Text

Enclosure 3, Areva Np Calculation 32-5012428-08, Davis-Besse Heat Balance Uncertainty.
	ML071070578
Person / Time
Site:	Davis Besse
Issue date:	04/12/2007
From:	; AREVA
To:	; Office of Nuclear Reactor Regulation
References
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Docket Number 50-346 License Number NPF-3 Serial Number 3198 Enclosure 3 AREVA NP Calculation 32-5012428-08 Davis-Besse Heat Balance Uncertainty April 2007

20697-10 (3I30/06'*

A CALCULATION

SUMMARY

SHEET (CSS)

AREVA Document Identifier 32-5012428-08 Title Davis Besse Heat Balance Uncertainty Calculation PREPARED BY: REVIEWED BY:

METHOD: M' DETAILED CHECK [] INDEPENDENT CALCULATION NAME Bret L. Boman NAME Todd Matthews SIGNATURE SIGNATURE *, 4 TITLE Eng Mgr DATE q/qI/7 TITLE Principal Eng DATE COST REF. TM STATEMENT:

CENTER 41917 PAGE(S) 37-38 REVIEWER INDEPENDENCE _

NAME z__

PURPOSE AND

SUMMARY

OF RESULTS:

Purpose - The objective of this calculation was to calculate Davis Besse's full-power reactor core power uncertainty value, also referred to as the "heat balance uncertainty," based on the planned installation of Caldon's ultrasonic feedwater flow metering equipment. Specific objectives were: (1) determine the minimum practical full-power core thermal power uncertainty in order to define the limits of Davis Besse's MUR power uprate; (2) determine the sensitivity of the core thermal power uncertainty to the individual measurements' uncertainty. This will assist Davis Besse in making decisions regarding the maintenance and modification of the instrumentation used in the core thermal power calculation; and (3) provide an accepted core thermal power uncertainty methodology to be used in future evaluations.

Summary of Results- The ASME Performance Test Code Methodology was used to calculate the expected core thermal power uncertainty to be achieved using the Caldon CheckPlusTM System ultrasonic flow meter. The analysis concluded that using the following instrument uncertainty values, the core thermal power uncertainty would be 0.369%, thus allowing a power uprate of 1.63% to be pursued.

Feedwater Flow Uncertainty of 0.29%

Feedwater Pressure Uncertainty of 14.6 psi (systematic) and 1.35 psi (random)

Steam Pressure Uncertainty of 1.42 psi (systematic) and 1.52 psi (random)

Steam Temperature Uncertainty of 1.56*F (systematic) and 0.153"F (random)

The other parameters (makeup, letdown, RCP heat, and ambient losses) are minor contributors. Their uncertainties are defined in the body of the report.

Rev. 01 - added the case for the MVP Uprate conditions. Rev. 02 - As-tested Caldon uncertainties evaluated. Rev. 03 -

removed assumption regarding random uncertainty values. Rev 04 & 05 evaluated a change in steam pressure uncertainties as directed by FENOC. Rev 06 complete revision to address comments and eliminate inconsistencies. Rev 07 incorporates the feedwater pressure uncertainty change into the MVP case. Rev 08 revised the feedwater flow uncertainty from 0.26% to 0.29%, updates References 3 and 21, and deletes Caldon proprietary attachments.

THE DOCUMENT CONTAINS ASSUMPTIONS THAT MUST BE VERIFIED PRIOR TO USE ON THE FOLLOWING COMPUTER CODES HAVE BEEN USED IN THIS DOCUMENT: SAFETY-RELATED WORK CODENERSION/REV CODENERSION/REV - YES Z NO AREVA NP Inc., an AREVA and Siemens company Page 1 of 71

AREVA NP 32-5012428-08 RECORD OF REVISIONS Revision Date Purpose 00 June 2001 Original Release 01 Oct. 2001 Define the uncertainty for the MVP operating conditions.

Changed a previous assumption on steam temperature, steam pressure, and feedwater pressure to an input by referencing a Davis Besse calculation package.

02 April 2003 In the previous revision feedwater flow and temperature uncertainty values were assumed.

Based on testing the assumed values have been confirmed as bounding. See assumption number 3.

03 May 2003 Based on input from FENOC the assumption regarding the validity of the random uncertainty values was removed.

04 July 2006 Removed Proprietary header. Fixed typos.

Revised Uncertainties for feedwater pressure.

05 August 2006 Revised Uncertainties for feedwater pressure (case 10). Added case 11 for as-tested Caldon LEFM uncertainties.

06 September 2006 Completely revised document to redefine the base case and remove inconsistencies created by multiple revisions.

07 October 2006 Revised the MVP section for the revised feedwater pressure uncertainty (pages. 27 &

30 only).

08 April 2007 Revised the feedwater flow uncertainty from 0.26% to 0.29% based on the replacement transducers. Updated References 3 and 21 to latest revisions, deleted previous attachments 1 and 4, changed 'FRA-ANP' to 'AREVA NP' and 'Appendix K' to 'MUR'.

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AREVA NP 32-5012428-08 TABLE OF CONTENTS Section Page RECO RD O F REVISIO NS ............................................................................ 2 1.0 O BJE C T IVE S ....................................................................................... 4 2.0 ASSUMPTIONS AND INPUTS ............................................................. 4 2.1 A SSU MPTIO NS ................................................................................ 4 2 .2 INP UT S ........................................................................................... . . 6 3.0 METHO DO LO G Y .............................................................................. 10 3.1 Industry Standard ............................................................................ 10 3.2 C aldon Experience .......................................................................... 10 3.3 AREVA NP Experience ................................................................... 10 3.4 Davis Besse Heat Balance Equations .............................................. 11 3.5 Davis Besse Heat Balance Instruments ........................... 12 4.0 CALCULATION INPUTS .................................. 14 4.1 MUR POWER UPRATE CONDITIONS ...................... 14 4.2 MVP POWER UPRATE CONDITIONS ............................................ 27 5.0 CA SES A NA LYZED ............................................................................ 31 6.0

SUMMARY

OF RESULTS .................................................................. 36

7.0 REFERENCES

..... ............................... ..... 37 APPENDIX A - Heat Balance Spreadsheets .............................................. 39 APPENDIX B - Excerpts from CTPA ........................................................... 51 APPENDIX C - Steam Line Pressure Losses .............................................. 54 ATTACHMENT 1 - CALDON Uncertainty Inputs - Telecon with Herb Estrada

. ............................... °...

........................... °............................... .I °... . ....... 60 ATTACHMENT 2 - Revised CALDON Flow Uncertainty Values ................. 62 ATTACHMENT 3 - Davis Besse Instrument Uncertainty Values ................. 64 3

AREVA NP 32-5012428-08 1.0 OBJECTIVES The objective of this calculation was to calculate Davis Besse's full-power reactor core power uncertainty value, also referred to as the "heat balance uncertainty,"

based on the planned installation of Caldon's ultrasonic feedwater flow metering equipment. Specific objectives were:

Determine the minimum practical full-power core thermal power uncertainty in order to define the limits of Davis Besse's MUR power uprate.

" Determine the sensitivity of the core thermal power uncertainty to the individual measurements' uncertainty. This will assist Davis Besse in making decisions regarding the maintenance and modification of the instrumentation used in the core thermal power calculation.

Provide an accepted core thermal power uncertainty methodology to be used in future evaluations.

2.0 ASSUMPTIONS AND INPUTS The assumptions and inputs used in these calculations are presented in this section.

2.1 ASSUMPTIONS The following assumptions were used in these calculations. None require further verification before using the results of this calculation.

(1) The core thermal power analysis (CTPA) software uses three methods for computing core power (see Section 3.3). It is assumed that the secondary power method is being used at 100% power. This assumption is reasonable because page 5 of Reference 7 states, "A switch is incorporated in CTPA so that the output from the secondary side heat balance is used in the core power distribution calculation above a specified power level, and the output from the delta T method is used at or below the specified power level."

"It is recommended that this power level be set at 50% (this is the initial setting). However, the switch is adjustable and may be set at any power level equal to or greater than 15%

of rated power."

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AREVA NP 32-5012428-08 (2) The correspondence between the plant computer IDs and the variables used in CTPA was not formally provided to AREVA NP. Thus, the information shown is assumed.

(3) The following values were assumed. Because the results are not sensitive to these values as shown by the calculations, herein, they do not require verification.

Feedwater Pressure = 1005 psia Makeup Temperature = 100°F Makeup Pressure = 2250 psia Letdown Pressure = 2250 psia Makeup Flow Systematic Uncertainty = 5%

Makeup Flow Standard Deviation = 10%

Makeup Temperature Systematic Uncertainty = 51F Makeup Temperature Standard Deviation = 2°F Makeup Pressure Systematic Uncertainty = 50 psi Makeup Pressure Standard Deviation = 50 psi Letdown Flow Systematic Uncertainty = 5%

Letdown Flow Standard Deviation = 10%

Letdown Temperature Systematic Uncertainty = 50 F Letdown Temperature Standard Deviation = 20 F Letdown Pressure Systematic Uncertainty = 50 psi Letdown Pressure Standard Deviation = 50 psi (4) In addressing the steam pressure instrument location effects, a + 20 %

uncertainty on the steam line pressure losses was assumed based on engineering judgment. The heat balance uncertainty is insensitive to this assumption.

(5) In calculating the steam line unrecoverable losses, the elbows were assumed to have a 1.5 diameter bend radius (R/D = 1.5) based on past experience with piping systems. The previous assumption accounts for a variation in steam line pressure loss that would encompass any variation in steam line bend radius. The heat balance uncertainty is insensitive to this assumption.

(6) Letdown flow is measured downstream of the letdown cooler and pressure reducing orifice. The conditions used for evaluating the letdown density were 120OF and 150 psia. The potential variations in these conditions would not affect the heat balance uncertainty calculation.

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AREVA NP 32-5012428-08 2.2 INPUTS The following inputs were used to calculate the core thermal power uncertainty:

(1) The Caldon LEFM CheckPlus MT System ultrasonic feedwater flow meter provides a measurement of the feedwater flow and feedwater temperature.

