ML20082D840
| ML20082D840 | |
| Person / Time | |
|---|---|
| Site: | Fort Calhoun  |
| Issue date: | 11/30/1983 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
| To: | |
| Shared Package | |
| ML19274C105 | List: |
| References | |
| CEN-257()-NP, CEN-257(0)-NP, NUDOCS 8311230079 | |
| Download: ML20082D840 (219) | |
Text
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CEtP257 (0)-NP STATISTICAL COMBINATION OF UNCERTAINTIES PART 1 NOVEMBER, 1983 i
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E POWER SYSTEMS RSAES88Po!S$$$A3 P PDR
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s LEGAL NOTICE THIS REPORT WAS FREPARED AS AN ACCOUNT OF WORK SPONSORED BY COlWUSTION ENGINEERING, INC. NEITHER COM8USTION ENGINEERING NOR ANY PERSON ACTING ON ITS SEHALF:
A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR 1RFLIED INCLUDING THE WARRANTIES OF PITNESS FOR A PARTICULAR PURPOSE OR MERCHANTA88UTY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS;OR B. ASSUMES ANY UA81LITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, METHOD OR PROCESS DISCLOSED IN THIS REPORT.
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t CEN-257 (0)-NP STATISTICAL COMBINATION OF UNCERTAINTIES METHODOLOGY PART 1: AXIAL POWER DISTRIBUTION AND THERMAL MARGIN / LOW PRESSURE LSSS FOR FORT CALHOUN l
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ABSTRACT This report describes the methods used to statistically combine uncertainties fcr the Axial Power Distribution ( APD) LSSS and Thermal Margin / Low Pressure (TM/LP) LSSS for Fort Calhoun.
A d3 tailed description of the uncertainty probability distributions and the stochastic simulation techniques used is presented. The total uncertainties presented in this report are expressed in percent overpower (P fd n , Pfdl) units, assigned to the APD LSSS and the TM/LP LSSS at the 95/95 pr;bability/ confidence limit.
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l TABLE OF CONTENTS Chapt'r Page 1.0 Introduction 1.1 Purpose 1-1 1.2 Background 1-1 13 Report Scope 1-3 1.4 Summary of Results 1-3 1.5 References for Section 1.0 1-3 2.0 Analysis 2-1 2.1 Objective of Analysis 2-1 2.2 Analytical Techniques 2-1 2.3 TM/LP LSSS Stochastic Simulation 2-2 2.4 Axial Power Distribution LSSS Stochastic Simuistion 2-3 2.5 Functional Models 2-3 2.6 Evaluation of Uncertainty Factors 2-4 2.7 References for Section 2.0 2-4 30 Results and Conclusions 3-1 31 Results of Analyses 3-1 32 Lapact on Margin to SAFDL 3-3 33 References for Section 3.0 3 -4 App ndix A. Description of CESCU Calculational Method A-1 B. Basis for Uncertainties Used in Statistical B-1 Combination of Uncertainties Program B1 Axial Sbspe Index Uncertainties B-4 B2 Measurement Uncertainties B-31 B3. Trip System Processing Uncertainties B-39 C. Summary of Previous Methods for Combining Uncertainties C-1 i i
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LIST OF TABLES Table _P ag,e 1-1 NSSS Parameters Affecting Fuel Design Limits 1-5 2-1 Operating Space Used for Statistical Analysis 2-7 3-1 Uncertainties Associated with the Axial Power Distribution LSSS and the TM/LP LSSS 3-5 3-2 Impact of Statistical combination of Uncertainties on Margin to SAFDL 3-6 LIST OF FIGURES Figure Pm 2-1 Thermal Margin Uncertainty Analysis 2-5 2-2 Linear Heat Rate Uncertainty Analysis 2-6 l
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3 DEFINITION OF ACRONYMS AND ABBREVIATIONS ACU Axial shape index calibration uncertainty A00 Anticipated Operational Occurence(s)
APD Axial Power Distribution APU, TPU Processing uncertainty
'ARO All rods out L ASI Axial shape index after epplication of uncertainties LSSS ASI DNB Axial shape index after inclusion of the DNB LSSS uncertainties s
LSSS ASI GR Axial shape index after inclusion of GR LSSS uncertainties B Unless sepcifically defined in context as representing AT Power, B is used interchageably with Q, core power.
B DNB P
fdn after application of uncertainties B
WR Pfdl after application of uncertainties B gg MR overpower including uncertainties B L333 Power limit for MR LSSS B Available overpower margin g p, B,p,, Reference B,p, for calculating the constants in the TM/LP trip equation LSSS B
DNB Power level after inclusion of DNB LSSS uncertainties and allowances LSSS B
LHR Power level after inclusion of linear heat rate L3SS uncer-tainies and allowances B
OP"k(h)
B OP8k(h) axial shape inder uncertainties BMU Power measurement uncertainty Value of the power measurement uncertainty sampled by SIGMA BMU k (h) in trial k(h).
BOC Beginning of Cycle j _CEA Control Element Assembly CECOR Computer code used to monitor core power distributions CETOP Computer code to determine the overpower limits due to thermal-hydraulic conditions iv J
CE-1 DNBR DNB Ratio calculated by the TORC /CE-1 correlation DBE Design Basis Event (s)
Di Value of simulation point i DNB Departure from Nucleate Boiling DNBR Departure from Nucleate Boiling Ratio EOC End of Cycle F Primary coolant flow rate f Number of degress of freedom DNB F Coolant flow used in the generation of (Pfdn' I p) ordered pairs of data F Engineering factor on local heat flux 9
Fq, F" q Synthesized three-dimensional core power peak FP Planar radial peaking factor F Integrated radial peaking factor R
H Height of core Y Core average axial shape index I External shape index n
th assembly Ig Axial shape index for the i I Peripheral axial shape index I QUIX-calculated core average axial shape index If QUIX-calculated I p QUIX calculated value of Ipusing the rod shadowing factor Ih(RSF) method I
R ROCS-calculated core average axial shape index If ROCS-calculated I p ROCS power distribution based values ofpI using the If(AWF) assembly wei5hting factor method ROCS power distribution based values ofpI using the rod If(RSF) shadowing factor method Ip I pcalculated CECCR C I calculated CECOR I
L Power in lower half of core LCO Limiting Condition (s) for Operation
- LHS Latin Hypercube Sampling LHR Linear Heat Rate LPD Local Power Density LSSS Limiting Safety System Setting (s) f V
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MDNBR Minimum DNBR ,
MOC Middle of Cycle Mwt Megawatt (s) thermal MTC Moderator Temperature Coefficient N Sample size NSSS Nuclear Steam Supply System (s)
P Reactor coolant system pressure P(J) Average power in axial node J Pg Axially integrated power of assembly i P Power to the fuel design limit on fuel centerline melt fdl P
fdl h Value of P fdl from simulation h DNB P Pressure used in calculating the (Pfdn'Ip) ordered pairs of data P
fdn Power to DNBR SAFDL P Overpower from CETOP from the sampled input parameters in fdnk simulation k P Variable 1 w pressure trip limit vtr DNB P, , Variable pressure to achieve DNB at the LSSS limit LSSS,DNB P Variable pressure to achieve DNB at the LSSS limit including vtr uncertainties PDIL Power Dependent Insertion Limit MKPU Pressure Measurement Uncertainty
, PU Uncertainty in predicting local power at the fuel design limit
! P(x) Normalized power level at core height x
( Q Core power, auctioneered higher of flux power or T power QUIX Computer code used to solve the 1 dimensional neutorn diffusion equation RCS Reactor Coolant System RDT Pressure equivalent of the total trip unit and processing delay time for the DBE exhibiting the most rapid approach to the SAFDL on DNBR ROCS Coarse mesh code for calculating power distributions RPS Reactor Protection System RSU Peripheral shape index uncertainty R(x) Rod shade.ing factor at core height x vi l
S Sample standard deviation SAFDL Specified Acceptable Fuel Design Limit (s)
SAU Shape annealing factor uncertainty SCU Statistical Combination of Uncertainties SIGMA Stochastic Simulation Code SMLS Statistically combined uncertainties applicable to the APD LSSS T Azimuthal tilt allewance AZ T, , Tin Reactor coolant cold leg, inlet temperature DNB T Inlet c lant temperature used in the calculation of in (Pfdn' I p) ordered pairs of data 4
LSSS,DNB T Final inlet coolant temperature for LSSS calculation in T Reactor coolant hot leg temperature h
TMLL Thermal Margin Limit Line(s)
TM/LP Thermal Margin / Low Fressure TMU Temperature measurement uncertainty TORC /CE-1 Thermal hydraulic calculational model including CE-1 critical heat flux correlation TPD Allowance for Transient Power Decalibration TPU Trip processing uncertainty U Power in upper half of core VHPT Variable High Power Trip Wcy g Core average linear heat rate Weyg Peak Generated linear heat rate limit corresponding to the SAFDL on fuel centerline melt Wi Weighting factor of assembly 1 i
x Axial position l
X Sample mean Z i th value of a normally distributed random variable with i
zero mean and unit standard deviation
- a Shape annealing factor f
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. - , _ _ _ - . . _ . - - = .
( c) , ( 8) , ( y) Coefficients in the P$r v equation C Population mean a Population standard deviation y Axial shape index correction term UO (r) [
.1 p R' g, J
u* C g C 1 Xf Chi-squared deviate with f degrees of freedom I
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1.0 INTRODUCTION
1.1 PURPOSE Th) purpose of this report is to describe a method for statistically combining the uncertainties involved in the analog protection and monitoring system setpoints. The following uncertainties are considered:
- 1. Uncertainty in predicting integrated radial pin power
- 2. Uncertainty in predicting local core power density
- 3. Power measurement uncertainty 4 Shape annealing factor uncertainty
- 5. Shape index separability uncertainty
- 6. Axial shape index calibration uncertainty
- 7. Processing uncertainty
- 8. Flow measurement uncertainty
- 9. Pressure measurement uncertainty
- 10. Temperature measurement uncertainty ,
1.2 BACKGROUND
1.2.1 Protection and Monitoring System Th3 Enalog protection and monitoring systems in operation on the Fort Calhoun Nuclotr Steam Supply System has been designed to assure safe operation of the rsactar in accordance with the criteria established in 10 CFR 50, Appendix A.
This is demonstrated in the Final Safety Analysis Report (FSAR) and subsequent roload licensing amendments.
This is achieved by specifying:
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- 1. Limiting Safety System Settings (LSSS) in terms of parameters directly monitored by the Reactor Protection System (RPS);
- 2. Limiting Conditions for Operation (LCO) for reactor system parameters; and
- 3. LCOs for equipment performance.
1-1
The LSSS, combined with the LCO, established the thresholds for protection systa action to prevent exceeding acceptable limits during Design Basis Events (DBE) where changes in DNBR and LHR are important. The limits addressed by the RPS cre:
- 1. The reactor fuel shall not experience centerline melt; and
- 2. The departure from nucleate boiling ratio shall have a minimum allowable limit corresponding to a 955 probability at a 95%
confidence level that DNB will not occur.
Th3 RPS trips jointly provide protection for all A00s. The RPS providing prierry protection from centerline melt is the Axial Power Distribution (APD) trip. The RPS providing primary DNB protection is the Thermal Margin / Low PresIure (TM/LP) trip.
l Th3 design of the RPS requires that correlations including uncertainties be tpplied to express the LSSS in terms of functions of monitored parameters.
Th se functions are the trip limits which are then set into the RPS. A list of pr.rameters which affect the calculation of limits for linear heat rate and DNB protsetion is shown in Table 1-1. A more detailed discussion of C-E setpoint methodology may be found in Reference 1-1.
1.2.2 Previous Uncertainty Evaluation Procedure Tha nethods previously in use for the application of uncertainties to the subjset limits are presented in Reference 1-1 and summarized in Appendix C.
As noted in Reference 1-1 these methods assume that all applicable uncer-teinties occur simultaneously in the most adverse direction even though not all of the uncertainties are systematic; some are random and some contain both sy;timatic and random characteristics. This assumption is extremely cenr4rvative. This report documents the methodology used to statistically
( csmbine uncertainties explicitly.
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13 REPORT SCOPE Th3 scope of this report encompasses the following objectives:
- 1. To define the methods used to statistically combine uncertainties applicable to the Thermal Margin / Low Pressure (TM/LP) and Axial Power Distribution (APD) LSSS;
- 2. To document the probability distributions associated with these uncertainties.
3 To evaluate the aggregate uncertainties as they are applied in the determination of the TM/LP and APD LSSS.
Th3 cethods presented in this report are applicable to the Fort Calhoun Unit 1 R3actsr (Omaha Public Power District).
1.4
SUMMARY
OF RESULTS Tha analytical methods presented in Section 2.0 are used to show that a stoch2stic simulation of uncertainties associated with the APD LSSS and TM/LP LSSS results in aggregate uncertainties of [ 1% and [ ]%, respectively, at c 95/95 probability / confidence limit.
Tha total uncertainties previously applied to the APD LSSS and the TM/LP LSSS cre'approximately [ ]% and [ 3%, respectively. Therefore, the use of the ststistical combination of uncertainties provides a reduction in conservatism in thi margin to SAFDL of approximately ( 3% and [ ]%, respectively.
1.5 REFERENCES
1-1 CENPD-199-P, Rev. 1-P, "C-E Setpoint Methodology,d March, 1982.
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TABLE 1-1 NSSS PARAMETERS AFFECTING FUEL DESIGN LIMITS DNBR
- 1. CORE POWER
- 2. AXIAL POWER DISTRIBUTION
- 3. RADIAL POWER DISTRIBUTION 4 AZIMUTHAL TILT MAGNITUDE
- 5. CORE COOLANT INLET TEMPERATURE
- 6. PRIMARY COOLANT PRESSURE
- 7. PRIMARY COOLANT MASS FLOW LINEAR HEAT RATE
- 1. CORE POWER
- 2. AXIAL POWER DISTRIBUTION 3 RADIAL POWER DISTRIBUTION
- 4. AZIMUTHAL TILT MAGNITUDE l
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, -- - . _ _ . _ . . _ _ . - _ - - _ . - . - - - - _ _ - - _ _ ~ . . _ . _ _ .
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I 2.0 ANALYSIS 2.1 OBJECTIVES OF ANALYSIS The cbjectives of the statistical andysis are to determine overall uncertainty factors to be applied to the TM/LP LSSS and the APD LSSS. These uncertaintv i festa.rs are determined such that there is a 95% probability at a 95% confidence icv:1 that the combined effect of uncertainties on the LSSS limits will not cxceed these factors.
2.2 ANALYTICAL TECHNIQUES Th3 techniques used to evaluate the uncertainty factors are similar to those used on other CE plants employing Analog Reactor Protection Systems as d: scribed in References 2-1 and 2-2. Minor changes have been made to aescamodate the earlier generation protection system in use at Ft. Calhoun.
Th . CESCU stochastic simulation methodology (Ref. 2-3) is used to determine the
, cv;rcll uncertainty factors. In this method the same calculations as the SIGMA /CETOP combination described in References 2-1 and 2-2 are performed in a moro automated manner. Details of the CESCU method are provided in Appendix A.
Th3 p:rticulars of the analysis for Ft. Calhoun are provided below.
-23 TM/LP LSSS STOCHASTIC SIMULATION For the TM/LP LSSS, DNB overpower (Pfdn) is the dependent variable of intcrest. Core coolant inlet temperature, reactor coolant system pressure, and tot 4 core power are monitored directly by the TM/LP trip system. Total int 33 rated radial' peaking factor, peripheral axial shape index, and RCS. coolant ficw rate are monitored by other systems and must be included in the TM/LP LSSS l
cvelustions.
Figuro 2-1 is a flow chart representing the simulation sequence for the TM/LP LSSS. For each simulation trial, a value of overpower obtained using sampled valuas of uncertainties about nominal conditions is calculated. This value is comp red to the overpower calculated at nominal conditions by taking the ratio cf tha two values. This simulation sequence is repeated over several thousand sata of nominal operating conditions covering the operations space for the 2-1
plant. The resulting _ distribution of the ratio of nominal overpower to ov:;rpower incorporating uncertainties is used to determine the overall unc:rtainty factor on the TM/LP LSSS.
The cperating space for the analysis is defined by establishing ranges for RCS pr0ccure, flow, radial peaking (FRI ), axial shape index (ASI) and core coolant inlet temperature. The ranges for F R I and ASI are set to r:caonably bound core operating limits for both present and future cycles. The
-rang 3 of flow rate is set to cover flows from a minimum to a maximum value which might occur with the present plant configuration. The pr' essure range is bounded by the value of the high pressurizer pressure trip setpoint and the icwor pressure limit of the TM/LP trip system. Core coolant inlet temperature osvars a range established by the combination of core power and inlet t0rp;rature resulting in the highest temperature at which the secondary safety velv;s open and the lowest temperature at which the low secondary pressure trip octurs.
The ranges of conditions used in the analysis are listed in Table 2-1.
2.4 AXIAL POWER DISTRIBUTION LSSS STOCHASTIC SIMULATION For the axial power distribution ( APD) LSSS, the power to peak linear heat rate (Pfdl) is the dependent variable of interest. Axial shape index and total e ro power are monitored directly by the APD trip system. Total integrated 3-D T
nucisse peaking (Fg) is monitored by other systems and must be included in the APD LSSS evaluations.
Figure 2-2 is a flow chart representing the simulation sequence for the APD
! LSSS.
Fcr cach simulation trial, a value of overpower (Pfdl) btained using campisd values of uncertainties about nominal conditions is compared to a value of overpower computed at nominal conditions. This simulation sequence is rspgnted several thousand times to obtain a distribution of uncertainty factors
' in tha same fashion as the TM/LP uncertainty evaluation. The operating space for analysis is defined by the ranges of ASI and FR I listed in Table 2-1.
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2.5 FUNCTIONAL MODELS The use of stochastic simulation to evaluate the effect of uncertainties on cynilable overpower margin requires models to compute overpower. For the TM/LP anclysis, CETOP-D (Ref. 2-4) is used to compute DNB overpower for given inputs of.etre inlet temperature, pressure, RCS flow rate, F R, T and axial power dictribution. The CETOP-D model and base deck used are described in Part 2 of this topical report.
Fcr the APD analysis, the following expression is used to evaluate Pfd1*
(Wetg) (100.0)
P (2-1) fdl I
(Fg) (WAVG) wh:ror Wu= Peak generated linear heat rate limit corresponding to centerline fuel melt WAVG : Core average linear heat rate at 100% power T Synthesized 3-D power peaking factor Fg
.Th2 value of the 3-D peaking factor is obtained by combining the maximum values of axial peaking factor (F Z) from the sampled power distribution with the campled integrated radial peaking factor. ,
'2.6 EVALUATION OF UNCERTAINTY FACTORS Th3 output of each stochastic simulation analysis consists of several thousand dtta points representing the ratio of nominal overpower to overpower including th3 effects of uncertainties. These data points are analyzed using non-parametric statistical methods to determine the 95% probability /95% confidence limit on the ratio.
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2.7 REFERENCES
2.1 " Statistical Combination of Uncertaintie s ," CEN-124(B)-P, Part 1, December,1979; Part 2 ' January,1980; Part 3, March,1980.
2-2 " Statistical Combination of Uncertaintie s ," CEN-123(F)-P, Part 1 December,1979; Part 2, January, 1980; Part 3, February,1980.
2-3 D. S. Moelling, R. Goldstein, F. J. Berte, " Reduction of Uncertainty Penalties in the Calculation of PWR Core Performance Safety Limits," TIS-7489, October, 1983 2-4 Letter from W. C. Jones (OPPD) to R. A. Clark (NRC), " Fort Calhoun Cycle 8 Reload Application," February 18, 1983 l
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OMAHA PUBLIC Ficure
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POWER DISTRICT LINEAR HEAT RATE UNCERTAINTY ANALYSIS 2_I-FORT CALHOUN NuclCor Power Plant 2-5
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POWER DISTRICT THERMAL MARGIN UNCERTAINTY ANALYSIS FORT CALHOUN ,2-2 Nuclear Power Plant 2-6
f TABLE 2-1 OPERATING SPACE USED FOR STATISTICAL ANALYSIS Coro Inlet Temperature (T )
e 465 F - 5800F Pressurizer Pressure (P) 1765 psia - 2400 psia Int 0 grated Radial Peak (FT) 1 35 - 2.5
, Axici Shape Index ( ASI) - 0.4 - +0.4 Core Coolant Flow Rate (% of Design Flow) 77 - 120 l
2-7 r ---- -- - -
e y 1--v-.: yw t- yrw - ,
- p e- - -3iw < -
30 RESULTS AND CONCLUSIONS 31 RESULTS OF ANALYSES Th3 cnalytical methods presented in Section 2 have been used to show that a stochastic simulation of uncertainties associated with the APD LSSS and the TM/LP LSSS results in combined uncertainties of ( 35 and [ ]%.
respectively, at a 95/95 probability / confidence limit.
Tablo 3-1 shows the values of the individual uncertainties which were stctistically combined to yield the above combined uncertainties. Appendix B c ntcins a further discussion of the bases for these individual uncertainties.
Th3 combined uncertainties are in units of percent overpower (Pfdl and Pfdn) and are applied in the generation of the APD and TM/LP LSSS as discussed below (Reference 3-1).
3 1.1 Axial Power Distribution LSSS The fuel design limit on linear heat rate corresponding to fuel centerline melting is represented by the ordered pairs (P fd1' I). p A lower bound is drawn under the " flyspeck" data such that all the core power distributions analyzed are accommodated. This lower bound is reduced by the applicable un:Grtainties and allowances to generate the LSSS as follows:
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(3-2) l 3-1
wheros LSSS B
LHR verpower limit for APD LSSS SMLS : Statistically combined uncertainties applicable to the APD LSSS TPD Allowance for transient power decalibration LSSS 3
ASI UiR Axial shape index associated with B 3 1.2 TM/LP LSSS The fuel design limit on DNBR for the TM/LP LSSS is presented by a combination of the ordered pairs (Pfdn' I) p and the DNB thermal margin limit lines. A lower bound is drawn under the " flyspeck" data such that all the core power distributions analyzed are accommodated. This lower bound is reduced by cpplicable uncertainties as follows:
(3-3)
I (3 4) wh:ro:
B gp, 3 Available overpower margin l SMDS : Statistically combined uncertainties applicable to the TM/LP LSSS ASI DNB = Axial shape inder associated with B 0p,.
Both components of the TM/LP LSSS can be represented by the following equations:
(3-5)
(3-6) 32
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(3-8) whero Q,(S),(y) : Coefficients B Core power, 4 of rated power DNB LSSS, DNB Py ,7 : Variable pressure to achieve DNB at the L33S limit including uncertainties RDT Pressure equivalent of the total trip unit processing delay time for the DBE exhibiting the most rapid approach to the SAFDL on DNBR LSSS B
= Power level after inclusion of DNB LSSS uncertainties and allowances TPD : Allowance for transient power decalibration LSSS'DNB S DDNB Tin Core inlet temperature associated with the P y DNB Tin Inlet coolant temperature used in the calculation of (Pfdn '
Ip ) ordered pairs of data.
32 IMPACT ON MARGIN TO SAFDL Tha motivation for using a statistical combination of uncertainties is to irprcve NSSS performance through a reduction in the analytical conservatism in the margin to the SAFDL. This section contains a discussion of the margin obtSinable through a reduction in this conservatism.
i Ttblo 3-2 lists the uncertainty values previously used on this plant. The i approximate worth of each of these uncertainties in terms of percent overpower margin (Pfdl, Pfdn) is also shown.
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Tha total uncertainties previosuly applied to the APD LSSS and the TM/LP LSSS ar3 approximately. [ ] and [ ), respectively. The uncertainties resulting from the application of the statistical combination of uncertainties pr gram are approximately [ ] and ( ). The use of the statistical combination of uncertainties provides a reduction in conservatism in the margin to SAFDL of approximately [ ] and [ 1, respectively.
Although the conservatism in the margin to SAFDL has been reduced , a high d:grce of assurance remains that the SAFDL will not be violated. ,
33 REFERENCES 3-1 CENPD-199-P, Rev. 1-P, "C-E Setpoint Methodology," March, 1982.
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TABLE 3-1 UNCERTAINTIES ASSOCIATED WITH THE APD LSSS AND THE TM/LP LSSS Untertainty' APD LSSS DNB LSSS Ctro power (% of rated power) 12% 125 .
Priccry coolant mass flow (1 design)" NA Prictry coolant pressure (psid) NA Cora coolant inlet temperature (OF) NA P4wer distribution (peaking factor) [ .
