ML20133H359

Statistical DNBR Evaluation Methodology

ML20133H359
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Site:	Surry, North Anna, 05000000
Issue date:	07/31/1985
From:	Richard Anderson, Basehore K, Berryman R VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
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ML18143B651	List: ML20133H359
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VEP-NE-2, NUDOCS 8510170079
Download: ML20133H359 (67)

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Statistical DNBR Evaluation Methodology VEP-NE-2 July,1985 6

VIRGINIA POWER NORTHCAROLINA POWER WEST VIRGINIA POWER ri '0079 B '.)1 0 0 8 ADOCK 05000?'80 PDP

PAGE 1 s

VEP-ME-2

[ STATISTICAL DMBR EVALUATION METHODOLOGY

[

by

[ R. C. Anderson l

MUCLEAR ENGINEERING ENGIMEERING AND CONSTRUCTION DEPARTMENT VIRGINIA POWER RICHMOND, VIRGINIA L

July~ 1985 Recommended for Approvals M. L. Basdhore, Supervisor f Muclear Engineering Approved by,*

km. - __ .

R. M. Berryman, Director .

Nuclear Engineering

PAGE 2 CLASSIFICATI0M/ DISCLAIMER The data, information, analytical techniques and conclusions

[

in this report have been prepared solely for use by Virginia Power (ths Company), and they may not be appropri~ ate for use in situations other than those for which they were specifically proPared. The Company therefore makes no claim or warranty whatsoever, express or implied, as to their accuracy, usefulness, or applicability. In particular, THE COMPANY MAKES MO WARRANTY OF MERCHAMTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, MOR SHALL ANY WARRANTY BE DEEMED TO ARISE FROM COURSE OF DEALING OR USAGE OF TRADE, with respect to this report or any of the dtha, information, enclytical techniques, or conclusions in it. By making this report ovcilable, the Company does not~ authorize its use by others, and cnv such use is expressly forbidden except with the prior written I

cyproval of the Company. Any such written approval shall itself be dacced to incorporate the disclaimers of liability and disclaimers of warranties provided herein. In no event shall the Company be lichle, under any legal theory whatsoever (whether contract, tort, uctranty, or strict or absolute liability), for any property l

dcange, mental or physical injury or death, loss of use of property, or other damage resulting from or arising out of the use, authorized or unauthorized, of this report or the data, information, and analytical techniques, or conclusions in it.

PAGE 3 ABSTRACT Virginia power has developed a methodology for the statistical j troatment of uncertainties in evaluating the Departure from Mucleate Boiling Ratio (DNBR) in a nuclear reactor core.

Proviously, these uncertainties were treated in a conservative datorministic fashion, with each parameter assumed to be I

alcultaneously and continuously at the worst point in its uncortainty range with respect to the DNBR. Statistical combination of some of these uncertainties permits a conservative concideration of each uncertainty, while providing a more realistic ovoluation of the DMBR margin.

This report documents Virginia power's methodology, and is becod upon typical uncertainties. Some of the uncertainties which havo previously been treated deterministically are herein treated statistically. A Statistical DMBR Limit (SDL) of 1.44 for the COBRA /W-3 code / correlation combination for Morth Anna has thus been obtained for this example, which provides protection from DMB with botter than 95% probability at a 95% confidence level.

I l

PAGE 4 l

i ACKNOWLEDGEMENTS  ;

The author would like express his appreciation for the

. tochnical assistance of Mr. K. L. Basehore in the development of this methodology, as well as the contributions of Mr. G. A. Meyer, i Mr. D. A. Tarnsworth, Mr. J. H. Jones and Ms. A. S. Heller of Babcock C Wilcox. Also to be noted are the contributions of Mr. N.

A. Smith, Mr. M. G. Matras, Mr. J. G. Miller, Mr. K. L. Maddock and Mro. A. S. pegram in both the methodology development and proparation of the documentation.

i I

1

_ _ __ , _ _ ~

PAGE 5 1 TABLE OF CONTENTS Page Title Page.............................................. 1 Cicssification/ Disclaimer............................... 2 Abatract................................................ 3 Acknowledgements........................................ 4 Table of Contents....................................... 5 Liot of Figures......................................... 6 List of Tables.......................................... 6 McConclature............................................ 7 1.0 Introduction........................................ 9 2.0 Methodology Description............................. 19 3.0 Core-wide DMB Probability Calculation............... 51 4.0 Application to Reactor Protection................... 56 5.0 conclusions......................................... 59 RGforences.............................................. 61 App 3ndix A.............................................. 63 1

= - -

PAGE 6 LIST OF FIGURES Page 1.1.1 Components of DNBR Margin......................... 14 2.3.1 Subchannel Modeling of Hot Assembly in 6-channel Mode 1................................ 34 2.3.2 Comparison of 6-Channel Model DNBR's to Production Model Results.......................... 35 2.4.1 Probability Density Function of COBRA DNBR's at Statapoint G (Limiting Case)................... 39 2.4.2 Multiplier k(95) of' Equation (2.4.5) on Logarithmic 5cale................................. 41 2.6.1 Probabilistic Daturmination of DNBR Limit.......... 50 3.0.1 Core-wide DNB Probability Analysis................ 54 LIST OF TABLES Page 1.1.1 Treatment of Uncertainties........................ 15 2.1.1 Statistically-Treated Parameters and Uncertainties.............................'.... 27 l