The uncertainty values for these measurements were not finalized at the time of the original calculation and were thus based on Revision 0 of Reference 21. The initial values used were:

Combined uncertainty feedwater flow and feedwater temperature

= 0.32% full power Feedwater Flow Rate Systematic Uncertainty = 0.30%

Absolute Standard Deviation of Mean Feedwater Flow Measurements = 0 (based on Caldon input, the random effects are near negligible and included in the systematic uncertainty)

Feedwater Temperature Systematic Uncertainty = 0.6°F Absolute Standard Deviation of Mean Feedwater Temperature Measurements was determined to be 0.24728 0 F (see the calculation section) in order to achieve the combined uncertainty of 0.32%.

After the original calculation, the Davis Besse Caldon LEFM CheckPlus M

T System ultrasonic feedwater flow meter was tested at Alden labs. Based on this testing, the following values used determined (Reference 21, Section 2, Result 4):

Combined uncertainty feedwater flow and feedwater temperature

= 0.29% full power Feedwater Flow Rate Systematic Uncertainty = 0.26%

Absolute Standard Deviation of Mean Feedwater Flow Measurements = 0 (based on Caldon input, the random effects are near negligible and included in the systematic uncertainty)

Feedwater Temperature Systematic Uncertainty = 0.10°F Random Feedwater Temperature Uncertainty = 0.561F. This corresponds to two standard deviations. Thus, the Absolute Standard Deviation of Mean Feedwater Temperature 6

AREVA NP 32-5012428-08 Measurements = 0.28°F (i.e., 0.56/2). However, to achieve the combined uncertainty of 0.29%, this value was increased to 0.460 F (see case 3).

However, subsequently the transducers were changed and Caldon revised the feedwater flow uncertainty from 0.26% to 0.29%, Reference

22. Thus, the final values used were:

Feedwater flow systematic flow uncertainty = 0.29%

Feedwater Temperature Systematic Uncertainty = 0.1 0°F Random Feedwater Temperature Uncertainty = 0.46 0 F (2) The following random uncertainties for steam temperature, steam pressure, and feedwater pressure were provided by Davis Besse, Attachment 3. Note: that these values are based on the existing instrumentation and because they are based on plant measurement variations include both random error and some part of the systematic uncertainty. While some part of the systematic uncertainty is double-accounted, this is conservative.

Random Uncertainties Steam Temperature = 0.153°F Steam Pressure = 1.52 psi Feedwater Pressure = 1.35 psi (3) Aside from the feedwater flow uncertainty, the steam measurements have the largest impact on the core thermal power uncertainty. The following instrumentation uncertainties were used in the base calculations, References 20 and 23.

Two values are shown below: (1) "single" which refers to a single instrument, and (2) "dual" which refers to the total uncertainty based on one instrument per feedwater/steam loop. Since each loop's instruments will normally be operable, the "dual" uncertainties were used in the base analyses. The steam temperature uncertainty was also varied in the calculations to demonstrate its impact.

The rationale for using the "dual" loop uncertainties is as follows. The Caldon feedwater flow and feedwater temperature values were provided as a lumped parameter for total feedwater flow rather than on a per feedwater train basis. Thus, the heat balance uncertainty calculations 7

AREVA NP 32-5012428-08 were performed on a total feedwater flow basis. The uncertainties for steam temperature, steam pressure, and feedwater pressure were provided as both "single" which refers to individual measurements in each feedwater/steam train and as "dual" in which individual uncertainties were combined using the square root sum of the squares. For example, the "single" steam temperature is 2.2°F while the "dual" value is 1.56 0 F. The "dual" value is the "single" value divided by the square root of 2 which is equivalent to 2.2/(2.) 0*. Ifthe heat balance had been performed on a per feedwater train basis, the "single" values would have been used but during the uncertainty calculation process the "single" values would have been statistically combined to effectively yield the "dual" values.

Note: to achieve full power operation, the loops would be operating at comparable conditions. Thus, the steam temperature, steam pressure, feedwater flow, etc. would be nearly the same for the "A" and "B"loops.

Systematic Uncertainties (Refs. 20 and 23)

Feedwater Pressure = 20.63 psi (single); 14.60 psi (dual)

Steam Temperature = 2.2°F (single); 1.56°F (dual)

Steam Pressure = 2 psi (single); 1.42 psi (dual)

(4) Nominal Letdown Flow Rate = 45 gpm (Reference 9)

= 45 gal/min + 7.4805 gal/ft3

61.7 Ibm/ft3

60 min/hr = 22,270 Ibm/hr based on a letdown density = 61.7 Ibm/ft 3 (at 150, psia and 120 0 F).

Note: the effects of Boron on makeup and letdown water density were neglected. Due to the insensitivity of makeup and letdown flow on the total heat balance uncertainty, there is no effect of this omission.

(5) Nominal Makeup Flow Rate = 22,270 Ibm/hr (Set equal to letdown flow rate)

= 22,270 Ibm/hr + 62.4 Ibm/ft 3

7.4805 gal/ft3 + 60 min/hr = 44.5 gpm based on a makeup density = 62.4 Ibm/ft 3 (at 2250, psia and 100 0F)

(6) RC Pump power. From Appendix B and Reference 6, QRCP = 0.8*6.181 Mw/RCP

4 RCP

1000 kw/Mw

3413 Btu/hr/kw

= 6.75e7 Btu/hr 8

AREVA NP 32-5012428-08 (7) The systematic uncertainty in RC pump heat was taken from Reference 6 as, eQRCP = 4.928e6 Btu/hr (8) Reference 6 provides an ambient heat loss rate of 5.12e6 Btu/hr with an uncertainty of 2.5e6 Btu/hr. However, Reference 24 uses an ambient heat loss of 0.653 MWt (2.23e6 Btu/hr), which is used herein. Both values were shown to have a negligible effect on the core power uncertainty.

(9) Since the RCP heat input and RCS heat losses are not typically measured values and because they have a negligible effect on the core power uncertainty, no random uncertainties were used.

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AREVA NP 32-5012428-08 3.0 METHODOLOGY A discussion of heat balance uncertainty methodology is presented herein.

3.1 Industry Standard The ASME provides a standard methodology for estimating instrument-related uncertainties, Reference 1. Both individual instruments as well as resultants from multiple instruments are treated. Instrument uncertainties are classified as either systematic related or random errors. Systematic errors are defined as that portion of the total measurement uncertainty that remains constant in repeated measurements of the true value. Systematic errors may arise from imperfect calibration corrections, data acquisition systems, data reduction techniques, etc.

Random errors are defined as that portion of the total measurement uncertainty that varies in repeated measurements of the true value. Random errors may arise from non-repeatability in the measurement system, environmental conditions, data reduction techniques, and measurement methods.

Provisions for co-dependent errors that may occur due to using the same apparatus to measure different parameters or calibrating different parameters against the same standard are also presented.

3.2 Caldon Experience In performing MUR uprates for other plants, Caldon calculated the power uncertainties for their Check and CheckPlusTM Systems, References 2 and 3.

However, neither of these reports addressed the B&W plants. Since the OTSG provides superheated steam, the equations presented therein are not applicable.

3.3 AREVA NP Experience AREVA NP has performed secondary heat balance calculations including uncertainty calculations for secondary thermal power, core thermal power, and RCS flow for a number of B&W plants. Examples of these are References 4-6.

The methodology used in these calculations is consistent with those of the ASME, Reference 1. The governing equation is presented and then differentiated with respect to the contributing measurements. The products of the partial derivatives and individual measurement uncertainties are squared, summed, and then square-rooted to solve for the core thermal power uncertainty.

For example, from Reference 6, the uncertainty in steam generator "A" secondary power is:

E(QA) = [(oQA/oWfw X F-Wfw)2 + (aQA/-Ts X STS)2 + (aQA/oTfw x FTfw)2 +

2 (aQA/*Ps x Eps) 2 + (aQA/aPfw x pfw) ]0.5 10

AREVA NP 32-5012428-08 Where E(QA) = steam generator thermal power uncertainty QA= steam generator thermal power Wfw = feedwater flow Ts = steam temperature Tfw = feedwater temperature Ps = steam pressure Pfw = feedwater pressure P = measurement uncertainty for feedwater flow, feedwater pressure, feedwater temperature, steam pressure, and steam temperature 3.4 Davis Besse Heat Balance Equations Davis Besse plant computer software was reviewed to define core thermal power calculation methodology and corresponding input variables. The nuclear steam system (NSS) application software (NAS) software consists of data reduction, nuclear, thermal/hydraulic, and utility programs to support plant operation, performance monitoring, and fuel management. The core thermal power analysis (CTPA) module of NAS computes the core power level. The equations used to calculate core power are contained in Reference 7 and are reproduced here and Appendix B as the basis for the heat balance uncertainty calculation.

The expression for core power in terms of a secondary side heat balance is:

QCor = WFWA (AHSGA )+ WFWB (AHSGB )+ Qcorri Where WFWA, WFWB Feedwater flow, OTSG A and B AHSGA, AHSGB Enthalpy change, OTSG A and B Qcor-l Correction for letdown, makeup, RC pumps, and surface heat loss Within the code listing, formulations were provided for the heat balance.

Computer code excerpts are provided in Appendix B.

The NAS software will eventually be replaced by the Fixed Incore Detector Monitoring System (FIDMS), Reference 18. This software contains core thermal power analysis algorithms, which are effectively the same as those in NAS.

Some improvements to the NAS calculations have been made including an adjustment for the AP between the steam pressure and temperature locations (this is discussed further in Section 5). Currently FIDMS is running in parallel with NAS; results show that the calculated core thermal power from NAS and FIDMS agree within a few tenths of Mwt.

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AREVA NP 32-5012428-08 3.5 Davis Besse Heat Balance Instruments A listing of Davis Besse computer points that are input to the current (pre-Caldon instrumentation) core thermal power calculation is provided for information. This table was provided informally to AREVA NP. "Both" refers to both the primary

("Prim") and secondary heat balance methods.