- 1. Separability See Table 1 of Appendix B1
- 2. Calibration (asiu) 3 Shape Aimealing (asiu) ,
- 4. Monitoring system processing (asiu)
- 5. Monitoring system processing (psia)
Nitant cFor complete description of tnese uncertainties, see Appendix B.
ocDesign flow = 190,000 GPM aco2 a values C000 Includes ( )
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TABLE 3-2 IMPACT OF STATISTICAL COMBINATION OF UNCERTAINTIES ON MARGIN TO SAFDL Approximate Values of Equivalent Overpower Margin (%)
DNB APD Unscrtainty Value LSSS LSSS
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Pow:r 2% of rated C:ro coolant inlet 0
tacperature 2F R; actor coolant system prctsure 22 psid Axial shape index:
Separability Shape annealing C:libration R;acter coolant system flow ]
P;cking factors 6% DNB, 7% APD Equipment processing:
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Istel uncertainty applied Total prsvicu' sly Total uncertainty statistically combined i Net c rgin gain -.
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APPENDIX A Description of CESCU Calculational Methodology f
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, APPENDI'X A s
- Description of CESCU Calculational Methodology
. 11 3 A.1 INTRODUCTION Th3 CESCU calculational methodology is - a stochastic simulation (Monte Carlo) method designed to determine the overall uncertainty factor to be applied to DNB-overpower and LHR-overpower limits in an automated manner. It can acionatodate the calculations required for determining these factors as applied to the TM/LP and APD LSSS limits and _ the DNB-overpower and KW/FT monitoring liEits (LCO's). The basic computational and statistical algorithms are those d scribed in previous SCU topical reports for C-E analeg plants (References
- A-1 and A-2) .
- A.2 STRUCTURE CESCU ' consists of four functional modules: a nominal condition selection modulo, a sampling module, a functional model module, and a statistical
-anclysis module.
Tha first module selects sets of nominal operating conditions (Tc, P, F, F R' ASI) such that the joint operating space defined is completely covered in the EnElysis. The range of e ach variable and the number of intervals to be c:nsidered within the range are specified. This method partitions the joint cperating space into hypercubes using a factorial sampling scheme ( Reference A-3). Random samples are drawn from each hypercube to provide nominal 1
' cperating conditions for the stochastic simulation analysis.
The second module samples the uncertainties according to the specified
_prebtbility distributions. For each set of nominal operating conditions g".nerated by the first module, another set of conditions is generated by the I rmpling ~ module. This set represents the nominal conditions perturbed by j samplsd values of the uncertainties.
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f The probability distributions of uncertainties can be represented as uniform
(*Etributions, Gaussian distributions, or as a histogram (frequency table) r:prasentation.
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Tha third module contains the functional models used for the DNB-overpower and GR-overpower calculations. For DNB-overpower the CETOP-D code (Reference A 4) is used to calculate the power to the DNBR limit for any input values of prssgure, temperature, flow, radial peak, and axial power distribution. The appr:priate CETOP-D base deck provides the other information required to apply CETOP to a specific plant and reload core. For MR overpower a synthesized 3-D peck (Fq) is computed from the exial peaking factor (Fz) of the axial power I Overpower (Pfdl) is distribution and the integrated radial peak (FR).
givsn by:
(Weg) (100.0)
Pfdl = (A-8)
T (WAVG) (Fg)
A-4
{
In cach case, the nominal and corresponding perturbed sets of input conditions aro used to calculate overpower values with anc without uncertainties. The b sic axial power distributions (shapes) are drawn from (.
1 Uncertainties in ASI (
1 .
J. Therefore, the fclltwing calculational scheme is used to relate uncertainties in ASI to
.cycrpower.
Tha cxial shape seen by the excore detectors is related to the core average cxici shape provided by QUIX (Reference A -5) by several factors. These fact:rs are obtained by calculation or, measurement and are subject to some unscrtainty. A 40-node core average axial shape is selected from a (-
-1. The core average axial shape index, I, is calculated frca this shape.
- L-U I ; 20 L+U U=I P(J) (A-9)
Jul (A-10) 40 L=I P(J) (A-11)
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To relate this to the peripheral shape index inferred by the excores, the following relation is used:
[- 3 (A-12) where:
A-5
A Th3 [ ] have uncertainties associated with them. These uncertainties were ured to generate representative values of ( ). Using these values, c:rrcsponding values of Ip are computed to obtain a AI value, which is the p
difference between the mean value of Ip and the Ip value including unsertainties. This is converted to overpower units by applying a multiplier rcprosenting a conservative value of the sensitivity of overpower to ASI.
During each simulation trial, k, the value of perturbed DNB overpower produced by CETOP is modified by additional uncertainty values to produce a final cverpower value. The final value is given by (A-13)
-t Fcr each simulation trial in the LHR-overpower calculation. [.
P
- I the modified overpower value fdlh. Ihus, th] LHR overpower including uncertainties, BLHRh ' 18
[ ] (A-14)
Tht ratio of nominal overpower to perturbed overpower is calculated for each simulation trial. These ratios are input to the final function module for statistical analysis.
A-6
- .- . . - - =..
4 Th3 fourth and final module of the CESCU method performs the statistical analysis of the set of overpower ratios. The mean, median, and variance of the
' dst 3 are computed and the data are ordered arithmetically for use in non-
. parametric analysis.
R7f;rnces A-1 ' Statistical Combination of Uncertainties," CEN-124(B)-P, Part 1, December 19719; Part 2, January 1980; Part 3, March 1980.
A-2 " Statistical . Combination of Uncertainties," CEN-123(F)-P, Part 1 December 1979; Part 2, January 1980; Part 3, February 1980.
A-3 McKay, M. D., et al., " Report on the Application of Statistical Techniques to the Analysis of Computer Codes," LA-NUREG-6526, MS, Los Alamos Scientific Laboratory, October,1976.
A-4 Letter from W. C. Jones (OPPD) to R. A. Clark (NRC), " Fort Calhoun Cycle 8 Reload Application," February 18, 1983 A-5 System 80 PSAR, CESSAR, Volume 1, Appendix 4A, Amendment No . 3 June 3.
-1974.
f l
I I
l A-7 l__ _. _ - _ _ _ _ __ _ _ , . . . _ . - _ . _ _ . . . . - . _ _ _ - _ _ _ . . _ . _ - --
APPENDIX B Basis for Uncertainties Used in Statistical Combination of Uncertainties l
B-1 l
i APPENDIX B 1
LIST OF TABLES Title Pm l B1-1 ' Uncertainty [ l Components for the Evaluation B-15 ef-the Peripheral Shape Index B1-2 Cycle 8 ar.d Cycle 9 BOC and EOC ( l Data B-16 B1-3 [ ] B-17 B1-4 [ B-18
]
B1-5 [ ] Index Normality Tests B-19 B1-6 Bantlett Pooling Tests B-20 B1-7 ( ) Comparison of lI B-21 B1-8 Measured Values of Shape Annealing Factors B-22 B1-9 Measured Shape Annealing Factors for Fort Calhoun B-23 B1-10 [ ] Standard Deviation of the Shape Annealing B-25 Factor for Each Channel j B1-11 Data for the Alternate Method Shape Annealing Factor B-26 l Uncertainty Evaluation B2-1 Sources of Flow Measurement Uncertainty for Omaha Reactor B-35 l B2-2 Components of Pressurizer Pressure and Coolant Temperature B-36 Uncertainty i
lB2-3 Peaking Factor Uncertainties B-37 B2-4 Components of Calorimetric Power Uncertainty B-38 B-2 l
LIST OF FIGURES Title Page B1-1 Fort Calhoun Shape Annealing Factor Cycle 8 Test Data B-28 CEA Position 25 B1-2 Fort Calhoun Shape Annealing Factor Cycle 8 Test Lata B-29 CEA Position 14 B1-3 Variation of Shape Annealing Factor Uncertainty With B-30 Shape Annealing Factor l
l B-3
Appendix B1 B1.1 Objectives of this Analysis Th2 f4ur peripheral shape index uncertainties which are incorporated into the setpoint analyses are: 1) the Separability Uncertainty, 2) the Calibration Unsertainty. 3) the Shape Annealing Factor Uncertainty, and 4) the Processing Uncertainty (uncertainties in the electronic processing of excore detector signels). Prior to the development of the methodology to combine these uncertainties statistically, they were combined additively to yield a net un2ertainty (Reference B1-1). The purpose of this part of the SCU program is to dsvelop the data base necessary- to support a procedure for statistically
. combining these four components of the axial shape index uncertainty. Table B1 sh:ws the values of the shape index uncertainties developed in this program.
B1.2 General Strategy Erch of the components of the axial shape index uncertainty is investigated in this Appendix in order to justify their statistical combination.
Tha Separability Uncertainty accounts for the difference between the core avirrge axial shape index and the peripheral axial shape index. This unctrtainty has four components:
- 1. -[ ]
- 2. '[ ]
3 [ l 4 [ ]
Tha Calibration Uncertainty accounts for errors introduced into the protection l
( system when the excore detec tor system is periodically adjusted to match I m2arured parameters of the core's power distribution.
The Shape Annealing Factor Uncertainty accounts for the error in the i
matsurement of the shape annealing factor.
I l
l l
B-4 l
Tha Processing Uncertainty accounts for the uncertainty in Ip calculated by
'the protection system. This uncertainty is taken into account by its explicit
.rcpresen at tion 'in the stochastic simulation procedure used to statistically combine all the uncertainties.
-B1.3 - Speeific Uncertainty Evaluations B1.3.1 Separability Uncertainty Tha Separability Uncertainty is a calculational unc er tain ty. . It is the unc%rtainty associated with inferring a peripheral shape index, I, p from a giv n known core average shape index I. The one dimensional shape anclysis used in the development of setpoints correlates the power to centerline melt (Pfdl) and the power to DNB, (Pfdn) to the core average cxici shape. Since the excore detector,5 respond only to the power distribution n0tr the periphery of the core, a calculated relationship is needed between I End I.
p This relationship, represented in the setpoint development by incorporation of the rod shadowing factors in QUIX (Reference B1-2), is currently calculated be means of the three dimensional code RCCS (Reference B1-3). The uncertainty in this calculation is the Separability Uncertainty.
i Tha Separability Uncertainty consists of four components: [
]. The components of the Separability Uncertainty are discussed in detail below.
l l
B1 3 1.1 1 1 l
l t .
B-5
Rod Shadowing Factor Method The peripheral axial shape index I pis defined in the following manner:
Du-Do I
p (B1-1) whsre Dg = x R(x) E (x) (B1-2)
' H/2 H/2 Dg a JdxR(x)P(x) (B1-3) 0 wh;rs D,D g are g the powers at the periphery of the upper and lower half of the core, respectively.
P (x) is the core average power distribution R(x) is the. rod shadowing factor for the rod configuration inserted at position x.
H is the height of the core.
Th2 rod shadowing factors are derived from the product of rodded and unrodded 2D pswer distributions and the assembly weighting factors, which account for tha contribution of each assembly to the excore detector response to a given powsr distribution.
m
'M t
l B-6
Asrembly Weighting Factor Method
'Th] Assembly Weighting Factor ( AWF) method consists of the following criculation of I :
p Wi P-I g t i
I p
- (B1-4) i i i wh' ire Pg is the axially integrated power of fuel assembly i I is the axial shape index of assembly i t
Wg is the weighting factor of assembly i Tha W g values are computed for those core edge assemblies which are the principal source of the excore detector's response.
Tha result of this procedure is that (
J.
[
]. This component of the separability uncertainty is es sh:wn in Table 1 along with the other components.
B1. 3.1.2 E ]
- =
~
_ B-7
'l
- 3. Ft. Calhoun Unit l's fuel loading patterns for Cycles 8 and beyond are modified low leakage designs. Only Cycle 8 and 9 designs
, curr;ntly exist and can provide appropriate data for the different rod einfigurations. [
J. It 10, therefore , conservative to assume that a C J.
This difference from previously reported [ ] unc.ertaintie s (Rafercnce B1-1 and B1-2) is partially due to the differences between Ft.
Cr;1h un Unit 1 and the BG&E and FP&L units' radial diameters (Ft. Calhoun has 133 assemblies, the others, 217 assemibies) and lead bank rod patterns (Ft.
C:1houn: 1 center and 4 peripheral CEAs, the others: 1 center. and 9 periph ral CEAs).
B1.3.1.3 Assembly Weighting Factor Uncertainties Th3 third component in the Separability Uncertainty consists of (
- 3. The AWF method is described in Section B1.3 1.1.
g _.
B-8
i
'[ 1. The k0 95/95 value is given in. Table B-1.
l B1.3.1.4 Uncertainty in the [
} l The fourth component of the Separability Uncertainty consists of the :
-t
.], the uncertainty in the calculated power
' distribution also results in a component of the Separability Uncertainty.
Sinse .Ft. Calhoun Unit 1 has a different diameter than do the Calvert Cliffs Units 1 and 2, St.- Lucie Unit 1, and Millstone point Unit 2 its [ ]
compIrisons of [ ] and [ ] should not be expected to st tistically correlate with those previously reported (References B1-1 and B1-
- 2) .. Consequently, only Ft. Calhoun data was examined for these two variables.
[ ] data points from Cycles 5, 6, and 7 of Ft. Calhoun's operation wero examined for Normality and Poolability using the W-test (Reference B1-6) '
and the Bartlett test (Reference B-18). All [ ] sets of data satisfied the n rmality and poolability conditions (Tables B-3, B 4, and B-5) .
_Fer: _,
Since 1e above result also [
J.
B1 3 2 Uncertainty on I, Calibration - of the excore detectors relative to the axial shape index as macsured by [
l
]. The components of this measurement uncertainty l censist of the uncertainty in [
] modeling the reactor power distribution.
B-9
Tho eclibration is performed [
- 3. This calibration is done near an ASI of zero so that
. ac:;urt . , of the shape annealing factor has minimal impact on the calibration recult.
Th3 measurement uncertainty on I is analyzed herein by a comparison of
[ 3. Differences between I '[ l were studied to determine uncertainties statistically. The mean and standard deviation of the respective diff;rences for each cycle were calculated, after which the data were examined ta datermine whether the cycle by cycle data could be pooled.
l Tcble B1-7 shows the standard deviations of the( } comparison of
__I.
B1 3 3 Shape Annealing Factor Uncertainty Th2 shape annealing fac to r , a, is an experimentally measured value which
, rslates the external axial shape index I, to the peripheral axial shape indsx, I .
p I
p
= aI, (B1-6)
( This factor accounts for the fact that the excore detectors respond to the power in both the upper and lower portion of the core. This signal mixing j yiolds shape annealing factors which are larger for detectors which are far from the periphery than for detectors which are near the periphery. The theorstical lower limit of a is unity.
B-10 l
The shape annealing factor is measured [ ] by inducing a xenon cGaillction ir. the core and measuring the external shape index of the j th cxtr.ro channel (If) along with the internal axial shape index 5 cs Ecsured by the CECOR system using incore instruments. The [
] slope of I versus Ij is the shape annealing factor : At the ~ b ginning of life I is assumed to be equal to I. p [
] as discussed ab;v3.
OPPD measured the Ft. Calhoun reactor's shape annealing factors using axial xcnon cscillations at the [ J. Available data for Cycle 1 consists of ccre average ASI's and [ '] from the excores. The dcts from Cycle 8 consists of core average ASI's, [
1.
Figurcs B1-1 and B1-2 provide plots of some of the Cycle 8 Ft. Calhoun I, -Io test data. These plots illustrate the fit of the straight line to th2 data.
In th2 Fort Calhoun Unit, the Safety Channel ex-ecre ASI, which is directly used to feed the APD LSSS trips, is also monitored with the plant computer.
Tha value monitored is the average Ie for the four ex-core channels multiplied by a c:nstant. This constant is the shape annealing factor for the average Ie signsl. Ie is averaged over a period of 10 min. For Cycle 1 the shape
! cnnsaling factor built into the calculation was 2.8. The value used for Cycle 8 w:s 2.86. This yields a [ ] indication of the monitored variables sinca both of these values are [ l than the measured shape annealing fcotgrs.
Vclu3s of the shape annealing factor for other C-E developed operating l reactors, which were reported in Reference B1-9 are also shown in Table B1-8.
l GPPD is, currently planning to replace the plant computer monitoring system with l cna that accounts for the individual c's for each of the ex-core channels.
Since individual channel SAF data is not readily available for Cycle 1, and sinc 2 the individual channel s's are very close to the average a in Cycle 8, it is reasonable to assume that the uncertainty relationship of the Cycle 1 and l Cyclo 8 [
B-ll
). Rese values are given in Table B1-
- 8. Table B1-9 shows the [ 1, and their individual
[ 3. deviations from the average of them all. Bis result is listed in Tablo B-10, along with the individual channel [ l standard deviation d;to for the other C-E reactors, as reported in References B1-5 and B1-9 Tha crror analysis previously performed on the Table B1-10 data , excluding the Ft. Calhoun information, resulted in a 95/95D ] standard deviation of
[ ].
Alt rnative presentation of the raw data for these same oscillations (R,ferences B1-10 and B1-11) also supported the validity of using this value of the SAF uncertainty. Since the available Ft. Calhoun . shape annealing factor tcct data is [ '], this alternative procedure was used. Table B1-11
. pr sents the data for this type of analysis for the other C-E reactors. Figure B1-3 presents Tables B1-9 and B1-11, all the shape annealing factor
[ ] standard deviation data, as a function of the average shape annacling factor. Over the range of SAF's shown, the [ ] standard d;vistion is less than [ ], thus the statistically determined value
[ 1 is a conservative estimate of the uncertainty of the
- sh:pe annealing factor for the Ft. Calhoun reactor.
B1 3 4 Processing Uncertainty Th3 Processing Uncertainty is discussed in Appendix B3 B1.4 [ J of the Peripheral Shape Index Uncertainties Th2 following [ ] have been identified in the development of p ripheral shape index uncertainties.
O i
e =
l B-12
y .
I Equation B1-10 is an identity. Equation B1-11 follows from the assumption that
't 1.
Equation B1-12 and the results summarized in Table 1 are used in the stochastic i simulctor described in Appendix A of this report.
1 B1.5 REFER ENCES
[ B1-1 "C-E Setpoint Methodology," CENPD-199-P, Rev. 1-P, March 1982.
B1-2 System 80 PSAR, CESSAR, Volume 1, Appendix 4A, Amendment No.
l I 3 June 3, 1974.
t B-13 L
!) B1-3 "The ROCS and DIT Computer Cod es for Nuclear Design",
CENPD-266-P, December 1981.
B1-4 A. Jonsson, W. B. Terney, M. W. Crump, "Evalution of Uncertainty in the Nuclear Power Peaking Measured by the Self-Powered Fixed In-Core Detector System", CENPD-153-P Rev. 1-POA, May 1980.
81-5 Statistical Combination of Uncertainty, Part 1," CEN-124 (B)-
December 1979 B1-6 " Assessment of the Assumption of Normality", ANSI N 15.15-197 B1-7 M. S. Bartlett, " Properties of Sufficiency Statistical Te st s ," Proc . o f Roy. Soc , A, 160, 1937, 268082.
B1-8 N. S. Dixon and F. J. Massy, " Introduction to Statistical Analysis," McGraw-Hill,1969
< B1-9 Statistical Combination of Uncertainties Part 1, CEN-123 (F)-
1980.
B1-10 Response to Second Round Questions on the Statistical Combination of Uncertainties Program (CEN-123 (F)-P, Part 1-3, Part 2, September 1981.
B1-11 "The Shape Annealing Factor Component of the Axial Shape Index Uncertainty at Millstone Point Unit 2," CEN-247(N)-P, March 1983 4
B-14 l
l l
TABLE B1-1 UNCERTAINTY [ ) COMPONENTS FOR THE EVALUATION OF THE PERIPHERAL SHAPE INDEX II)
K 095/95 (asiu) K(f)(2) Bias I. Separability Uncertainty g
II. Calibration Uncertainty (")
III. Shape Annealing Uncertainty (n)
IV. Monitoring System Processing UncertaintyI ") (asiu) - -
Nst2s on Table 1 (1) All components of the peripheral shape index have been tested for normality, and where indicated , satisfy that distributional requirement (n) .
(2) f a degrees of freedom.
(3) This Uncertainty is conservatively ( ).
l (4) This K o95/95 is for consistent sets of input data used by the uncertainty processors.
I I
B-15 l
t - - - -
TABLE B1-2 C 3
% LCad Bank 1 Second Bank BOC8 ECC8 BOC9 EOC9 AVG Insertion Insertion 0 -
25 -
35 -
45 -
50 -
55 -
65 05 75 15 82 22 85 25 90 30 95 35 1
1
\
i B-16
TABLE B1-3 Rod Bank Insertion i 1 All Rods Out (ARO)
R:g Bank 1 (25%)
Reg Bank 1 (355)
Rig B:nk 1 (45%)
Reg Bank 1 (505),
R:g Bank 1 (555),
R:g Bank 1 (655), Reg Bank 2 (05%)
. R:g Bank 1 (75%), Reg Bank 2 (15%)
Rig Bank 1 (82%), Reg Bank 2 (22%)
rig Bank 1 (85%), Reg Bank 2 (25%)
R;g Bank 1 (90%), Reg Bank 2 (30%)
Rig Brnk 1 (955), Reg Bank 2 (35%) .,
B-17 i
TABLE B1-4
. a
. . _ _ _ _ . 2.
OMAHA SCU NORMALITY TESTS n s2 s w sample size variance standard dev. test stat. Significance bias Cysla 5 Cyclo 6 J
. Cyclo 7 Totti
'T B-18
TABLE B1-5 OMAHA SCU NORMALITY TEST 1
n s2 s w sample size variance standard dev. test stat. Significance bias Ft. Calhoun Cyclo 5 Cycle 6 Cycle 7 Totsi ,
f f
B-19
TABLE B1-6 BARTLETT POOLING TESTS f
Number of Degrees Calculated Chosen Par a- of Standard Stand ard CGtcr Freedom yj v F (v ,v ) F (v ,V ) Deviation Deviation 2 cale 1 2 theor 1 2 9
E e l
I I
l l
B-20
TABLE B1-7 ROCS-CECOR COMPARISON OF I C 1 Mean Stand ard Number of Value, Deviation R actor Data Points asiu asiu t
- 1. St. Lucie I Cycle 1
- 2. St. Lucie I Cycle 2
- 3. Calvert Cliffs I Cycle 1 4 Cnivert Cliffs I Cycle 2
- 5. Calvert Cliffs I Cycle 3
- 6. C21 vert Cliffs II Cycle 1
- 7. Calvert Cliffs II Cycle 2
- 8. Millstone II Cycle 1
, 9. Millstone II Cycle 2
- 10. Fcrt Calhoun Cycle 5
- 11. Fort Calhoun Cycic 6
- 12. Fcet Calhoun Cycle 7 1
- 13. Fort Calhoun Cycles 5, 6, 7 r
'Thsse two cycles were pooled and were the basis of the uncertainty on I fcr Calvert Cliffs and St. Lucie 1.
+Th2se three cycles were pooled (Item 13). This pooled value is the basis of the uncertainty on i for Ft. Calhoun.
B-21
TABLE B1-8 MEASURED VALUES OF SHAPE ANNEALING FACTORS OPPD Cycle 1 Cycle 1 Cycle 1 Nov. 24-Dec.3, 1973 Dec. 6-8, 1973 Dec. 22-24, 1973 (ARO) (ARO) Bk4 13.45 Ins.
- f Cycle 8 April 11 - April 14, 1983 Ch nnel Bk4 0 121 Ins. Bk4 0 15 Ins.
D e
B-22
w TABLE B1 8
, (continued)
, N St. Lucie 1 ,
Cycle 1 Cycle 1A Cycle 2 Cycle 3*
June 1976 Jan. 1977 June 1978 June 20, 1979 Ch nn-1 505 Power SOS Fower 805 Power 801 Power Mw A s r
n, B ,
C t
- . l lD 's 1
'A. s ss J
10
' Note that a new streaming shield was placed in St. Lucie 1 at EOC2.
This new streaming shield changed the shape annealing factors.
C_^1v'rt Cliffs Unit 1
,7
. t -
Cycle 1 Cycle 2 Feb. 1975 April 7, 1977 Ch nnni 801 Power 50% Power 5
6 A
B C
D' _
s B-23 x
h.
.~ - . , - - , , . , - , , , - , . _ . ,,n~ w -._-- - - - ,-n-.r- . --me- ,-,. - ---, , ,,r -c
TABLE B1-8 (continued)
C-1 vert Cliffs 2 Cycle 1 .