2.2.1 Nominal Statapoints for DNBR Calculations......... 30 2.2.2 Sample Random Operating Conditions................ 31 2.4.1 DNBR Distribution Summary Statistics.............. 40 3.0.1 Generic Rod Power Census for Morth Anna........... 53 3.0.2 Corn-wide DNB Probability Iteration Summary....... 55 '

4.0.1 Treatment of Parameters in Statistical Methodology....................................... 58 A.1 Retained DNBR Margin for Wertinghouse Standard 17x17 Fuel............................... 66 i

l MOMENCLATURE PAGE 7 l

VARIABLE DEFINITION CHF Critical heat flux (MBTU/hr/ft2) r CHIm Statistical CHI 2 distribution variable CV Coefficient of variation (-)

DDL Deterministic DNBR limit (-)

DMB . Departure from Mucleate Boiling DNBR Departure from Mucleate Boiling Ratio C-)

EFF Effective flow fraction (-)

F(z) Cumulative normal distribution function (-)

Fdho Engineering enthalpy-rise factor (-)

Fdhn Nuclear enthalpy-rise factor (-)

FSE Engineering heat flux factor (-)

Fnz Axial peaking factor (-)

L Gin Core-average mass flux (Mlbm/hr/ft2) l k Multiplicative constant (-)

kC95) Multiplier on SIGMA to obtain upper 95X confidence limit (-)

M Mean measured-to-predicted ratio (-)

Mu Mean value of a parameter 1

n Mumber of observations (-)

q' Heat flux (MBTU/hr/ftz)

RAMMOR(SEED) Standard normal random variable (-)

RAMUMICSEED) Standard uniform random variable (-)

SDL Statistical DNBR Limit (-)

VARIABLE DEFINITION SEED Starting point for random number generators SHRF Stack Height Reduction Factor (-)

SIGMA Standard deviation SIGMA (Code) DNBR uncertainty component due to code SIGMA (Model) DNBR uncertainty component due to use of 6-channel model SIGMACP/C) DNBR standard deviation due to parameter and correlation uncertainties SIGMA (P/C,95) Upper 95% confidence limit on SIGMA (p/C)

SIGMACTotal) Upper 95% confidence limit on total DNBR standard deviation SIGMAC95) Upper 95% confidence limit on any standard deviation TDC Thermal diffusion coefficient Y Normally distributed variable k 2 Standard normal random variable

\

1.0 - INTRODUCTION PAGE 9 s

Chapter ,1.0: Introduction n

[ Virginia Power has traditionally performed DNBR analyses with cpecified design uncertainties applied in a deterministic manner (i.e. they are compounded). Such analyses assume that each Pcrameter is at the worst end of its uncertainty range with respect to the DNBR. Thus a typical deterministic transient analysis begins with an initial temperature at 4*F greater than the nominal value, the pressure at 30 psi less than nominal, and so forth. Each Porameter is assumed to have varied from its nominal value to the full extent of its uncertainty, in the direction which is worst with respect to the DNBR. Such a methodology is clearly conservative, and acceptable to the NRC; Virginia Power's original licensed core thermal / hydraulic procedure was thus based upon a doterministic treatment of uncertainties.

A number of methodologies 2-' have been developed which treat F these uncertainties by means of statistical rather than doterministic combination. Statistical combination maintains the onme uncertainty on each parameter, but permits a more realistic combination of the independent variable errors. The NRC has cpproved5-7 such statistical methods, i

The following text describes Virginia Power's internally doveloped statistical DNBR evaluation methodology. This procedure develops a revised DNBR limit, known as the Statistical DNBR Limit (SDL), by statistically analyzing uncertainties which were previously compounded in the models or in the transient analysis

1.0 - INTRODUCTION PAGE 10 s

/ cothodology. The SDL is greater than the original 1.30 limit of 5

the W-3 CHF correlation, but it provides the standard against which more realistic DNBR analysis results may be compared.*

( For the purposes of this methodology topical report, sample calculations have been performed for the North Anna power Station using typical uncertainties. The result is a DMBR margin gain of about 13X; a comparable gain would be expected in a sample surry analysis. In order to actually implement this methodology on a plant-specific  !

bcsis, separate packages for the Morth Anna and Surry power stations, which are based upon uncertainties determined from plant-specific data, will be submitted to the NRC for review.

l n parameters with statistically-treated uncertainties are used for DNBR calculations in best estimate form, rather than by setting the parameter at the conservative and of its uncertainty range.

The core thermal / hydraulic decks still treat some parameters in a conservative (deterministic) manner, however, and thus are not best-estimate decks.

)

1.0 - INTRODUCTION PAGE 11 1.1 Deterministic Methodology Review In this section, the philosophy of the deterministic DNBR ovoluation methodology will be reviewed, and important terms will bo defined and discussed. These definitions will permit a clearer 1

understanding of the similarities and differences between the doterministic and statistical methodologies, as well as assist in illustrating the manner in which important parameters are treated in both approaches.

Methodology philosophy. The treatment of the components of onch DNBR calculation is illustrated in Figure 1.1.1. In the doterministic methodology, the calculated DMBR at hot full power is loss than its best estimate value due to the conservative influence of retained DNBR margin, deterministically-treated uncertainties I cnd design conservatisms. The deterministic DMBR limit is set by cdding a correlation uncertainty factor to the point at which DMB i

occurs, i.e. at a DNBR of 1.0. The difference between the two points is operating margin, which provides an adequate DMBR margin for abnormal operation or system transients such as the Loss of Fleu Accident (LOTA).

