Ys, YL

ER-1182NP Rev. 1

Swirl Rate = Average 1 5 ,

8 4 ,

2 G , 1 3 [

V -V V -V V -V V -V] 2·Ys 2·Ys 2·yL 2·yL

= = =

normalized velocities measured along outside chords normalized velocities measured along inside chords

Normalized chord location for short and long paths

Prepared by: JJL Reviewed b~{ RSH t ~ Schlumberger-Private

Trade Secret & Conlidentia Commercia lnfomiation


Swirl rates less than 3% are low and are typically observed in models with only planar connections. Swirl rates greater than 3% are considered "swirling". Swirl rates greater than 10% are considered to have strong swirl.

3.3.1.1 Swirl Rate Results

The following figure summarizes the absolute value of swirl rate observed during the calibrations. [

]

Figure 10: Summary Swirl Rate for Tests

Trade Secret&



ER-1182NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~


\


3.3.2 Flatness Ratio Definition

Cameron uses the flatness ratio (FR) to quantify how flat the velocity profile is. FR is defined as:

Where:

V1, V4, Vs. Vs V2, VJ, V6, V1

= =

FR= [ V1 + V4 + Vs + Vs J v2 + v3 + v6 + v1

velocities measured along the outside chords (or short paths) velocities measured along the inside chords (or long paths)

When a velocity profile is perfectly flat, then FR equals 1.0. When a velocity profile is laminar, then the FR equals approximately 0.38. The limits of 0.38 and 1.0 represent extremes. The FR is a function of Reynolds number but also is strongly influenced by the hydraulics upstream of the flow meter.

Typical feedwater applications have FR in the range of 0.78 to 0.95. Downstream of flow conditioners, the velocity profile tends to be pointier and the FR value is lower, 0.78 to 0.82. Downstream of elbows and tees the velocity profile tends to be flatter and the FR value is higher, 0.85 to 0.95, where reducing tees produce the flatter profiles (e.g., higher FR values). The actual range at a given plant is dependent upon site upstream conditions (for example the hydraulic fittings such as tees, elbows, etc.). The tests are summarized in the following figure. [

]




ER-1182NP Rev.1



Figure 11: Summary of Flatness Ratios for Tests

Prepared by: JJL Reviewed bY.: RSH ~~ Schlumberger-Private

4.0 METER FACTOR ACCURACY ASSESSMENT

Measurement Systems

Page 19

This section documents the methodology for calculating the uncertainty or accuracy of the meter factor. This report was produced using a process and quality assurance consistent with the requirements of ASME PTC 19.1 and ANSI/NCSL 2540-2-1997 (see References 6, 11, 16 and 17). The approach to determination of the set points is to combine the random (Type A) and systematic (Type B) terms by the means. of the RSS approach given that all the terms are independent, zero-centered and normally distributed.

First, the sensitivity of the calculated flow to each independent variable or input is determined. Once the sensitivities to the independent variables have been calculated, then the independent variables' uncertainties are calculated and multiplied with their sensitivity coefficient, such as calibration facility, timing errors, etc. The 95% confidence level uncertainty bounds are calculated for each element (uncertainty coverage for each term is 95%).

The evaluation of the sensitivity coefficients is performed by determining the independent variables in the mass flow (and volumetric flow) calculation. For example, if volume flow is a function of independent variables X1, X2, ... , Xn, as follows:

Q = f(Xl, X2, ... , Xn)

The uncertainty effect of specific independent variables on the flow measurement is calculated by partial differentiation of the above equation. Expressing the result as a per unit sensitivity:

dQ = [X1iQ](~X1)+[XiiQ](~Xi)+ ....... +[XniQ](~Xn). Q QOX:1 X1 QoX.2 Xi QoXn Xn

Where the terms in the brackets are the sensitivity coefficients for X1, X2, ... , Xn. The magnitudes and signs of each uncertainty for a given flow measurement are then bounded by 95% confidence intervals.

ASME PTC 19 .1 demonstrates that by combining the independent uncertainty contributions as the root sum square, the overall uncertainty in volumetric flow is bounded by a 95% confidence level.