Dec. 27, 1976 Ch nn"1 505 Power A
B C
D X
Y Millstone Point 2 Cycle 1 Cycle 1 Feb. 6-9, 1976 March 11, 1976 Ch nnel , 501 Power 801 Power B
C D
. -1 B-24
l l --
i TABLE B1-9 MEASURED SHAPE ANNEALING FACTORS FOR FORT CALHOUN Measurements SAF 6)
Cy lo 8, CEA position 12% IN Cyalo 8, CEA positon 15 IN Cy210 1, Nov 29-Dec 3,1973 ARO Cy le 1 Dec. 6-8, 1973 ARO
_ Cyclo 1, Dec. 22-24, 1973 (13 45-In)
Average a an [ ]
B-25
TABLE B1-10 IFRACTIONAdSTANDATiD DEVIATION OF THE SHAPE ANNEALING FACTOR FOR EACH CHANNEL
[ ]
Number of Standard Deviation Plant & Degress of Freedom per Channel Ch nn*1 f
=
St. Lucie 1 1
Crivert Cliffs 1 Millstone Point 2 l Millstone Point 2 l
l l
Fcrt Calhoun 1
- L O( 3 B-26
l TABLE B1-11 DATA FOR THE ALTERNATE METHOD SHAPE ANNEALING FACTOR UNCERTAINTY EVALUATION St. Lucie 1 Cycle (1, 2) Cycle 1A (50%, 80J Power) Cycle 36 4 Detector _a () a : ;
a B
C D i 9
1 10 . (
C-1 vert Cliffs 1
{
Cycle 1,
- 1
- a. . .. l {
B C
D Millstone 1 Cycle 1 (Reanalysis) Cycle 1 (Reanalysis)
[ [ 3
_ i
' .]i _
c .1
- 3. ., J a_ t ,a B
C D
.. . 1. a B-27
FIGURE B1-1 FORT CALHCUN SHAPE ANNEALING FACTOR CYCLE 8 TEST DATA 452 POWER AU. CHANNELS g, Cib PCS M (13% Ins) 3, a.15 --
8.15 L ID --
- s. la E a. 85 --
- s. es E -
4 -
g .
S s.es .- a. ca ik -
-e. 25 --
-a. 25
-e. la -
-0.la
-e.15 --
-0.15
-S.20 - - -
-c.20
-0. la -c. 25 2. 20 a. as B.10 EX-CORE A5; (ASILD B 28
h FIGURE B1-2 FORT CALHCUN SHAPE ANNEALING FACTCR CYCLE 8 TEST DATA 45x rovsa ALL 04ANfELS CEA ar POS = 14 (l% Ins) -
B.29 - - -
B. 22 B.15 -- -
B.15 ,
B.18 -- -
R. IB
@ 3.25 -- -
2.25 g . .
g . _
g w B.98 - --
C. 20 g . _
-B. 85 - - -B. 05
-9.10 -
.- -0.12 l_
-0.15 - -
-0.15
-8.29 4 y
-2.23
-3.10 -0.95 8.20 2. 35 3,10 EX-CCRE ASI (ASlu)
B-29
FIGUPI B1 3 VARIATION OF. SHAPE ANNEALING FACTOR. UNCERTAINTY WITH S%PE ANNEALI?E FACTOR m
W W
W W
W W
W W
W M
W W
W W
es eu 9
W W
m W
W W
W W
W W
W W
W W
W W
W W
W W
W D
em I
- 1. 0 2. 0 3. C 4. e G
B-30 -
l B2 Measurement Uncertainties I
l l
l l
I l
1 i
1 h
B-31
Appendix B2 B2.1 Basis for Flow Uncertainty The system rate for the Fe'>t Calhoun reactor is measured by means of the pump cccing A P method. This method makes use of measured presst:re differentials acrx2 the four pumps and pump casing AP vs. flow rate curves detarmined from t0sto en the pumps by the pump manufacturer.
Th3 c:asurement uncertainty on the system flow rate is evaluated by examining the uncertainties in each input parameter used in the flow determination. The un ert31nties come from three major sources:
A. Uncertainties arising from the pump calibration tests carried out by pump manufacturer.
B. Uncertainties arising from measurements taken at the reactor site.
C. Uncertainties arising from differences in pump installation between the pump test loop and the reactor site.
Tcble B2-1 provides a listing of the individual component uncertainties for cach of the major sources of uncertainties. The overall uncertainty on system fif.w rate is determined by [
.] uncertainty. The resulting overall (2a) uncertainty is found to b3 [ ] or ( ,,
) of the minimum al .owable indicated flow rate.
B2.2 Monitored Thermal-Hydraulic Parameter "ncertainty Distributions Th3 process instrumentation used in the TM/LP LSS3 and LCO consists of mersurements of cold leg primary coolant temperature and pressurizer pressure.
Unscrtianties in hot leg temperature measurements are considered in the cveluntion of the core power uncertainty and the primary coolant flow rate uncertainty.
Tho uncertainties in cold leg temperature and pressurizer pressure measurements are cbtained by considering the sources of uncertainty listed in Table B2-2.
Tha vclues of uncertainty listed are those specified by the instrument supplier 4
B-32
i far the worst case normal environment conditions. The distributions are c:nsidered to be normally aistributed about the normal signal with the un2ert inty listed equal to 2 standard deviations, j B2 3 . Power Peaking Factor Uncertainties
-Th] 3D Pcwer Peaking Factor Uncertainty (F g) and the Integrated Radial Power Pxking Factor Uncertainty (F R) used in these Fort Calhoun analyses (Table B2-
- 3) aro 'more conservative than those reported in C-E's uncertainty topical r port (Reference B2-1).
B2.4 OPPD Core Thermal Power Accuracy The unsertainty in core thermal power is derived from consideration of the calcrimetric relationships outlined in Equation B2- 1.
B, + B3-Be -B b Pwr n (B2-1) 3, 412, 141 where:
Pwr a core thermal power, MW Bw feedwater flow x (steam enthalpy - feedwater enthalpy), BTUhr B1 miscellaneous heat losses, BTU /hr Be a heat input due to pressurizer heaters and reactor coolant pumps, BTU /hr l
l Bb blowdown flow x (steam enthalpy), BTU /hr l
I
! Bectu;p each of the components of the heat balance equation (Eq. B2-1) are
! ind3 pendent of each other and because several of the components have multiple inputs (e.g. the RCP heat input is the sum of four individual pump power
. rcadings), the calorimetric power uncertainty is given by Equation 2.
Pwr a (2(( Pwr/ Mfw) Mfw)2 + 2(( Pwr/ Tfw) Tfw)2 +
2(( Pwr/ Pfw) Pfw)2 + 2(( Pwr/ Psec) Psec)2
(( Pwr/ B1) B1)2 + (( Pwr/ Qpzr) Qpzr)2 l
4(( Pwr/ Qp) Op)2 = 2(( Pwr/ Mbd) Mbd)2 +
i 2(( Pwr/ Tbd) Tbd)2)1/2 (B2-2) l B-33 l
l l
whera Mfw a feedwater flow, lb/hr Tfw a feedwater temperature, OF Pfw a feedwater pressure, psia Psec : secondary pressure, psia Qpzr a pressurizer heater power, KW Op RCP work power, KW Mbd a blowdown flow, Ib/hr Ibd a blowdown temperature, OF.
Tha 12 sigma value of each variable is given in Table B2 4 .
Tha I, ] total of [ ] is ( 3, giving a confidence Icvsl of ( l.
B2.5 References B2-1 A. Jonsson, W. B. Terney, M. W. Crump, " Evaluation of Uncertainty in the Nuclear Power Peaking Measured by the Self-Powered, Fixed In-Core Detector System," CENPD-153-P, Rev.1-P-A, May 1980.
l l
l l
l B-34
TABLE B2-1 SOURCES OF FLOW MEASUREMEffr UNCERTAINTIES FOR OMAHA REACTOR Equivalent Vessel Flow
- 1. Pump Test Loop Sources Rate Uncertainty 92c A. Test Loop Venturi Calibration B. Venturi AP C. Pump Casing AP D. Pump Curve Fit
. TOTAL 3( ) .
Equivalent Vessel Flow
- 2. R'setor Site Source Rate Uncertainty 82c A. Pump Cssing LP TOTAL 1 +2 b l .
Equivalent Vessel Flow
- 3. Test Loop to Reactor Site Variations Source Rate Uncertainty 92c A. Differences in Pump Casing Suction Pressure Tap Azimuthal Location Between Test Loop and Site and Difference in Suction Leg Geometry [ }
B. Pump Casing Area Differences Relative to Test Loop Casing TOTAL 3 1+2+3 k . .
[ ]
B-35 i
TABLE B2-2 COMPONE!frS OF PRESSURIZER PRESSURE AND COOLANT TEMPERATURE UNCERTAINTIES S nsor Pressure Temperature
?
R fcrence Accuracy 4
Ambisnt Temperature Effect Ambicnt Pressure Effect Drift C 11 Radiction Effect Power Supply Repr:ducibility ;
Sign =1 Conditioner Reference Accuracy N/A Ambicnt Temperature Effect N/A Drift [ ] N/A Powir Supply N/A Precision Resistor R2farence Accuracy ( ) [., "1 ~
TOTAL L J ( )
i l
I l
B-36 1
, - - , _ _ . . _ _ . . . _ , _ ._m _r , . _ _ _ - . , _ _ . - - - - . _ . -
TABLE B2-3 PEAKING FACTOR UNCERTAINTIES Praking Factor Uncertainty (1 of Power)
FR I I*
Fg [ ]+
+ Including [ !)
i n
i i
B-37
TABLE B2 4 COMPONENTS OF CALORIMETRIC POWER UNCERTAINTY V'rirble Error (MW) Error (1 Core Power)
Feedw;ter flow Feedwater temperature Fcedw ter pressure See:ndary pressure Misesilaneous losses Proscurizer heaters RCP h3at input Bicwd wn flow Blowdtwn temperature Tatel ( )
l
( 3-38 l
l r
l
- - - . .- . - - . _ _ . , _ . _ ~ . . _ . _ _ . . _ . . . - - , . _ _ _ . . _ _ , - . ,
B3 Trip System Processing Uncertainties l
l l
l B-39
Appendix B3 B3 Trip and Monitoring System Processing Uncertainties Th3 trip and monitoring systems discussed in this report recieve signals from the process and nuclear instrumentation and calculate the required signals to b3 compared against trip and monitoring setpoints. The uncertainty in these calculations as performed by the analog circuitry installed at the plant is inaluded in the overall combination of uncertainties.
. The simulation package models the process variable signal uncertainty at the point where the signal enters the reactor protection system trip circuits. The signcl uncertainty is the combined result of the allowed component tolerances in dcvices such as temperature and pressure sensors, resistors, power supplies, and transmitters. The combined effect of the allowed tolerances is estimated t
using a linearized form of the circuit model. The first-order terms produced by linaarizing the model are used to root-sum-square the individual component tolerances. . As the form of the probability density function for these talercnces is unknown, they are assumed to be Gaussians with the tolerance band rcpecsenting a 13 standard deviation limit. The assumption of a Gaussian
. distribution is generally satisfactory for representing the accuracy of tanuftetured components.
Th2 ccmbined effect of the individual uncertainties is also a Gaussian, as any linsar transformation of a Gaussian processi is also Gaussian. In the event l' that the individual uncertainty distributions are not Gaussians, as is assumed, j
tha central limit theorem shows that a linear combination of arbitrary I distributions tends to be Gaussian in form as the number of terms in the summation increase.
l As th2 overall uncertainties for each processor will depend to some degree upon the setpoints dialed in to the system, a simulation study was performed where nminci 'setpoints were varied in a random fa shion. [
3.
B-40
APPENDIX C Summary of Previous Methods For Combining Uncertainties C-1
Appendix C The 00thods previously used for the application of uncertainties to the LSSS ar3 presented in Reference C-1 and are summarized in this Appendix.
C.1 Limiting Safety System Setting on Linear Heat Rate ( APD LSSS)
Th] fuel design limit on linear heat rate at fuel centerline melt is rcprcsented by the ordered pairs (P I ).
p A lower bound is drawn under fdl' this " flyspeck" data such that all the core power distributions analyzed are C :opunodated. Using the previous methodology this lower bound was reduced by th] cpplicable uncertainties and allowances to generate the Local Power Density LSSS cs follows:
(C-1)
(C-2) wheros Tg = Azimuthal Tilt Allowance PU = Uncertainty in predicting local core power at the fuel design limit BMU = Power masurement uncertainty SAU = Shape annealing factor uncertainty RSU = Shape inder separability uncertainty l ACU = Axial shape index calibration uncertainty APU = Processing uncertainty C.2 Limiting Safety System Setting on DNBR (TM/LP LSSS)
Tha fuel design limit for the TM/LP trip on DNBR is represented by a combination of the ordered pairs (P fdn' p) and the DNB TMLL. A lower l
bound is drawn under the " flys peck" data such tnat all the core power l distributi0ns analyzed are accommod ated . Using the previous methodology this Icw;r bound was reduced by applicable uncertainties and allowances as follows:
C-2 1
L
1 1
(C-3)
(C-4) wher0:
Both components of the DNB LSSS were then represented by the following equations:
(C-5)
(C-6)
(C-7)
(C-8)
~
-t wheros l
l l
l RDT = Pressure equivalent of the total trip unit and processing delay l
time for the DBE exhibiting the most rapid approach to the SAFDL on DNBR.
PMU = Pressure measurement uncertainty l TPU' s Processing uncerainty l BMU = Power measurement uncertainty l TMU = Temperature measurement uncertainty l
l C.3 References C-1 CENPD-199-P, Rev.1-P,, "C-E Setpoint Methodology," March 1982.
1 l
l C-3
L t
COMBUSTION ENGINEERING, INC.
\
l O
bauu msu i ei ii .
CEN-257(0)-NP 9
STATISTICAL COMBINATION OF
~
UNCERTAINTIES PART 2 NOVEMBER, 1983 EGL COMBUSTION ENGINEERING, INC.
_. ._ J
LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED i BY CORSUBTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF:
A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IIWLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTAStuTY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS;OR R. m8m' ANY UABILITIES WITH RESPECT TO THE USE OF,OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, 1 METHOD OR PROCESS DISCLOSED IN THIS REPORT. l l
i L
STATISTICAL COMBINATION OF UNCERTAINTIES Combination of System Parameter Uncertainties in Thermal Margin Analysis for Fort Calhoun Nuclear Unit 1 l
l 1
J
ABSTRACT This report describer the methods used to statistically combine system
- parameter uncertainties in the thermal margin analyses for Fort Calhoun Nuclear
- Unit 1. A detailed description of the uncertainty probability distributions l and r;sponse surface techniques used is presented. This report demonstrates
.that there will be at least 95% probability with at least 95% confidence that
- th] limiting fuel pin will avoid departure from nucleate boiling (DNB) so long
- as tha minimum DNB ratio found with the best estimate design CETOP-D model remains at or above 1.22.
O O
ii
TABLE OF CONTENTS i
TITLE PAGE i
~ Abstract 11 Tablo of Contents 111
-List cf Figures v List of Tables vi
' Nomenclature and Abbreviations vii Subscripts and Superscripts viii (1.0 Suneary of Results 1-1
- 2.0 Introduction 2-1 !
2.1 Deterministic Method 2-2 2.2 Statistical Method 2-2 3.0 Sources of Uncertainty 3-1 3.1 State Parameters Used in the Study 3-2 3.1.1 Method for Selecting State Parameters 3-2 3.1.2 Axial Shape Sensitivity 3-4 ,
3.1.3 Primary System Flowrate Sensitivity 3-4 !
3.1.4 Pressure and Temperature Sensitivity 3-5 3.1.5 Final Selection of Most Adverse ASI 3-5 3.1.6 Most Adverse State Parameters 3-5 3.2 Radial Power Distribution 3-6 3.3- Inlet Flow Distribution 3-6 l
3.4 Exit Pressure Distribution 3-8 3.5 Enthalpy Rise Factor 3-8 3.6 Heat Flux Factor 3-8 l
3.7 Clad 0.D. 3-9 3.8 Systematic Pitch Reduction 3-9 l 3.9 Fuel Rod Bow 3-10 1
3.10 CHF Correlation 3-10 l 3.11 TORC Code Uncertainty 3-11 l l
111 J
TABLE OF CONTENTS (cont)
- 4.0 MDNBR Response Surface 4-1
! 4.1 TORC ~Model Used 4-1 4.2 Variables Ilsed 4-2 4.3 Experiment Design 4-3 4.4 Design Matrix 4-4 4.5 Response Surface 4-4
- 5.0 Combination of Probability Distribution Functions 5-1 5.1 Method 5-1 5.2 Results 5-1 5.3 Analytical Canbination 5-1 26.0 Application to Design Analysis 6-1 6.1 Statistically Derived MDNBR Limit 6-1 6.2 Adjustments to Statistically Derived MONBR Limit 6-2 6.3 Application to TORC Design Model 6-3 7.0 Conclusions 7-1 7.1 Conservatisms in the Methodology 7-1 8.0 Rsferences 8-1
- Appendix Apptndix A: Detailed TORC Analysis Used to A-1 Genarate Response Surface ,
1 iv
\
?
LIST OF FIGURES
- Figura Number Title Page 3-1 ~ N Inlet Flow Distribution (3-Pump) 3-13 Used to Generate Response Surface 3-2 Core Exit Pressure Distribution 3 (3-Pump) Used to Generate Response Surface 3-3 Core Wide Radial Power Distribution 3-15 Used to Generate Response Surface 3-4 Hot Assembly Radial Power Distribution 3-16 Used to Generate Response Surface 3-5 Channel Numbering Scheme for Stage 1 3-17 TORC Analysis 3-6 Intermediate (2nd Stage) TORC Model 3-18 s Used in Generating Response Surface 3-7 Subchannel (3rd Stage) TORC Model 3-19 Used in Generating Response Surfats
-N-1 Resultant MDNBR Probability Distribution 5-4 Function ,
i l
s 4
l l
l V l
LIST OF TABLES Tablo Na. Title Page 3-1 Ranges of Operating Conditions 3-20 for Which Response Surface is Valid 3-2 Determination of the Most Adverse 3-21 Axial Shape Index 3-3 Determination of Most Limiting 3-22 Flow Rate 3-4 Determination of Most Adverse 3-23 Operating Conditions 3-5 Final Selection of the Most 3 Adverse Axial Shape Index 3-6 Inlet Mass Velocity Ratio 3-26 4-1 System Parameter Included as 4-6 Variables in the Response Surface 4-2 Coefficients for MDNBR Response 4-7 Surface 5-1 Probability Distribution Functions 5-5 Combined by SIGMA A-1 Coded Set of Detailed TORC Cases Used A-2 to Generate Response Surface A-2 Comparison of TORC and Response Surface A-3 MDNBR for Cases Used to Generate Response Surface vi
. _ _ _ . . _ . - _ _ _ ._ )
N0ENCLATURE AND AB8REVIATIONS b- coefficient in response surface c constant in response surface f arbitrary functional relationship k number of independent variables in response surface
- n number of items in a sample p.d.f. probacility distribution function psd pounds per square foot psia pounds per square inch (absolute) x system parameter -
y state parameter z MDN8R values predicted by response surface ASI axial shape index (defined in Table 3-2)
CE Combustion Engineering CHF Critical Heat Flux DN8 Departure from Nucleate Boiling DNBR Departure from Nucleate Boiling Ratio F Fahrenheit F"q engineering heat flux factor MDN8R Minimum Departure from Nucleate Boiling Ratio T temperature T-H thennal-hydraulic a constant used to code system parameters (Table 4-1) 8 constant used to code system parameters (Table 4-1) n coded value of system parameters (Table 4-1) y mean ,
a standard deviation A denotes difference between two parameters vii
~ ' _ _ _ . _ - _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _
subscripts denotes vector quantity _
1 index in conditions at reactor core inlet j index superscripts denotes estimate m
- degrees average value viil 1
1.0 Sumary of Results Methods were developed to combine statistically the uncertainties in reference thermal margin (detailed TORC) analyses. These methods were applied to Fort Calhoun Nuclear Unit 1. This work demonstrated that there will be at least 951 probability with at least 95% confidence that the limiting fuel pin will avoid departure from nucleate boiling (DNB) so long as the Minimum DNBR Ratio (MDNBR) found with the best-estimate design CETOP-D model remains at or above 1.22. The 1.22 MNBR limit includes allowances for reference analysis input uncertainties but does not take into account uncertainties in operating conditions (e.g., monitoring uncertainties).
h e
1 -1
2.0 Introduction CE's thermal margin methodology for Fort Calhoun Nuclear Unit I has been modified by the application of statistical methods. This report focuses en the statistical combination of reference thermal-hydraulic (T-H) code input uncertainties. This combination was accomplished by the generation of.a Minimum DNBR (MONBR) response surface and the application of Monte Carlo methocs.
A complete description of the methods used in the statistical combination is provided in this report. The remainder of this section outlines the previous deterministic and the new statistical thermal margin methods.
52ction 3.0 describes the sources of uncertainty that were considered in this effort. Section 4.0 describes the MONBR response surface. The application of Monte Carlo Methods is discussed in Section 5.0, and results are presented. Finally, Section 6.0 descr:bes the changes in d; sign analyses that result from this work, in particular, the resultant MDNBR limit of 1.22 which accommodates the T-H uncertainties described in this report.
2-1
.= . _ _ . - - _ - ----- - D
2.1 Deterministic Method Two types of problem dependent data are required before a detailed T-H code can be applied. The first type of data, system parameters, describe the physical system, such as the reactor geometry, pin-by-pin radial power
, distributions, inlet and exit ficw boundary conditions, etc. These are not monitored in detail during reactor operation. The second type of data, state parameters, describe the operational state of the reactor. State parameters are monitored while the reactor is in operation and include the core average inlet temperature, primary loop flow rate, primary loop pressure, etc.
C-E thermal margin methods (2-1) utilize the TORC (2-2) and CETOP-D (2-3) codes and the CE-1 CHF correlation (2-4) with two types of models. The first model, detailed TORC, is tailored to yield best estimate MDNBR prediction:: in a particular fuel assembly for a specific power distribution. Both system and state parameter input are used in a detailed TORC model. The second model, the CETOP-D design model, requires only state parameter data and may be applied to any fuel assembly for any power distribution that is expected to occur during a particular fuel cycle. System parameters are fixed in the design model so that the model will yield either accurate or conservative EMBR predictions for all operating conditions within a specified range.
Design model EMBR results are verified by comparison with results from the detailed model of the limiting assembly in the deterministic method.
After the design model is shown to yield acceptable (i.e., accurate or conservative) results, additional adjustment factors are applied to account for uncertainties in system parameter input to the detailed model. For example, engineering factors are applied to the hot subchannel of the design model to account for fuel fabrication uncertainties. These adjustment factors, though arrived-at statistically, are applied in a deterministic manner. That is, although each adjustment factor represents a 95/95 probability / confidence limit that the particular parameter deviation from nominal is no worse than described by that factor, all factors are applied simultaneously to the limiting subchannel. This is cquivalent to assuming that all adverse deviations occur simultaneously in the limiting subchannel.
2.2 Statistical Method The probability of all adverse system parameter deviations from nominal occurring simultaneously in the limiting subchannel is extremely remote.
With a more reasonable, demonstrably conservative method, the probability of system parameter input being more adverse than specified can be taken !
into account statistically, as described herein.
The improved methodology involves a statistical combination of system parameter uncertainties with the CHF correlation uncertainties to determine a revised design ENBR limit. Sincs uncertainties in system parameters are taken into account in the derivation of the new MDNBR >
limit, no other allowance need be made for them. A best estimate design :
CETOP-D model is therefore used with the revised MDNBR limit for thermal margin analysis. This best estimate design model yields conservative or 2-2 I
i
l
! accurate W NBR results when compared with a best estimate detailtd model.
The resultaht best estimate design model and increased WNBR limit ensure eith at least 95% probability and at least a 95% confidence level that the liciting fuel pin will avoid departure from nucleate boiling if the predicted MONBR is not below the limit E MBR.
2-3
- _ - _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ J
l l
3.0 Sources of Uncertainty Four types of uncertainty are identified in MONBR predictions from the TORC code:
- 1) numerical solution parameter uncertainty
- 11) _ code uncertainty 111) state parameter uncertainty l iv) systcm parameter uncertainty Numerical solution parameters are required input that would not be necessary if analytic methods could be used (e.g., radial mesh siza, axial mesh size, convergence criteria, etc.). The uncertainties associated with these
!parametcrs are dealt with in a conservative manner (3-1) in C-E's present
. methodology.
i The numerical algorithms in the TORC code represent approximations to thee icons;rvative equations of mass, momentum, and energy. Because of the
- apprcximations involved, an inherent code uncertainty exists. This uncertainty
- is iglicitly dealt with in the CE-1 CHF correlation as discussed in Section
- 3.11. However, according te the NRC guidelines (3-5) an additional penalty is
- incorp: rated into the present analysis to take into account the TORC code
'uncsrtainty explicity.
lStato parameters define the operational state of the reactor. Uncertainties in
'thisa parameters are included when the CETOP-0 model is ' incorporated into the op: rating algorithms.
-As' explained in Section 2.1, system parameters describe the physical l environment that the working fluid encounters. This report establishes the equivalent MDNBR uncertainty that results from a statistical combination of uncertainties in system parameters.
3-1.