Retained DMBR Margin. " Retained DNBR margin" consists of DNBR Ponalties which are not required as a part of Virginia power's 1 doterministic DMBR evaluation methodology. This margin includes such parameters as a conservatively low thermal diffusion coofficient, the absence of a mixing-vane grid (which adds turbulence to the subchannel flow) in the core hydraulic model and

1.0 - INTRODUCTION PAGE 12 m

j n conservatively low W-3 CHT correlation coefficient. These 1 parameters could be used to provide additional DMB margin, if L nocessary; however, by their inclusion they provide DNBR margin as a contingency factor. The retained DMBR margin has traditionally

( boon used to offset the rod how penalty, and is discussed in Appendix A.

Conservative Assumptions. The "deterministically-treated uncertainties" and " design conservatisms" consist of those parameters whose values are part of the Virginia Power SMBR nothodology design basis. They include such parameters as a conservatively low core flow (thermal design flow), conservatively

~

/ high values for the radial and axial power peaking factors, and conservative biases on the initial operating conditions in transient analysis. The tuo categories differ only in that the "doterministically-treated uncertainties" have been selected for statistical treatment in Virginia Pouer's statistical methodology, while the " design conservatisms" have not. Thus from Tab 3a 1.1.1 it may be seen that the "deterministically-treated uncertainties" cro those which are associated with the code, correlation, flow, prossure, temperature, power, engineering and nuclear enthalpy-rise inctors and effective flow fraction; the " design conservatisms" rofer to the deterministic treatment of the effect of rod how, the calculational component of the nuclear enthalpy-rise factor, the inlet flou maldistribution, fuel densification and the nuclear exial factor.

1.0 - INTRODUCTION PAGE 13 Correlation Uncertainty. The " correlation uncertainty" is taken directly from an analysis of the W-3 data base. In the L doterministic methodology, the traditional W-3 CHT correlation linit of 1.30 is based solely upon the mean and the standard doviation of the measured-to-predicted CHT data ratio; in Virginia Power's statistical methodology, however, the Statistical DNBR Linit is based upon a statistical combination of the correlation otendard deviation with other uncertainties.

I e

1.0 - INTRODUCTION PAGE lie

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2.75 -

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s Retained i Retained 2.50 - Margin DNBR Margin Design Conserva-Design i eism, 2.25 -

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Operating Determinis- ,/ Margin j1.75 -

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$ istic DNBR Probabilit y Limit Correlatiort/

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Correlation Uncertainty Parameter Factor Uncertainty 1.00 Deterministic Statistical DNBR Evaluation DNBR Evaluation Figure 1.1.1 - Components of DNBR Margin l

1.0 - INTRODUCTION PAGE 15 Table 1.1.1 s Treatment of Uncertainties g Uncertainty Deterministic Statistical Methodology Methodology Treatment Treatment Core-uide DMB Mot treated Statisticsl code Not treated Statistical -

CHF Correlation Deterministic Statistical Flow Deterministic Statistical Prossure Deterministic Statistical 1

Tonperature Deterministic Statistical Power Deterministic Statistical Engineering Deterministic Statistical Enthalpy-rise (Fdhe)

Muslaar Deterministic Statistical Enthalpy-rise (Fdhn),

consurement s

Effective Flow Deterministic Statistical Frcction Red Bou DMBR Penalty Applied

• DNBR Penalty Applied

• Muclear Deterministic Deterministic Enthalpy-rise (Fdhn),

eniculational Inlet Flow Deterministic Deterministic Mn1 distribution Fu21 Densification Deterministic Deterministic Axial Factor Fnz Deterministic Deterministic Engineering Heat Deterministic Eliminated as Flux Factor FSE Unnecessary; see Reference 8 8 See Appendix A.

1 s 1.0 - INTRODUCTION PAGE 16 1.2 Statistical Methodology Overview s

e Methodology philosophy. In Virginia Power's statistical DNBR ovaluation methodology, the calculated DNBR at any statapoint is reduced from the best estimate value by only the retained DNBR norgin and the design conservatisms. The parameters which were doscribed as "deterministically-treated" in the deterministic nothodology are instead included in the development of the DNBR licit itself. There, they are described as " statistically-treated uncertainties." Those parameters induce a DNBR uncertainty due to their independent random variation, which will be described as the "porameter-induced uncertainty." This uncertainty is coupled with the correlation uncertainty and three other factors. Those factors era a code uncertainty, a model uncertainty and a factor due to the

, consideration of core-wide DMB probability. In the statistical nothodology, the DNBR limit thus consists of five components, as opposed to the single component in a deterministic approach. The correlation uncertainty was discussed in Section 1.1; the remaining four terms, which were not considered in the deterministic cathodology, are summarized below. More discussion will be provided in the development of the model and in the chapters which follow.

1 Code Uncertainty. A code uncertainty must be applied because 1

of two factors. Those factors account for the effect of analyzing a full core with a correlation which was based only upon steady state test bundle data, and the effect of performing analyses with i

1

1 1.0 - INTRODUCTION PAGE 17 tho Virginia Power COBRA code when the W-3 data were reduced with Wootinghouse's THINC code.

Model Uncertainty. The model uncertainty accounts for differences between the simple core thermal-hydraulics model with.

which the statistical DNBR limit has been derived and the sophisticated model which is normally used for production eclculations. Had the SDL been developed with the more complex model, a model uncertainty would not need to be included.