The allocation of uncertainties for meter factor for the flow meter ( consistent with the Cameron Topical report) is shown in Table 5 below. Using the data in Table 5 and the root mean square summation technique indicated for combining independent uncertainties of relatively the same magnitude, the total uncertainty due to MF is computed.

ER-1182NP Rev. 1 Prepared by: JJL Reviewed by: RSH'2 lf Schlumberger-Private

Table 5: Uncertainty Summary for Meter Factor

RMS values rounded to closest 0.01 %

Measurement Systems

Page20


(All terms are treated as normal distributions with k = 2, e.g., 95% coverage)

4.1 Facility Uncertainty

A facility uncertainty of [ ] has been budgeted and this figure appears in the table above.

4.2 Measurement Uncertainty

Appendix B calculates the uncertainties in the volumetric flow measurement (excluding meter factor) of the flow meters used for this test. The results are summarized below in Table 6. [

For this report, Loop C was used to represent the system in the analysis.

3 See Reference 14.

ER-1182NP Rev. 1 Prepared by: JJL Reviewed b~t.: RSH f ~ Schlumberger-Private



Measurement Systems

Page 21

Table 6: Uncertainties in Volumetric Flow Measurements (All Figures rounded to two decimal points)


4.3 Extrapolation - Profile Variation Allowance At the plant, it is likely that the hydraulic conditions will not equal those tested during the calibration. In particular, the plant's Reynolds numbers are higher than that achievable at the laboratory (approximately 20 million vs. -2 million). Further, the plant may have a lower wall roughness than the test pipes used at the laboratory.

[

]

[

]

[

]

The numerical calculation of meter factor is illustrated below.




ER-1182NP Rev. 1 Prepared by: JJL Reviewed bY-: RSH ffe Schlumberger-Private



Measurement Systems

Page 22



Measurement Systems

Page 23

Using this analysis, a meter factor extrapolation of [ ] is predicted from the average calibration Reynolds number (-2e6) to the plant application (-20e6). The flatness ratio extrapolation is approximately [ ] for the same range.

[

4.4 Modeling Sensitivity Uncertainty

For the Farley Unit l, 12 different models were tested. Using this population, the population statistics are calculated. [

]

4.5 Data Scatter - Mean Meter Factor Uncertainty

Each average (mean) meter factor is computed using all of the meter factor measurements made for that flow element. The uncertainty in mean meter factor addresses the 95% confidence limits on the uncertainty in that mean. Each set of data at a given flow rate is treated as a separate datum, since in fact the profile varies with flow rate (i.e., Reynolds Number) as shown in Section 3 .2. Section 4.4 shows that meter factor is essentially independent of hydraulic configuration. Hence the precision with which the meter factor for a specific flow element is determined is enhanced by including all calibration data for that flow element. Accordingly the meter factor is determined as follows:

• Loop A from the [ • Loop B from the [ • Loop C from the [

] measurements of tests A-1 through A-4 ] measurements of tests B- l through B-4 ] measurements of tests C-1 through C-4

The calculation of the uncertainty of the mean proceeds as follows:



]






Measurement Systems

Page 24


Using the above methodology, the uncertainty in the mean meter factor is computed to be as follows:

. [ . [ . [

ER-1182NP Rev.1 Prepared by:


JJL

] ] ]


Reviewed b~,'.: RSH ~ 't

5.0 l.

2.

3.

4.

5.

6.

7.

8.

9.

IO.

11.

12.

13.

14.

15.

16.

17.

18.

19.

REFERENCES

Measurement Systems

Page 25

ALD-1167 Rev 2, Hydraulic Calibration Plan for Farley Unit 1 Chordal Spool pieces

2006 South East Asia Flow Workshop Paper, "The Relative Merits of Ultrasonic Meters Employing Between Two and Eight Paths", Gregor Brown, Don Augenstein, Terry Cousins, Herb Estrada

EFP-68, Commissioning Procedure for LEFMCheck Chordal Systems

EFP-55, Profile Factor Determination at a Flow Measurement Facility

Moody, L. F., "Friction Factors for Pipe Flow," ASME Transactions, V. 66, 1944, pp. 671-694

National Bureau of Standards and Technology, "Experimental Statistics Handbook 1991"

Murakami, M., Shimizu, Y., and Shiragami, H., "Studies on Fluid Flow in Three-Dimensional Bend Conduits," Japan Society of Mechanical Engineering (JSME), Bulletin V. 12, No. 54, Dec. 1969,pp. 1369-1379.