)
3.1 StathParametersUse{intheStudy Gen: ration of response surface which simultaneously relates MDNBR to both system and state parameters would require an excessive number of detailed TORC analys:s. Consequently, a conservative approximation is made and a response surfaca relating MONBR to system parameters only is created. To achieve consIrvatism, it is necassary to generate the surface for that set of state parameters which maximizes the sensitivity of MONBR to system parameter variations. That is, the response surface can be described as:
PONBR = g(x,yo )
wh2ra: _x, is the vector of system parameter 3, and yo_ the vector of state parameters, is selected such that blMoa6 A) , ,,x; mum 3 21. _4_
Th2 set of state parameters, yo, that satisifies the above relation, is rafcrrcd to as the most adverse sat of state parameters. The generation of tha rcsponse surface is discussed in Section 4.3.
I j3.1.1 Method for Selecting State Parameters
- Allowable operating parameter ranges are presented in Table 3-1. These ranges larsbaseduponreactorsetpointsincludingmeasurementuncertainty. The r;sp
- nse surface must he valid over these ranges. As intficated above, a single snt of operating conditions is chosen from these ranges to maximize the sensitivity of MDNBR to Eystem parameters, i This sst of state conditions is determined from detailed TORC analyses in the following manner. Three TORC analyses are performed for a single set of l
op2 rating conditions. In the first analysis, nominal system parameters are 3-2.
used and the enre average heat flux is chosen to yield a MONBR in the neighbor-
. hood of 1.19. A second TORC analysis uses the same heat flux and operating conditicns but has all system parameters (i.e., pitch, clad 0.D., enthalpy Iris]) psrturbed in an adverse direction (i.e., MONBR decreases). A third TORC
- analysis uses the same heat flux and operating conditions but has all system
- parametcrs perturbed in an advantageous direction (i.e., MONBR increases). The MON 8R from the " adversely perturbed" analysis is then subtracted from the
- nominal" MONBR to yield a MONBR(ADVERSE) for the chosen set of operating conditions and the same is done for the TORC analysis where system parameters
- are "p;rturbed advantageously". That is,
" Nominal" MONBR " Adversely Perturberi" MONBR (3.1)
ENBRADVERSE=
MONBRADVANTAGE00S=
" Nominal" MONBR " Advantageous Perturbed" MONBR (3.2)
The p2rcent change in MONBR is then determined according to the following
.ralaticnships:
% ChangeA0 VERSE = ( MONBRADVERSE /" Nominal" MONBR) x 100 (3.3)
/
%Cha W AnVANTAGECUS= f MONBR ADVANTAGEOUS " Nominal" MONBR) x 100 This process is repeated for several sets of operating condi: ions to establish
.tha s:nsitivity of the MONBR throughout the allowable opera *ing range. Sets of opIrating conditions used in this sensitivity study are chosen to envelop
- tha required ranges shown in Table 3-1. The set of state parameter values
- which maximizes the quantity (% ChangeADVERSE + % ChangeADVANTAGE0US) is
,ch:stn as the most sentitive set of state parameter values. This set is
- referred to as the set of "most adverse" state parameter values and is used in
- dstsrmining the response surface.
iSinco MONBR is a smoothly varying function of these state parameters (3-2), it
- is likely that the theoretical set of most adverse state parameters will be l
3-3.
similar to the most adverse set found by the method dnscribed above.
. Sir.ilarly, it is also highly unlikely that MONBR sensitivities observed with tha theoretical most adverse set will differ appreciably from MONBR s ssnsitivities which occur using the most adverse set found by the above method.
Inist flow and. exit pressure boundary conditions for the model are shown in Figure 3-1 and 3-2. Core-wide and hot assembly power distributions are shown in Figure 3-3 and 3-4 respectively. The detailed TORC analysis (3-1) consists
=of three stages. A core-wide analysis is done on the first stage, in which l cach fuel assembly near the limiting assembly is modeled as an individual channal. Crossflow boundary conditions from the first stage are applied in the
. sec:nd stage to a more detailed model of the neighborhood around the limiting assembly. Each quadrant of the limiting assembly is represented by a channel in tha second stage analysis. Cross flow boundary conditions from the second stage.,,are applied to the subchannel model of the limiting assembly hot quadrant in tha third stage, and the MONBR is calculated. TORC models for the first, s:cend, and third stages of the model used in the sensitivity study are shown in Figures 3-5, 3-6, and 3-7 respectively.
3.1.2 Axial Shape Sensitivity 0; tailed TORC analyses as described in Section 3.1.1 are performed to dittrmine the most adverse Axial Shape Index ( ASI) to be used in the analysis.
Data from these calculations are listed in Table 3-2. From these results it is concluded that (asiu) are the prime candidates for the most advarse ASIS.
l 3.1.3 Primary System Flowrate Sensitivity Having selected the probable most adverse ASIS in Section 3.1.2, detailed TORC
'analysss as tiescribed in Section 1.1.1 are performed to determine the most adv;rsa flow rate to be used in this analysis. Data from these calculations are listed in Table 3-3. , Based upon the results pres,ented in this table, it is concluded that for ASI = , both percent and percent flow rates are tha most adverse ones. For ASI = percent flow rate is the most advarsa one.
3-4.
l l
I f3.1.4 Pressure and Temperature Sensitivity Having determined the probable most adverse ASIS and flow rates in Sections 3.1.2 and 3.1.3, respectively, detailed TORC analyses are performed using the method described in Section 3.1.1 to determine the pressure and temperature to be us:d in defining the response surface. Data from this analysis are found in Table 3-4 Also included in this table are the results obtained from an
~
analysis performed with ASI = The reason for including this ASI in the prasInt analysis is based upon the past experience (previous SCtl programs) in which this ASI was found to be the most adverse one. From the results prasented in Table 3-4, it is c,oncluded that the most adverse flow rate, prsssure and temperature are ,
percent,p psia and , respectively and tha probable most adverse ASI is 3.1.5 Finai Selection of Most Adverse ASI Having determined the most adverse flowrate, pressure and temperature in S:ctions 3.1.3, and 3.1.4, and the probable most adverse ASIS in Section 3.1.2, detailed TORC analyses are performed using the method described in Section 3.1.1 for the final selection of the most adverse ASI. Data from these calculations are listed in Table 3-5. As expected, the sensitivity results obtainId with each ASI are very close to one another. The final most adverse ASI is -0.079)
. J 3.1.6 Most Adverse Parameters As cxplained in Section 3.1, the set of state parameters' chosen for use in gin: rating the response surface should maximize MONBR sensitivity to variations in system parameters; this is the most adverse set of state parameters. The most sensitive set of parameters is chosen so that the resultant MONBR unc:rtainty will be maximized. This introduces conservatism into the overall tr2atment of uncertainty.
3-5.
. i
c Fran Sections 3.1.2, 3.1.3, 3.1.4, and 3.1.5 it is seen that the state para- -
, met rs which maximize MDNBR sensitivity are:
l _ -.
where 100% design flow is 197,000 gpm.
3.2 Radial Power Distribution Inh 2rsnt conservatism in the thermal margin modeling methodology makes it unnicsssary to account for uncertainties in the radial power distributions that are uspd in, TORC DN8 analyses.
' 3.3 Inlet Flow Distribution An inist flow boundary condition is used in detailed TORC analysis. Ratios of tha lccal to core average mass velocity are input for every flow channel in the ccro-wide analysis. The inlet flow distribution used in the detailed TORC cases to generate the Minimum DNBR response surface 1,s shown in Figure 3-1.
Tha core inlet flow distribution in Figure 3-1 is derived from scaled flow model test results for the Omaha reactor. The number of test runs on the flow modal is very limited. Because of this factor, the following procedure was adopt;d to define the core inlet flow distribution and to account for uncsrtainties in the core inlet flow data.
A quarter core or quadrant map of the 4-pump core inlet flow distribution was constructed by " folding over" the core-wide flow distribution map from the
' single 4-pump test run made on an open-core version of the Omaha model. The basis for this folding over technique is that the reactor geometry has quadrant symmetry and the flow distribution is also expected to be generally symmetric 3-6.
a
a quadrant basis. The resulting quadrant map (designated Map #1) has four bs rved values of inlet flow per fuel assembly location, except for locations un thn ctre centerlines. There, fuel assemblies have fewer observed values.
average quadrant core inlet flow distribution map (designated Map #2) was
< hen constructed by averaging the observed values in each fuel . assembly ccaticn based on up to four observed values.
he quadrant Map #1 containing all of the observed inlet flow values was (xamined to identify the lowest observed fuel assembly inlet flow value for
<ach fu21 assembly location. Each of these lowest observed values was further keducId by the measurement error of Wj /W = 0.03. These minimum inlet flew
'alu s for each fuel assembly were then also recorded on the average quadrant ra inlet flow distribution Map #2.
i (t this point, each assembly box in Map #2 has two inlet flow factor values, a uadrant averaged value and a minimum value. The final 4-pump inlet flow
.istribution map, designated Map #3 was determined by first selecting the ccatien of the limiting hot fuel, assembly. The inlet flow factors for the hot ssembly and its immediate neighbors were obtained from the minimum values for ha appropriate assembly locations in Map #2. The inlet flow factors for the emaining fuel assembly locations were obtained from the quadrant averaged actors in Map #2, but adjusted upwards by an equal increment that offsets the lost" flow at the hot assembly and its imediate neighbors. The resulting sora inlet flow map constitutes the final Map #3 for 4-pump operation.
'he 3-pump core inlet flow distribution map was constructed using the above
. scribed 4-pump open-core inlet flow distribution Map A3 and test data from an arlicr Omaha reactor flow model tested withh a closed core. The closed core
.ata consisted of 4-pump and 3-pump test data. A core-wide inlet flow
.iffcr:nce map was obtained from the closed-core data that provided the nformation:
Wh inlet j inlet a q
_ W}
W/4-pump W/3-pump 3-7.
.i
for each fuel assembly location. Adjustments were made to the flow inciement
- map to generate the equivalent map for an open-core. Typically, the quadrant
' clos;st to the non-operating cold leg has the largest flow increments between 3-pump and 4-pump operation. Increment values from this worst quadrant were subtracted from the final 4-pump quadrant Map #3 to arrive at the final 3-pump c:ra inlet flow map shown in Figure 3-1. Table 3-6 provi;as the quadrant avsraged values and the depressed (minimum) values of inlet mass velocity ratio for the limiting assembly location and its immediate neighbors.
Sinca inlet flow distribution uncertainties are taken into account in the dsterministic manner described above, these uncertainties are not included in
! tha statistical analysis described in this report.
3.4 Exit Pressure Distribution
! Sensitivity studies indicate that MDNBR is extremely insensitive to variations
- in tha exit pressure distribution (Ref. 3-4). Consequently, the exit pressure distribution need not be included in the MDNBR response surface.
i3.5 Enthalpy Rise Factor
!Tha engineering enthalpy rise factor accounts for the effects of manufacturing ideviations in fuel fabrication from nominal dimensions and specifications on i tha enthalpy rise in the subchannel adjacent to the rod with the MDNBR (3-3).
Tolcrance deviations in fuel pellet Mensity, enrichment, and diameter averaged
' ovgr the length of the fuel rods are used to compute this factor. Tolerance licits and fuel specifications ensure that this factor may be characterized lctns3rvatively by a norma,1 p.d.f. with a mean of and standard deviation at 95% confidence of .
3.6 Heat Flux Factor Tha cngineering heat flux factor is used to take into account the effect on local h:at flux of deviations from nominal design and specifications that occur in fabrication of the fuel, Random variation in pellet enrichment, initial pallet density, pellet diameter, and clad outside diameter (0.D.) contribute to 3-8
tha effects represented by the engineering heat flux factor. Tolerance limits and fual specifications ensure that this factor may be characterized conssrvatively by a normal p.d.f. with a mean of and standard deviation 6 at 951 confidence of .
3.7 Clad 0.0.
Variations in clad diameter change subchannel flow area and also change the 1ccal heat flux. The impact of both random and systematic variations in fuel
' clad 0.0. on the local heat flux is accounted for by the engineering factor on hIat flux, discussed in Section 3.6. The effect of random variations in clad 0.0. on subchannel flow area is included in the rod bow penalty, discussed in S2ction 3.9 The effect of systematic variations in clad 0.0. on the subchannel hydraulic parameters is addressed here.
Manufacturing tolerances on the fuel clad allow for the possibility that the l clad diameter will be systematically above nominal thrcughout an entire fuel assembly. That is to say, the mean as-built value of the clad 0.0 may differ
' from the nominal value. The distribution of the meal clad 0.0. for fuel assemblies may be characterized by a normal p.d.f. As-built data for 14 x 14 typa Exxon fuel indicate that on conservative bases the maximum_
mean value of
' tha systematic clad 0.0 at the 95% confidence level is inches and the i '
standard deviation of the mean at the 95% confidence level is inches.
l Tha double accounting for both the adverse effect of a decrease in clad 0.D. in l tha Engineering facter on heat flux and the adverse effect of a systematic, i incraase in clad 0.0. on subchannel flow area adds conservatism to the l analysis. -
1 I
i 3.8 Systematic Pitch Reduction i
Tha rod bow penalty, discussed in Section 3.9, takes into account the adverse effcct on MDNBR that results from random variations in fuel rod pitch. The rod bow ptnalty does not take into account the adverse effect of systematic variations in fuel rod pitch. This systematic pitch reduction effect must be discussed separately.
3-9.
Manufacturing tiolerances on fuel assemblies allow for the possibility that the ,
ps-built fuel pitch will be less than nominal throughout an entire fuel bssembly. Thus the systematic pitch refers to the mean value of the pitch in an assembly. The systematic pitch distribution is assumed to be a normal pistribution characterized by the mean value of the pitch and the standard scviationofthatmeanvalue.
As-built gap width data for 14 x 14 type Exxon fuel indicate that on conserva-
)ivebasesthe minimum mean value of the systematic gap width at the 95%
fonfidence level is , ,,
inch 4s and the standard deviation of the mean at the 95% confidence level is inches. This combined with the information 1 ' ~
provided on clad 0.D. in Secticn 3.7 gives minimum mean value of the systematic
~ ~
Ditch at the 95% confidence level equal to inches and the standard
~ ~
kviation of the mean at the 95% confidence level' equal to inches.
p.9 Fuol Rod Bow I
he fual rod bow penalty accounts for the adverse impact on MONBR of random pariaticns in spacing between fuel rods. The methodology for determining the od bow penalty is the subject of a C-E topical report (3-6). Rod bow perialties for the Fort Calhoun Nuclear Unit have been derived by application of hhemethodsofAppendixGofthatreport(3-7). The penalty at 40,000. MWD /MTU burnup is 0.5% in MDN8R. This penalty is applied directly to the new MONBR imit dsrived in Section 6.
p.10 CHF Correlation
%Do C-E 1 Critical Heat Flux (CHF) correlation (3-8) (3-9) is used in the TORC sode(3-1)todeterminewhetheradeparturefromnucleateboiling(DNB)will 1
3-10 l
't occu r. This correlation is based on a set of 731 data points. The mean of the ratio of observeyi to predicted CHF using the CE-1 correlation is 0.99983, while ,
tha standard deviation of that ratio is 0.06757. CHF correlation uncertainty may b3 characterized by a normal distribution with a mean 0.99983 and standard d viation of 0.06757. This yields a 1.13 WNBR limit to satisfy the criterion of "95% probability at the 95% confidence level that the limiting fuel pin does n;t cxperience DNB". However, because the NRC staff has not yet concluded its review of the CE-1 correlation, a 5% penalty has been applied; this raises the 95/95 WNBR limit to 1.19 This penalty may be conservatively treated by displacing the above normal distribution by +0.06 producing a displaced normal distribution with a mean of 1.06 (.99983 + 0.06) and the same standard deviation as above.
NRC has stated in the past during their reviews of C-E various SCU program rep;rts that the effect of so called " prediction uncertainty" in the CHF corralation must be included in the calculation of new MONBR limit. Inclusion of this uncertainty in the calculation has little effect on the MONBR limit, (MnNBR increases from 1.132 to 1.137) however, it has been incorporated into this analysis as discussed in Section 6.1 according to the guidelines provided by thm NRC in Reference (3-5).
l l 3.11 TORC Code Uncertainty l
Tha TORC computer code (3-1) represents an approximate solution to the conserva-l tion equations of mass, momentum, and energy. Simplifying assumptions were mada, and experimental correlations were used to arrive at the algorithms contained in the TORC code. Hence, the code has associated with it an inherent l calculational uncertainty. Comparisons between TORC predictions and experi-mental data (3-1) (3-10) have shown that TORC is capable of adequate predic-tions of coolant conditions. .
As.cxplained in Section 5.0 of Reference (3-10), the TORC code was used to d;termine local coolant conditions from data obtained during the CE-1 CHF exp;riments. These local coolant conditions were then used to develop the CE-1 3-11.
i
- CHF correlation. Thus, any calculational uncertainty in the TORC code is l
! implicitly included in the MDNBR limit that is used with the TORC /CE-1 package in thsrmal margin analyses.
- How2ver, NRC in their previous SCU reviews have consistently stated that iuncartainties exist for all subchannel codes, and that consistent application
- cf a code, such as in the case of DNB data analysis and DNB evaluation, does i n:t nullify this uncertainty. Based upon this argument, NRC has stated in the
- past that a 4% uncertainty (2r-value) must be imposed to cover code uncer-taintiss, plus an additional 1% (2r value) for transient code uncertainties.
l Acccrding to the NRC guidelines (3-5), the 4% and 1% values are combined
' statistically with the standard deviation of the response surface to assess the
- sffect of code uncertainties on the DNBR limit. As indicated in Section 6.2, a
- TORC code uncertainty penalty factor on MDNBR calculated based upon the NRC
. guid211nes (3-5) has been included in the present analysis.
I i
l l
l l
l l
3-12. !
i f
i l
FIGURE 31 INLET FLOW DISTRIBUTION (3-PUMP) USED TO GENERATE RESPONSE SURFACE 1
NOTE: Infonnation provided in this figure was also used in the sensitivity study.
3-13
FIGURE 3-2 CORE EXIT PRESSURE DISTRIBUTION (3-PUMP) USED TO GENERATE RESPONSE SURFACE l
- NOTE
- Information provided in this figure was also used l
in the sensitivity study.
3-14 l
~
~
FIGURE 3-3 CORE WIDE RADIAL POWER DISTRIBUTION USED TO GENERATE RESPONSE SURFACE NOTE: Information provided in this figunt was also used in the sensitivity study.
3-15
i- .
FIGURE 34 HOT ASSEMBLY ROD RADIAL POWER DISTRIBUTION NOTE: Information USED TO GENERATE RESPONSE SURFACE provided in this figure was also used in the sensitivity study.
3-16
l l
l I
NOTE: CIRCLED CHANNEL NUMBER k
DENOTES A FLOW CHANNEL IN WHICH SEVERAL ASSEMBLIES 1 2 HAVE BEEN " LUMPED" INTO T H ANALYSIS CHANNEL NUMBER IN FIRST STAGE TORC 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 8 -
___J i U a @ n a g g ;
I 1 I s- _. . _ _ ,1
.___,___3_. _
! 1 I i t e FIGURE 3-5 CHANNEL NUMBERING SCHEME FOR STAGE 1 TORC ANALYSIS
- 3-17
- F - W h
M m a
M FIGURE 3-6 INTERMEDIATE (2ND STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE 3-18
- - - - ~,---.-,.4, -
.,,-r,
. , ,, - , , . _ -.m- ,, -,, , y, . , - -. ._ , , , . ,
em' l
l l
FIGURE 3 7 SUBCHANNEL (3RD STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE 3-19
. .s..--
TABLE 3-1 Ranges of Operating Conditions for which Response Surface is Valid Operating Conditions Units Range Axial Shape Index *
-0.30<A.S.I.<+0.30 Inlet Temprature F 465<T
_j g580 System Pressure psia 1750<Psys<2400 System Flow % Design
- 75<W<120 NOTES *: See note (1) on Table 3-2 for definition of axial shape index
+ Thermal Margin Design Flow = 197,000 GPM i
l l
l l 3-20 l
l
4 TABLE 3-2 ,
Determination of Most Adverse Axial Shape Index Minimum DN8R Nominal System Parameters System Parameters '
% Change Adverse Axial System Adversely Advantageously + % Change Advantageous (2)
Shape Index Parameters Perturbed Perturbed t
-0.359
- -0.317 y -0.070 i
m
~
0.000 0.317 0.337 ;
L o L/2 (1) Axial shape index = I F,d, - / F zd, FZ = core average axial peaking
-L/2 o factor at axial location Z L/2 I F,d z O = core mid-plane
. -L/2 (2) See Section 3 L = active core length 1 Operating Teny = 545* F Conditions Pres. = 2l00 psia Flow = 75% design t
4
TABl.E 3-3 Determination of t.imiting Flow Rate
- Minimum DNRR Nominal System Parameters System Parameters % Change Adverse Axial Flow System Adversely Advantageously Shape Index +% Change AdvantageousI2)
Rate Parameters Perturbed Perturbed
- -0.070 120%
-0.070 100%
~
. us g -0.070 75%
- 0.000 120%
0.000 100%
i 0.000 751 1 . .
I
! Operating Conditions 100% Design Flow = 197,000 GPM i
- Temperature = 545*F
) Pressure = 2l00 psia j
1 l
i
'l i
l TARLE 3-4 a
Determination of Most Adverse Operating Conditions Minimun DNBR i i System System Axial Nominal Parameters !
Shape Temp / Press / Flow Parameters
! System Adversely Advantageously % Change Adverse }
Index *F / psia / % design Parameters Perturbed !
l -
Perturbed + % Change Advantageous '
j' -0.07 465 / 1750 / 75
-0.07 465 / 2400 / 75 u, -0.07 545 / 2100 / 75 i
n2 .
-0.07 580 / 1750 / 75 !
I
' l,
-0.07 580 / 2400 / 75 .-
j -0.07 465 / 1750 / 100
! -0.07 465 / 2400 / 100 i
-0.07 545 / 2100 / 100
-0.07 580 / 1750 / 100 I
-0.07 580 / 2400 / 100 j
0.000 465 / 1750 / 75 . . - - - . . .
i i
i
,r t
TABLE 3-4 (cont)
Determination of Most Adverse Operating Conditions Minimun ONRR System System Axial Nominal Parameters Parameters Shape Temp / Press / Flow System. Adversely ,
Advantageously 1 Change Adverse Index *F / psia / % design Parameters Perturbed Perturbed + % Change Advantagesus 0,000 465 / P400 / 75 h
0.000 545 / 2100 / 75 ~
0.000 580 / 1750 / 75 0.000 580 / 2400 / 75 Y
21 0.337 465 / 1750 / 75 -
0.337 465 / 2400 / 75 0.337 545 / 2100 / 75 0.337 580 / 1750 / 75 0.337 580 / 2400 / 75 0.337 580 / 1750 / 100 0.337 5R0 / 1750 / 120 . . . . . . . .
' l ' llll l l lli1 l li !
ljl
)
2 I
s u
o g
e ea st rn ea _
vv dd AA ee gg nn aa hh CC x %%
e d
I n +
p e
a h
S l
i a
x s A ry el e t sd s eue mob r aer -
5 e rgu
- v aat 3 d Pt r A ne -
E L
map B
t s ev td A o sA T M y S
e h
t f
o s r
n e o R t i R e yd t N ml e c D aeb e rsr l
e m u aru Pet S m vr i md e _
l a i n eAP t
n M s i y F S s
r l
aet me -
nt e s ism mya n oS r o N a - i _
P t i
d ===
n o
C e r
g u n t e x i ar e t ru l d a es an r psw iI p
e meo erl x 5 4 0 9 Ae 0 5 6 7 7 4 O TPF p 0 9 0 0 0 0 0 a 0 h 0 0 0 0 0 S -
0 - - - - -
"e y, l I \'
Table 3-6 Inlet Mass Velocity Ratios for the Limiting Assembly ,
and its Innediate Neighbors Fuel Quadrant Depressed (Minimum)
Assembly Averaged Value to Account for Number
- Value Uncertainty
~ = ., . -
- Assembly numbers refer to Figure 3-1.
3-26
-. ____ _________ _ _ __ i
4.0 N)NRR Response Surface A r;sponse surface is a functiMal relationship which involves several independent variables and one dependent variable. The surface is created by fitting the constants of an assumed functional relationship to data obtained from "experimeats".
The response surface provides a convenient means by which accurate estimate of a complex or unknown function 's response may be obtained. Since the response l surface is a relatively simple expression, it may be applied in analytic I tschniques where more complex functions would make an analytic solution !
intractable.
l In the present application, a single detailed TORC analysis is treated as an "cxper.i ment". A carefully selected set of detailed TORC " experiments" is conducted, and a functional relationship is fitted to the MONBR results. This r;sponse surface is then used in conjunction with Monte Carlo techniques to combine probability distribution functions (p.d.f's) for each of the independent variables into a resultant MONBR p.daf.