Core-wide DMB Probability Uncertaintv. Although a doterministic DNBR evaluation methodology considers only the probability of DMB occurring on the hot fuel rod, in this statistical methodology a full-core DMB probability analysis is parformed. This analysis is accomplished by conservatively calculating and summing the DH3 probability of every rod in the roactor core. The SDL is conservatively increased, if necessary, to ensure a minimum number of expected rods in DMB in the entire core if the SDL should be reached.

Virginia Power's statistical DMBR methodology treats every uncertainty which was considered in the datorninistic methodology.

Th3 two approaches differ only in the manner of treatment.

I conservatively, the statistical approach also considars additional uncertainties which were not considerad in the deterministic cyproach.

1.0 - INTRODUCTION PAGE 18 Table 1.1.1 lists each uncertainty and the manner in which it is treated in each methodology.r Deterministically-treated parameters are conservatively assigned a bounding value, in terms of effect upon the DNBR, in each methodology. Statistically-treated Perameters are accounted for as described in the following chopters. It thould be noted that every parameter is treated in tha statistical methodology with the exception of the engineering hant flux factor, which was shown in Reference 8 to be negligible.

Tho basis for excluding certain parameters from statistical troatment is discussed in Section 2.1.

n It is permissible to separate the components of a parameter uncertainty. For example, the 8% nu-lear enthalpy-rise (Fdhn) uncertainty is treated by incorporating 4% into the development of the Statistical DNBR Limit, while treating the remaining 4%

in a deterministic manner. The value of Fdhn uhich is used in the statistical models is thus 1.49, rather than the best-estimate 1.435, but less than the fully deterministic value of 1.55.

i

2.0 - METHODOLOGY DESCRIPTION PAGE 19 Chapter 2.0: Methodology Description s

g Chapter 2 provides details on Virginia power's statistical L

DNBR evaluation methodology, which will be discussed in the upccming sections. The methodology may be summarized as follows:

1. Statistically treated parameters and their uncertainties are defined.

2. At a specified set of nominal conditions, defined as a " nominal statepoint," 2000 sets of operating conditions in this sample analysis are determined by randomly varying each statistically-treated parameter about its nominal value according to its distribution. Each perturbation from a nominal statapoint is defined as a " random statapoint." Tor example, the pressure is treated as a normally distributed variable with

[ mean equal to its nominal value and standard deviation defined by its uncertainty.

3. The random statapoints are analyzed with the COBRA code, yielding a distribution of 2000 DNBR's at each nominal statapoint. Each random statapoint is multiplied by a random factor which accounts for correlation uncertainty.

4. The DNBR distribution is tested for normality with the D' normality test.

5. Steps 1-4 are performed at each of the nine different nominal statapoints which were selected for this sample analysis. The most conservative DNBR standard deviation which is obtained at any nominal statapoint is used in the further development of the Statistical DNBR Limit. This parameter standard deviation characterizes the combination of the " statistically-treated uncertainties" which were defined in Section 1.1 and the correlation uncertainty.

6. A total DNBR standard deviation is determined by combining the overall parameter / correlation standard deviation with factors I which account for the code and model uncertainties.

7. A DNBR limit for the nominal statapoint is determined from the absolute DNBR limit of 1.0, using the distribution mean and standard deviation to provide protection from DMB with 95X probability at a 95X confidence level for the hot fuel rod.

2.0 - METHODOLOGY DESCRIPTION PAGE 20

8. Using the DNBR standard deviation, a core-wide DMB probability ,

analysis is performed to determine the expected number of rods l in DNB when the hot fuel rod in the core is at the Statistical y DNBR Limit. This step is performed iteratively, if necessary, to find a SDL such that no more than 0.1% of the rods in the core are expected to be in DMB if the plant were to operate at the SDL. The Statistical DNBR Limit is thus defined by the more restrictive-of the two criteria

1) single rod DNB probability, or 2) a minimum number of rods expected to be in DNB at the DNBR limit.

2.0 - METHODOLOGY DESORIPTION PAGE 21 2.1 Operating Conditions and Associated Uncertainties s

( Each parameter which has a significant impact upon DNB is discussed below. The North Anna example illustrates how the I statistical DNBR evaluation methodology would be applied to either Morth Anna or Surry. The uncertainties were quoted from the North Anna UFSAR' with the exception of the effective flow fraction, for t which an estimated value was used. When a MRC submittal is propared to implement the statistical .DNBR methodology for a DPocific plant, the uncertainty magnitudes will be rigorously dotermined in an analysis of plant hardware and nonsurement/ calibration procedures. Just such an analysis leads to the conclusion that the pressure, temperature, flow, power and nuclear enthalpy rise factor uncertainties are all normally distributed. Although the previous statistical DMBR methodology submittals typically treat the engineering enthalpy-rise factor and offective flow fractions as normally distributed variables, they will be conservatively treated as uniformly distributed random variables in the Virginia Power analysis.

2.1.1 - Statistically-Treated Uncertainties Vessel Flow. The vessel mass flow is determined in a cocondary side enthalpy-rise calculation. For the sample calculation in this report, an uncertainty of 4.5% in the thermal dosign flow of 285,000 gym is quoted from Reference 9. This uncertainty yields a standard deviation of 4.5/1.645=2.74%. The 1.645 divisor is the a-value for a one-sided 95% confidence limit

2.0 - METHODOLOGY DESCRIPTION PAGE 22 on a normally distributed variable. In the statistical core model, a nominal flow of 289,200 gym Can increase of only 1.4%) will be I usod. Based upon Reference 10, this flow rate will bound the L

oxPected actual loop flows in plant operation with up to 11% steam e

generator tube plugging. An analysis of plant hardware and Procedures leads to the conclusion that vessel flow, as well as h power, core pressure and temperature are normally distributed; those parameters will be treated as such in this analysis.