Cameron Topical Report ER-SOP Rev 1, "Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM Check System", March 1997.

ER-551, Transducer Replacement Sensitivity

Westinghouse Research Laboratories Nov 3, 1972, "Integration Errors for Turbulent Profiles in Pipe Flow"

ASME PTC 19.1-1985, Measurement Uncertainty C,

Cameron Engineering Report ER-160P Rev 1, "Supplement to Topical Report ER 80P: Basis for a Power Uprate with the LEFM System", May 2000

Cameron Engineering Report ER-157(P-A) Rev. 8 and Rev. 8 Errata, "Supplement to Caldon Topical Report ER-80P: Basis for Power Uprates with an LEFM Check or an LEFM CheckPlus", May 2008

Alden Calibration Report for Farley Unit 1

Cameron Engineering Report ER 262 Rev l, "Effects of Velocity Profile Changes Measured InPlant on LEFM Feedwater Flow Measurement Systems", January 2002

NIST TN-1297, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results"

ANSI/NCSL 2540-2-1997, "U.S. Guide to the Expression of Uncertainty in Measurement"

ISO "Guide to the Expression of Uncertainty in Measurement"

IGHEM Flow Paper 2008 Milan, Italy, "Accuracy Validation of Multiple Path Transit Time Flowmeters"

ER-1182NP Rev.1 Prepared by: JJL Reviewed by: RSH·~~


Appendix A - Calibration Data

[

Measurement Systems

]


ER-1182NPRev.1 Prepared by: JJL Reviewed bY.: RSH ll~ Schlumberger-Private

Trade


Appendix B - Meter Uncertainty

B.1 - Inputs and Scaling B.2- Flow Uncertainty B.3- [ ] B.4-[



Measurement Systems


Reviewed bY.: RSH ~ \~

Appendix B.1

Inputs and Scaling

Measurement Systems


ER-1182NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~~


l

Appendix B.2

Flow Uncertainty

Measurement Systems


ER-1182NP Rev. 1 Prepared by: JJL Reviewed b~{ RSH yl~ Schlumberger-Private

Measurement Systems

Appendix B.3

I No attachment to follow, as Appendix is Propriet~ry in its Entirety

ER-1182NP Rev. 1 Prepared by: JJL Reviewed by: RSH ,e ~ Schlumberger-Private


Appendix B.4

[ ]

Measurement Systems





Reviewed bY.: RSH (l lfl ( UJ

SNC to NRG LAR Enclosure NL-19-0795

Attachment 8. ~ontc1in_s proprietary c1nd non-ptoprietc1ry versl9ns of r~port ER-1183. l.,Jnder 10 ¢FR 2.390, y.,ithhold_ fr~m, pl,lblic djscl0si.ir~ !:FM 183P Rev. 1.

Upon rem0val of ER-1183P Rev. 1, Attachment 8 ls :uncontrolled.

Attachment 8

Engineering Report: ER-1183P/NP Rev. 1, "Meter Factor Calculation and Accuracy Assessment for Farley Unit 2" & Caldon Application for Withholding Proprietary

Information from Public Disclosure CAW-19-04, accompanying Affidavit, Proprietary Information Notice, and Copyright Notice

Meast:Jrement Systems



METER FACTOR CALCULATION AND ACCURACY ASSESSMENT FOR FARLEY UNIT 2

Prepared by: Jonathan Lent Reviewed by: Ryan Hannas Reviewed for Proprietary Information by: Joanna Phillip~

July 2019

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSHp~


Measurement Systems

meron International Corporation ("Cameron") All information contained ioJbis publication is conf1 en I rtam:l-pr-E>f)i:ietar.y_~operty of Came~rotlocuonor use of these instructions, drawings, or photogroi,lu wit ~unfie ~swl'itten..pem1ission of an officer of

-Cameton ls-for6idden.