Davis-Besse Heat Balance Input Listing Point Instrument Description Units Range Heat Number Balance Method F673 MN FW 1 COMP FLOW, FY2B2 KPPH 0-7000 Both F674 MN FW 1 COMP FLOW, FY2B1 KPPH 0-7000 Both F679 MN FW 2 COMP FLOW, FY2A1 KPPH 0-7000 Both F680 MN FW 2 COMP FLOW, FY2A2 KPPH 0-7000 Both F718 RC LETDOWN FLOW KPPH 0-80 Both F738 RC MU FLOW 2 LOW RANGE GPM 0-50 Both F859 RC HLG TOTAL FLOW, RPS CH 1 MPPH 0-160 Prim F861 RC HLG TOTAL FLOW, RPS CH 2 MPPH 0-160 Prim F863 RC HLG TOTAL FLOW, RPS CH 3 MPPH 0-160 Prim F864 RC HLG TOTAL FLOW, RPS CH 4 MPPH 0-160 Prim P721 RC LOOP 1 HLG NR PRESS, RPS PSIG 1700- Both CH 1 2500 P722 RC LOOP 1 HLG NR PRESS, RPS PSIG 1700- Both CH 3 2500 P729 RC LOOP 2 HLG NR PRESS, RPS PSIG 1700- Both CH 2 2500 P730 RC LOOP 2 HLG NR PRESS, RPS PSIG 1700- Both CH 4 2500 P930 SG 1 MN FW NOZZLE PRESS PSIG 0-1500 Both P931 SG 1 OUT STM PRESS, PT12B1 PSIG 0-1200 Both P932 SG 1 OUT STM PRESS, PT12B2 PSIG 0-1200 Both P935 SG 2 MN FW NOZZLE PRESS PSIG 0-1500 Both P936 SG 2 OUT STM PRESS, PT12A1 PSIG 0-1200 Both P937 SG 2 OUT STM PRESS, PT12A2 PSIG 0-1200 Both T476 HPT IN TEMP FROM SG 2 Deg F 50-650 Both T477 HPT IN TEMP FROM SG 1 Deg F 50-650 Both T671 MN FW TEMP TO ICS, TTI-1 Deg F 0-600 Both T672 MN FW TEMP TO ICS, TT1-2 Deg F 0-600 Both T719 RC LOOP 1 HLG NR TEMP, Deg F 520- Prim RC3B1 620 T720 RC LOOP 1 HLG NR TEMP, Deg F 520- Prim 12

AREVA NP 32-5012428-08 Point Instrument Description Units Range Heat Number Balance Method RC3B33 620 T721 RC LOOP 1 HLG NR TEMP, RPS Deg F 520- Prim CH 1 620 T722 RC LOOP 1 HLG NR TEMP, RPS Deg F 520- Prim CH 3 620 T728 RC LOOP 2 HLG NR TEMP, Deg F 520- Prim RC3A1 620 T729 RC LOOP 2 HLG NR TEMP, Deg F 520- Prim RC3A3 620 T730 RC LOOP 2 HLG NR TEMP, RPS Deg F 520- Prim CH 2 620 T731 RC LOOP 2 HLG NR TEMP, RPS Deg F 520- Prim CH 4 620 T769 RC MU TK TEMP Deg .F 0-200 Both T780 RCP 1-1 DISCH CLG NR TEMP, Deg F 520- Prim RC4B1 620 T800 RCP 1-2 DISCH CLG NR TEMP, Deg F 520- Prim RC4B3 620 T820 RCP 2-1 DISCH CLG NR TEMP, Deg F 520- Prim RC4A1 620 T840P RCP 2-2 DISCH CLG NR TEMP, Deg F 520- Prim RC4A3 620 Z674B MN FW 1 STOP VLV DS 0 or 1 Both Z679B MN FW 2 STOP VLV DS 0 or 1 Both T821 RCP 2-1 DISCH CLG WR TEMP, Deg F 50-650 Both RC4A2 CLG : Cold Leg NR Narrow Range Instrument COMP: Compensated RC Reactor Coolant DS Digital Scan point, On or Off RCP: Reactor Coolant Pump FW: Feed Water System RPS: Reactor Protection System HPT High Pressure Turbine SG Steam Generator HLG Hot Leg STM Steam ICS Integrated Control System TK Tank LD Let down WR Wide Range Instrument MU Makeup MN Main 13

AREVA NP 32-5012428-08 4.0 CALCULATION INPUTS Inputs were calculated for two sets of conditions: (1) operating conditions for the MUR power uprate, and (2) operating conditions for the Maximum Value Program (MVP) uprate.

4.1 MUR POWER UPRATE CONDITIONS Reference 1 provides step-by-step instructions for calculating the uncertainty of a result. These were implemented as follows:

(a) Define measurement process 1 (1) Review test objectives and test duration.

The "test" objective is to continuously calculate the core thermal power and ensure the plant is operated within its licensed power.

(2) List all independent measurement parameters and their nominal levels.

The independent measurement parameters and their nominal values 2 are comprised of the following values in Table 1.

TABLE I - Nominal Heat Balance Parameter Values Nominal Symbol Description Units Value Basis WFW Feedwater Flow Rate Ibm/hr 1.184E+07 Ref. 10 TS Steam Temperature F 596 Ref. 10 PS Steam Pressure psia 930 Ref. 10 TFW Feedwater Temperature F 455 Ref. 10 PFW Feedwater Pressure psia 1005 Assmptn 3 WMU Makeup Flow Rate Ibm/hr 2.227E+04 Ref. 9 TMU Makeup Temperature F 100 Ref. 9 PMU Makeup Pressure Psia 2250 Assmptn 3 WLD Letdown Flow Rate Ibm/hr 2.227E+04 Ref. 9 TLD Letdown Temperature F 557 Ref. 10 1 The alphanumeric heading and subheading nomenclature as well as the text (e.g., reference to "test") from the ASME Performance Test Code (Ref. 1) is used herein.

2" nominal" refers to the expected value at 101.7% of 2772 or 2819 Mwt core thermal power. The 101.7% value was the initial guess of the maximum achievable power. Thus, the nominal values were calculated at this power level in Reference 10.

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AREVA NP 32-5012428-08 I

PLD Letdown Pressure psia 2250 Assmptn 3 QRCP RCP Power Btu/hr 6.75E+07 Ref. 6 QLOSS Ambient Heat Loss Btu/hr 2.23E+06 Ref. 24 Water Properties:

Steam Enthalpy = 1253.356 Btu/Ibm 3 at 596 0F and 930 psia Feedwater Enthalpy = 436.041 Btu/lbm at 4550 F and 1005 psia Makeup Enthalpy = 73.957 Btu/Ibm at 100°F and 2250 psia Letdown Enthalpy = 555.518 Btu/Ibm at 5570 F and 2250 psia (3) List all calibrations and instrument setups that will affect each parameter. Be sure to check for uncertainties in measurement system components that affect two or more measurements simultaneously (correlated uncertainties).

Except for the Caldon ultrasonic flow meter, the other instruments (feedwater pressure, steam temperature, steam pressure, makeup:

flow, pressure, temperature, letdown: flow, pressure, temperature) are maintained and calibrated by Davis Besse. An instrument uncertainty calculation should exist for each instrument.

(4) Define the functional relationship between the independent measurement parameters and the test result.

The expression for core power in terms of a secondary side heat balance is shown below. This is equivalent to the equations used by CTPA.

QC = W-,w (HsA - HFwA )+ WmW6 (HsB - HFB )+ QLD - QMU - QRCP + QLOSS Where WFWA, WFWB Feedwater flows in Loop A & B HSA, HFWA, HSB, HFWB Steam & feedwater enthalpies for Loops A & B QLD = WLD HLD Heat loss due to primary side letdown flow QMU = WMU HMU Heat added due to makeup and net seal injection QRCP Heat added due to RC pumps QLOSS Ambient heat losses from the RCS WLD, WMU Letdown and Makeup Flow Rates HLD, HMU Letdown and Makeup Enthalpies (b) List Elemental Error Sources (1) Make a complete and exhaustive list of all possible test uncertainty sources for all parameters.

3 Water properties were based on STP published values.

15

AREVA NP 32-5012428-08 Not needed to calculate the core thermal power uncertainty.

(c) Calculate the Systematic and Random Standard Deviation for Each Parameter Uncertainties for each parameter are shown below:

TABLE 2- HEAT BALANCE PARAMETER UNCERTAINTY VALUES Absolute Systematic Absolute Standard Symbol Description Units Uncertainty Deviation Of the Mean Value Basis Value Basis WFW Feedwater Lbm/hr Initial Value = Input 1 0 Input 1 Flow Rate 0.30% of nominal flow Final Value 0.29% of nominal flow TS Steam F 2.2(single) Input 3 0.153 Input 2 Temperature 1.56 (dual)

PS Steam psia 2 (single) Input 3 1.52 Input 2 Pressure 1.42 (dual)

TFW Feedwater F Initial Value = Input 1 Initial Value Input 1 Temperature 0.6 = 0.24728 Final Value = Final Value 0.10 = 0.46 PFW Feedwater psia 20.63 (single) Input 3 1.35 Input 2 Pressure 14.60 (dual)

WMU Makeup Ibm/hr 5% of Assmptn 3 10% of Assmptn 3 Flow Rate nominal flow nominal flow TMU Makeup F 5 Assmptn 3 2 Assmptn 3 Temperature PMU Makeup psia 50 Assmptn 3 50 Assmptn 3 Pressure WLD Letdown Ibm/hr 5% of Assmptn 3 10% of Assmptn 3 Flow Rate nominal flow nominal flow TLD Letdown F 5 Assmptn 3 2 Assmptn 3 Temperature PLD Letdown psia 50 Assmptn 3 50 Assmptn 3 Pressure QRCP RCP Power Btu/hr 4.93e6 Input 7 0 N/A QLOSS Ambient Btu/hr 2.5e6 Input 8 0 N/A Heat Loss (d) Propagate the Systematic and Random Standard Deviations 16

AREVA NP 32-5012428-08 (1) The systematic and random (sample) standard deviations of the independent parameters are propagated separately all the way to the final result.

(2) Propagation of the standard deviations is done, according to the functional relationship defined in step (a)(4) above, by using the Taylor series method. This requires a calculation of sensitivity factors, either by differentiation or by computer perturbation.