Pressure. Reference 9 notes an uncertainty in the control of Prossurizer pressure of 30 psi. The standard deviation is thus 30/1.645=18.2 psi. The nominal pressurizer pressure is 2250 psia t at hot full power.

Inlet Temperature. The evaluated temperature uncertainty in Roference 9 is 4*T. The uncertainty standard deviation on the thormal design inlet temperature of 555.9'T is thus 4/1.645=2.43'F.

This temperature is based upon the current vessel average toaperature of 587.8'r, nominal pressure of 2250 psia and a nominal flow rate of 289,200 gym as noted above.

Power. An uncertainty of 2% in the measurement of core power generation is stated in Reference 9, yielding an uncertainty stendard deviation of 2/1.645=1.22%. This uncertainty is applied

) to the nominal heat flux, which is 0.19489 MBTU/hr/ft2

2.0 - METHODOLOGY DESCRIPTION PAGE 23 Engineering Enthalpy-Rise Hot-Channel Factor. Fdhe accounts for uncertainty in the hot-channel enthalpy-rise, and is applied as a multiplier on the heat flux rate in the hot channel. In a best ostimate analysis, Fdhe is set equal to 1.0. A conservative bounding value of 1.02 is stated in Reference 9. As stated

' Proviously, be Fdhe will treated as a uniformly distributed variable. ,

l

_Muclear Enthalpy-Rise Hot-Channel Factor (Measurement

_Canyonent). Ydhn is effectively the maximum two-dimensional radial power factor. For this parameter, Reference 9 lists a design value of 1.55 and uncertainty components of 4% calculational and 4%

cocsurement. The measurement error has been found to vary normally and randomly with respect to the calculated value of Fdhn, and thus will be treated statistically. Because of difficulty in evaluating the probability density function of the calculational component, however, it will be treated deterministically. This analysis will thus be performed with a nominal Fdhn of 1.49 and an uncertainty of 4%. The uncertainty standard deviation is thus 4/1.645=2.43%.

Effective Flow Fraction (EFF). A portion of the vessel flow bypasses the reactor core and is unavailable for core heat transfer. The EFF is that portion of flow which does not bypass tho core. The leakage paths are the spray nozzles into the upper hand, the rod control cluster guide tubes, the vessel / core barrel gap and the baffle plate gaps. For the deterministic analyses of Roference 9, a conservatively low EFF of 95.5% is specified. In

2.0 - METHODOLOGY DESCRIPTION PAGE 24 l

Virginia Poue.r's statistical DNBR methodology, best estimate values of the EFF and its uncertainty are employed. For this sample calculation a value of 96.5% uith an uncertainty of IX was used.

Plent-specific values for the flow fraction and uncertainty, when datermined, are expected to be close to these values. At each rendom statapoint, the core mass flux is calculated from Vessel Mass Flow

• EFF Gin = ----------------------- . (2.1.1)

Core Flow Area Engineering Heat-Flux Hot-Channel Factor. FSE is a multiplier on the heat flux which accounts for manufacturing tolerances on the fual which influence the heat flux, and is described in Reference

11. FSE was applied as a 1.03 multiplier on the heat flux only during DNBR calculations and does not affect energy deposition in thn coolant; that uncertainty is treated by the Fdhe multiplier which was discussed above. In the Virginia Power statistical core thormal/ hydraulic models, however, the heat flux spike (FSE) has baon removed. The omission of this factor is supported by the NRC cyproval of WCAP-8174e, in which they stated in part: "...We concur with the conclusion of WCAP-8174 that a special DNB heat flux spike need not be incorporated into Westinghouse reactor dooigns using Westinghouse type mixing vane grids. Therefore, WCAP-8174 may be referenced in license applications as an accepted topical report when it is used to support this conclusion."

s 2.0 - METHODOLOGY DESCRIPTION PAGE 25 2.1.2 - Design Conservatisms s

Rod Bou. In Virginia power's original core thermal-hydraulic b models, the hot-channel fuel pin pitch was reduced in the doterministic analysis in an attempt to accommodate the effects of rod-to-rod pitch variation. However, the need for such a factor was eliminated by the separate application of a rod how penalty to thG retained DNBR margin. As a result, the pitch reduction became a simple contingency penalty. In Virginia power's statistical DNBR ovoluation methodology, the hot-channel pitch reduction has been #

rocoved from the models. However, the~ elimination of the pitch roduction also reduces some of the retained DNBR margin for North i Anna, and is discussed further in Appendix A. The rod bow phonomenon was not treated statistically because of difficulty in codeling the random variation thereof. The rod bou penalty will continue to be offset by the remaining retained DNBR margin.

Nuclear Enthalpy-Rise Hot-Channel Tactor (Calculational Camponent). As noted above, 4% of the total 8% uncertainty in the radial power factor may be attributed to calculational uncertainty.

In both the deterministic and statistical'-methodologies, this pcrameter is treated as a multiplier on the measured value of Tdhn.

This factor was not treated statistically due to difficulty in .

\

ovoluating its probability density function.