4.1 TORC Model Used Four-pump and three-pump inlet flow distributions are compared with radial pow 2r distributions to determine the limiting location for DNB analysis. For tha purpose of generating the response surface, the limiting location is d2 fined as the assembly in which the impact of system parameter uncertainties on MONBR is the greatest. The inlet flow distribution (3-pump) used in the generation of the response surface is shown in Figure 3-1. The core-wide and limiting assembly radial power distributions used to generate the response surface are shown in Figures 3-3 and 3-4, respectively.
The first stage TORC model used in thi,s analysis is shown in. Figure 3-5. The limiting assembly occurs in location of this model. Second and third stage modals used in this analysis are show"n"in Figures 3-6 and 3-7, respectively.
4-1.
4.2 Variables Used A careful examination of the sources of uncertainty discussed in Section 3 shows that several of these sources of uncertainty can be omitted from the r;sponse surface.
As explained in Section 3.2, inherent conservatism in the thermal margin modaling methodology factors makes it unnecessary to account for uncertainty in the radial power disribution used in DNB analyses. Hence, the radial power distribution was omitted from the response surface.
Since the inlet flow distribution uncertainties are taken into account using dit;rministic methods, as explained in Section 3.3, these uncertainties are not included in the statistical analysis.
The sensitivity study discussed in Section 3.4 indicates that large perturba-tions in the exit pressure distribution have negligible effect on the predicted MONBR. Thus, the exit pressure distribution is not included in the response surface.
The heat flux factor (F ")q is applied to the MDNBR calculated by TORC in the following manner:
MDNBR TORC M1NBR = (4.1)
Fuq Since the functional relationship between MDNBR and Fq " is known, the heat flux factor is not used in generating the response surface. Instead, this factor is combined with the resultant surface, as explained in Section 4.5.
A method has already been developed (4-1) to account for rod bow uncertainty
- . fer C-E fuel . No rod bow effects are included in the response surface.
4-2.
Inst::ad, the rod bow penalty determined with existing methods (4-1) is applied to the design limit MDNBR as discussed in Section 6.2.
The calculational uncertainty associated with MONBR predictions using the TORC /CE-1 package is inplicitly included in CHF distribution uncertainty, as explained in Sections 3.10 and 3.11. Hence, no explicit allowance for code unc';rtainty is included in the response surface. However, as discussed in Section 3.11, NRC in their previous SCU reviews has consistently imposed a p:nalty factor on MONBR to account for the TORC code prediction uncertainty.
In the present analysis, this penalty has been taken into account according to tha NRC guidelines as discussed in Section 6.2.
The system parameters included as variables in the response surface are listed in Table 4-1.
4.3 Experimental Design An orthogonal central composite experimental design (4-2) is used to generate the response surface applied in this study. The total number of experiments nIed:d to generate a response surface using this experiment design is 2k + 2k + 1 whera k is the number of variables to be considered. The desired response surface consists of three variables, hence 15 " experiments" or detailed TORC analyses were needed for a full orthogonal central composite design. The results of these experiments may then be manipulated by means of the least squares estimator b,_ = (n' n}'1 {n') z (4.2) 4-3.
l
wh;re z is the vector of experimental results, to yield the coefficients which define the response surface.
3 3 3 3 2
z,,, o MDN8Rg3 = b, + E bj ng + I b9g (ng -c)+ I b g3 ng nj (4.3) i<j In the above equations, the nj are coded values of the system parameters (xj) to be treated in the response surface, as indicated in Table 4-1.
The bj represent the constants found from the TORC results by means of Eq.4.2, and e is a constant determined by the number of experiments conducted.
The number of TORC analyses needed to' generate the response surface could be r;duced significantly if some of the interaction effects (i.e., bg3ngn3) wera neglected. However, such interaction effects are included in the present method.
4.4 Design Matrix The set of experiments used to generate the response surface is referred to as tha design matrix. This matrix, in coded form, comprises the second through fourth columns of the matrix cited in Eq. (4.2). Both coded and uncoded v2rsions of the design matrix used in this study are presented in Appendix A alcng with resultant MDNBR values. The design matrix was constructed such that each independent variable included in the response surface extends just l b;ycnd the 2a range of its associated p.d.f.
4.5 Rasponse Surface l
Equation (4.2) was solved numerically using the data in Appendix A.
Cosfficients for the response surface as given by Eq. (4.3) are presented in Table 4-2. Comparisons made between TORC predicted MDNBR and response surface pr: dictions show excellent agreement. The 95% confidence estimate of the resp:nse surface standard deviation is 0.000411.
4-4.
The heat flux factor is included analytically in the response surface by combining Eq. (4.1) with Eq. (4.3). The final relationship is given by 3 3 3 3 i .
- M" o
+g,Iff"1 E D.fi ("i - c) + _]
,j I b gj ng nj ) (4.4)
- - i*j .
Th0 coefficient of determination, r, provides an indication of how well the r;sponse surf ace explains the total variation in the response variable (4-3).
WhIn r = 1, a true model has been found. The r value associated with the response surface generated in this work is 0.99995 which indicates that this response surface is a very good model.
Another indication of model performance is provided by the standard error of cstimate (4-4). The standard error for the response surface is 0.000197. The ralative error is 0.017% indicating that this model performs very well.
l I
4-5.
TABLE 4-1 System Parameters Included as Variables in the Response Surface Coded Values
- Index System Parameter Variable (i) aj Sj Enthalpy Rise X I 1 Factor Systematic X 2
2 Pitch (in)
Systematic X 3
3 Clad 0.D. - -
(in)
- Variables coded according to relation nj = X$- og O
i 0 at nominal where the aj conditions andare chosen the such that sj are chosen nj =t hat the interval such l
of the response surf ace will include 6, 2e intervals l
of each of the system parameters.
l l
l I
l 4
4-6
TABLE 4-2 Coefficients for MDNBR Resporse Surface Response Surface Coefficient Coefficients Values b
o b;
bp b
3 b jj b pp b
33 b ig b
i3 b
23 c
3 3 3 3 b, + I I bgg (n - c) + i=1 I MDNBR = I b R.S. i=1 bg n$ + i=1 j=1 g3 ng n)
(
4-7 l
l
(
I J.O Combination of Probability Distribution Functions The EN8R response surface discussed in Section 4 is applied in Monte Carlo methods to combine numerically the system parameter probability distribution functions (p.d.f.'s) discussed in Section 3 with the CHF correlation uncertainty. A new 95/95 ENBR limit is than selectad from the resultant p.d.f. This new limit includes the effect of system parameter uncertainties and thus may be used in conjunction with a best estimate design TORC model.
-3.1 Method I The SIGMA code applies Monte Carlo and stratified sampling techniques to combine arbitrary p.d.f's numerically (5-1). This code is used with the J rcsponse surface to combine system parameter p.d.f's witn the CE-1 CHF correlation p.d.f. into a resultant MDNBR p.d.f. The methods used to achieve this combination are discussed below.
Th] effect of system parameter uncertainties on MDNBR is combined with the effect of uncertainty in the CHF correlation by computing a t.MDMBR caused by deviation of the system parameters from nominal:
amNBR = EN8Rg,3,- WNBRNOM (5.1) where WN8Rg$ is the MDNBR found by substituting the set of system parameters Int 6 the response surface and MDNBR NOM is the MDNBR value predicted by the response surface with nominal system parameters. A point is then randomly chosen from the CHF correlation p.d.f. and combined with the WNBR from Eq. (5.1) to yield a MDNBR value:
ENBR = EMBRCHF + A M NBR (5.2)
This process is repeated by the SIGMA code for 2000 randomly selected sets of system parameters and randomly selected points from the CHF correlation p.d.f., and a resultant WNBR p.d.f. is generated.
Tha system parameter p.d.f's input to SIGMA are listed in Table 5-1. Both "b:st estimate" and 95% confidence estimates of the standard deviation are included. Standard deviations at the 951 confidence level are input to SIGMA to ensure that the standard deviation of the resultant MDNBR p.d.f is at least at the 95% confideace limit.
32 R sults The resultant WNBR p.d.f is shown in Fig. 5-1. The mean and standard d;viation of this p.d.f. are 1.00041 and 0.075551, respectively. As Fig. 5-1 indicates, the resultant WNBR p.d.f. approximates a normal distribution.
@.3 Analytical Combination -
An approximate yalue of the standard deviation of the resultant MDNBR p.d.f may be found by analytic methods. These methods are based upon the 5-1
I assumption that the uncartainties are small deviations from the mean (5-2). Given a functional relationship y = f('x g ,x2 ' " Xn) (5.3) the effects of small perturbations in x on y may be found from Ay i dy 1 ( ) AXg+( ) AX2 +****+ ( ) A* n (5.4)
Hence, if several independent normal distributions are combined by the relationship expressed in Eq. (5.3), the variance of the resultant p.d.f. is 2
'y 2 1(a ) o,}2 ,(sax ) *2 + ****
- I x)
- n (5.5) where the partial derivatives are evaluated at the mean value of the xj's.
The response surface relates E NBR to system parameters by the relationship found on Table 4-2:
3 3 3 3 2
MON 3RRS " Do +I D I bgg (ng - c) + I I b jj nj nj (5.6) i=1 1 "i +i=1 i=1 j=1 i<j where x, - og (5.7)
'i " 3 9
Applying Eq. 5.5 to the response surface yields the following expression for the variance:
- }
ORS I x ) *1 (5.8)
Differentiating Eq. (5.6) and (5.7) with respect to , and xj:
N =
bg + 2byg nj + b (5.9) n ij nj an4 , 1 (5.10) ax g 9
j Substituting Eq. (5.9) and (5.10) into Eq. (5.8) results in a relation between the resultant NMBR variance and the system parameter variances:
3 3 2 c x4 2 l
=I (3) (5.11)
(bg + 2bjg nj +j=1+1 bgj nj)
I ORS i=1 1 5-2 '
This equation is simplified when evaluated at the mean values of the ng: (i .e. , n = 0 )
, 2 3 2 , ,i 2
b '
'RS ,"q[1 i (5.12)
The CHF correlation p.d.f and system parameter p.d.f.'s are related to the resultant MNBR in Eq. (5.1) and Eq. (5.2), and the heat flux factor is related by Eq. (4.1). The resultant MDNBR variance is given by 2 2 2 2
c MD_NBR-" 'R.S. + 'CHF + 'Fo" .
2 2 2 (5.13)
MDN3R Fq" (uR.S.+uCHF) where DR.S. % 0 Substituting values from Tables 4-1, 4-2, 5-1, and Section 4.5 into Eq.
(5.1 ) and Eq. (5.13) yields:
o m MBR = 0.07311 which is in good agreement with the value predicted by the SIGMA code simulation using the response surface.
5-3
0.10 i i I ' ' '
I i
N FREQUENCY = 2000 TRUE GAUSSIAN N = NUMBER OF POINTS IN INTERVAL 0 ACTUAL DISTRIBUTION 0.08 -
(DNBR-1/2ADNBR DNBR+1/2ADNBR) OBTAINED FROM MONTE -
CARLO CODE AND 0 o RENSE SNM O
0.06 - O -
o z
W i
O O
w "g 0.04 -
00 0.02 - -
O 0.00 a i i I
) 0.60 0.70 0.80 0.M 1.M lM D I DNBR 1
4 FIGURE 5-1 l RESULTANT MDNBR PROBABILITY DISTRIBUTION FUNCTION l
( -. -
TABLE 5-1 Probability Distribution Functions Combined by SIGMA Distribution Mean Standard Deviation at 95% Confidence Enthalpy Rise Factor Heat Flux Factor ,,+'
Systematic Pitch (in) ,j /
/
Systematic Clad 0.0. /
(in) - - - -
,s
/
CE-1 CHF Correlation 0.99983 0.07065 , /
go
, ./
j
/
/
, c'*
,/
,,f '
./*
..a*
/
,/
l
/
d
,r 5-5 i
6.0 Application to Design Analysis
' ,,,,- - - ,q This section discusses the application of the st,atJJfirdM7Wrived MONRR p.d.f l
to d; sign analyses. Determinist 1cyt'ud6.'6gy (6-1) involves use of a design
, l modal for TORC analysisf4d?"
includes deterministic allowances for system parameter uncytfihties. These deterministic penalties are replaced with a highp,.%IBR limit in the statistical methodology. This higher MONBR limit is 3,ddsId with a "best estimate" design model in thermal margin analyses.
6.1 Statistically Derived MDNRR Limit The MDNBR p.d.f. described in Secthn 5.0 is a normal distribution having a mean of 1.00041 and a standard deviation of 0.0755509. This standard deviation is at least -at the 95% confidence level. These values were e ,puted by means ,
of Monte Carlo methods as discussed in Section 5.0. A comi ison of TORC r:sults and response surface predictions indicates that the lo error associated with the response surface is og = 0.000197 ; at the 95% confidence level this value is e =
.0001974 g5/1.15 = 0.00041077.
s95 According to the NRC guidelines as discussed in Section 3.10, the effect of prediction uncertainty in CHF correlation on MDNBR is calculated as follows:
2 2 2 2 11DNBR " R.S + CHF + Fq" From this 2 2 2 2
" R.S
- f1DNBR ~ "CHF - Fq" Substituting the numerical values in the above equation yields:
2 c g, = (0.0755509)2 (0.07065)2 (0.015)2 = 0.0004915 Th2 5% penalty factor proposed in the NRC guidelines can now be applied to oCHF to account for the prediction uncertainty in CHF correlation and o pgygg recomputed:
oMDNBR = (0.0004915) t (0.07065*1.05)2 + (0.015)2
= 0.078864 6-1.
l
v Since a finite number of points (2000) were used in Monte Carlo methods, the r;sultant MONBR standard deviation adjusted for finite sample size is 3, ... 0.078864*/1999 1
%.<,$.[w'999( 0.94854)
N + .- = 0.080969
~m TherootsumsquareoftheadjustehNDNBR 5t,andard deviation and the response surface standard deviation at the 95% confidenc6 leval is:
a tot (0.0809691 2 + (0.00041077)2 = 0.080970
=3 The 95% confidence estimate of the mean becomes 1.00041 + 1.645 (0.078864) = 1.00331 yf2000 Since the resultant MDNBR p.d.f is a normal distribution, as shown in Figure 5-1, the one-sided 95% probability limit is 1.645o. Hence there is a 95%
probability with at least 95% confidence that the limiting fuel pin will not Gxp;rience DNB if the 5"st estimate design model TORC calculation yields a MDNBR value greater than or equal to 1.00331 + 1.645*0.080970 = 1.137.
6.2 Adjustments to Statistically Derived MDNBR Limit The statistical MDNBR limit derived in Section 6.1 contains no allowance for the adverse impact on DNBR of fuel rod bowing. C-E has , applied an NRC method for taking rod bow into account in DNBR calculations (6-2) as discussed in S;ction 3.9 This appliation shows that the penalty depends on batch average burnup. For the CE's 14 x 14 type fuel for Fort Calhoun Nuclear Unit, this p:nalty is 0.5% in MONBR at a burnup of 40 GWD/MTU. Thus, the new limit, including an allowance for rod bow is (1.137*1.005) or 1.1427.
Tha NRC has not yet completed review of the application of the CE-1 CHF correlation (6-3) to non-uniform axial heat flux shape data (6-4).
6-2.
.i
Consequently, a 5% penalty was applied to the 1.13 PONBR limit by the NRC. The intG; rim MDNBR limit for use with the CE-1 CHF correlation, pending NRC approval of C-E's non-uniform axial heat flux shape data, is 1.19. For the purpose of this study, a conservative application of this penalty is to shift the mean of th2 MDNBR p.d.f. by 0.06. This shift results in a MDNBR limit of 1.2027.
Finally, as discussed in Section 3.11, a penalty factor calculated bassd on the NRC guidelines is applied to the above MDNBR limit of 1.2027 to take into account the TORC code prediction uncertainty. A conservative value of 1.011 for this factor is applied to the above MDNBR limit.
Tha final value of the MDNBR limit becomes 1.2027*1.011 = 1.216, roundedup$o 1.22.
Thus, the new MDNBR limit which contains allowances for uncertainty in the CHF correlation and system parameters as well as a 0.5% rod bow penalty, the NRC imp; sed code uncertainty penalty, and the NRC imposed 5.0% CE-1 correlation p:nalty is'1.22.
6.3 Application to TORC Design Model Statistical combination of system parameter uncertainties into the MONBR limit pr:cludes the need for deterministic application of penalty factors to the design TORC model. The design TORC model used with the new MDNBR limit of 1.22 consists of best estimate system parameters with no engineering factors cr other adjustments to accommodate system parameter uncertainties. The inlet flow split will, however, cor.tinue to be chosen such that the best estimate design TORC model will yield accurate or conservative MDNBR predictions when compared with MDNBR values from detailed TORC analyses (6-1) which include d;terministic allowances for inlet flow distribution uncertainties.
l 6-3.
l- - - - . -. . ..
i 7.0 Conclusions Us3 of a 1.22 PONBR limit with a best-estimate design CET0p-D model for Fort Calhcun Nuclear Unit will ensure with at least 95% probability and 95%
confidence, that the hot pin will not experience a departure from nucleate bailing. The 1.22 MONBR limit includes explicit allowances for system parameter uncertainties, CHF correlation uncertainty, rod bow, the NRC penalty for TORC code uncertainty and the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation.
7.1 Conservatisms in the Methodology S,veral conservatism are included in the present application. The significant censervatisms include:
- 1) combination of system parameter p.d.f. 's at the 95% confidence level to yield a resultant MDNBR at a 95% + confidence level
- 11) use of pessimistic system parameter p.d.f. 's 111) use of the single most adverse set of state parameters to generate the response surface iv) application of the 5% interim penalty imposed by the NRC on the CE-1 CHF correlation v) application of additional NRC CHF correlation uncertainty penalty vi) explicit application of NRC imposed code uncertainty penalty l 7-1.
u
i f
8.0 References 3.1 section 2.0 References (2-1) " TORC Code: Verification and Staplified Modeling Models". CINPD-206-P, ,
January 1977. ,
l (2-2) " TORC Code: A Computer Code for Determining the Thermal Margin of a l Reacter Core". CEIFO-161-P. July 1975. j (2-3) Letter from W. C. Jones (OPPD) to R. A. Clark (NRC), " Fort i Calhoun Cycle 8 Reload Application", February 18, 1983. l (2-4) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-t Fuel Assemblies with Standard Gries. Part 1: tiniform Axial Power Distribution". CEMPD-162-P. September 1976.
8.2 section 3.0 References ,
(3-1) " TORC' Code: A Computer Code for Determining the Thermal Margin of i a Reactor Core. CEMPO-181-P. July 1975, pp. 5-1 to 5-4.
l (3-2) " Final Safety Analysis Report", Fort Calhoun Station Unit No.1, AEC Occket No. 50-285, Exhibit F-17 Volume 1, May 1971 Fig. 3.5-5.
l (3-3) ibid, Subsection 3.5.5.2. l (3-4) " Statistical Combination of Uncertainties Part 2*, CEN-124(3)-P. !
January 1980.
(3-5) Telecon from Galen Hesson (Battelle); NRC Reviewer of Statistical Combination of Uncertainties Methodology for System 80 Reactors to Tom Bracke (Con 6ustion Eng.), August 3,1983.
(3-4) " Fuel and Poison Rod Bowing". CEMPO-225 P. October 1976.
(3-7) " Fuel and Poison Red Bowing - Supplement 3". CEMPO-225-P.
Supplement 3. June 1979.
(3-8) "CE Critical Heat Flux: Critical Heat Flux Correlation for CE Fuel Assemblies with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution", CENPD-162-P, September 1976.
(3-9) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 2: Nonuniform Axial Power Distribution", CENPD-207-P, June 1976.
(3-10) " TORC Code: Verification and Simplified Mod 611ng Methods",
CENPD-206-P, January 1977.
8-1 m- -
-..----------,--,,,.--,,-~,,-e, -
, , ,,-+,,,w-,, -,_c,w.,. ee,y-,,p.-m_,_., ,, , , , - - - , - ,,s-w,-- w ow=,.='-v
8.3 References for Section 4 (4-1 ) " Fuel and Poison Rod Bowing, Supplement 3", CENPD-225 o, June 1979.
(4-2) R. H. Myers, Response Surface Methodology , Allyn and Bacon, Inc.
. Boston,1971.
(4-3) N. R. Uraper H. Smith, Applied Regression Analysis , John Wiley
& Sons, New York,1966, p. 62.
(4-4) ibid., p.118 -
8.4 References for Section 5 (5-1) F. J. Berte, "The Application of Monte Carlo and Bayesian Probability Techniques to Flow Prediction and Determination",
Combustion Engineering Technical Paper TIS-5122, presented at the Flow Measurement Symposium, sponsored by the National Bureau of Standards, Gaithersburg, Maryland, February 23-25, 1977. '
(5-2) E. L. Crow, F. A. Davis, M. W. Maxfield, Statistical Manual ,
Dover Publications, Inc., New York,1960.
8.5 References for Section 6 (6-1) " TORC Code: Verification and Simplified Modeling Methods",
CEMPD-206-P, January 1977.
(6-2) " Fuel and Poison Rod Bowing Supplement 3", CENPD-225-P, Supplement 3-P June 1979.
(6-3) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution", CENPD-162-P, September 1976.
(6-4) "C-E Critical Heat Flux; Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Girds, Part 2: Nonuniform Axial Power Distribution" CENPD-207-P June 1976.
l l
l 8-2
h Appendix A: Detailed TORC Analyses Used To Generate Response Surface An orthogonal central composite experimental design (A-1) was used to generate the response surface (R 5) used in this study. All first order interaction effects (i.e. xy terms) were retained.in the R 5. The R S used in this study included tnree variables. The coded set of detailed TORC analyses performed to generate the R S is presented in Table A-1; variables were coded as shown in Table 4-1. The actual values of the input parameters are presented in Table A-2 along with the resultant MNBR values. .
l References
( A-1) R. H. Myers Response Surface Methodology, Allyn & Bacon, Inc.,
Boston,1971, p.133. .
l t
A-1
f TABLE A-1 Coded Set of Detailed TORC Cases Used to Generate Response Surface Case Enthalpy Systematic Systematic Number Rise Factor Pitch Clad 0.D.
1 -1.00 -1.00 -1.00 2 -1.00 -1.00 1.00 3 -1.00 1.00 -1.00 4 -1.00 1.00 1.00 5 1.00 -1.00 -1.00 6 1.00 -1.00 1.00 7 1.00 1.00 -1.00 8 1.00 1.00 1.00 9 0.00 0.00 0.00 10 -1c22 0.00 0.00 11 1.22 0.00 0.00 12 0.00 -1.22 0.00 13 0.00 1.22 0.00 14 0.00 0.00 -1.22 15 0.00 0.00 1.22 See Table 4-1 for Coded Relationships i
l (A-2)
l
- , i l
a _ -
u d
i s
e _ -
- R R
B e N c e .
Oa s Mf nCR r ERB eu pON cS sTD t.
a e M _
f e R rs _
un S o p
es se nR d 2
o pe e -
l CR _
- st i RR A ea aON R r tTO E e e M _ -
L dn D B ne A aG T
Co Rt O
Td c .
e ,
f s it D. -
oU a0
. m ns ed oe t a ss sl i a yC rC S a
pr mo of
_ c C
i t
ah mc et ti sP . -
y S
y . _
p r l eo ast hic tRa n F .
E -
r ee "
sb am 6 7 8 9 0 1 Cu 1 2 3 5 1 N 1 w
TARLE A-? (cont)
Comparison of TORC and Response Surface MONRR 1
for Cases lised to Generate Response Surface -
i
- Enthalpy Detailed Response l Case Rise Systematic Systematic TORC TORC l . Number Factor Pitch Clad 0.D. MDNBR MONBR Residual j - - - _ _ _ _ _ - -
12
! 13 l
l 14 x 15 l L - -
i l
Note: All the residuals are zero because when the MDNBRs are rounded off to 3rd decimal place, j they are the same for detailed TORC and response surface l
1
-l l
1 I
i i
I ,
1
h f"
i
.i.
COMBUSTION ENGINEERING, INC.
- _ - - - - - - - - - - - - l
CEN-257(0)-NP STATISTICAL COMBINATION OF . .
~
UNCERTAINTIES PART 3 NOVEMBER, 1983 l
=! POWER E=HSYSTEMS CCMBUSTICN ENGINEERING, INC.
1 LEGAL NOTICE THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY ColMUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF:
A. MAKEC ANY WARRANTY OR REPRESENTATION, EXPRESS OR lRFLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOO, OR PROCESS DISCLOSED IN THl3 REPORT MAY NOT INFRINGE PdlVATELY OWNED RIGHTS;OR R. ASEUMES ANY UA51UTIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, METHOD OR PROCESS DISCLOSED IN THIS REPORT.