ER-1183NP Rev. 1


Engineering Report No. ER-1183NP Rev. 1 July 2019

Prepared by: JJL


-

Reviewed bY-: RSH ~~

Measurement Systems

Table of Contents

1.0 INTRODUCTION ............................................. ,,,0,,, •••••••••••••••••••••••••••••••••••••••••••••••• 1

I.I SCOPE .......................................................................................................................... I 1.2 BACKGROUND .......................................................................................................... I 1.3 REPORT SUMMARY ................................................................................................. 2

2.0 CALIBRATION TESTS .......................................................................................... 3

2.1 METER SETUP ........................................................................................................... 3 2.2 INST ALLA TI ON SITE MODEL ................................................................................ 3 2.3 CALIBRATION DATA AND PARAMETRIC TESTS .............................................. 6

2.3.1 TEST COLLECTION PROCEDURE .......................................................................... 7

3.0 METER FACTOR CALCULATION .................................................................... 8

3.1 METER FACTOR DEFINITION .......................................................................... -...... 8 3.2 TEST RESULTS .......................................................................................................... 8 3.3 MEASURED VELOCITY PROFILES ...................................................................... 12

3.3.1 SWIRL RATE DEFINITION ..................................................................................... 15 3.3.2 FLATNESS RATIO DEFINITION ........................................................................... 17

4.0 METER FACTOR ACCURACY ASSESSMENT .............................................. 19

4.1 FACILITY UNCERTAINTY .................................................................................... 20 4.2 MEASUREMENT UNCERTAINTY ........................................................................ 20 4.3 EXTRAPOLATION - PROFILE VARIATION ALLOWANCE .............................. 21 4.4 MODELING SENSITIVITY UNCERTAINTY ........................................................ 23 4.5 DATA SCATTER - MEAN METER FACTOR UNCERTAINTY ........................... 23

5.0 REFERENCES ....................................................................................................... 25

APPENDIX A - CALIBRATION DATA ..................................................................... 26

APPENDIX B - METER UNCERTAINTY .................................................................. 27

ER-1183NP Rev.1 Prepared by: JJL Reviewed by~t



ER-1183NP Rev 1, Meter Factor Calculation and Accuracy Assessment for Farley Unit 2

1.0 INTRODUCTION

1.1 Scope

This report documents calibration and uncertainty analysis of the Farley Unit 2 flow elements SIN 4400010594-004 (Loop A), SIN 4400010594-005 (Loop B), and SIN 4400010594-006 (Loop C).

This report includes:

• Meter factor(s) (e.g., profile factor) and meter factor uncertainty • Description of the hydraulic models • Description of the tests conducted . [ ]

1.2 Background

The flow meter uses measurements of the fluid velocity projected onto acoustic paths to determine the volumetric and mass flow. The meter makes the transit time measurements of ultrasonic energy pulses that travel between transducers and combines these with the distance separating the transducers to calculate the velocity. The flow meter uses eight acoustic paths that are arranged as two crossing planes, each plane containing four chords (essentially two four path meters). The meter calculates volumetric flow by numerically integrating the fluid-velocity chord length product along the chords.

The calibration test was performed at Alden Research Laboratories (Alden), an independent hydraulic laboratory. Alden can provide flow rates up to -16,000 gpm. For these hydraulic models, the piping pressure losses and cavitation limited the maximum calibration flow rate to .,..14,000 gpm.

During the calibration, reference flow rates were determined by Alden using a weigh tank, fill times, fluid temperature and barometric pressure measurements. All elements of the lab measurements including weigh tank scale, time measurements, thermometers and pressure gages, are traceable to NIST standards. In order to determine the meter factor, the flow meter outputs are compared against the reference flow rates.

The Farley Unit 2 calibration test procedure was ALD-1168 Rev. 2, which provided overall guidance for the test setup and test scope.

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RS~


Trade


Trade Secret & Confidential Cornmercial Information

1.3 Report Summary


a. Table l provides the Farley Unit 2 meter factors and uncertainties when calibrated in the installation model. Refer to Section 4 for a detailed summary.