Inlet Flow Maldistribution. The core' inlet flow is not uniform, but varies from assembly to assembly by a few percent. As noted in Reference 1, this uncertainty may be treated by modeling

s

, 2.0 - METHODOLOGY DESCRIPTION PAGE 26

~

tho hot assembly as receiving only 95% of the core average flow, l Tho balance of the flow is made up in the core-edge assemblies. The troatment of this uncertainty as a Design Conservatism was noted in Soction 1.1 and is the same in both the deterministic and statistical methodologies. A deterministic treatment was chosen for this variable due to the difficulty in modeling the randon 1

variation of the phenomenon, j

Fuel Densification. The effect of fuel densification may be treated by the application of a Stack Height Reduction Factor (SHRF), which effectively serves as a multiplier on the core-average heat flux. The use of the SHRF multiplier is al'o s a Design Conservatism, a'nd occurs in both the deterministic and statistical methodologies.

Core-Average Axial peaking Factor (Fnz). Fnz is the cere-average value of the peak-to-average axial power factor, and in a Design Conservatism. In both the deterministic and statistical methodologies, the expected power profiles are examined en a reload basis to verify that an axial factor of 1.55 hounds the actual core conditions. Difficulty in statistically modeling the profile's random variation precluded its statistical treatment at this time. .

The parameters which will be statistically treated, as well as thoir nominal values and uncertainties, are listed in Table 2.1.1.

s

, 2.0 - METHODOLOGY DESCRIPTION PAGE 27 1

J s

TABLE 2.1.1 Statistically-Treated Parameters and Uncertainties Parameter Nominal Uncertainty Standard value Deviation s

Pressurc 2250 psia 30 psi 18.2 psi Inlet Temp 555.9'T 4*F 2.43'F Heat Flux 0.19489 2% 1.22%

MBTU/hr/ft2 Flow Rate 289,200 gym 4.5% 2.74%

Effective Flow 0.965 1.0% --

Fraction Radial Factor 1.49 4.0% 2.43%

Tdhe 1.00 2% --

Notes the standard deviation of each normally distributed uncertainty is obtained by dividing it by 1.645, the absolute value of the =-value for a one-sided 5% lower tail. The standard deviation is not used in the analysis of the uniformly distributed uncertainties.

s 2.0 - METHODOLOGY DESCRIPTION PAGE 28 1

/ 2.2 Random Variation of Operating Conditions s

The nominal statapoints chosen for analysis are presented in Table 2.2.1. The statapoints were chosen to represent nonz-bounding conditions across a full rabge of DNBR-limited occidents. A wide range of power, flow, temperature and pressure uno thus examined. These statapoints span the full range of prossure/ temperature / power transients and lou flow accidents.

Multiple sets of random statapoints were generated at each nominal ,statepoint by independently varying each statistically-treated parameter according to the probability distribution of its uncertainty. To accomplish this task, Virginia Power's on-line random number generators RAMMOR and RAMUNI in the SAS11 package were employed. RAMMOR generates a normally l distributed random number with mean zero and standard deviation ono, and has been shown to be normal by the D' normality test.13 RAMUNI generates a uniformly distributed random number on the interval (0,1).

In application, a randomly generated pressure about 2250 psia una calculated by the expression

' PRESSURE = nominal value

+ [ standard deviation *RAMMOR(SIED)] (2.2.1)

=

2250.0 + [18.2*RAMMOR(SEED)] (2.2.2) whore 18.2 is- the standard deviation of the pressure uncertainty from Table 2.1.1. Repeated calculations with equation (2.2.2) will

'~

- . - - ~ -

= _ - - .m.- _ _ _ _ _ . _ _ _ . - . . _ .

2.0 - METHODOLOGY DESCRIPTION PAGE 29 s

yiold a distribution of pressures with mean 2250 psia and standard s

doviation 18.2 psia. This uncertainty was treated additively; I those which are expressed as a percent were treated cultiplicatively. For example, HEATTLUX = 0.19489 * [0.0122*RANNOR(SEED) + 1.01. (2.2.3)

Sicilarly, a uniformly distributed variable would be calculated by EFF = 0.965 * [2*0.01*{RANUNICSEED)-0.5) + 1.01. (2.3.4)

Ecch parameter was treated appropriately, independently varying, to pzcduce a set of random statapoints. An example is shown in Table 2.2.2. Unique seeds were used in the random number generators at ovory step in this simple Monte Carlo process. A total of 2000 cuch random statapoints were generated for each nominal statapoint, providing a satisfactory balance between the statistical requirement of a large data base and the need to minimi=a computer costs. The use of those statapoints in the thermal-hydraulic cnalysis will be discussed in Section 2.4.