STATISTICAL COMBINATION OF UNCERTAINTIES METHODOLOGY PART 3:
DEPARTURE FROM NUCLEATE BOILING AND LINEAR HEAT RATE LIMITING CONDITIONS FOR OPERATION FOR FORT CALHOUN f
ABSTRACT The three parts of the Statistical Combinatin of Uncertainties (SCU) report d: scribe a method for statistically combining uncertainties involved in the cclculation of the limits for the Reactor Protection and Monitoring Systems (RPS). Part 1 of the SCU report describes the application of these new methods far the development of the Axial Power Distribution (APD) and thermal Margin / Low Pressure (TM/LP) Limiting Safety System Settings (LSSS's). Part 2 d: scribes the statistical basis for a revised Departure from Nucleate Boiling
.Rr,tio (DNBR) corresponding to the Specified Acceptable Fuel Design Limit (SAFDL).
This part of the report, Party 3, describes the methods used to statistically combine uncertainties for the calculated departure from nucleate boiling (DNB) and linear heat rate (LHR) Limiting Conditions for Operation (LCO).
Descriptions of the probability distributions of the LCO-related uncertainties tnd the stochastic simulation techniques developed for this program are pratented. The total uncertainties presented in this report are expressed in percent overpower (P fd n , Pfdl) units for the DNB and LHR LCO respectively, at the 955 probability /95% confidence level limit.
Since the Required Overpower Margin (ROPM) is used to determine the LCO studies p;rformed to determine the sensitivity of ROPM to these uncertainties are also discussed.
i
,+A TABLE OF CONTE!rrS Chnpter Page Abstract i TLblo of Contents ii Lict of Tables iv List of Figures v Definitions of Acronyms and Abbreviations vi 1.0 Introduction 1-1 1.1 Purpose 1-1 1.2 Background 1-1 1.2.1 Protection and Monitoring System 1.2.2 Previous Uncertainty Evaluation Procedure 1.2.3 Design Basis Event Transi. nt Analysis Evaluation .
13 Report Scope 1-2 1.4 Susunery of Results 1-3 1.5 References for Section 1.0 1-3 2.0 Analysis 2-1 2.1 General 2-1 2.2 Objective of Analysis 2-1 2.3 Analysis Techniques 2-1 231 General Strategy 2.3.2 DNB LCO Stochastic Simulation 233 LHR LCO Stochastic Simulation 2.4 Analyses Performed 2-3 2.4.1 DNB LCO Uncertainty Analysis 2 4.1.1 Simulation 2.4.1.2 ASI Uncertainty Simulation 2.4.1 3 Processing Uncertainty Simulation 2.4.1.4 Overpower Calculations with Respect to DNB LCO 2.4.1.5 Combination of Uncertainties 2.4.2 LHR LCO Uncertainty Analysis 2.5 References for Section 2.0 2-5 ii 1
TABLE OF CONTENTS (continued) 3 0 _ Results and Conclusions 3-1 31 Results of Analysis 3-1 3.1.1 DNB LCO 3 1.2 LHR LCO 32 Impact of Statistical Combination of Uncertainties 3-3 3 2.1 Lapact on Margin to Limits 3 2.2 Impact on Consequences of DBE's 33 References for Section 3 0 3-4 Appendix A. Basis for Uncertainties Used in Statistical Combination of Uncertainties A1 Axial Shape Index Uncertainties A-2 A2 Measurement Uncertainties A-2 A3 Monitoring System Processing Uncertainties A-2 A4 - Reference for Appendix A A-2 B. Summary of Previous Methods for Combining Uncertainties B1 LHR LCO B-2 B2 DNB LCO B-3 B3 References for Appendix B B-4 C. Treatment of Uncertainties in Transient Analysis C1 Objective of Analysis C-2 C2' General Strategy C-2 C3 Analyses performed for Evaluation of ROPM for the Limitin,t DBE's C-6 L C.3 1 Loss of Coolant Flow Event C.3.2 Single Full Length CEA Drop Event C4 Conclusions C-17 C5_ References for Appendix C C-17 iii l
l
LIST OF TABLES f
Ch7pter 1 Pm 1-1 Variables Affecting the LCO-Related Uncertainty 1-4 1-2 NSSS Parameters Affecting the DNB and LHR LCO's 1-5 Ch pter 3 3-1 Uncertainties Associated with the DNB and LHR LCO's 3-5
, 3-2 Impact of Statistical Combination of Uncertainties on Margin to Limits 3-6 Appendix C C-1 Design Basis Events and RPS Trip Prot'ection C-19 C-2 Design Basis Events and Important Parameter Changes C-20 C-3 Uncertainties C-21 C4 Key Input Parameters Used in the Loss of Coolant Flow Event C-22 C-5 Sequence of Events for the Loss of Coolant Flow Event C-23 C-6 Key Input Parameters Assumed in the Single Full Length i CEA Drop Event C-24 C-7 Sequence of Events for the CEA Drop Event C-25 l
iv
_ _ - _ . _ _ . . . ~ . . _ _ _. . _ . . _ __- _._. _._ _-
LIST OF FIGURES Ch7pter 2 M 2-1 Ex-core Detector Monitored DNB LCO Uncertainty Analysis 2-6 Appendix C C-1 Loss of Coolant Flow Procedures Used to Determine Required Overpower Margin C-26 C-2 loss of Coolant Flow Required Overpower Margin (DNB) at 100% Power C-27 C-3 ' toss of Coolant Flow ROPM vs. Axial Shape Index C-28 C-4 Loss of Coolant Flow Core Power vs. Time C-29 C-5 - Loss of Coolant Flow Core Heat Flux vs. Time C-30 C-6 Loss of Coolant Flow RCS Temperature vs. Time C-31 C-7 loss of Coolant Flow RCS Pressure vs. Time C-32 C-8 CEA Drop Event Procedure Used to Determine Required Overpower Margin C-33 C-9 CEA Drop Event Required Overpower Margin (DNB) at 1005 Power C-34 C-L' CEA Drop Evnt R0PM vs. Axial Shape icdex C-35 C-11 Single Full Length CEA Drop Core Power vs. Time C-3 6 C-12 Single Full Length CEA Drop Core Heat Flux vs. Time C-37 C-13 Single Full Length CEA Drop RCS Temperature vs. Time C-38 C-14 Single Full Length CEA Drop RCS Pressure vs. Time C-39 V
DEFINITION OF ACRONYMS AND ABBREVIATIONS ACU Axial shape index calibration uncertainty A00 Anticipated Operational Occurence(s)
APD Axial Power Distribution APU Axial Shape Index Processing uncertainty ARO All Rods Out .
ASGT Asymmetric Steam Generator Transients ASI Axial Shape Index ASI DNB Axial Shape Index associated with Pfdn LCO LCO Axial Shape Index associated with P ASkHR fdl ASIU Axial Shape Index Units B Unless sepcifically defined in context as representing T power, B is used as core power
-B 3 Rod average power at which fuel design limit or DNBR is reached for initial steady state B Power at which fuel design limit on DNBR is reached for 2
transient conditions LCO B
DNB Power level after inclusion of all DNB LCO uncertainties and allowances LCO B
LJiR Power level after inclusion of the LHR LCO uncertainties and allowances BMU Power Measurement Uncertainty BMU g Kth sampled value of BMU BOL Beginning of Life i B Available Overpower Margin OPM ,
B OPM Mean value of B OPM distribution B
OPMk The final B OPM calculated from the Kth simulation trial
'1 95/95 B B at lower 95% probability /95% confidence level of B OPM OPM distribution CEA Control Element Assembly CEAW CEA Withdrawal CECOR Computer code used to monitor core power distributions Vi
CESEC Computer code used to simulate NSSS response to perturbations CETOP Computer code to determine the overpower limits due to thermal-hydraulic conditions CE-1 C-E's critical heat flux correlation CTM Centerline Temperature Melt D8E Design Basis Event (s)
~
.DNB Departu*e from Nucleate Boiling CNBR Departure from Nucleate Boiling Ratio F Primary coolant flow rate f Number of degrees of freedom F Fuel-densitication-dependent Power Peaking Augmentation Factor F
BH Coolant flow used to evaluate the ordered pairs (Pfdne Ip)
LCO F Flow component of the DNB LCO FNU Flow Measurement Uncertainty F Total 3D nuclear power peaking factor including the effect q
of augmentation factors T
F Total 3D nuclear power peaking factor including effects of q
tilt and augmentation factors Fr Integrated radial pin peaking factor F Core average axial power distribution peaking factor z
FTC Fuel Temperature Coefficient of Reactivity Fxy Planar Radial Peaking Factor I Axial Shape Index for the i th assembly t
I p
Peripheral Axial Shape Index I Core Average Axial Shape Index
-R I(r) Rod position dependent core average axial shape index for ROCS calculated power shape INCA Computer code used to calculate power shapes from instrumented signals I
p Peripheral Axial Shape Index R
I (r) Rod position dependent Peripheral Shape Index for ROCS p
calculated power shape vii l
- 7,RS(r) , 7p RSafety Rod configuration dependent peripheral shape index based on safety channel assembly weighting factors (I-Ip) ROCS , Difference between I and Ip for an ROCS calculated power distribution (I-Ip)CECOR Difference between I and Ip for a CECOR evaluated power distribution (IpROCS_7pCECOR) Safety Difference between ROCS and CECOR calculated Ip using the safety chennel assembly weighting factors k Stochastic simulation trial number K One-sided tolerance factor at the 95% probability /
95% confidence limit LCO Limiting Condition (s) for Operation LHR Linear Heat Rate
.LOF Loss of flow LSSS Limiting Safety System Setting (s)
MTC Moderator- Temperature Coefficient n Normal distribution N Total number of sampled cases in DNB LCO uncertainty analyses NA Not applicable NSSS , Nuclear Steam Supply System (s)
P Pressurizer pressure Pg Axially integrated power of assembly i P
3 Initial power level in CEA drop event analysis P
2 Final power level in CEA drop event analysis P
DNB System pressure used in the calculation of the ordered pairs (Pfdne Ip)
P Power to fuel design limit on linear heat rate fdl for LHR LCO including effects of azimuthal Phf P fdl tilt-P fdl P fdi for LHR LCO not including the effects of azimuthal tilt P Power to fuel c.esign limit on DNB including the fdn effects of azimuthal tilt P Power to fuel design limit on DNB fdn P
fdn k Overpower from the kth simulation trial CETOP i'
calculation viii
LCO Pressure component of the DNB LCO P
PLCS Pressurization level control system PLHGR Peak Linear Heat Generation Rate PPCS Pressurization Pressure Control System PMU Pressure Measurement Uncertainty PU Uncertainty in predicting local power at the fuel design limit QUIX Computer code for solving the one-dimensional diffusion equations
. RCS Reactor coolant system ROCS Coarse mesh code for calculating power distributions
- ROPM Required overpower margin RPS Reactor protection system RSU Shape index separability uncertainty RTD Resistance temperature devices SAFDL Specified acceptable fuel design limit LSAU Shape annealing factor uncertainty SCU Statistical Combination of Uncertainties SIGMA Stochastic simulation code SMD0 Statistically combined uncertainty applicable to the DNB LCO SMLO Statistically combined uncertainty applicable to the LHR LCO I
T AZ Azimuthal tilt allowance TC Primary coolant inlet temperature, cold leg temperature Th Primary coolant hot leg temperature T
DB Inlet coolant temperature used in calculating the ordered pairs (Pfdn' IP)
L Inlet temperature for the DNB LCO l Tfn b Inlet temperature for the DNB LCO after accounting
.Tfn' for the temperature measurement uncertainty ix
TM/LP Thermal Margin / Low Pressure TMU Temperature Measurement Uncertainty TORC /CE-1 Critical heat flux correlation used by CE W eyg Core average linear heat rate Weighting factor of assembly i for excore detector Wf set j 0 Maximum linear heat rate limit allowed by the LHR W[x LCO a Shape Annealing Factor ABOPM kth sampled overpower uncertainty due to ASI k
uncertainties AIp3 Uncertainty in kp due to uncertainty components other than electronic processing AIp2 Uncertainty in Ip due to electronic processing AP Pressure difference AT Temperature difference u Axial shape index correction term uC [
3 uR t 1
uC(r) [. .
3 US [ ]
G Standard deviation l
l l
X
1.0 Introduction 1.1 PURPOSE Part 1 of the SCU report (1-1) describes the application of C-E's method for statistically combining the uncertainties involved in the calculation of the linits for the axial power distribution ( APD) and thermal margin / low pressure liciting safety system settings (LSSS). Part 2 (1-2) describes the statistical b ris for the revised departure from nucleate boiling ratio (DNBR) limit to be used in the evaluation of LSSS and limiting conditions for operation (LCO).
The purpose of Part 3 of the report is to describe the method for statistically combining the uncertainties involved in the calculation of the limits for the DNB and LHR LCO's. Uncertainties for the variables listed in Table 1-1 are cinsidered.
1.2 BACKGROUND
1.2.1 Protection and Monitoring System Tha basic purposes and interactions of the LSSS and LCO's were previously diceribed in Section 1.2.1 of Part 1 of this report. Part 1 describes the function of the protection system; Part 3 describes the function of the DNB and LHR LCO's.
Operation within the DNB and LHR LCO's provides the necessary initial DNB and LHR margin to prevent exceeding acceptable limits during Design Basis Events (DBE's) where changes in DNBR and linear heat rate are important. A list of tha Nuclear Steam Supply System (NSSS) parameters which affect the calculation of these LCO's is shown in Table 1-2. A discussion of C-E setpoint methodology m:y be found in Reference 1-3 1-1
1.2.2 Previous Uncertainty Evaluation Procedure Th7 methods previously used to apply uncertainties to generate DNB and LHR LCO's are presented in Reference 1-3 and are summarized in Appendix B.
As noted in Reference 1-3. these methods assume that all applicable uncer-trinties occur simultaneously in the most adverse direction. This assumption is conservative. Not all of the uncertainties are systematic; some are random and some contain both systematic and random components. This report documents the methodology used to statistically combine the LCO-related uncertainties cxplicitly.
1.2.3 Design Basis Event Transient Analysis Evaluat, ion Th3 methods and rrocedures use in the reprt to analyze DBE's were approved by NRC in Reference 14. The purpose of these transient analysis evaluations is to demonstrate that the ROPM is relatively insensitive to the uncertainties trc.sted .
1 3 REPORT SCOPE Th) scope of this part of the SCU report encompasses the following objectives:
- 1. To define the methods used to statistically combine uncertainties applicable to the calculation of the DNB and LHR LCO's l
- 2. To determine the aggregate uncertainties as they are applied in the determination of the DNB and LHR LCO's 3 To demonstrate that the ROPM has a small sensitivity to the variables whose uncertainties are stochastically combined.
1-2
On3 requirement for achieving the objectives is to define the probability
.dittributions associated with the uncertaint es i being considered. The develop-Eent of those distributions which impact the LCO's differently than they irpasted the LSSS's is discussed in Appendix A. To achieve the third object-ivo, it is necessary to examine the sensitivity of ROPM to initial conditions f4r DNB and LHR-releted DBE's. These evaluations are discussed in Appendix C.
1.4
SUMMARY
OF RESULTS Th3 Enalytical methods presented in Section 2.0 are used to show that a stoch-catic simulation of uncertainties associated with the ex-core detector-monitored DNB and LHR LCO's results in aggregate uncertainties of [ ] and
[ 1, respectively, at a 95/95 probability / confidence level. The total unscrtainties previously applied to the ex-core DNB and LHR LCO's are cpprcximately [ ] and i 1, respectively. Therefore , the statistical combination of uncertainties program provides a reduction in the conservatism of the uncertainties applied in establishing the ex-core instrument monitored DNB End LHR LCO's of approximately [ ] and [ 1, respectively.
The DBE sensitivity evaluations, described in Appendix C, show that the rcquired overpower margin used in LCO generation is insensitive to the way uncertainties are combined.
1.5 REFERENCES
FOR SECTION 1 1-1 CEN-270-(0)-P, " Statistical Combination of Uncertainties," Part 1 November 1983 l
1-2 CEN-270-(0)-P, " Statistical Combination of Uncertainties," Part 2 November 1983 1-3 CENPD-199-P, Rev. 1-P, "C-E Setpoint Methodology," March 1982.
1-4 Letter, E. G. Tourigny (NRC) to W. C. Jones (OPPD) dated March 5, 1983, License Amendment 70 and SER for Cycle 8 Operation of Fort Calhoun Station Unit No.1, Docket No. 50-285.
1-3 L.
1 TABLE 1-1 VARIABLES AFFECTING THE LCO-RELATED UNCFRTAINTIES
- 1. Predicted integrated radial pin power at the fuel design limit
- 2. Power measurement
- 3. Shape annealing factor
- 4. Shape index separability
- 5. Axial shape index calibration
- 6. Equipment processing of detector signals
- 7. Flow measurement ,
- 8. Pressure measurement
- 9. Temperature measurement l
i l
l l
l l 1-4
TABLE 1-2 MSSS PARAMETERS AFFECTING THE DNB AND LHR LCO'S DNB
- 1. Core Power 2, Axial Power Distribution 3 Radial Power Distribution
- 4. Azimuthal Tilt Magnitude
- 5. Core Coolant Inlet Temperature
- 6. Primary Coolant Pressure
- 7. Primary Coolant Mass Flow LINEAR HEAT RATE
- 1. Core Power
- 2. Axial Power Distribution 3 Radial Power Distribution
- 4. Azimuthal Tilt Magnitude 1-5
i 1
e 2.0 ANALYSES 2.1 GENERAL Th2 following Sections provide a description of the analyses performed to statistically combine uncertainties associated with the DNB and LHR LCO's.
Thic - statistical combination technique is that described in Part 1 of this riport . The bases for the individual uncertainties not previously described in Part 1 (Reference 2-1) are presented in Appendix A. 'Ihe stochastic sinulation techniques are described below.
2.2 OBJECTIVES OF ANALYSES The cbjectives of the analyses presented in this section are:
- 1. To document the stochastic simulation techniques for the uncertainties asseciated with parameters that affect the LHR and the DNB LCO's.
- 2. To determine the 95/95 probability / confidence level uncertainty factors to be applied in calculating the LHR and DNB LCO's.
2 3 ANALYSIS TECHNIQUES 231 General Strategy Tha stochastic simulation method used for the statistical combination of the DNB and LHR LCO related uncertainties was described in Section 2 of Part 1 of this report (2-1) .
2.3 2 DNB LCO Stochastic Simulation Fcr the DNB LCO, DNB overpower (Pfdn) divided by the required overpower margin (ROPM) is the dependent variable of interest. The core coolant inlet t'mper atur e , reactor coolant system pressure and flow r ate , peripheral axial sh pe index and integrated radial peaking factor are the independent variables of interest. Aa demonstrated in Appendix C, R0PM is relatively insensitive to these independent variables. In addition, the maximum ROPM as a function of sh pe index is used as input to generate the LCO's. This reduces the 2-1
analytical evaluation of the dependent variable to consideration of the Pfdn's
. recponse . to the uncertainties of the independent variables. TORC /CE-1 (R3ferences 2-2, 2-3) is used to determine the functional relationship between i - Pfdn and the independent variables. The probability distribution of uncertainties associated with some of the independent variables have been discussed -in Appendix A of Part 1 of this report.
Th3 core coolant inlet temperature range of interest for the DNB LCO stochastic simulation is defined by:
(1) the temperature at which the secondary safety valves open, and (2) the temperature at which the low secondary pressure trip would occur i The reactor coolant system pressure range of interest for the DNB LCO stochastic simulation is defined by:
(1) the value of the high pressurizer pressure trip setpoint, and (2) the lower pressure limit of the thermal margin / low pressure trip It is noted that these ranges are the same as used in the LSSS stochastic sirulation (Ref. 2-1) and as such are bounding for the LCO.
Figure 2-1 is a flow chart representing the ex-core detector monitoring stochastic simulation of the DNB limits. This figure is similar to Figure 2-2 in P;rt 1.
l 233 LHR LCO Stochastic Simulation Fcr the LHR LCO, the LHR LCO overpower (P$) is the dependent varicble of interest. The three-dimensional (3D) pin power peak, the core avsrage power level and the peripheral axial shape index are the independent varicbles. The dependent variable is defined as:
i 0
LCO Whx x 100 P =
(2-1) fdl Wavg x F qT whsre W, ,0 is the peak linear heat rate allowed by the LHR LCO and is determined by analysis of DBE's.
2-2 1
W,,, is the core average generated linear heat rate at rated power pq T is the synthesized core power peak including the effects of azimuthal tilt and augmented power peaking due to fuel densification.
In all other ways, the stochastic simulation procedure for the LHR LCO is the game as the simulation procedure for the APD LSSS described in Section 2 3 3 of P rt 1.
2.4 ANALYSES PERFORMED 2.4.1 DNB LCO Uncertainty Analysis Evaluation of the combination of uretrtainties for the DNB LCO is similar to the TM/LP LSSS analysis reported in Part 1. The distributions of the uncer-
.tcinties of the following parameters are input to the analysis:
J j In order to combine the significant uncertainties in the same manner as shown in Figure 2-1 of Part 1, the LCO stochastic simulation sequence shown in Figure 2-1 of Part 3 was used.
2.4.1.1 Simulation The simulation process is carried out over all of the operating space, defined in Section 2.3.2, in the same manner as described in Section 2.4.1.1 of Part 1.
2-3
2.4.1.2 Axial Shape Index Uncertainty Simulation 2.4.1.2.1 Ex-Core Axial Shape Index At Fsrt Calhoun Unit 1, the digital display of safety channel information is used to monitor the LHR and DNS LCO's, in accordance with Technical Specification 2.10.4. hus, the basic relationships between the components of the cxial shape index uncertainty for LSSS, described in Appendix B1 of Part 1, cro clso appropriate for the LCO uncertainty analysis.
2.4.1 3 Processing Uncertainty Simulation 2.4.1.3 1 Ex-Core Instrument Processing The signals generated by the ex-core detectors are processed into an axial th;pe index (ASI) value, he electronic processing equipment introduces further uncertainty in these values. However , the safety channel information us;d is transferred to the digital display before the information is processed by the trip actuation evaluation circuits. Therefore, only the safety channel prcc ssing uncertainties need be included in the LCO processing uncertainties.
Sinn the axial power distribution and the ASI value used in each simulation calculation are correlated, this uncertainty is incorporated in the stochastic cycluation of the LCO.
l l 2.4.1.4 Overpower Calculation With Respect to DNB LCO As in Part 1, the overpower limits due to reactor thermal-hydraulic conditions cra determined by the code CETOP (Reference 2 4), which uses the CE-1 c rrelation. CETOP requires values of the pressure, inlet temperature, cycrrge coolant mass flow, and radial peaking factor, and calculates a limit on ovsrpower.
l i 2.4.1.5 Combination of Uncertainties As in Part 1, during each simulation trial (k), a calculation is performed to datarmine the ratio of the value of overpower at nominal (mean) conditions to the value at off-nominal conditions as the result of sampling values from the cppropriate uncertainty distributions. These uncertainties are combined by using the following relations:
2-4
2-2 wh:ro 2.4.2 LHR LCO Uncertainty Analysis Tha stochastic simulation calculation used for the APD LSSS uncertainty analysis in Section 2.4.2 of Part 1 was repeated for the LHR LCO uncertainty cnalysis with only minor changes. In the simulations, the overpower (P$)
is derived' from the technical specifications value of the LHR LCO limit.
The cxial shape index uncertainty and the processing uncertainty simulations of Sections 2.4.1.2 and 2.4.1.3 were also applied to this analysis.
2.5 REFERENCES
FOR SECTION 2 1 2-1 CEN-257(0)-P, " Statistical Combination of Uncertainties Part 1",
November 1983 2-2 CENPD-161-P, " TORC Code: A Computer Code for Determining the 'Ihermal Margin of a Reactor Core", July 1975 2-3 CENPD-206-P, " TORC Code: Verification and Simplified Idodeling Methods",
January 1977 2-4 C. Chiu, J. F. Church, "Three-Dimensional Lumped Subchannel Model and Prediction-Correction Numerical Method for Thermal Margin Analysis of PWR Cores", TIS-6191, June 1979 l
2-5
1 N o '
$(kk AXIAL POWER DISTRIBUTION 6
8"'E l T8 C
c- O E o PROBABILITY E fdn
- 3. M @ DISTRIBUTIONS P
' T
"@10 ON INPUT -> SAMPLING --D Fr "
=ga PAHAMETERS o MODULE F p 1
i ,
i I.