Table 1: Calibration Summary

b. The electronics worked within specifications [

C. [

Table 2: [



]

Reviewed b~,,: RSH ~ i






2.0 CALIBRATION TESTS The objectives for the calibration tests were to:

• Determine the meter factor in a piping configuration that models the installation site, • Determine the sensitivity of the meter factor to variations in the hydraulic model, • Determine the [. ]

2.1 Meter Setup

The meter was installed in accordance with portions of Cameron Engineering Field Procedure EFP-68. Specifically, the portions of EFP-68 accomplished:

• [ ]

• [ ]

• [ ]

[

]

2.2 Installation Site Model

The hydraulic model configuration was designed as a hydraulic duplicate of the principle hydraulic features of the in~tallation site (see Reference I for plant details). The general piping arrangement is shown in Figures I - 3 for Loops A - C respectfully. [

Trade




ER-1183NP Rev. 1 Prepared by: JJL Reviewed bv.: RSH ~~


ER-1183NP Rev. 1

(

\~ \_ 2•1" X 14· '

REO~CING TEE

LOOP A

Figure 1: Plant Hydraulic Configuration - Loop A

Prepared by: JJL



Figure 2: Plant Hydraulic Configuration - Loop B




Reviewed bY.: RSH e~

Figure 3: Plant Hydraulic Configuration - Loop C

2.3 Calibration Data and Parametric Tests


Reference I outlines the model tests and parametric tests performed. These parametric tests included variations to the model, such as changes to the upstream hydraulics. With these parametric tests, installation uncertainty is addressed.

The Farley Unit 2 parametric tests and calibration numbers are described in Table 3. The Farley Unit 2 test data is shown in Appendix A.

ER-1183NP Rev. 1 Prepared by: JJL Reviewed b~,'.: RSH (l\ Schlumberger-Private

Table 3: Test Summary (Reference ALD-1168)


Model tests consisted of 25 weigh tank runs over a range of different flow rates. Parametric tests consisted of 20 runs.

2.3.1 Test Collection Procedure

Weigh tank testing at a specific flow rate began by setting the proper flow in the flow loop using a remotely operated butterfly valve located downstream of the model. The flow meter data is

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~~



-----: Measurement Systems I

Page 8

collected using a serial connection to a laptop PC. The flow data is polled by the PC from the electronics at approximately 5-second intervals. The ported information contains a time stamp and volumetric flows, as well as signal data quality, and path velocity data. Velocity data for individual acoustic paths are recorded in order to evaluate the fluid velocity profile (see Figures 7, 8, and 9).

The test procedure at any given flow rate was as follows:

• Set the flow rate and allow flow to stabilize

• Alden personnel operate weigh tank run by moving the diverter valve.

• Cameron personnel separately record a start time and a stop time along with count values from the pulse output of each transmitter. This information is used to synchronize the ported data with the weigh tank data.

3.0 METER FACTOR CALCULATION

3.1 Meter Factor Definition The meter factor accounts for (typically small) biases in the numerical integration due to the hydraulics, dimension measurements and acoustics of the application. The flow meter software multiplies the result of the multi-path numerical integration by the meter factor to obtain the flow rate. For the Alden tests, the meter factor was set at 1.000.

The meter factor is calculated by the following equation:

MF= QAldcn

Qmeter

Where:

Q meter

QAtden

= Volumetric flow rate from meter (with meter factor set to 1.000)

= Volumetric flow rate based on Alden weigh tank

3.2 Test Results Appendix A tabulates the results of the individual calibration runs for each of the different hydraulic configurations. All tables contain for each weigh tank run:

• Alden certified flow rate.

• Meter flow rate averaged over the weigh tank fill period [ ]

. [ ]

Table 4 below summarizes the data [( ]

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH n.t Schlumberger-Private



Figures 4, 5, and 6 plot the meter factors for all the tests (note: for clarity only the average meter factor at each flow rate is plotted).