The core thermal power equation was differentiated with respect to the individual measured parameters to yield the following sensitivity coefficients:

OwfW =Qc//WFw = (Hs - HFW)

OPfw = DQc/PPFw = WFw aHJ/DPEw OTfw = DJQc/ITFw = WFw DIH/aTFw OPs = aQc/I2Ps = WEW aH/D/Ps OTs = aQc/aTs = WFw aJHJ/Ts 0

wmu r = Qc/aWMu = HMU OTmu = DQc/DTMu = WMU aJH/FJT OPmu = aQc/aPMu = WMU a)H/aP OWId = oQc/aWLD = HLD OTId = aQc/aTLc = WLD a)H/aT OPId = aQc/aPLD = WLD aH/o1P OQrcp = oQc/oQRCPs = 1 OQIoss = DQc/DQLoss = 1 In order to calculate these sensitivity coefficients, the water enthalpy differentials were computed.

For steam at 930 psia:

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AREVA NP 32-5012428-08 At T = 590'F, H = 1248.264 Btu/lbm At T = 600'F, H = 1256.687 Btu/Ibm a)H/aTs =- (1256.687 - 1248.264)/(600 - 590) = 0.842 Btu/Ibm/°F For steam at 5960F:

At P = 925 psia, H = 1253.921 Btu/Ibm At P = 935 psia, H = 1252.789 Btu/Ibm

-H/DPs = (1252.789 - 1253.921)/(935 - 925) = -0.1132 Btu/Ibm/psia For feedwater at 1000 psia:

At T = 4500F, H = 430.472 Btu/Ibm At T = 460'F, H = 441.637 Btu/Ibm

)H/DTfw =- (441.637 - 430.472)/(460 - 450) = 1.117 Btu/lbm/°F For feedwater at 455°F:

At P = 950 psia, H = 436.015 Btu/Ibm At P = 1050 psia, H = 436.067 Btu/Ibm DJH/aJPf = (436.015 - 436.067)/(950 - 1050) = 5.20e-4 Btu/Ibm/psia For letdown at 2250 psia:

At T = 550'F, H = 546.774 Btu/Ibm At T = 560'F, H = 559.306 Btu/Ibm o*H/oTLD = (559.306 - 546.774)/(560 - 550) = 1.2532 Btu/Ibm/°F For letdown at 5570F:

At P = 2300 psia, H = 555.429 Btu/Ibm At P = 2200 psia, H = 555.609 Btu/Ibm a)H/oPLD - (555.429 - 555.609)/(2300 - 2200) = -1.80e-3 Btu/Ibm/psia 18

AREVA NP 32-5012428-08 For makeup at 2250 psia:

At T = 90'F, H = 64.075 Btu/Ibm At T = 100°F, H = 73.957 Btu/Ibm DH/oTMu = (73.957 - 64.075)/(100 - 90) = 0.9882 Btu/Ibm/°F For makeup at 100'F:

At P = 2300 psia, H = 74.087 Btu/Ibm At P = 2200 psia, H = 73.826 Btu/Ibm lH/olPMu = (74.087 - 73.826)/(2300 - 2200) = 2.61e-3 Btu/Ibm/psia The water property derivatives are summarized in Table 3 below.

TABLE 3 - Water Property Derivatives

___H/aT, Btu/fIbm°F) @H/DP, Btu/(Ibm psi)

Steam (596 0 F, 930 psia) 0.842 -0.1132 Feedwater (4550 F, 1000 psia) 1.117 5.20e-4 Letdown (5570 F, 2250 psia) 1.2532 -1.80e-3 Makeup (100'F, 2250 psia) 0.9882 2.61e-3 Sensitivity Coefficients and Uncertainty Contributions The sensitivity coefficients and the uncertainty contributions were calculated using the values in Tables 2 and 3 as follows:

Feedwater Flow Rate The sensitivity coefficient, Owfw, was calculated using the previously defined partial derivative:

0wfw = DQC//WFW = (Hs - HFW) = 1253.356 -436.041 = 817.315 Btu/Ibm Using the systematic uncertainty of Bwfw = (0.30/100)

11.84e6 = 3.552e4 Ibm/hr, the systematic uncertainty contribution is:

2 2

[Owfw

Bww/2] 2 = [817.315

3.552e4/2] = 2.107e14 (Btu/hr) 19

AREVA NP 32-5012428-08 Using the random standard deviation Sx,wf = 0.0, the random uncertainty contribution is:

2

[OWfW

Sx,Wfw]2 = [817.315

0.0]2 = 0.0 (Btu/hr)

Feedwater Pressure The sensitivity coefficient, Opfw, was calculated using the previously defined partial derivative:

Opfw = aQc/aPFw = WFW aH/PFw = (11.84e6)(5.20e-4) = 6.157e3 Btu/hr/psi Using the single instrument, systematic uncertainty of Bpf = 20.63 psi, the systematic uncertainty contribution is:

2

[Opfw

Bp,/2] 2 = [6.157e3

20.63/2]2 = 4.033e9 (Btu/hr)

Using the dual instrument, systematic uncertainty of Bpfw = 14.60 psi, the systematic uncertainty contribution is:

2

[Opw

Bpwf/2] 2 = [6.157e3

14.60/2]2 = 2.020e9 (Btu/hr)

Using the random standard deviation Sxpf,= 1.35, the random uncertainty uncertainty contribution is:

2

[Opfw

Sx,pfw]

2

= [6.157e3

1.35]2 = 6.908e7 (Btu/hr)

Feedwater Temperature The sensitivity coefficient, OTfw, was calculated using the previously defined partial derivative:

0 Tfw = aQc/DTFw = WFv alH/aTFw = (11.84e6)(1.117) = 1.323e7 Btu/hr/°F Using the systematic uncertainty of Bmfw = 0.6 'F, the systematic uncertainty contribution is:

[OTf

BTfw/2] 2 = [1.323e7

0.6/2]2 = 1.574e13 (Btu/hr) 2 Using the random standard deviation Sx,Tfw = 0.24728 0 F, the random uncertainty uncertainty contribution is:

[OTfw

Sxmfw]2 = [1.323e7

0.24728]2 = 1.070e0 3 (Btu/hr) 2 Steam Pressure 20

AREVA NP 32-5012428-08 The sensitivity coefficient, Os, was calculated using the previously defined partial derivative:

Ops = aJQc/I)Ps = WFW alHl/Ps = (11.84e6)(-0.1132) = -1.340e6 Btu/hr/psi Using the single instrument, systematic uncertainty of Bps = 2.0 psi, the systematic uncertainty contribution is:

[Op,

Bps/2] 2 = [-1.340e6

2.0/2]2 = 1.796e12 (Btu/hr)2 Using the dual instrument, systematic uncertainty of Bps = 1.42 psi, the systematic uncertainty contribution is:

[Ops

Bps/2]2 = [-1.340e6

1.42/2]2 = 9.056el 1 (Btu/hr)2 Using the random standard deviation SxPs= 1.52, the random uncertainty uncertainty contribution is:

2

[EPS

Sx,ps]2 = [-1.340e6

1.52]2 = 4.150e12 (Btu/hr)

Steam Temperature The sensitivity coefficient, OTs, was calculated using the previously defined partial derivative:

OTs = aQc/aTs = WFW aH/lTs = (11.84e6)(-0.842) = -9.969e6 Btu/hr/°F Using the single instrument, systematic uncertainty of BT, = 2.2°F, the systematic uncertainty contribution is:

[OTsa

Bmsa/2] 2 = [-9.969e6

2.2/2]2 = 1.203e14 (Btu/hr) 2 Using the dual instrument, systematic uncertainty of BTs = 1.56 0 F, the systematic uncertainty contribution is:

2

[OTsa

BTsa/2] 2 = [-9.969e6

1.56/2]2 = 6.047e13 (Btu/hr)

Using the random standard deviation Sx,Ts = 0.153°F, the random uncertainty uncertainty contribution is:

2

[OPsa

Sx,Psa] 2 = [-9.969e6

0.153]2 = 2.327e12 (Btu/hr)

Makeup Flow Rate The sensitivity coefficient, OWmu, was calculated using the previously defined partial derivative:

21

AREVA NP 32-5012428-08 OWmu = oQc/oWMu = HMu = 73.96 Btu/Ibm Using the systematic uncertainty of BMU = 0.05 *2.227e4 Ibm/hr = 1.1 14e3 Ibm/hr, the systematic uncertainty contribution is:

[0MU

BMU/2] 2 = [73.96

1.114e3/2] 2 = 1.696e9 (Btu/hr) 2 Using the random standard deviation Sx,MU = 0.10*2.227e4 Ibm/hr =

2.227e3 Ibm/hr, the random uncertainty uncertainty contribution is:

2

[OMU

Sx,MU] 2 = [73.96

2.227e3]2 = 2.713e10 (Btu/hr)

Makeup Temperature The sensitivity coefficient, eTMU, was calculated using the previously defined partial derivative:

eTMU = aQc/oTMu = WMU lH/oTMu = (2.227e4)(0.9882) = 2.201 e4 Btu/hr/°F Using the systematic uncertainty of BTMU = 5.0 OF, the systematic uncertainty contribution is:

2

[eTMU

BTMu/2] =

2 [2.201e4

5.0/2]2 = 3.027e9 (Btu/hr)

Using the random standard deviation Sx,TMU = 2.0, the random uncertainty uncertainty contribution is:

[OTMU

Sx,TMU] =

2

[2.201 e4

2.0]2 = 1.937e9 (Btu/hr)2 Makeup Pressure The sensitivity coefficient, OPMU, was calculated using the previously defined partial derivative:

ePMu = aQc/oPMu = WMU olH/aPMu = (2.227e4)(2.61e-3) = 5.813el Btu/hr/psi Using the systematic uncertainty of BpMU = 50.0 psi, the systematic uncertainty contribution is:

2

[OPMU

BpMu/2] = [5.813el

50.0/2]2 = 2.112e6 (Btu/hr) 2 Using the random standard deviation Sx,PMU = 50.0, the random uncertainty uncertainty contribution is:

2

[OPMU

Sx,pMu] = [5.813el

50.0]2 = 8.446e6 (Btu/hr) 2 22

AREVA NP 32-5012428-08 Letdown Flow The sensitivity coefficient, OWLD, was calculated using the previously defined partial derivative:

OWLD = oQc/aWLD = HLD = 555.52 Btu/lbm Using the systematic uncertainty of BLD = 0.05 *2.227e4 Ibm/hr = 1.1 14e3 Ibm/hr, the systematic uncertainty contribution is:

2

[OLD

BLD/2] 2 = [555.52

1.114e3/2] 2 = 9.566e10 (Btu/hr)

Using the random standard deviation SxLD = 0.1 0*2.227e4 Ibm/hr =

2.227e3 lbm/hr, the random uncertainty uncertainty contribution is:

[OLD

Sx,LD]2 = [555.52

2.227e3]

2= 1.531e12 (Btu/hr) 2 Letdown Temperature The sensitivity coefficient, OTRD, was calculated using the previously defined partial derivative:

OTLD = o3Qc/oTLD = WLD olH/aTLD = (2.227e4)(1.2532) = 2.791 e4 Btu/hr/°F Using the systematic uncertainty of BTLD = 5.0 IF, the systematic uncertainty contribution is:

2

[OTLD

BTLD/2]

2 = [2.791e4

5.0/212 = 4.868e9 (Btu/hr)

Using the random standard deviation Sx,TLD = 2.0, the random uncertainty uncertainty contribution is:

2

[OTLD

Sx,TLD]

2

= [2.791e4

2.012 = 3.116e9 (Btu/hr)

Letdown Pressure The sensitivity coefficient, OPLD, was calculated using the previously defined partial derivative:

OPLD = oQc/oPLD = WLD -)H/-PLD = (2.227e4)(-1.80e-3) = -4.009el Btu/hr/psi Using the systematic uncertainty of BPLD = 50.0 psi, the systematic uncertainty contribution is:

23

AREVA NP 32-5012428-08

[OPLO

BPLD/2] 2 = [-4.009el

50.0/2]2 = 1.004e6 (Btu/hr) 2 Using the random standard deviation Sx,PLD = 50.0, the random uncertainty uncertainty contribution is:

2

[OPLD

SXPLD] 2 = [-4.009el

50.0]2 = 4.017e6 (Btu/hr)

RCP Power The sensitivity coefficient, OQrcp, was calculated using the previously defined partial derivative:

Oarcp = oQC/oQRCPs = 1 Using the systematic uncertainty of BQrcp = 4.93e6 Btu/hr, the systematic uncertainty contribution is:

[OQrcp

BQrcpI2] = [1

4.93e6/2] =

2 2 6.076e12 (Btu/hr) 2 Using the random standard deviation SxQrcp = 0.0, the random uncertainty uncertainty contribution is:

[OQrcp

Sx,Qrcp] = [1

0.0]2 = 0.0 2 (Btu/hr) 2 Ambient Heat Loss The sensitivity coefficient, OQioss, was calculated using the previously defined partial derivative:

OQIoss = oQc/aQLOsss = 1 Using the systematic uncertainty of B01 Qos = 2.50e6 Btu/hr, the systematic uncertainty contribution is:

2

[Oeloss

BQtoss/2] 2 = [1

2.50e6/2]2 = 1.563e12 (Btu/hr)

Using the random standard deviation Sx,QIoss = 0.0, the random uncertainty contribution is:

[OQIoss

Sx,eoIss]

2

= [1

0,0]2 = 0.0 (Btu/hr)2 The uncertainty contributions are summarized below in Table 4.

24

AREVA NP 32-5012428-08 TABLE 4 - HEAT BALANCE PARAMETER UNCERTAINTY CONTRIBUTIONS Systematic Random Symbol Description Uncertainty Contribution Uncertainty Contribution Absolute Relative Absolute2 Relative (Btu/hr) 2 (Btu/hr)

WFW Feedwater 2.107e14 71.29% 0.0 0.00%

Flow Rate TS Steam 6.047e13 20.46% 2.327e12 12.41%

Temperature PS Steam 9.056el1 0.31% 4.150e12 22.15%

Pressure TFW Feedwater 1.574e13 5.33% 1.070e13 57.09%

Temperature PFW Feedwater 2.020e9 0.00% 6.908e7 0.00%

Pressure WMU Makeup 1.696e9 0.00% 2.713e10 0.14%

Flow Rate TMU Makeup 3.027e9 0.00% 1.937e9 0.01%

Temperature PMU Makeup 2.112e6 0.00% 8.446e6 0.00%

Pressure WLD Letdown 9.566e10 0.03% 1.531e12 8.17%

Flow Rate TLD Letdown 4.868e9 0.00% 3.116e9 0.02%

Temperature PLD Letdown 1.004e6 0.00% 4.017e6 0.00%

Pressure QRCP RCP Power 6.076e12 2.06% 0.0 0.00%

QLOSS Ambient 1.563e12 0.53% 0.0 0.00%

Heat Loss Totals 2.956e14 100% 1.873e13 100%

Note: the systematic uncertainty contribution is an order of magnitude greater than the random uncertainty contribution. Thus, the significant contributors to the systematic uncertainty are the most important for defining the uncertainty. The values shown in Table 4 are presented graphically in the figure below to show the most significant uncertainty parameters.

25

AREVA NP 32-5012428-08 Systemtic Uncertairnies for Base Case m FeecMeter Flow Rate o Steam Tei~rpaftire mSteam Pressure m Feedmeter TejerAtre (e) Calculate uncertainty (1) Combine the systematic and random uncertainties to obtain the total uncertainty.

Reference 1 shows that the total uncertainty on the core thermal power is calculated using the following equation.

Result Uncertainty = 2*[JAbsolute 2] .

Systematic Uncertainty) 2 + (Absolute Random Uncertainty)

Absolute Systematic Uncertainty, BR = 2*(Absolute Systematic Uncertainty 05 Contribution)

BR = 2(2.956e14)05 = 3.4386e7 Btu/hr Absolute Random Uncertainty, 2 SR = 2*(Absolute Random Uncertainty 0 5 Contribution) .

2 SR = 2(1.873e13)05 = 8.6566e6 Btu/hr 2 2 5 Thus, the Core Thermal Power Uncertainty = [(3.4386e7) + (8.6556e6) ]°

3.546e7 Btu/hr On a percentage basis, Core Thermal Power Uncertainty

3.546e7/(2819*3413*1000) = 3.685e-3 = 0.369%

(f) Report 26

AREVA NP 32-5012428-08 Reference 1 provides a standard format for the uncertainty calculations. This format has been used for each of the cases analyzed (see Appendix A for the spreadsheet tables).

4.2 MVP POWER UPRATE CONDITIONS The preceding calculations were modified for the MVP power uprate conditions.

From Reference 19, the new operating conditions at a core thermal power of 3016 MWt are:

Feedwater flow rate, WFW = 12.72e6 Ibm/hr

Steam Temperature = 591°F The feedwater pressure (1005 psia), feedwater temperature (455°F), and steam pressure (930 psia) were unchanged from the MUR uprate conditions.

The affected parameters are those impacted by steam enthalpy and feedwater flow rate. These consist of:

1. Steam enthalpy, Hs

2. DH/aPs

3. 6 wfw = Qc/aWFw = (Hs - HFW)

4. OPfw = aQc/oPFw = WFW olH/DPFW

5. OTfw = DQc/aTFw = WFW a)H/aTFw

6. Op, = aJQc/IPs = WFW aHl/aPs

7. OTs = Qc/Ts = WFW a)H/aTs Steam Enthalpy = 1249.121 Btu/lbm at 591IF and 930 psia For steam at 591OF:

At P = 925 psia, H = 1249.704 Btu/Ibm At P = 935 psia, H = 1248.535 Btu/Ibm

@H/aPs =- (1248.535 - 1249.704)/(935 - 925) = -0.1169 Btu/Ibm/psia 27

AREVA NP 32-5012428-08 Sensitivity Coefficients and Uncertainty Contributions The sensitivity coefficients and the uncertainty contributions were calculated using the values in Tables 2 and 3 and in this section as follows:

Feedwater Flow Rate The sensitivity coefficient, ewfw, was calculated using the previously defined partial derivative:

OW = aQc/DWFw = (Hs- HFW) = 1249.121 -436.041 = 813.080 Btu/Ibm Using the systematic uncertainty of Bwf = (0.30/100)

12.72e6 = 3.816e4 Ibm/hr, the systematic uncertainty contribution is:

2 2

[Owfw

Bwfw/2] 2 = [813.080

3.816e4/2] = 2.407e14 (Btu/hr)

Using the random standard deviation S,,wfw = 0.0, the random uncertainty uncertainty contribution is:

[Ewfw

SxWw]

2

= [813.080

0.0]2 = 0.0 (Btu/hr) 2 Feedwater Pressure The sensitivity coefficient, Opfw, was calculated using the previously defined partial derivative:

OPfw = DQC/aPFW = WFW H/aPFW = (12.72e6)(-5.20e-4) = -6.614e3 Btu/hr/psi Using the single instrument, systematic uncertainty of Bpf = 20.63 psi, the systematic uncertainty contribution is:

2

[OP*

Bpfw/2] =

2 [6.614e3

20.63/2]2 = 4.654e9 (Btu/hr)

Using the dual instrument, systematic uncertainty of Bpfw = 14.60 psi, the systematic uncertainty contribution is:

2

[Opfw

Bpfw/2] 2 = [6.614e3

14.60/2]2 = 2.331e9 (Btu/hr)

Using the random standard deviation Sx,,pfw = 1.35, the random uncertainty uncertainty contribution is:

2

[OPf

SxPfw] 2 = [6.614e3

1.35]2 = 7.973e7 (Btu/hr) 28

AREVA NP 32-5012428-08 Feedwater Temperature The sensitivity coefficient, eTm, was calculated using the previously defined partial derivative:

OTf = aQc/aTFw = WFW alH/@TFw = (12.72e6)(1.117) = 1.421e7 Btu/hr/IF Using the systematic uncertainty of BTfw = 0.6 OF, the systematic uncertainty contribution is:

[OTfw

BTrf/2] 2 = [1.421 e7

0.6/2]2 = 1.817e13 (Btu/hr)2 Using the random standard deviation Sx,TmW = 0.24728 0 F, the random uncertainty uncertainty contribution is:

2

[OTfw

Sx,,T] 2 = [1.421e7

0.24728]2 = 1.235e13 (Btu/hr)

Steam Pressure The sensitivity coefficient, Ops, was calculated using the previously defined partial derivative:

Ops = DQc/DPs = WFW alH/DPs = (12.72e6)(-0.1169) = 1.487e6 Btu/hr/psi Using the single instrument, systematic uncertainty of Bps = 2.0 psi, the systematic uncertainty contribution is:

2 fops

Bps/2] 2 = [1.487e6

2.0/2]2 = 2.21 le12 (Btu/hr)

Using the dual instrument, systematic uncertainty of Bps = 1.42 psi, the systematic uncertainty contribution is:

2 2

[ops

Bps/2] = [1.487e6

1.42/2]2 = 1.115e12 (Btu/hr)

Using the random standard deviation Sx,Ps = 1.52, the random uncertainty uncertainty contribution is:

2

[ops

Sx,Ps] 2 = [1.487e6

1.52]2 = 5.109e12 (Btu/hr)

Steam Temperature The sensitivity coefficient, OTs, was calculated using the previously defined partial derivative:

6 Ts = aQc/ITs = WFW a)H/aTs (1 2.72e6)(-0.842) = 1.071 e7 Btu/hr/°F 29

AREVA NP 32-5012428-08 Using the single instrument, systematic uncertainty of BTs = 2.2°F, the systematic uncertainty contribution is:

[eTsa

BTsa/2] 2 = [1.071e7

2.2/2]2 = 1.388e14 (Btu/hr)2 Using the dual instrument, systematic uncertainty of BTs = 1.56°F, the systematic uncertainty contribution is:

2

[eTsa

BTsa/2] 2 = [1.071e7

1.56/2]2 = 6.979e13 (Btu/hr)

Using the random standard deviation Sx,-rs= 0.153'F, the random uncertainty uncertainty contribution is:

[Opsa

Sx,Psa] 2 = [1.071e7

0.153]2 = 2.685e12 (Btu/hr) 2 The uncertainty contributions are summarized below in Table 5.

TABLE 5- HEAT BALANCE PARAMETER UNCERTAINTY CONTRIBUTIONS REVISED FOR MVP CONDITIONS Systematic Uncertainty Random Uncertainty Symbol Description Contribution Contribution Absolute Absolute2 (Btu/hr) 2 (Btu/hr)

WFW Feedwater 2.407e14 0.0 Flow Rate TS Steam 6.979e13 2.685e12 Temperature PS Steam 1.115e12 5.109e12 Pressure TFW Feedwater 1.817e13 1.235e13 Temperature PFW Feedwater 2.331E+09 7.973e7 Pressure Note: there are some insignificant round-off differences between these values and those shown in the Appendix A spreadsheets.

30

AREVA NP 32-5012428-08 5.0 CASES ANALYZED The preceding heat balance uncertainty equations were input into a spreadsheet and the following cases were analyzed:

1) Definition of "Random" Feedwater Temperature Uncertainty

2) Base Case (Dual Loop PFW, Ts, Ps Uncertainties)

3) Definition of "Random" Feedwater Temperature Uncertainty to match the as-tested Caldon LEFM uncertainties

4) Revised Case 2 using the Revised Feedwater Flowmeter Transducer Uncertainty

5) Reduced Steam Temperature Uncertainty

6) Single Loop PFW, Ts, Ps Uncertainties

7) Instrument Location Effects

8) Instrument Locations Effects (continued)

9) Alternate Steam Pressure Location 10)Insensitivity to Assumed Values for Makeup Flow, Letdown Flow, RCP Power, Ambient Losses 11)MVP Base Case (Dual Loop PFW, Ts, Ps Uncertainties)

Case 1 - Definition of "Random" Feedwater Temperature Uncertainty The Caldon CheckPlus TM System equipment was originally specified with a combined 0.32% feedwater flow-temperature uncertainty. This is a systematic uncertainty that includes the random effects. The equations derived herein treat the feedwater flow and feedwater temperature as separate uncertainties. To account for the combined uncertainty, the individual feedwater flow and temperature uncertainties were input to the equations and then an additional "random" feedwater temperature uncertainty was varied until the combined uncertainty was obtained. Specifically, the 0.30% feedwater flow and 0.6 0F feedwater temperature uncertainties were input to the spreadsheet and the "random" feedwater temperature uncertainty was varied until the 0.32% total heat balance uncertainty was achieved (all the other uncertainties were set to zero).

The resulting value of the random uncertainty is 0.24728 0 F as shown in Appendix A.

31

AREVA NP 32-5012428-08 Case 2 - Base Case Using Initial Caldon Uncertainties and Dual Loop PFw T, Ps Uncertainties The base case core thermal power uncertainty was determined using the dual loop uncertainties for feedwater pressure, steam pressure, and steam temperature, where "dual loop" refers to a single instrument in each steam line.

The resulting core thermal power uncertainty is 0.369%.

Note: the values provided in this spreadsheet serve as the spreadsheet benchmark since the values agree with the calculations shown in Section 4.

Case 3 Definition of "Random" Feedwater Temperature Uncertainty to Match the as-tested Caldon LEFM uncertainties After the original calculation, the Davis Besse Caldon LEFM CheckPlusTM System ultrasonic feedwater flow meter was tested at Alden labs. Based on this testing, the following values were determined (Reference 21, Section 2):

Combined uncertainty feedwater flow and feedwater temperature

= 0.29% full power Feedwater Flow Rate Systematic Uncertainty = 0.26%

Feedwater Temperature Systematic Uncertainty = 0.10°F Random Feedwater Temperature Uncertainty = 0.56°F. This corresponds to two standard deviations. Thus, the Absolute Standard Deviation of Mean Feedwater Temperature Measurements = 0.28 0 F (i.e., 0.56/2).

However, to achieve the combined uncertainty of 0.29%, this random feedwater temperature uncertainty value was increased to 0.461F.

Case 4 Revised Case 2 with New Transducer Uncertainty After the flowmeter testing, the transducers were changed and Caldon revised the feedwater flow uncertainty from 0.26% to 0.29%, Reference 22. Case 1 was re-run using the following flowmeter uncertainties:

Feedwater flow systematic flow uncertainty = 0.29%

Feedwater Temperature Systematic Uncertainty = 0.10°F Random Feedwater Temperature Uncertainty = 0.460 F 32

AREVA NP 32-5012428-08 When combined with the other heat balance uncertainties, the total heat balance uncertainty is 0.367%, which is marginally less than Case 2 that used the pre-test uncertainties.

Case 5 - Reduced Steam Temperature Uncertainty To determine whether further reductions in the heat balance uncertainty are possible through the reduction of the steam temperature uncertainty, a case was analyzed with a steam temperature uncertainty of 1.1F which corresponds to (2)-05 times the base case uncertainty of 1.561F (this would be representative of adding a second independent temperature transducer to each steam line). The resulting core themal power uncertainty value is 0.349%.

Case 6 - Single Loop PFw Ts Ps Uncertainties In the event that only instrumentation from a single loop were available, the heat balance uncertainty would be 0.401% based on the following systematic uncertainties: feedwater pressure = 20.6 psi, steam pressure = 2 psi, steam temperature = 2.2 OF.

Cases 7 and 8 - Instrument Location Effects Feedwater pressure, feedwater temperature, steam pressure, and steam temperature are used to calculate the feedwater and steam enthalpies used in the heat balance calculation. Ideally, these measurements would be conducted at the steam generator inlet and outlet nozzles to achieve a heat balance free from instrument location errors. Since this is not possible, the instrument location effects should be factored into the heat balance calculation and heat balance uncertainty calculation. The new FIDMS CTPA software provides a means where the AP can be included in the heat balance calculation.

The temperature change between the steam generator and the instrument location will be immeasurable. Thus, the effects of temperature location errors are perceived as negligible.

There will be appreciable pressure differences between the measurement locations and the steam generator. For the feedwater pressure, this is not significant as evidenced by the small systematic uncertainty contribution of feedwater pressure as shown in Table 4. Steam pressure, however, does have an impact and should be addressed.

OTSG outlet pressure is sensed in the 26" steam lines downstream of the steam generator. From Appendix C, there is a 3 psi unrecoverable pressure loss between the outlet nozzle and the pressure transducer location. It is recommended that this pressure loss be taken into account in FIDMS' CTPA software.

33

AREVA NP 32-5012428-08 If the adjustment is made, then the only addition to the uncertainty is the uncertainty on the AP calculation. Assuming, that the line loss has a calculational uncertainty of 20% (assumption no. 4), the additional steam pressure uncertainty factor is 0.2*3, or 0.6 psi. The line loss uncertainty can be considered independent of the instrumentation uncertainty and thus combined in a square-root-sum-of-the-squares method.

Steam pressure uncertainty = [(2.0)2 + (0.6)2]0.5 = 2.09 psi Using two pressure instruments, the uncertainty = 2.09*205 = 1.48 psi The resulting core thermal power uncertainty for this Case 7 is 0.367% and is unchanged from the base case.

If the pressure difference adjustment is not made within the heat balance calculation and/or plant computer software, then the addition to the uncertainty is the uncertainty on the AP calculation plus the AP itself. Assuming, that the line loss has a calculational uncertainty of 20%,

Steam pressure uncertainty = [(2.0)2 + (3*1.2)210.5 = 4.12 psi Using two pressure instruments, the uncertainty = 4.12*2-0.5 = 2.91 psi The resulting core thermal power uncertainty for this Case 8 is 0.369%.

Case 9 - Alternate Steam Pressure Location In the event that turbine header pressure instruments were used instead of the steam generator outlet pressures, pressure adjustments would be required in the FIDMS CTPA software (i.e., 15 or 20 psi would need to be added to account for the steam line losses between the two locations). These values are based on the line loss calculations shown in Appendix C. Assuming, that the line loss has a calculational uncertainty of 20%, an additional steam pressure uncertainty factor must be considered. The line loss uncertainty can be considered independent of the instrumentation uncertainty and thus combined in a square-root-sum-of-the-squares method.

Steam pressure uncertainty = [(2.0)2 + (0.2*20.0)2]05 = 4.47 psi Steam pressure uncertainty = [(2.0)2 + (0.2*15.0)2]05 = 3.61 psi Using both steam lines, the uncertainty = [(4.47/2)2 + (3.61/2)2]0.5 = 2.87 psi The resulting core thermal power uncertainty for this case is 0.369%.