MAXIMUM VALUE OF Th ---D ELECTRONIC l
Tc ---D PROCESSING g i z CORE J g UNCERTAINTIES W 'p AVERAGE 1, g o c) ASI opm og j,
- 'f Cm 6 z o mQ
- n m Al
. ~e G P2 4
hg z - -
1 r q .g i g '
ASI ---> OVERPOWER AB -g ASI ,P1 vs i OPm P
z -i
>g --> CORREC- $
UNCERTAINTY SENSITIVITY
=
, Pida + ABopm + BMU rm gg#}
TIONS RELATION g -
PROCESSORS m - _
j 1
1 1
POWER
____ , MEASUREMENT (BMU) BUILDUP UNCERTAINTY DISTRIBUTION ON UNCERTAINTIES _
OVERPOWER FOR N CASES ,
' ~'
. .fi .
i
)
1 l
30 RESULTS AND CONCLUSIONS 3.1 RESULTS OF ANALYSES The statistical analytical methods presented in Section 2 have been used to show that a stochastic simulation of uncertainties associated with the ex-core monitored DNB and LHR LCO result in combined uncertainties of (7.8%) and
[9 5%), respectively, at a 95/95 probability / confidence level.
Tcble 3-1 shows the values of the individual uncertainties which were st:tistically combined to yield the above combination. Appendix A contains a further discussion of the bases for these individual uncertainties.
'the combined uncertainties are in units of percent overpower (P fd n ' fdl) cnd are applied as such in the generation of the LCO limits as discussed b;1ow (Reference 3-1).
3 1.1 DNB LCO The fuel design limit on DNBR for the DNB LCO is represented by a combination of the ordered pairs (Pfdn, ASIDNB). A lower bound is drawn under the
" flyspeck" data such that all the core power distributions analyzed are bound ed . This lower bound is reduced by applicable uncertainties as follows:
l (3-2) l I
(3-2) j where:
B b - DNB power limit for LCO after inclusion of uncertainties and allowances P - Power to fuel design limit on DNB including the effects of fdn azimuthal tilt 3-1 l
l
SMD0 - Statistically combined uncertainties applicable to the DNB LCO ASIDNB- Axial shape index associated with Pfdn
, Temperature, pressure and flow components of theeDNB LCO are represented by cqu;tions as follows:
(3-3)
(34)
(3-5)
~ -
whero:
FMB, pMB,Tg B : Coolant conditions used in the calculations of (Pfdn' I )p ordered pairs of data.
3 1.2 LHR LCO Th3 excore detector monitored LCO on litiear heat rate is represented by the crdired pairs (P fd1' I). A lower t,cund is drawn under the " flyspeck" data p
such that all the core power distributions analyzed are bounded. This lower bsund is reduced by the applicable uncertainties and allowances to generate the LCO as follows:
(3-7) l where:
b B - Linear Heat Rate Power Limit for LCO after inclusion
! of uncertainties.
l 3-2 l
i i - .. -
PLf [ - The power to the LCO linear heat rate limit including the effects of azimuthal tilt.
SMID - Statistically combined uncertainty applied to the LHR LCO 32 IMPACT OF STATISTICAL COMBINATION OF UNCERTAINTIES 3.2.1 IMPACT ON MARGIN The motivation for using a statistical combination of uncertainties is to iIpreve NSSS performance through a reduction in analytical conservatism in the unacrtainties which must be taken into account. This section contains a discussion of the margin obtainable through a reduction in this conservatism.
Tible 3-2 lists the uncertainty values previously used on Fort Calhoun Unit 1.
Th3 cpproximate worth of each of these uncertainties in terms of percent over-power margin (Pfdn, Pfdl) is shown.
Ihn total uncertainties previously applied to the excore monitored DNB and IJIR LCO are approximately [17.8%) and (18.653, respectively. The use of the stctistical combination of uncertainties justifies a reduction in the conser-vttism in the uncertainty of approxiutately [9 2%] and [8 35], respectively.
Although the conservatism in the uncertainty has been reduced, a high degree of rsgurance remains that acceptable limits will not be exceeded.
3.2.2 IMPACT ON CONSEQUENCES OF DBE'S l Th3 plant technical specifications restrict operation to within the DNB, LHR cnd squipment LCO's. The statistical combination of uncertainties only impacts the DNB and LHR LCO's. For transient analyses of DBE*s, where changes in DNB rnd LHR are significant, the appropriate LCO establishes the limits on initial etnditions assumed in the analyses. Thus, the impact of uncertainties on these linits and, consequently, on the initial conditions for the transients, must be l
t cycluated.
3-3 ,
L :
As cxplained in previous sections, the LCO's are generated based on the P fdn (fcr DNB), Phf (for LHR) and the R0PM for the limitiag A00. As explcined in Appendix C, the maximum ROPM which bounds the maximum variations in the ROPM due to the range of uncertainties is used to generate these LCO's.
Sinso the uncertainties will be combined statistically, the conservatism in the uncertainties used to generate the LCO's are reduced. However, the DNB and LHR LCO's based on the methodology presented in this report will provide at least a 955 probability at a 955 confidence level that acceptable limits will not be cxceeded during DBE's initiated from the extremes of the LCO's.
33 REFERENCES FOR SE0 TION 3.0 31 CENPD-199-P, Rev.1-P, "C-E Setpoint Methodology," March 1982.
3-4
TABLE 3-1 UNCERTAINTIES ASSOCIATED WITH THE DNB AND LHR LCO'S Un ertainty LHR LCO DNB LCO Coro power ($ of rated power) g,25 125 Prizary coolant mass flow (5 Design flow)* NA i ]
Primary coolant pressure (psia) NA [ ]
Coro coolant inlet temperature (F C) NA [ ]
P wer distribution (peaking factor) [ ]
Axici Shape Index
- 1. Separability (asiu) See Table A-1 of Appendix A1
- 2. Calibration (asiu) [ -] (- ]
3 Shape Annealing (asiu) ( )
- 4. Monitoring system processing (asiu)(2c) ( )
Nnt7: For complete description of these uncertainties, see Appendix A.
- Decign Flow: 190,000 gpm 3-5
l TABLE 3-2 IMPACT OF STATISTICAL COMBINATION OF UNCERTAINTIES ON MARGIN TO LIMITS FOR EXCORE MONITORING l l
Approximate Values of Equivalent Overpower Margin Previous DNB LHR
- Uncertainty Value LCO LCO
, m P2wer 25 Coro coolar.t inlet 2F temperature R; actor coolant system 22 psid pr:s:ure Axici shape index:
Separability [ ]
Shape Annealing [ ]
Calibration [ tl R; actor coolant system ( ]
flow Perking factors 6%, 7%
Equipment processing:
DNB LCO [ ]
LHR LCO [ ]
Tct31 uncertainty applied previously Tat:1 uncertainty statistically combined Net gargin gain _
.. . -_ .-_. , . . --. . . . - . = - _ , _ _ _ _ - ,
APPENDIX A Basis for Uncertainties Used in Statistical Combination of Uncertainties 1
l l
l l
l 1
l l
A-1
A.1 ' Shape Index Uncertainties At Fort Calhoun Unit 1, the safety channel instruments, which supply some of the input information to the trip system, also supply information for monitoring the shape index of the LCO's. This shape index information is supplied to the LCO monitors before the trip system evaluation of shape index is performed. Consequently, except for the processing uncertainty for shape ind:x uncertainties described for the LSSS in Appendix A-1 Part 1 (Reference A-
- 1) are appropriate for evaluation of the LCO shape index uncertainty. The LCO shape index processing uncertainty should include only that part of the LSSS proccasing uncertainty attributed to the ex-core detectors, and must exclude that portion of the uncertainty due to the trip system shape index evaluation circuits. The processing uncertainties are described in A.3 below. The other shape index uncertainties are given in Table A-1.
A.2 , Measurement Uncertainties The description of the measurement uncertainties given in Appendix B2 of Part 1 is also valid for the DNB LC0 uncertainty evaluation.
'A.3. Monitoring System Processing Uncertainties A.3 1 Excore Monitoring System Th3 description of the Trip System Processing Uncertainties given in Appendix B3 cf Part 1 is valid for the Fort Calhoun excore aonitored DNB LCO because the arme instruments are used.
A. 4 References for Appendix A A-1 CEN-257-(0)-P " Statistical Combination of Uncertainties Part 1,"
November 1983 A-2 1
TABLE A-1 Uncertainty [ ] Components for the Evaluation of the LCO Related Peripheral Shape Index(l) k 95/95 ASIU K(f)(2) Bias
- 1. Separability Uncertainty -
--,em _, ,
- 2. Calibration uncertainty (")
- 3. Shape annealing uncertainty (")
4 Processing uncertainty ("I LHR (ASIU)
DNB (PSIA)
Not7s on Table A1-1:
(1) All components of the peripher al shape index have been tested for l
normality and where indicated, satisfy that distributional requirement (n).
(2) f - degrecs of freedom l (3) The [ ] is conservatively ( )
l 1
(4) For the [ ], see Table 2 of Appendix B1 Part 1 l
l (5) 2 Sigma values for consistent sets of input to the uncertainty processors l A-3 l
l
l l
APPENDIX B Sununary of Previous Methods for Combination Uncertainties ed B-1
APPENDIX B Th3 methods previously used for the application of uncertainties to the LCO's aro presented in Reference B-1 and are summarized in this appendix.
8,1 LHR LCO The LCO limit on linear heat rate is represented by the ordered pairs (P I)*
p fdl' A Icwer bound is drewn under this " flyspeck" data such that all she core power distributions analyzed are bounded. Using the previous methodology this lower bound was reduced by the application uncertainties and allowances to generate the LHR LCO as follows:
(B-1)
(B-2) where:
(B-3) l LCO W,,x = Core average linear heat rate i
l F = Planar radial peaking factor xy I
i F Core average axial power distribution peaking factor 2
i F,yg = Fuel densification-dependent power peaking augmentation factor '
l Tg = Azimuthal tilt allowance l
PU = Uncertainty in predicting local power at the fuel design limit B-2
MU = Power measurement uncertainty SAU = Shape annealing factor uncertainty RSU = Shape index separability uncertainty 1 i
ACU = Axial shape index calibration uncertainty APU = Processing uncertainty B.2 DNB LCO The fuel design limit for the DNB LC0 is represented by the ordered pairs (P fdn ' Ip). A lower bound is drawn under the " flys peck" data such that all the analyzed core power distributions are bound ed . Using the previous methodology this lower bound was reduced by applicable uncertainties and cllowances to obtain ex-core monitoring limits as follows:
(B-4)
(B-5) where:
Pfdn - Power to fuel design limit on DNB MU - Power measurement uncertainty I
Othsr components of the DNB LCO were thea represented by equations as fc11ows: (B1-1)
(B-6)
(B-7) i t . -
B-3 l
i
(B-8)
PMU - Pressure measurement uncertainty TMU - Temperature measurement, uncertainty FMU - Flow measurement uncertainty B.3 References for Appendix B B-1 CENPD-199-P, Rev. 1-P, "C-E Setpcint Methodology," March, 1982.
s e
B-4
e APPENDIX C TREATMENT OF UNCERTAINTIES IN TRANSIENT ANALYSES k
e C-i
APPENDIX C TRANSIENT ANALYSES C.1 Objective of Analysis As stated in Section 31, the DNB and LHR LCO's are generated from the fc11owing: .
- 1. The P fdn (for DNB) and Ph (for LHR) for the reload core.
- 2. Statistically combined process variable uncertainties.
- 3. The DNB and LHR Required Overpower Margin (ROPM) for the limiting A00.
The cethods used to combine uncertainties were discussed previously. The cbjectives of this appendix are:
- 1. Ta evaluate the impact of statistically combining uncertainties on the s31ection of initial conditions used in the transient analysis of DBE's.
- 2. TO determine the magnitude of the variation in ROPM attributable to the uncertainties.
C.2 General Strategy This section of the appendix provides the basis for analyzing the Loss of Csolant Flow (4 Pump LOF) and Single Full Length CEA drop (CEA drop) events to dst:rmine the variation of the ROPM due to statistically combining uncertainties.
Th7 Design Basis Events (DBEs) applicable to Fort Calhoun Station Unit 1 are presented in Table C-1. This table also lists the RPS trips which intervene to asIuro _ that acceptable limits
- are not exceeded. The table also identifies which of these events has the potential of yielding the maximum ROPM used to gen::rcte DNB or LHR LCOs, or for setting the pressure bias input used to cattblish the TM/LP LSSS.
CTh3 term " acceptable limits" is used in this appendix to include limits on DNBR, kw/ft, and dose rates, etc.
C-2
This table shows that most of these events can be classified in the following manner:
- 1. The events where action of the Thermal Maring/ Low Pressure (TM/LP) trip or the Axial Power Distribution ( APD) trip is necessary to prevent exceeding acceptable limits.
- 2. The events where action of RPS trips and/or sufficient initial steady state targin is necessary to prevent exceeding acceptable limits.
- These two categories of events are further discussed below.
C.2.1 Events Where Action of TM/LP and LPD Trips is Necessary to Prevent Exceeding Acceptable Limits The TM/LP trip limits are calculated assuming a conservative pressure bias factor. This bias factor accounts for the margin degradation due to proc;ssing, equipment and RTD response time delays for the most rapid DBE. By ac::unting for these effects in a conservative manner, the TM/LP trip will be actuated when necessary to ensure that the DNBR limit is not exceeded.
AD stated in Reference C-1, the maximum pressure bias factor may be obtained frca the RCS Depressurization event, the CEA Withdrawal (CEAW) event or Excess load event. However, the CEAW event now has been classified (in Reference C-2) as nst requiring the TM/LP trip. Thus, this event is no longar analyzed to
~
dstcrmine the pressure bias factor. It is analyzed to determine ROPM as d::sribed in Reference C-2. The pressure bias factor calculated is therefore derived from either the RCS Depressurization event (which is the most rapid d2prcssurization event where mitigation by the TM/LP trip is necessary) or the ExcIss Load event.
Th) pressure bias term from either the RCS Depressurization event or Excess Load event, caluclated using the methods and procedures given in Reference C-1, is the maximtm pressure bias term for the entire operating range of system parameters allowed by the Technical Specification LCO. Since the methods and the initial conditions used in this analysis are selected in the same manner as d scribed in Reference C-1, there is no need to perform a sensitivity study on the calculated value of the pressure bias term. That is, the method of C-3 i
combining uncertainties (either statistical or deterministic) does not affect the way in which the TM/LP trip is used for protection for DBEs where actuation of the TM/LP trip is required.
Th3 Gvents listed in Table C-1 where action of the LPD trip is necessary to prevent the kw/ft limit from being exceeded do not require any bias term for input to the APD trip limits. These limits already include a three percent pow:r bias to account for any transient variations in the measured power rclative to the actual power. Since none of the DBE requiring the APD trip
, rasult in a three percent margin degradation from the time of APD signal to the tima of maximus kw/ft, the bias for the APD trip is adequate. The method of combining ~ uncertainties has no impact on the method of analysis or on the input d ta selected for transients requiring the actuation of the APD trip to ensure th t the kw/ft SAFDL limit is not exceeded.
C.2.2 Events for Which Intervention of RPS Trips and/or Sufficient Initial Steady State Thermal Margin Maintained by LCO is Necessary to Prevent Exceeding Acceptable Limits DBEs ' listed in this category are not protected by the TN/LP and LPD trips beetuse some of the parameters (such as core mass flow rato or radial peaking fGstor), that are important in some DBEs are not directly monitored by the TM/LP and APD trips. For these DBEs, the mitigating effects of other RPS trips and/cr sufficient initial steady state taargin maintained by operating within the LCO is necessary to ensure that acceptable limits are not exceeded.
Th2 DBEs in this category can be further grouped according to a single key parameter change which has the greatest impact on the margin degradation. A grcuping of DBEs in this manner is presented in Table C-2.
To dstermined the sensitivity of ROPM to the magnitude of uncertainties listed in Tcble C-3 during an event characterized mainly by a decrease in the core mass flow rate, the 4 Pump LOF event was analytad. This event was analyzed beccuse it bounds all events characterized by decreases in the core mass flow rate, since all of these events are characterized by the same principal physical effects.
C-4
The CEA drop event was analyzed to determine the variation of ROPM due to the method of calculating uncertainties for events characterized by increase s in integrated radial ar.d planar peaking factors (F r, Fx y) . This event was taalyzed because a dropped CEA results in higher rF and Fxy increases than the Asymmetric Steam Generator events and it provides the limiting input (i.e.,
highest R0PM) used in establishing the DNB LCO.
Th3 rsaults have shown insensitivity of ROPM to the magnitude of uncertainties far the 4 Pump LOF and CEA drop events. The same conclusion may be applied to the CEA withdrawal event, which is expected to always be less limting than the
' CEA drop event. It can be stated that the CIA Withdrawal event will not become liciting from the standpoint of establishing LCOs due to variations in the R0PM cttributable to the process variable uncertainties considered in the analysis.
Therofore, an ROPM sensitivity analysis has not been performed for this event.
C.2.3 Impact of Statistically combined Uncertainties on DBEs with Other Limits The statistical combination of uncertainties are only used to establish DNB and LHR LCOs and LSSS. Therefore, it impacts only the DNB. and LHR-related LCOs i cnd LSSS. Statistically combining uncertainties does not impact events with othsr limits (such as deposited energy, time to lose Technical Specification allowed shutdown margin , etc.) . 1her efore , events with other limits will be anclyzed using the same methods and selecting the initial conditions in the s=3 way as previously reported in the USAR (Reference C-3) or as updated by apprcved reload license amendments.
l l
l
! l l
C-5
C.3 Analyses Performed for Evaluation of ROPM for the Limiting DBEs C.3 1 Loss of Coolant Flow Event (4 Pump LOF)
C.3 1.1 Description of Transient The key input parameters for the 4 pump LOF event are determined from the d:scription of the transient given below.
The 4 pump LOF event is asstaned to be initiated by the simultaneous loss of AC power to all four reactor coolant pumps. After the loss of power, the flow starts coasting down rapidly. In a very short time (about 2 seconds) the low ficw trip setpoint is reached. After a delay for processing the trip signal,
( 0.65 seconds), and decay of the magnetic flux for the holding coils (.0.5 seennds), the CEAs start dropping into the core. After the scram 3CEAs reach chout 205 insertion for an initially top peaked axial shape (or 55% insertion f4r o bottom peaked shape), the CEAs have inserted sufficient negative rcactivity to drop the core heat flux below that required to turn around the transient DNBR. The transient minimum DNBR occurs when the margin gain due to the rate of heat flux decay (after scram) equals the margin loss due to the rato of flow decrease. The minimum DNBR occurs within 3 5 to u.5 seconos of the initiation of this event.
Sinco the minimum DNBR is reached within the first 4.5 second s , the power distributions and the peak linear heat generation rate have not had time to chings. The core inlet and fuel temperatures will not change appreciably, sin 30 the loop cycle time ( 12.0 seconds) and the fuel time constant ( 6.0 sec2nds) are larger than the time required to terminate the transient DNBR.
Thus, the margin degradation for this event is determined primarily by:
- 1. The core flow coastdown
- 2. The signal processing time delay 3 The holding coild time delay 4 The low flow trip setpoint
- 5. The available scram worth *
- 6. The CEA reactivity versus insertion characteristics.
C-6
C.3 1.2 Criteria of Analysis This event is classified as an A00 and hence is analyzed relative to the fall: wing criteria:
1
280 x Burnup (MWD /MT)
- 2. Centerline taeperature melt 2 < 50800 F - -
50,000 (MWD /MT)
Notest (1) CE-1 DNBR shall have a minimum allowable limit corresponding to a 955 probability at a 95% confidence level that DNB will not occur on the limiting rod. In this study, a DNBR limit of 1.22 was used (see Reference C-4 for austification).
(2) The CTM SAFDL is a criterion for this event, but this SAFDL is never exceeded since there is no increase in PLHGR during this event.
C.3 1 3 Input Parameters and Initial Conditions Th2 purpose of this study L.4 to evaluate how much predicted margin degradations vary because of the way the uncertainties of initial conditions are ecmbined.
' An Enalysis parametric in
- 1. the initial coolant temperature,
- 2. initial RCS pressure (pressurizer pressure),
3 initial core mass flow rate,
- 4. initial axial shape index ,
- 5. integrated radial peaking factor, and
- 6. initial core power w s performed to determine the sesntivity of ROPM to these parameters. Other parameters were assumed to be at their limiting values to maxi:cize the calculated margin degradation. The input parameters used in the analysis of th) 4 Pump LOF event are presented in Table C-4 A brief justification of valu3s selected is given below.
C-7
The key parameters for the loss of coolant flow event were identified earlier ca the flow coastdown, the RPS delay times, the low flow analysis trip setpoint cnd the scram reactivity versus insertion characteristics.
The flow coastdown assumed in the analysis is generated by CESEC-III using the i plicit reactor coolant pump model. This model produces a conservative constdown, consequently, yielding a larger margin degradation due to a lower absolute flow at time of minimum DNBR.
Th3 low flow analysis trip setpoint of 935 assumed is one correspoding to the tinimum allowed Technical Specification limit for initial 4-pump flow. The RPS trip processing response delay time and holding coil magnetic flux decay time i occused in the - analysis are the maximum delay times allowed by the Technical Specific ation. This results in the largest margin degradation since it takes lenger for the CEAs to start dropping into the core and tnus takes a longer time period to twn around the transient DNBR. The scram reactivity versus insertion characteristics assumed in the analysis were calculated according to the s;3thods given in Reference C-1.
Oth:r important parameters are the available scram worth and the moderator and
, fu 1 temperature reactivity coefficients (MTC and FTC). The available scrs=
wortha were conservatively c alculated , including an allowance for the most rcactive CEA being stuck in the fully withdrawn position after the trip.
A beginning-of-cycle (BOC) MTC was used in the analysis, since a positive MTC in combination with the slight increase in the coolant temperature accelerates
! the rcte of increase of both the coolant temperature and heat flux prior to trip. Both theses effects cause the transient DNBR to decrease at a faster rato. The least negative FTC was asstaned for the same reasons.
C.3 1.4 Method of Analysis for the Four Pump LOF Tha Nuclear Steam Supply System (NSSS) response to the 4 pump LOF event was sistulated using the digital computer code CESEC-III described in References C-5 thrcugh C-7. - The thermal hydraulic code CETOP (Reference C-8) incorporating 1 the CE-1 correlation and a 1.22 DNBR limit was used to calculate the thermal Ergin degradation during the event. These codes are the same as described in I the previously approved license submittal (Reference C-9) except for the use of C-8
,e3 y _- - , . , _ . - , . , , . _ . _ , _ - , . - , _ , , . . , _ , . _ , . , , , . < _ . - . . . - . , _ . -.-e_,,m . . - . -,.
0 DNBR limit of 1.22 rather than the 1.19 value used previously. The methodology used is described in Reference C-10.
The calculative procedures used in the analysis to determine the DNB R0PM
- d: pend upon the initial axial power distribution. The methods used to analyze 4 pump LOF are axial shape index dependent because credit for the heat flux decay is taken only when the initial minimum CE-1 DNBR is located in an axial regica of the core where the scram rods have passed the axial node of minimum DNBR before the time of minimium DNBR is reached.
. The CESEC-CETOP method of analysis is schematically presented in Figure C-1.
This Eethod for analyzing the event is discussed below.
C.3 1.4 CESEC-CETOP
- 1. Limiting axial power distributions, characterized by shape ind ex , are d;termined from a large sample ( 2,000) of possible distributions which are calculated as a function of axial shape index, core burnup, and CEA ctnfiguration, using the QUIX code (Reference C-11). The limiting axial power shapes are those distributions that produce the lowest initial steady state power to a DNBR limit of 1.22 at a given axial shape index. The power at which the limit is reached is predicted by the CETOP code.
- 2. The initial core power, initial RCS flow rate, initial pressurizer pressure (RCS pressure), initial coolant inlet temperature, and the scram reactivity versus insertion associated with the axial power distribution of interest are input to CESEC to obtain the time dependent values of core average heat flux, RCS pressure, coolant inlet temperature and the core mass flow rate.
CESEC-III solves the conservation equations for mass flow and momentum to cbtain the RCS flow coastdown values. The general forcing functions for the fluid momentum equations consist of the pump torque values from the raanufacturer's four quadrant curves, wherein the torque is related to pump angular velocity and discharge rate.
- 3. A set of CETOP cases are run with the time dependent values of core heat flux, temperature, RCS pressure and core mass velocity along with the initial values of integrated radial peaking factor , the axial power distribution and the net uncertainties to determine the time of minimum DNB R.
C-9 1
4 The core mass velocity at the time of minimum DNBR in combination with the initial values of RCS pressure, inlet temper ature , axial power dsitribution, integrated radial peaking factor, core average heat flux and the not uncertainties are used to determine the power to the DNB limit.
This power is denoted B2'
- 5. A CETOP cace is also run with the initial steady state system parameters, including the effects of statistically combined uncertainties, to determine the power to DNB limit. This power is denoted B .3
- 6.- The R0PM is then defined (Reference C-1) to be:
(C-1)
C.3 1.5 Results The results of the sensitivity analysis performed over the range of uncertainties for the variables listed in Table C-3 about the nominal base etnditions listed in Table C-4 are presamted in Figure C-2. This figure prosents the ROPM as a function of initial axial shape index obtained for the event initiated from the nominal base cone itions and also at the conditien:
rcsulting in the maximum variation in the ROPM due to the uncertainties.