, 2.0 - METHODOLOGY DESCRIPTION PAGE 30 l

}

s Table 2.2.1 Nominal Statapoints for DNBR Calculations

( State- Inlet Pressure Power Flow Tdhn Description Point Temp. (psia) (X) CX) (-)

A 560.0'T 1875 108 100 1.49 Core Thermal Limit

. Statapoint B 541.7*F 1875 118 100 1.49 Core Thermal Limit Statapoint C 571.0*F 2000 105 100 1.49 Core Thermal Limit Statapoint D 548.9'F 2000 118 100 1.49 Core Thermal Limit Statapoint E 602.2'T 2250 90 100 1.535 Core Thermal Limit Statapoint F 562.4'T 2250 118 100 1.49 Core Thermal Limit Statapoint G 619.3*F 2400 80 100 1.573 Core Thermal Limit Statapoint H 570.1*F 2400 118 100 1.49 Core Thermal Limit Statapoint I 555.9'T 2250 100 69.5 1.49 Loss of Flow Statapoint

s 2.0 - METHODOLOGY DESCRIPTION PAGE 31

(

s J

s TABLE 2.2.2 Sample Randon Operating Conditions Pressure Temperature Heat Mass Fdha Radial (psia) (*F) Flux Flux (-) Factor

{

(MBTU/ (M1bm/ (-)

hr/ft2) hr/ft2) 2014.6 545.0 0.23340 2.45728 1.0104 1.5025 2016.1 549.2 0.23659 2.53693 1.0035 1.5451 f 2023.4 548.8 0.23399 2.56237 0.9964 1.5154 1959.4 546.7 0.23049 2.47318 1.0145 1.4677 1996.1 553.6 0.23302 2.57118 1.0043 1.5030 1962.0 545.1 0.22688 2.55500 1.0062 1.4566 2002.5 545.1 0.23513 2.40207 1.0194 1.5092 2008.8 553.7 0.22938 2.55909 0.9804 1.4829 2014.6 548.3 0.23459 2.60379 0.9913 1.4765 1989.5 547.3 0.23045 2.60231 1.0174 1.5481 Note: This table is a sample set of ten of the 2000 random statapoints which were generated at nominal statapoint D.

s 2.0 - METHODOLOGY DESCRIPTION PAGE 32 s

2.3 Core Thermal / Hydraulic Model s

r A 6-channel North Anna model was used to perform DNBR ociculations with the sets of randomly generated operating conditions. This model resolves both the hot typical and hot thimble cells. The division of the hot assembly into four of the six subchannels is shown in rigure 2.3.1; the rest of the core is ocdeled concentrically by the remaining two subchannels.

Sixty-one benchmark cases across a wide range of operating conditions were run to compara the 6-channel model to Virginia Power's detailed North Anna thermal-hydraulic model which is used for production calculations. These conditions varied cystematically from 1800 to 2400 psia, from 80% to 120% power and from 525'r to 575'T inlet temperature. A wide range of DNBR's was thus examined. It should be noted that all of the Monte Carlo DNBR calculations will be performed with the COBRA thermal / hydraulics code and a code model which is similar to but slightly less complex then the production model, rather than with a response surface codel. As a result, it was not necessary to benchmark the 6-channel model over the full range of Monte Carlo conditions, but it will be sufficient to show that the difference due to the relative model complexities with the same code is small over a wide rcnge of conditions.

A scatter plot of 6-channel DMBR's versus their production nodel counterparts, as calculated by the COBRA /W-3 combination, is shown in Figure 2.3.2. The agreement is clearly excellent. The

s 2.0 - METHODOLOGY DESCRIPTION ,PAGE 33 scan ratio of the 6-channel model DMBR and the production model

(

DNBR was 1.012, with a standard deviation of 0.0099. The peak

( orror was 3.01X across a very wide range of DNBR; by conservatively cotting this value equal to the maximum uncertainty at a one-sided 95% confidence level, the model standard deviation SIGMA may be calculated from

(

SIGMA (Model) = 0.0301 / 1.645 (2.3.1)

= 0.0183. (2.3.2)

It should be noted that using the peak error provides the 98th parcantile for this data base, rather than a 95X bound. The model uncertainty will be incorporated into the development of the SDL in Soction 2.5.

I l

s s 2.0 - METHODOLOGY DESCRIPTION PAGE 34 L

{

- / O v  %

l 6 Channel 2 - Hot Typical Cell Channel 1 Channel 3 - Surrounding I -

Channel 4 - Remainder of Assembly Channels 5,6 - Remainder of Core .

Figure 2.3.1 - Subchannel Modeling of Hot Assembly in 6-channel Model

s 2.0 - METHODOLOGY DESCRIPTION PAGE 35 r

l L

3.6

{

• 3 2-~

l .

2.8 .

6 H

A

• N N 2 . 4-.

E L

e C

0 8 .

R 2.0-A M

D N .

B .

1.6-R 8

• 1.2-0.8 '

0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.5 PRODUCTION MODEL MON 8R$

Figure 2.3.2 - Cooperison of 6-Channel Model DMBR's to Production Model Results i

ii i

2.0 - METHODOLOGY DESCRIPTION PAGE 36 2.4 DNBR Calculations s

r The 6-channel model was used with the COBRA code to analyze L

occh random statapoint. With 2000 random statepoints at each of f the nine nominal statepeints from Table 2.2.1, a total of 18,000 DNBR calculations were performed. The 18,000 COBRA calculations provided a large data base from which the Statistical DNBR Limit could be determined. Each COBRA DNBR was multiplied by a random

{

variable to include the effect of the correlation uncertainty as follows:

l DNBR = DNBR * [1 + 0.123*RANNOR(SEED)] (2.4.1) in which 0.123 is the W-3 correlation standard deviation, quoted from Reference 14. This uncertainty is applied multiplicatively bocause it is not independent of the parameter-induced 'DNBR vcriation. The combined result was then subjected to the statistical analysis described below.

The DNBR means, standard deviations and coefficients of variation at each statapoint are presented in Table 2.4.1. The probability density function of the 2000 DNBR's at nominal statapoint G, which proved to be the limiting statapoint, is presented in Figure 2.4.1. The COBRA DNBR's at statapoint G were taalyzed a second time with a different SEED in equation (2.4.1);

no significant differences from the Table 2.4.1 statistics were observed.