34

AREVA NP 32-5012428-08 Case 10 - Insensitivity to Assumed Values for Makeup and Letdown Flow, Pressure, and Temperature To demonstrate the core thermal power uncertainty to the assumed uncertainties relative to makeup and letdown flow, pressure, and temperature, a case was analyzed in which each of the uncertainties were doubled. The resulting uncertainty only increased from 0.367% to 0.370%, thus demonstrating the insensitivity of these values.

Case 11 - MVP Base Case (Dual Loop PFW, Ts*Ps Uncertainties)

To determine the effects of the larger MVP uprate on the heat balance uncertainty, case 2 was repeated for at the 3016 Mwt feedwater flow and steam temperature conditions. Even though there are differences in the secondary operating conditions at the larger power uprate, no significant effect on the heat balance uncertainty was observed as the resulting core thermal power uncertainty is 0.367% (which matches Case 4 to three significant figures).

35

AREVA NP 32-5012428-08 6.0

SUMMARY

OF RESULTS The ASME Performance Test Code Methodology was used to calculate the expected core thermal power uncertainty to be achieved using the Caldon CheckPlusTM System ultrasonic flow meter. The analysis concluded that using the following instrument uncertainty values, the core thermal power uncertainty would be 0.367%, thus allowing a power uprate of 1.63% to be pursued. This is based on:

Feedwater Flow Uncertainty of 0.29%

" Feedwater Temperature Uncertainty of 0.1 *F (systematic) and 0.46°F (random*)

Feedwater Pressure Uncertainty of 14.6 psi (systematic) and 1.35 psi (random)

" Steam Pressure Uncertainty of 1.42 psi (systematic) and 1.52 psi (random)

Steam Temperature Uncertainty of 1.56 0F (systematic) and 0.1530 F (random)

The other parameters (makeup, letdown, RCP heat, and ambient losses) are minor contributors. Their uncertainties are defined in the body of the report.

This result is valid for both the MUR and MVP uprates.

"Random" as described herein corresponds to one standard deviation as opposed to two standard deviations. The Caldon published random uncertainty of 0.56°F corresponds to two standard deviations or 0.28°F. The 0.28*F value was increased to 0.46°F to match the Caldon published combined flow uncertainty (see Case 3).

36

AREVA NP 32-5012428-08

7.0 REFERENCES

(1) ASME PTC 19.1-1998, Test Uncertainty, Instruments and Apparatus, American Society of Mechanical Engineers, NY, NY, 1998.

(2) Caldon, Inc. Engineering Report-80P Revision 0 (Proprietary Version),

Topical Report - "Improving Thermal Power Accuracy and Plant Safety While Increasing Operating Power Level Using the LEFM V/TM System,"

March 1997. (For Information Only)

(3) Caldon Topical Report Caldon, Inc. Engineering Report-157P Revision 5 (Proprietary Version), Topical Report - "Supplement to Topical Report ER-TM or LEFM CheckPlus TM 80P: Basis for a Power Uprate With the LEFM,/

System.". (For Information Only)

(4) AREVA NP Document 32-1119395-00, Calculated Uncertainty in Qprimary," May 1980.

(5) AREVA NP Document 32-1142654-00, "Error Equations for RC Flow Calculation," May 1983.

(6) AREVA NP Document 32-5001078-01, "CR-3 Heat Balance Uncertainty Calc," March 1998.

(7) AREVA NP Document 75-1103982-02, "Core Thermal Power Analysis Module (CTPA), 1983.

(8) AREVA NP Document 32-5007853-01, "DAVIS-BESSE CYCLE 13 OLC DBU," May 2000 (9) AREVA NP Document 51-5005750-00, "DBNPS Design Basis Validation for the Makeup and Purification System," October 1999.

(10) AREVA NP Document 32-5011757-00, "DB App. K Power Uprate - New Operating Conditions," March 2001.

(11) Bechtel Drawing M-203A Rev. 20, "Piping Isometric Main Steam System Ctmt. Bldg. Steam Gen. 1-1."

(12) Bechtel Calculation No. 1.38 Rev. 0.

(13) Idelchik, I.E., Handbook of Hydraulic Resistance, Second Edition, Hemisphere Publishing Co., Washington DC, 1986.

(14) Ladish General Catalog No. 55, "Forged and Seamless Welding Pipe Fittings, Cudahy, WI, 1971.

37

AREVA NP 32-5012428-08 (15) Crane Technical Paper No. 410, "Flow of Fluids Through Valves, Fittings, and Pipe," 2 4 th Printing, King of Prussia, PA, 1988.

(16) Bechtel Drawing M-203B Rev. 16, "Piping Isometric Main Steam System Ctmt. Bldg. Steam Gen. 1-2."

(17) Bechtel Drawing M-203C Rev. 11, "Piping Isometric Main Steam System Turbine Building."

(18) AREVA NP Document 51-5003544-00, "FIDMS Methodology," September 1999.

(19) AREVA NP Document 32-5013080-00, "DB 3016 Mwt Power Uprate -

New Operating Conditions," June 2002.

(20) Davis Besse Calculation No. C-ICE-083.01-004 Rev. 01, "Loop Uncertainty for Main Feedwater & High Pressure Turbine Main Steam Temperature & Pressure."

(21) Caldon, Inc. Engineering Report: ER-202 Revision 2, "Bounding Uncertainty Analysis for Thermal Power Determination at Davis Besse Nuclear Power Station Using the LEFM/+ System," July 2004.

(22) Letter from Ed Madera (Cameron) to Tim Laurer (Davis Besse), "Cameron Measurement Systems Response to Transducer Replacement Sensitivity," dated March 8, 2007. (Attachment 2)

(23) Davis Besse Calculation No. C-ICE-083.01-004 Rev. 03 Addendum No. 2, "DB Loop Uncertainty for Main Feedwater & High Pressure Turbine Main Steam Temperature & Pressure."

(24) AREVA NP 38-5038413-00, "Revision of NAS QHTRS Variable."

Retrievable from Davis-Besse records center and thus acceptable references for this calculation.

38

AREVA NP 32-5012428-08 APPENDIX A - Heat Balance Spreadsheets The methodology developed in Section 5 was programmed in Excel for ease of evaluating various inputs. The Excel spreadsheet was verified by comparing the results of Case 2 with those listed in Section 5.

39

AREVA NP 32-5012428-08 Case 1 - Definition of "Random" Feedwater Temperature Uncertainty All uncertainties except feedwater flow and feedwater temperature set to zero.

Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.55E+04 0 8.170E+02 2.105E+14 0.OOOE+00 93.05% 0.00%

TS Steam Temperature F 596 0 0 9.969E+06 0.OOOE+00 0.OOOE+00 0.00% 0.00%

PS Steam Pressure Psia 930 0 0 -1.340E+06 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TFW Feedwater Temperature F 455 0.6 0.24728 -1.323E+07 1.574E+13 1.070E+13 6.96% 100.00%

PFW Feedwater Pressure Psia 1005 0 0 -6.157E+03 0.OOOE+00 0.OOOE+00 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 0.OOE+00 0.OOE+00 7.396E+01 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TMU Makeup Temperature F 100 0 0 2.201 E+04 0.OOOE+00 0.OOOE+00 0.00% 0.00%

PMU Makeup Pressure Psia 2250 0 0 5.812E+01 0OOOE+00 0.OOOE+00 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 0.OOE+00 0.OOE+00 5.555E+02 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TLD Letdown Temperature F 557 0 0 2.791 E+04 0.OOOE+00 0.000E+00 0.00% 0.00%

PLD Letdown Pressure Psia 2250 0 0 -4.009E+01 0.OOOE+00 0.OOOE+00 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 0.OOE+00 0 1.OOOE+00 0.OOOE+00 0.OOOE+00 0.00% 0.00%

QLOSS Ambient Heat Loss Btu/hr 0.00E+00 0.00E+00 0 1.OOOE+00 0OOOE+00 0.000E+00 0.00% 0.00%

2.263E+14 1.070E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621E+09 3.009E+07 6.541E+06 3.079E+07 0.32 HSB Steam Enthalpy Btu/lbm 1250 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/lbm 433 DHFW/DT -1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 HLD Letdown Enthalpy Btu/Ibm 555.52 DHLD/DT 1.2532 DHLD/DP -1.80E-03 40

AREVA NP 32-5012428-08 Case 2 - Base Case Using Dua) Loop Instrument Uncertainties Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.55E+04 0 8.173E+02 2.107E+14 0.OOOE+00 71.29% 0.00%

TS Steam Temperature F 596 1.56 0.153 9.969E+06 6.047E+13 2.327E+12 20.46% 12.42%

PS Steam Pressure psia 930 1.42 1.52 -1.340E+06 9.056E+1 1 4.150E+12 0.31% 22.15%

TFW Feedwater Temperature F 455 0.6 0.24728 1.323E+07 1.574E+13 1.070E+13 5.33% 57.09%

PFW Feedwater Pressure psia 1005 14.6 1.35 -6.157E+03 2.020E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.14%

TMU Makeup Temperature F 100 5 2 2.201 E+04 3.027E+09 1.937E+09 0.00% 0.01%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.03% 8.17%

TLD Letdown Temperature F 557 5 2 2.791 E+04 4.868E+09 3.116E+09 0.00% 0.02%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 1.000E+00 6.076E+12 O.OOOE+00 2.06% 0.00%

OLOSS Ambient Heat Loss Btu/hr 2.23E+06 2.50E+06 0 1.OOOE+00 1.563E+12 0.OOOE+00 0.53% 0.00%

2.956E+14 1.873E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr Qc Core Thermal Power Btu/hr 9.621 E+09 3.438E+07 8.657E+06 3.546E+07 0.36852537 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/lbm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 HLD Letdown Enthalpy Btu/lbm 555.52 DHLD/DT 1.2532 DHLD/DP -1.80E-03 41

AREVA NP 32-5012428-08 Case 3 - Definition of Randon Feedwater Temperature Uncertainty for As-Tested Caldon Flowmeter All other terms set to zero Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.08E+04 0 8.173E+02 1.583E+14 0.OOOE+00 99.72% 0.00%