Figuro C-3 shows a plot of the ROPM varia', ion, ROPM, as a function of axial sh pe index. It should be noted that the absolute value of the ROPM is plant and cycle specific; however, the maxiram margin variation may not be plant and cynlo specific . The maximum variation in the ROPM, shown in Figure C-3 as a function of axial shape index, will be added to the cycle specific ROPM ociculated for the nominal base conditions to obtain the maximum ROPM during th3 Gvent. This maximum ROPM will be used to establish the DNB LCO.
Tha sequence ofe vents during a 4 pump LOF event is presented in Table C-5.
The NSSS response during this event is presented in Figures C 4 to C-7 for the ocse with an axial shape index of 0.0.
C-10
C.3 1.6 Conservatisms in the Analysis Methods l
Tha purpose of this section is to identify the conservatisms that are included in th] methods used to calculate the ROPM on DNBR during a 4 pump LOF event.
~1. The magnetic flux decay of the holding coil assumed in the analysis is 0.5 seconds. A more realistic value based on field test data is 0.4 seconds.
~
- 2. . The low flow response time assumed in the analysis is 0.65 seconds, which 10 conservative by at least 0.1 second based on field measurements. !
l 3 The CEA drop time value of 31 seconds assumed in the analysis is for j slowest CEA. The maximum drop time to 90% insertion is allowed by l
Tcchnical Specifications is 2.5 seconds.
4 The flow coastdown generated by CESEC-III is conservative with respect to the actual coastdown characteristics.
- 5. The ROPM is calculated without taking credit for the higher value of RCS pressure at the time of minimum DNBR. The higher RCS pressure at the time of minimum DNBR will lower the ROPM for this event.
In R]ference C-12 a "best estimate" case was run to quantify the conservatisms cutlined above. The ROPH for this best eatimate case was conservative by
[' j with respect to the transient analysis case. The results of the best I citicate case showed that due to the slower flow coastdown and the higher lower l
l ficw trip setpoint assumed in the best estimate case, the l'ow flow trip was initicted at the same time as in the safety analysis case. However, the faster 1
i RPS rcsponse time, the faster time to decay the magnetic flux of the holding l
coil and the faster insertion of the shutdown CEAs turned around the transient DNBR faster relative to the safety analysis case, , Due to the slower flow coastdewn, the absolute flow at the time of minimum DNBR was higher than in the transiint case. A best estimate analysis for the Fort Calhoun Station would also show positive gains.
Ta Ensure that the SCU ROPM analysis were conservative, the four pump Loss of i Flow svent was analyzed using deterministic methods (with all uncer tainties l
C-11 l
cpplied in the most adverse direction). Bis analysis indicated that the SCU derived R0PMs were conservative with respect to the deterministically derived values.
C.3 2 Sinale Full Length CEA Drop Event (CEA Drop)
Tha key input parameters for the CEA Drop event are determined from the d::cription of the transient given below.
A CEA Drop event is asstaned to occur as a result of:
- 1. An inadvertent interruption of power to the CEA drive magnetic clutch, or
- 2. A mechanical or electrical failure in the mechanical brake in the CEA mechanism when the CEA is being moved.
Th2 drop of a CEA into the core reducea che fission power in the vicinity of th] dropped CEA and adds negative reactivity on a core-wide basis. The n:gative reactivity causes a prompt drop in power and thus the heat flux. he cagnitude of this prompt power decrease depends upon the worth of the dropped CEA. Since the turbine is operated in the load limit mode (i.e., no turbine admission valve motio'n occurs), a power mismatch exists between the primary and sec:ndary s ystem. He power mismatch initially causes the primary side to coold down. The decrease in the fuel and moderator temperatures in conjunction with an assumed highly negative fuel temperature and moderator temperature 1
l coefficients adds positive reactivity. The positive reactivity added by the feedbacks compensates for the negative reactivity added by the dropped CEA within approximately 200 seconds.
Th) initial decrease in the coolant temperatures also causes the pressurizer pr:srure to decrease (the analysis conservatively assumes that the pressurizer icv 01 and pressur . control systems are inoperative) . In addition, the dropped CEA also causes an asymmetry in the radial power distribution and the radial power peaks. Tne radial peaks increase as a result of this distortion and achicve a new, " tilted" asympotite state. At approximatley 200 seconds, the power and the core heat flux have returned to their initial values. Be coolant inlet temperature and RCS pressure achieve a new, lower, steady state vclua. We DNBR also achieves a new, lower, steady state value.
C-12 l
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drop worth at any time during core life. The maximum radial peaking factor change results in the highest ROPM. Assuming the[ ] drop worth of the CEA at any time during core life producing the [ j distortion is also conservative since it minimizes both the pressure and inlet temperature decreases. (It should be noted that the analysis conservatively assumes an inconsistent set of radial peaking factor changes and CEA drop worth.
Realistically, a L 1 worth dropped CEA will not produce the[ ]
radial peaking factor increases.)
The most negative values of the Moderator Temperature Coefficient (MTC) and the
- Fuel Temperature Coefficient (FTC) were assumed in the analysis. The negative FTC and MTC in conjunction with the decreasing coolant and fuel temperatures insert positive reactivity. The positive reactivity inser ted offsets the negative reactivity insertion initially by the dropped CEA and thus enables the core heat flux to return to a value aproaching its initial level. The uncertainties on the FTC asssumed are given in Table C-6. All control systems are assumed to e in the manual mode. The key control systems for this event are the Pressurizer Pressure Control System (PPCS) and Pressurizer Level Control System (PLCS). The PPCS and PLCS are assumed to be in the manual mode because this allows the primary pressure to drop during the transient and thus minimizes the pressure at time of einimum DNBR. This results in the larges DNBR margin degradation during the event.
C.3.2.!! Method of Analysis for the CEA Drop Event The Nuclear Steam Supply System (NSSS) response to a single full length CEA drop event was simulated using the digital computer code CESEC-III, described in References C-5 through C-7. The thermal hydraulic design code CETCP described in Reference C-8, used the CE-1 correlation and a DNBR limit of 1.22 to calculate the thermal margin degradation during the transient.
~
C.3 2.5 Required Overpower Margin for CEA Drop C.3.2.5.1 Required Overpower Margin on DNBR The calculational procedure used in the analysis to determine DNB RCPM is presented in Figure C-8. This procedure consists of the following steps:
.., # .g, Idhi~N%
.x'
/ *. , '
.,w g,
,;E
- 1. Determining the pseudo hot channel power distribution both before CEA drop ,i ."M'p . N. ,'Q= . g7 ? '-D and after CEA drop. The integrated radial peaking factors are synthesized s'~ % , . : ,.
- from the core average axial power distribution and planar radial power N ..[h distributions if explicit 3-D physics calculations are not performed. k...bhYk,Y
. f , . . ..t lf ,,,l1 .l * '
- 2. Simulating the CEA drop event using CESEC to determine the final values of r,g f + j ',,-.
4 / t.f 4- . 7 core average heat flux, RCS pressure and inlet temperature.
I g . , :s . s. ..
1 e:pi 3 bnning the CETOP code to determine the rod average power at which the 4.M.7, n: , q y'f,kc( .
final design limit on DNBR is reached for the initial steady state N ' , . ....+t 'C e,
W W; u ..".
t.
par ameter s, including the e f fects of those uncertainties which were w .. ,
3 combined statistically. This value of power is denoted B). .Y'3'i<A
, y. 3 ...j
-d 4 The maximum heat flux, final inlet temperature and RCS pressure , the post- V 3.]g g.,.,. { t[
drop integrated radial peaking factor , the post-drop axial power 6 distribution , the uncertainties and the final value of the core average h s '.K ; ,
7-eer .s mass velocity are input to CETCP to determine the power at which the fuel /
- geygg .
design limit on DNBR is reached for the transient conditions. This power . ,. ,'.j - .. Q .,
s .
is denoted B2 ' Mb~Y .
h,$h?. ,b. . .h
.. n
- 5. The ROPM is then defined as: _ i *' J .". ,
gg',A
% jp
~ '
(C-3)
Mb y , 3 ,4 , ,,. i l T+--r f" %,[
'; y r 7,g :
"} '..g. ;. l.n s e
'5... ev $
5 where P 3 is the initial core heat flux and P 2 is the final core heat flux. - ll C.3.2.5.2 Required overpower Margin on PLHGR (kw/ft) .
I e
i The ROPM on linear heat rate is calculated by the procedures given in Chapter 8 of Reference C-1. Since the methods used to analyze the PLHGR have not changed _
and since there is no sensitivity of this ROPM due to statistically combining uncertainties, no analysis is required.
C-15
,1-C.3.2.6 Results The results of the sensitivity analyses performed for the CEA drop event is _
presented in Figure C-9 This figure presents the R0PM as a function of _
initial axial shape index obtained for the event initiated from the nominal .
base conditions and also at the conditions resulting in the maximum variation in the R0PM due to the uncertainties. The maximum variation in the R0PM _
( AROPM), shown in Figure C-10 as a function of axial shape index, will be added to the cycle specific R0PM calculated for the nominal base conditions to obtain the maximum .ROPM during the event. This maximum ROPH will be input to establish the DNB LCO. --
. =
The sequence of events during a CEA drop event is presented in Table C-7 The NSSS response during this event is presented in Figures C-11 to C-14.
C.3 2.7 Conservatism in Analytical Methods The purpose of this section is to identify the conservatisms that are included in the methods used to calculate the ROPM on DNBR during a CEA drop event.
These conservatisms are qualitatively identified below. An example case is _
presented and compared with the safety analysis results of previous sections to quantify the conservatism.
- 1. The analysis assumed a boundD.g value for the integrated rdial peaking .
factor changes which is conservative by 2%. The analysis also assumed a minimum CEA drop worth, which does not produce the maximum integrated [
radial peaking factor changes. The use of consistent set of CEA drop worth _
and the integrated radial peaking factor change will lower the margin degradation.
- 2. No credit for the actuation of the pressurizer pressure and level control system is taken in the analysis. The actuation df the pressurizer pressure and level control system would maintain the RCS pressure at a higher value thereby lowering the margin requirement for this event.
3 The moderator temperature coefficient assumed in the analysis is '
0
-2.7x10 4 A o / F. Current Technical Specifications limit the MTC to
-2.5x10~1o / F.
C-16 ,
Reference C-12 quantifies the conservatism outlined above by running a "best estimate" case. The ROPM for this best estimate case was conservative by _.
[ ] with respect to the transient analysis case. A best estimate analysis for the Fort Calhoun Station would also show positive gains. -
To ensure that the results of the SCU ROPM analysis were conservative, the Single Full Length CEA Drop event was analyzed using deterministic methods (with all uncertainties applied in the most adverse direction). This analysis indicated that the SCU derived R0PMs were conservative with respect to the deterministically derived values.
C.4 Conclusions =
Based on the results of the sensitivity studies, it can be concluded that:
- 1. The ROPM is relatively insensitive to the range of uncertainties on the initial conditions. The maximum ROPM established by the sensitivity study
^
is used to generate the LCOs.
- 2. The use of a constant maximum ROPM at each axial shape index to generate the LCOs eliminates the need to stochastically simulate the ROPM variations in calculating the net aggregate uncertainty.
3 The use of the maximum R0PM also ensures with a high degree of confidence that acceptable limits for the DBEs will not be exceeded.
C.5 References for Appendix C C-1 CENPD-199-P, Rev. f-P, "C-E Setpoint Methodology," March, 1982.
C-2 CEN-121(B)-P, " Method of Analyzing Sequential Control Element Arsembly Group Withdrawal Event for Analog Protected Systems," November,1979 C-3 Fort Calhoun Station Unit 1 USAR Docket No. 50-285. .
C-4 CEN-257(0)-P, " Statistical Combination of Unc er tai ntie s , Part ? -
Combination of System Parameters Uncertainties in Thermal Margin Analyses for Fort Calhoun Station Unit 1," November,1963 C-17
C-5 CENPD-107, "CESEC Topical Report," July, 1974 C-6 "CESEC, Digital Simulation of a Combustion Engineering Nuclear Steem #. ~
Supply System," December,1981, transmitted as Enclosure 1-P to LP-82-001, , ,
January 6,1982.
C-7 CEN-234(C)-P, Louisiana Power and Light Company, Waterford Unit 3, Docket 50-382, Response to Questions on CESEC, December,1982.
C-8 CEN-191(B)-P, "CETOP-D Code Structure and Modeling Methods for Calvert <
Cliffs Units 1 and 2," December 1981. .
C-9 Letter, E. G. Tourigny (NRC) to W. C. Jones (OPPD), dated March 15, 1983.
License Amendment 70 and SER for cycle 8 Operation of Fort Calhoun Station Unit 1, Docket 50-285. '
C-10 OPPD.NA-8303-P, " Omaha Public Power District Transient and Accident Methods Verification," September,1983. -
1 C-11 System 80 PSAR, CESSAR, Vol.1, Appendix 4A, Amendment No. 3, June,1974 C-12 CEN-124(B)-P, " Statistical Combination of Uncertainties Part 3 - C-E Calculated Departure from Nucleate Boiling and Linear Heat Rate Lir:iting '
Conditions for Operation for Calvert Cliffs Units 1 and 2," March, 1980. ,
2 e
n a e i
C-18 l l
\
TABLE C-1 DESYGN BASIS EVENTS AND RPS TRIP PROTECTION Limiting Input to Establish Setpoints DBE RPS Trip LCO LSSS CEA Withdrawal High Power and No No Variable High Power
' Borsn Dilution TM/LP arid /or APD No No Loss' of Load TN/LP and/or APD No No Exessa Load TM/LP and/or APD No Yes Logs of Feedwater 'TM/LP and/or APD No No Exo:Es Feedwater TM/LP and/or APD No No RCS Depressurization TM/LP and/or APD No Yes 1423 of Coolant Flow low Flow Yes No loss of AC Power low Flow No* No CEA Drop None Yes No Asymmetric Steam' AP Across Steam No No Generator Transients Steam Generator
, (input to TM/LP)
CEA' Ejection High Power or Variable No No High Power Seized Pump Rotor low Flow No No Stoam Line Rupture low Steam Generator Level No No
, or low Steam Pressure Stoam Generator Tube TM/LP and/or APD No No Rupture
'Th3 DNBR transient for this , DBE is covered by the loss of coolant flow DBE transient analysis.
Y
~
C-19 I
TABLE C-2 DESIGN BASIS EVENTS AND IMPORTANT PARAMETER CHANGES Parameter Changes Most Important Design Basis Event to Margin Degradation Loco of Forced Primary Coolant Flow Decrease in Ccre Mass Flow Rate
~*
Loca cf Non-Emergency AC Decrease in Core Mass Flow Rate Seized Rotor Decrease in Core Mass Flow Rate CEA Drop Increase in Integrated Radial and Planar Peaking Factor Asymmetric Steam Generator Transients Increase in Integrated Radial and Planar Peaking Factor CEA Withdrawal Increases in Core Posar and Core Coolant Inlet Temperatures 4
C-20
TABLE C-3 UNCERTAINTIES Uncertainties Values
- 1. . Uncertainty in integrated radial pin power (F )
r 10I
- 2. Uncertainty in local core power density (F q) 27%
- 3. Power measurement uncertainty 125 4 Shape Index uncertainty 'e
- 5. Flow measurement uncertainty
- 6. Pressure measurement uncertainty 122 psia Temperature measurement uncertainty 0
- 7. 32F CCROPH is an input value used to generate the LCOs. The ROPM vlaues are gin: rated parametrically in axial shape index. The uncertainty associated with any given value of axial shape index is accounted for explicitly in the anelyses which determine the LCOs and does not have to be accounted for in the transient analysis.
C-21
l TABLE C-4 KEY INPUT PARAMETERS USED IN THE LOSS OF COOLANT FLOW EVENT Parameter Units Values Initici Power Level 5 of 1500 MWt 100.0*
CF Initici Inlet Temperature 54 5' Initici RCS Flow Hate gpm 208,280'
- Initici Pressurizer Pressure psia 2075' Integrated Radial Peaking Factor -
-ARO 1.70'
-Lead Bank Inserted 1.75' Low Flow Analysis Trip Septoint 5 of initial flow 93.0 Flow Coatdown Fraction of initial Generated
. flow vs. time by CESEC-III Trip Delay Time sec 0.65 Holding Coil Delay Time sec 0.5 CEA Drop Time sec 3.1 Moderator Temperature Coefficient x10#ap /0F 4.5 Fu:1 Temperature Coefficient --- 0.85 Multiplier CEA Scram Worth 1 -6.18 Initial Axial Shape Index asiu -0.359 to +0 337 CDcos not include uncertainty. The uncertainties for these parameter s are given in Table C-3 C-22 y
TABLE C-5 SEQUENCE OF EVENTS FOR THE LOSS OF COOLANT FLOW EVErr Time Event Value 0.0 Loss of Power to all Four Reactor ---
Coolant Pumps 1.90 Low Flow Trip 935 of initial flow 2.55 Trip Brenkers open ---
3 05 CEAs Begin to Drop into Core ---
4.75 Maximum RCS Pressure, psia 2099 C-23
TABLE C-6 KEY INPUT PARAMETERS ASSUMED IN THE SINGLE FULL LENGTH CEA DROP EVETT Range of Parameter Units Values
. Initic1 Core Power Level 1 of 1500 MWt 100* *
-Initici Inlet Temperature CF 545' Initici RCS Pressurizer Pressure psia 2075' Initici Integrated Radial Peaking 1.758 Factor F , Lead Bank Inserted 25%
r Initici RCS Flow Rate gpm 208,280 Initici Axial Shape Index asiu -0.359 to +0.337 CEA Drop Worth 5 -0.28 Intcgrated Radial Peaking Factor % 16.96 Chingo Moderator Temperature Coefficient x10~"ap/0F -2.7 Fu:1 Temperature Coefficient 1.15 Multiplier CValuas quoted are without uncertain tie s. The uncertainties for these paramaters were given in Table C-3 C-24
TABLE C-7 SEQUENCE OF EVEffrS FOR THE CEA DROP EVENT Time (sec) Event Setpoint or Value 0.0 CEA Begins to Drop Into Core ---
1.0 CEA Reaches Full Inserted Position 1005 Inserted 1.22 Core Power Level Reaches Minimum 65 3% of initial and Begins a Return to Power due to Reactivity Feedbacks 200.0 Reactor Coolant System Pressure 1996 Reaches a New Steady State Value 200.0' Core Heat Flux Returns to its 95.2% of initial Maximum Value S
O C-25
LOW R0W ANALYSIS
- MASS R0W RATE
~
SCRAM REACTIVITY W INITIAL HEAT RUX LOW FLOW TRIP RESPONSE * - INITIAL AXPD TIME AND HOLDING COIL TIME DEPENDENT VALUES OF TIN. PRESSURE. MASS FLOW RATE. AND HEAT FLUX n
CETOP TO DETERMINE 2
TIME OF MIN! MUM DNBR
CETOP TO DETERMINE 6--- INITIAL TIN ---* CETOP TO DETERMINE POWER TO ONS LIMIT -
- INITIAL PRESSURE ; POWER TO DNB LIMIT WITH MASS FLOW RATE " WITH INITIAL m!TM MPD m AT TIME OF MINIMUM CCN0!TIONS. DENOTE INITIAL FR W ONBR. DENOTE THIS THIS POWER AS 81 UNCERTAINTY ~
POWER 82
- --- INITIAL HEAT FLUX W B2 I o
^
81
\-
LassOfCoolantFlaw OmahaPublicPowerDistrict Figure ProcedureUsedToDetermine90PM FortCalhounStation-UnitNo.1 C-1 C-26
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-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.46' AXIAL SHAPE INDEX,ASIU LossOfCoolantFlow OmahaPublicPowerDistrict Figure R0PM (DNB) At 100% Pcwer FortCalhounStation-UnitNo.1 C-2 C-27
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.40 -0.30 -0.20 -0.10 0.00 0.k0 0.20 0.30 0'.40 AXIAL SHAPE INDEX,ASIU LossOfCaolantFlow OmahaPublicPowerDistrict Figure AROPM vs Axial Shape Index FortCalhounStation-UnitNo.1 C-3 C-28
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LossOfCoolantFlow Ca:anaPublicPowerDistrict Figure !
CorePowervsTime FortCalhounStation-UnitNo.1 C-4 !
C-29
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LessOfCaolantFlow CmahaPublicPowerDistrict ! Ficure CareHeatFluxvsTime FortCalhounStation-UnitNo.i: C-5 C-30
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LossOfCaolantFlow OmahaPublicPowerDistrict l Ficure .
RCSTemperaturesvsTime FortCalhounStatian-UnitNo.1i C-6 :
C-31
2250 i i , i i 2200 -
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1900 - -
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1800 0 5 10 15 20 25 30 TIME, SECONDS l
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i LossOfCaolantFlow l CaanaPuolicPaxerDistrict Ficure '
RCSPressurevsTime iFortCalhounStation-UnitNo.i. C-7 C-32
SYNTHESIZE 3-D PSEUDO HOT CHANNEL BEFORE DROP AXIAL AND PLAMAR RADIAL - PWR DISU!Bm0NS 3-0 PSGC0 .
POWER DISTRIBUTIONS HOT CHt.NNEL IF EXPLICIT 3-D PHYSICS CALC. ARE NOT PERFORMED POWER AFTER DROP 3-0 PSEUDO HOT CHANNEL POWER
- INITIAL T!N "
CG WP mm -
g ==-INITIAL PRESS.-e.
DROP EVENT
- INITIAL MASS MTC. FTC WITH CESEC FLOW RATE INITIAL HEAT ,
FLUX FINAL VALUES OF PRESSURE. Tf '
MASSFLCWRAfE AND HEAT FLUX
<r .,
CETOP TO DETERMINE CETCP TO CETEFli!NE
! PC'4ER TO DNB LIMIT l POWER TO DN8 LIMIT
- FOR TRANSIENT ; UNCERTAINTY ; FOR INITIAL l
COM0!TIDMS. DENOTE CCN0!TIONS. CENOTE THIS POWER 82 THIS POWER SI l B2 l
o 1
i CEADropEvent OmahaPublicP0'nerDistrict Fiaure
~
ProcedureUsedToDetermineR0PM FortCalhounStation-UnitNo.1 C-8 C-33
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cr .
~ ' 0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 010 AXIAL SHAPE INDEX, ASIU CEADrcpEvent OmahaPublicPowerDistrict Figure R0PM (DNB) At 100% Power FortCalhounStation-UnitNo.1 C-9 C-34
(~
w i
s M -
<3
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-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 AXIAL SHAPE INDEX, ASIU CEADrapEvent OmahaPublicPowerDistrict Fiaure 2
AROPMvsAxialShaceIndex FortCalhounStation-UnitNo.1 C10 C-35
4 110 i i i i i i i i i 100 - -
5 90 - -
E o 80 -- -
S.
70 - -
o '
y 60 - -
d 5
c.
50 - -
g 40 - -
5 1 30 - -
E 8 20 - -
10 - -
1 0
0 20 40 60 80 100 120 140 160 180 200 TIME, SECONDS i
l i,
SingleFullLengthCEADrop OmahaPuolicP0'derDistrict , Figure ,
CoreP0'dervsTime Fort Calhoun Station-Unit !!0. i; C-!! '
C-36
110 , , , , , , , , i 100 - -
a E 90 .- -
8 80
-g - -
Ei 70 - -
e d 60 - -
5
' 50 - -
x" 40 -
h dc 30 -
i E 20 - -
O 10 - -
0 0 20 40 60 80 100 120 140 160 160 200 TIME, SECONDS SingleFullLengthCEADrop OmanaPublicPowerDistrict Figure i CoreHeatFluxvsTime FortCalhounStation-UnitNo.i; C-12 i C-37
600 i i i i i i i i i 590
["tl't -
' 580 - -
S o
570 T ,y,y,,, -
1
$ 560 - -
5 S 550 - -
F h 540 -
530 - -
' ' ' ' ' ' ' ' I 520 l 0 20 40 60 80 100 120 140 160 180 200 l i
TIME, SECONDS I
i l
l SingleFullLengthCEAOrop OmahaPublicPowerDistrict ! Figure RCSTemaeraturesvsTi.me Fort Calhoun Station-Unit No. i! C-13 .
C-38
2300 , , , , , , , , i 2250 - -
2200 - -
5 m
o- 2150 - -
Y
@ 2100 - -
'O C
' 2050 - -
O C
2000 - -
4 1950 - -
1900 0 20 40 60 80 100 120 140 '160 180 200 TIME, SECONDS l
l l
i l 1 i
l l
SingleFullLengthCEADrop OmanaPublicPower. District Figure ACSPressurevsTime FortCalhounStation-UnitNo.1 C-14 ;
C-39 1
t e
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