Table 4: [

ER-1183NP Rev. 1 Prepared by:


JJL




Figure 4: Loop A - Meter Factors vs. Flow




Reviewed by: RSH '2,~


Figure 5: Loop B - Meter Factors vs. Flow




Reviewed bY.: RSH~t


Figure 6: Loop C - Meter Factors vs. Flow

3.3 Measured Velocity Profiles


Using the flow meter it is possible to measure and understand the actual hydraulic velocity profile. Appendix A has the velocity profiles observed during each model test. [

]

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH~~


Trade Secret & Confidenti, Commerci: lnformatior


ER-1183NP Rev.1


Figure 7: Loop A Test A-1 (Model) Velocity Profile

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ER-1183NP Rev. 1


Figure 8: Loop B Test B-1 (Model) Velocity Profile

Prepared by: JJL Reviewed b~f.: RSH ~\~ Schlumberger-Private


Figure 9: Loop C Test C-1 (Model) Velocity Profile

Measurement Systems

Page 15

3.3.1 Swirl Rate Definition

Swirl can be measured by the flow meter. Cameron quantifies swirl rate with a swirl rate calculation, as follows:

Where:

V1, V4, Vs. Vs V2, V3, V6, V1 ys, YL

ER-1183NP Rev. 1

Swirl Rate = Average 1 5 , 8 4

, 2 6

, 7

J [V -V V -V V -V V -V] 2·Ys 2·Ys 2·YL 2·yL

=

=

normalized velocities measured along outside chords normalized velocities measured along inside chords

Normalized chord location for short and long paths

Prepared by: JJL Reviewed b~: RSH ~ ~


-- ------,

Trade Secret & Confidentia Commercia Information


Swirl rates less than 3% are low and are typically observed in models with only planar connections. Swirl rates greater than 3% are considered "swirling". Swirl rates greater than 10% are considered to have strong swirl.

3.3.1.1 Swirl Rate Results

The following figure summarizes the absolute value of swirl rate observed during the calibrations. [

]

Figure 10: Summary Swirl Rate for Tests

Trade Secret&



ER-1183NP Rev. 1 Prepared by: JJL Reviewed b~: RSti6l}\



3.3.2 Flatness Ratio Definition

Cameron uses the flatness ratio (FR) to quantify how flat the velocity profile is. FR is defined as:

Where:

V1, V4, Vs, Vs V2, VJ, V6, V1

= =

FR= [V, + V4 +Vs+ Vs] V2 + V3 + V6 + V1

velocities measured along the outside chords (or short paths) velocities measured along the inside chords (or long paths)

When a velocity profile is perfectly flat, then FR equals 1.0. When a velocity profile is laminar, then the FR equals approximately 0.38. The limits of 0.38 and 1.0 represent extremes. The FR is a function of Reynolds number but also is strongly influenced by the hydraulics upstream of the flow meter.

Typical feedwater applications have FR in the range of 0.78 to 0.95. Downstream of flow conditioners, the velocity profile tends to be pointier and the FR value is lower, 0. 78 to 0.82. Downstream of elbows and tees the velocity profile tends to be flatter and the FR value is higher, 0.85 to 0.95, where reducing tees produce the flatter profiles (e.g., higher FR values). The actual range at a given plant is dependent upon site upstream conditions (for example the hydraulic fittings such as tees, elbows, etc.). The tests are summarized in the following figure. [

]

ER-1183NP Rev. 1 Prepared by: JJL Reviewed b~: RSH ~ ~



ER-1183NP Rev. 1



Figure 11: Summary of Flatness _Ratios for Tests

Prepared by: JJL Reviewed bY.: RSH·~'t\


4.0 METER FACTOR ACCURACY ASSESSMENT

Measurement Systems

Page 19

This section documents the methodology for calculating the uncertainty or accuracy of the meter factor. This report was produced using a process and quality assurance consistent with the requirements of ASME PTC 19.l and ANSI/NCSL 2540-2-1997 (see References 6, 11, 16 and 17). The approach to determination of the set points is to combine the random (Type A) and systematic (Type B) terms by the means of the RSS approach given that all the terms are independent, zero-centered and normally distributed.