TS Steam Temperature F 596 0 0 9.969E+06 0.OOOE+00 0.OOOE+00 0.00% 0.00%

PS Steam Pressure psia 930 0 0 -1.340E+06 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+1 1 3.701 E+1 3 0.28% 100.00%

PFW Feedwater Pressure psia 1005 0 0 -6.157E+03 0.OOOE+00 0.OOOE+00 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 0.OOE+00 0.OOE+00 7.396E+01 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TMU Makeup Temperature F 100 0 0 2.201 E+04 0.OOOE+00 0.OOOE+00 0.00% 0.00%

PMU Makeup Pressure psia 2250 0 0 5.812E+01 0.OOOE+00 0.OOOE+00 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 0.OOE+00 0.OOE+00 5.555E+02 0.OOOE+00 0.OOOE+00 0.00% 0.00%

TLD Letdown Temperature F 557 0 0 2.791 E+04 0.OOOE+00 0.OOOE+00 0.00% 0.00%

PLD Letdown Pressure psia 2250 0 0 -4.009E+01 0.OOOE+00 0.OOOE+00 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 0.OOE+00 0 1.OOOE+00 0.OOOE+00 0.OOOE+00 0.00% 0.00%

QLOSS Ambient Heat Loss Btu/hr 0.OOE+00 0.OOE+00 0 1.OOOE+00 0.OOOE+00 0.OOOE+00 0.00% 0.00%

1.587E+14 3.701E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621 E+09 2.519E+07 1.217E+07 2.798E+07 0.29080499 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 42

AREVA NP 32-5012428-08 Case 4 - Base Case Using New Feedwater Flowmeter Transducer Uncertainty Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 73.89% 0.00%

TS Steam Temperature F 596 1.56 0.153 9.969E+06 6.047E+13 2.327E+12 22.69% 5.16%

PS Steam Pressure psia 930 1.42 1.52 -1.340E+06 9.056E+1 1 4.150E+12 0.34% 9.21%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+1 1 3.701E+13 0.16% 82.15%

PFW Feedwater Pressure psia 1005 14.6 1.35 -6.157E+03 2.020E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.06%

TMU Makeup Temperature F 100 5 2 2.201 E+04 3.027E+09 1.937E+09 0.00% 0.00%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.04% 3.40%

TLD Letdown Temperature F 557 5 2 2.791 E+04 4.868E+09 3.116E+09 0.00% 0.01%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 I.OOOE+00 6.076E+1 2 0.OOOE+00 2.28% 0.00%

QLOSS Ambient Heat Loss Btu/hr O.00E+00 2.50E+06 0 1.0OOE+00 1.563E+12 0.OOOE+00 0.59% 0.00%

2.664E+14 4.505E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621E+09 3,265E+07 1.342E+07 3.530E+07 0.36687916 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/lbm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 43

AREVA NP 32-5012428-08 Case 5 - Reduced Steam Temperature Uncertainty Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 83.41% 0,00%

TS Steam Temperature F 596 1.1 0.153 9.969E+06 3.006E+13 2.327E+12 12.74% 5.16%

PS Steam Pressure psia 930 1.42 1.52 -1.340E+06 9.056E+11 4.150E+12 0.38% 9.21%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+11 3.701E+13 0.19% 82.15%

PFW Feedwater Pressure psia 1005 14.6 1.35 -6.157E+03 2.020E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.06%

TMU Makeup Temperature F 100 5 2 2.201E+04 3.027E+09 1.937E+09 0.00% 0.00%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.04% 3.40%

TLD Letdown Temperature F 557 5 2 2.791 E+04 4.868E+09 3.116E+09 0.00% 0.01%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 1.OOOE+00 6.076E+12 0.OOOE+00 2.57% 0.00%

QLOSS Ambient Heat Loss Btu/hr 0.OOE+00 2.50E+06 0 I.OOOE+00 1.563E+1 2 0.OOOE+00 0.66% 0.00%

2.360E+14 4.505E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621E+09 3.073E+07 1.342E+07 3.353E+07 0.34851553 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 44

AREVA NP 32-5012428-08 Case 6 - Single Loop Uncertainties Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 60.19% 0.00%

TS Steam Temperature F 596 2.2 0.153 9.969E+06 1.203E+14 2.327E+12 36.76% 5.16%

PS Steam Pressure psia 930 2 1.52 -1.340E+06 1.796E+12 4.150E+ 12 0.55% 9.21%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+1 1 3.701 E+1 3 0.13% 82.15%

PFW Feedwater Pressure psia 1005 20.63 1.35 -6.157E+03 4.033E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.06%

TMU Makeup Temperature F 100 5 2 2.201 E+04 3.027E+09 1.937E+09 0.00% 0.00%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.03% 3.40%

TLD Letdown Temperature F 557 5 2 2.791 E+04 4.868E+09 3.116E+09 0.00% 0.01%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 1.OOOE+00 6.076E+12 O.OOOE+00 1.86% 0.00%

QLOSS Ambient Heat Loss Btu/hr O.OOE+00 2.50E+06 0 1.OOOE+00 1.563E+12 0.OOOE+00 0.48% 0.00%

3.271E+14 4.505E+1 3 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621E+09 3.617E+07 1.342E+07 3.858E+07 0.40102689 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 7.3.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 HLD Letdown Enthalpy Btu/lbm 555.52 DHLD/DT 1.2532 DHLD/DP -1.80E-03 45

AREVA NP 32-5012428-08 Case 7 - Instrument Location Effects (Adjustment Incorporated)

Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 73.87% 0.00%

TS Steam Temperature F 596 1.56 0.153 9.969E+06 6.047E+13 2.327E+12 22.69% 5.16%

PS Steam Pressure psia 930 1.48 1.52 -1.340E+06 9.837E+11 4.150E+12 0.37% 9.21%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+11 3.701E+13 0.16% 82.15%

PFW Feedwater Pressure psia 1005 14.6 1.35 -6.157E+03 2.020E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.06%

TMU Makeup Temperature F 100 5 2 2.201E+04 3.027E+09 1.937E+09 0.00% 0.00%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.04% 3.40%

TLD Letdown Temperature F 557 5 2 2.791E+04 4.868E+09 3.116E+09 0.00% 0.01%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 1.OOOE+00 6.076E+12 0.OOOE+00 2.28% 0.00%

QLOSS Ambient Heat Loss Btu/hr 0.OOE+00 2.50E+06 0 1.OOOE+00 1.563E+12 0.OOOE+00 0.59% 0.00%

2.665E+14 4.505E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertainty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr %

Qc Core Thermal Power Btu/hr 9.621E+09 3.265E+07 1.342E+07 3.530E+07 0.36692518 HSB Steam Enthalpy Btu/Ibm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 HLD Letdown Enthalpy Btu/Ibm 555.52 DHLD/DT 1.2532 DHLD/DP -1.80E-03 46

AREVA NP 32-5012428-08 Case 8 - Instrument Location Effects (Adjustment Not Incorporated)

Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 73.10% 0.00%

TS Steam Temperature F 596 1.56 0.153 9.969E+06 6.047E+13 2.327E+12 22.45% 5.16%

PS Steam Pressure psia 930 2.91 1.52 -1.340E+06 3.803E+12 4.150E+12 1.41% 9.21%

TFW Feedwater Temperature F 455 0.1 0.46 1.323E+07 4.373E+1 1 3.701 E+1 3 0.16% 82.15%

PFW Feedwater Pressure psia 1005 14.6 1.35 -6.157E+03 2.020E+09 6.908E+07 0.00% 0.00%

WMU Makeup Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 7.396E+01 1.696E+09 2.713E+10 0.00% 0.06%

TMU Makeup Temperature F 100 5 2 2.201 E+04 3.027E+09 1.937E+09 0.00% 0.00%

PMU Makeup Pressure psia 2250 50 50 5.812E+01 2.112E+06 8.446E+06 0.00% 0.00%

WLD Letdown Flow Rate Ibm/hr 2.23E+04 1.11E+03 2.23E+03 5.555E+02 9.566E+10 1.531E+12 0.04% 3.40%

TLD Letdown Temperature F 557 5 2 2.791E+04 4.868E+09 3.116E+09 0.00% 0.01%

PLD Letdown Pressure psia 2250 50 50 -4.009E+01 1.004E+06 4.017E+06 0.00% 0.00%

QRCP RCP Power Btu/hr 6.75E+07 4.93E+06 0 1.OOOE+00 6*076E+12 0.OOOE+00 2.26% 0.00%

QLOSS Ambient Heat Loss Btu/hr 0.OOE+00 2.50E+06 0 1.OOOE+00 1.563E+12 0.OOOE+00 0.58% 0.00%

2.693E+14 4.505E+13 100.00% 100.00%

Absolute Absolute Absolute Relative Nominal Systematic Random Uncertain ty Uncertainty Symbol Description Units Value Uncertainty Uncertainty Btu/hr Qc Core Thermal Power Btu/hr 9.621E+09 3.282E+07 1.342E+07 3.546E +07 0.36858151 HSB Steam Enthalpy Btu/lbm 1253.356 DHS/DT 0.842 DHS/DP -0.1132 HFWB Feedwater Enthalpy Btu/Ibm 436.041 DHFW/DT 1.117 DHFW/DP -5.20E-04 HMU Makeup Enthalpy Btu/Ibm 73.96 DHMU/DT 0.9882 DHMU/DP 2.61 E-03 HLD Letdown Enthalpy Btu/Ibm 555.52 DHLD/DT 1.2532 DHLD/DP -1.80E-03 47

AREVA NP 32-5012428-08 Case 9 - Use of Turbine Header Pressure Instruments Absolute Absolute Relative Relative Absolute Absolute Systematic Random Systematic Random Nominal Systematic Std. Dev. Absolute Uncertainty Uncertainty Uncertainty Uncertainty Symbol Description Units Value Uncertainty of the Mean Sensitivity Contribution Contribution Contribution Contribution WFW Feedwater Flow Rate Ibm/hr 1.18E+07 3.43E+04 0 8.173E+02 1.969E+14 0.OOOE+00 73.13% 0.00%

TS Steam Temperature F 596 1.56 0.153 9.969E+06 6.047E+13 2.327E+12 22.46% 5.16%

PS Steam Pressure psia 930 2.87 1.52 -1.340E+06 3.699E+12 4.150E+12 1.37% 9.21%