First, the sensitivity of the calculated flow to each independent variable or input is determined. Once the sensitivities to the independent variables have been calculated, then the independent variables' uncertainties are calculated and multiplied with their sensitivity coefficient, such as calibration facility, timing errors, etc. The 95% confidence level uncertainty bounds are calculated for each element (uncertainty coverage for each term is 95%).

The evaluation of the sensitivity coefficients is performed by determining the independent variables in the mass flow (and volumetric flow) calculation. For example, if volume flow is a function of independent variables X1, X2, ... , Xn, as follows:

Q;: f(Xl,X2, ... , Xn)

The uncertainty effect of specific independent variables on the flow measurement is calculated by partial differentiation of the above equation. Expressing the result as a per unit sensitivity:

dQ =[X'~](~X')+[Xi~](~X2)+ ....... +[Xn~](~X"). Q Qo'X, X, Qo'Xi Xi Qo'Xn Xn

Where the terms in the brackets are the sensitivity coefficients for X1, X2, ... , Xn. The magnitudes and signs of each uncertainty for a given flow measurement are then bounded by 95% confidence intervals.

ASME PTC 19 .1 demonstrates that by combining the independent uncertainty contributions as the root sum square, the overall uncertainty in volumetric flow is bounded by a 95% confidence level.

The allocation of uncertainties for meter factor for the flow me'ter ( consistent with the Cameron Topical report) is shown in Table 5 below. Using the data in Table 5 and the root mean square summation technique indicated for combining independent uncertainties of relatively the same magnitude, the total uncertainty due to MF is computed.

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~ \\-


Table 5: Uncertainty Summary for Meter Factor

RMS values rounded to closest 0.01 %

Measurement Systems

Page 20



4.1 Facility Uncertainty

A facility uncertainty of [ ] has been budgeted and this figure appears in the table above.

4.2 Measurement Uncertainty Appendix B calculates the uncertainties in the volumetric flow measurement ( excluding meter factor) of the flow meters used for this test. The results are summarized below in Table 6. [

]

For this report, Loop A was used to represent the system in the analysis.

3 See Reference 14.

ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ~.




Measurement Systems

Page 21

Table 6: Uncertainties in Volumetric Flow Measurements (All Figures rounded to two decimal points)


4.3 Extrapolation - Profile Variation Allowance At the plant, it is likely t~at the hydraulic conditions will not equal those tested during the calibration. In particular, the plant's Reynolds numbers are higher than that achievable at the laboratory (approximately 20 million vs. -2 million). Further, the plant may have a lower wall roughness than the test pipes used at the laboratory.

[

]

[

]

[

]

The numerical calculation of meter factor is illustrated below.




ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH'9~


- -----:



Measurement Systems

Page 22



Reviewed bY.: RSH ~ t

Measurement Systems

Page 23

Using this analysis, a meter factor extrapolation of [ ] is predicted from the average calibration Reynolds number (-2e6) to the plant application (-20e6). The flatness ratio extrapolation is approximately [ ] for the same range.

[

4.4 Modeling Sensitivity Uncertainty For the Farley Unit 2, 12 different models were tested. Using this population, the population statistics are calculated. [

4.5 Data Scatter - Mean Meter Factor Uncertainty Each average (mean) meter factor is computed using all of the meter factor measurements made for that flow element. The uncertainty in mean meter factor addresses the 95% confidence limits on the uncertainty in that mean. Each set of data at a given flow rate is treated as a separate datum, since in fact the profile varies with flow rate (i.e., Reynolds Number) as shown in Section 3.2. Section 4.4 shows that meter factor is essentially independent of hydraulic configuration. Hence the precision with which the meter factor for a specific flow element is determined is enhanced by including all calibration data for that flow element. Accordingly the meter factor is determined as follows:

• Loop A from the [ • Loop B from the [ • Loop C from the [

] measurements of tests A-1 through A-4 ] measurements of tests B-1 through B-4 ] measurements of tests C-1 through C-4

The calculation of the uncertainty of the mean proceeds as follows:

[





Trade Secret & Confidential Commercial Information·

ER-1183NP Rev. 1 Prepared by: JJL Reviewed by~ 't Schlumberger-Private

Measurement Systems

Page 24


Using the above methodology, the uncertainty in the mean meter factor is computed to be as follows:

. [ . [ . [

ER-1183NP Rev. 1 Prepared by:


JJL

] ] ]


Reviewed b~,'.: RSH ~ f

5.0 REFERENCES

Measurement Systems

Page 25

1. ALD-1168 Rev 2, Hydraulic Calibration Plan for Farley Unit 2 Chordal Spool pieces

2. 2006 South East Asia Flow Workshop Paper, "The Relative Merits of Ultrasonic Meters Employing Between Two and Eight Paths", Gregor Brown, Don Augenstein, Terry Cousins, Herb Estrada

3. EFP-68, Commissioning Procedure for LEFMCheck Chordal Systems

4. EFP-55, Profile Factor Detennination at a Flow Measurement Facility

5. Moody, L. F., "Friction Factors for Pipe Flow," ASME Transactions, V. 66, 1944, pp. 671-694

6. National Bureau of Standards and Technology, "Experimental Statistics Handbook 1991"

7. Murakami, M., Shimizu, Y., and Shiragami, H., "Studies on Fluid Flow in Three-Dimensional Bend Conduits," Japan Society of Mechanical Engineering (JSME), Bulletin V. 12, No. 54, Dec. 1969, pp. 1369-1379.

8. Cameron Topical Report ER-80P Rev 1, "Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM Check System", March 1997.

9. ER-551, Transducer Replacement Sensitivity

10. Westinghouse Research Laboratories Nov 3, 1972, "Integration Errors for Turbulent Profiles in Pipe Flow"

11. ASME PTC 19.1-1985, Measurement Uncertainty

12. Cameron Engineering Report ER-l 60P Rev 1, "Supplement to Topical Report ER SOP: Basis for a Power Uprate with the LEFM System", May 2000

13. Cameron Engineering Report ER-157(P-A) Rev. 8 and Rev. 8 Errata, "Supplement to Caldon Topical Report ER-SOP: Basis for Power Uprates with an LEFM Check or an LEFM CheckPlus", May 2008

14. Alden Calibration Report for Farley Unit 2

15. Cameron Engineering Report ER 262 Rev 1, "Effects of Velocity Profile Changes Measured InPlant on LEFM Feedwater Flow Measurement Systems", January 2002

16. NIST TN-1297, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results"

17. ANSI/NCSL 2540-2-1997, "U.S. Guide to the Expression of Uncertainty in Measurement"

18. ISO "Guide to the Expression of Uncertainty in Measurement"

19. IGHEM Flow Paper 2008 Milan, Italy, "Accuracy Validation of Multiple Path Transit Time Flowmeters"

ER-1183NP Rev. 1 Prepared by: JJL Reviewed b~t RSH ~u Schlumberger-Private

Appendix A - Calibration Data

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Measurement Systems

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ER-1183NP Rev. 1 Prepared by: JJL Reviewed bY.: RSH ·~\\


Trade

I Secret & Confidential Commercial lnfonnation

Appendix B - Meter Uncertainty

B.1 - Inputs and Scaling B.2 - Flow Uncertainty B.3 - [ ] B.4-[

ER-1183NP Rev. 1

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Prepared by: JJL


Measurement Systems


Reviewed bY.: RSH (l ~

Appendix B.1

Inputs and Scaling

Measurement Systems


ER-1183NP Rev. 1 Prepared by: JJL Reviewed by~


Appendix B.2

Flow Uncertainty

Measurement Systems


ER-1183NP Rev.1 Prepared by: JJL Reviewed bY.: RSH (2\J' Schlumberger-Private

Measurement Systems

Appendix B.3


ER-1183NPRev.1 Prepared by: JJL Reviewed bY.: RSH ~~ Schlumberger-Private


Appendix B.4

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Measurement Systems



ER-1183NP Rev. 1 Prepared by: JJL Reviewed by: RSH ~~


Engineering Report: ER-11 SONP Rev. 1 BOUNDING UNCERTAINTY ANALYSIS … · 2019. 11. 20. ·...

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Transcript of Engineering Report: ER-11 SONP Rev. 1 BOUNDING UNCERTAINTY ANALYSIS … · 2019. 11. 20. ·...