The DNBR distribution at each nominal statapoint was tested

1 2.0 - METHODOLOGY DESCRIPTION PAGE 37 with the D' n'ormality test, and all passed. For 2000 observations, 95% confidence in the assumption of normality requires that L 25,110$D'525,340; at statapoint G, the limiting case, the eclculated D' statistic uns 25,173.

The largest standard deviation due to the parameters and correlation, SIGMACP/C), for any of the DNBR distributions was 0.2028 at statapoint G. A 95% upper confidence limit on SIGMACP/C)

{

10 found from SIGMA (P/C,95) = k(95)

• SIGMA (P/C) (2.4.2) l = 1.0268

• 0.2028 (2.4.3)

0.2082 (2.4.4) uhere 2* (n-1) kC95)

[-----------------------18*5 (2.4.5)

({2*n-3}8's - 1.64532 cud n=2000, the number of observations. Equation (2.4.2) is an upper 95% confidence limit on the estimated variance of a variable, es developed in Reference 15:

(n-1)

• SIGMA 2 SIGMA (95) 5 ----------'----- (2.4.6)

CHI 2 where SIGMA is the estimate of the distribution standard deviation.

and CHI 2 is the lower value of the cumulative CHIz distribution corresponding to a one-sided 95% confidence limit. CHI 2 is actimated in Reference 16 by the asymptotic expression CHIz = 0.5 * [z + (2*n-3)**5]z (2.4.7)

_____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ _ _ - _ _ _ _ _ _ _ - - _ _ _ _ _ _ _ _ _ _ - __ J

2.0 - METHODOLOGY DESCRIPTION PAGE 38 in which z=-1.645, the 0.05 point (1.0-0.95=0.05) of the cumulative normal distribution. Substituting Equation (2.4.7) into Equation

( (2.4.6), setting z=-1.645 and setting k(95) equal to SIGMAC95)/ SIGMA yields Equation (2.4.5). .

A plot of kC95) versus n appears in Figure 2.4.2, illustrating

( th3 accuracy with which SIGMA may be known by developing a large dcta base. The selection of n=2000 provides a satisfactory balance b3 tween minimizing computer time and minimizing k(95).

2.0 - METHODOLOGY DESCRIPTION PAGE 39 2.5 r

12NE = EQUIVAIENT MORMAL CURVE DIAMOND = MONTE CARIA DATA 2.0- o 4

a

• a p 1.5-t 0

m .

A a

I L

I T

Y 1.0-D s

a s

I '

0.5-o 0.0 0.6 1.0 1.4 1.8 2.2 MINIMUM DNS RATIO (MOMBRI Figure 2.4.1 - Probability Density Tunction of COBRA DNBR's ht StatePoint G (Limiting Case) l l

2.0 - METHODOLOGY DESCRIPTION PAGE 40 I

TABLE 2.4.1 DMBR DISTRIBUTION

SUMMARY

STATISTICS Statapoint Mean DNBR Standard DNBR Coefficient f DNBR Deviation of Variation A 1.40 0.1848 13.2%

B 1.41 0.1853 13.1%

C 1.41 0.1878 13.3%

D 1.42 0.1877 13.2%

E 1.40 0.1954 13.9%

F 1,41 0.1947 13.8%

j G 1.40 0.2028 14.5%

H 1.41 0.1960 13.9%

I 1.41 0.1888 13.4%

l l

f 2.0 - METHODOLOGY DESCRIPTION PAGE 41 2 .0 n

1.5-4 I 8 I 1.5-G n

R M

U L

T I

'P L 1.4-1 E

R

-)

1.2-1.0 5 5 10 100 1000 10000 NUMBER OF 088ERVRT10NS Figure 2.4.2 - Multiplier k(95) of Equation (2.4.5) on Logarithmic Scale 1

1 I

2.0 - METHODOLOGY DESCRIPTION PAGE 42 i

2.5 Total DMBR standard Deviation To develop a statistical DMBR Limit, it is necessary to consider all of the components of a DNB ratio and their uncertainties. Besides those parameters which are to remain doterministically treated, each calculated DMBR has the following f cross of uncertainty:

1) Correlation uncertainty.

2) Influence of " statistically-treated uncertainties."

3) Uncertainty in core application of steady state bundle test data.

4) Uncertainty in COBRA application of W-3 test data.

In addition, in the development of the SDL a model uncertainty must b2 considered, since the 6-channel model and not the production codel was used. Each term has an uncertainty standard deviation which must he quantified and appropriately combined with every other term to determine a total standard deviation and hence the SDL. For the purposes of this analysis, items 3-4 above will be grouped and treated as a " code uncertainty."

Correlation Uncertainty. Reference 14 notes that the W-3R correlation, including both the R-grid factor and F-factor, is

. conservatively modeled at a 95% confidence level by a normal diotribution with a standard deviation of 0.123. Traditionally, this uncertainty is compounded by designing to a DMBR limit of 1.30, although Reference 14 notes that the required statistical protection is provided by a lesser limit of only 1.28. In

2.0 - METHODOLOGY DESCRIPTION PAGE 43 contrast, Virginia Power's statistical DNBR methodology combines tho correlation uncertainty statistically with the other uncertainties noted above. The methodology is not dependent upon the W-3 correlations another correlation, with its unique data atendard deviation, could also have been used, f Parameter-Induced Uncertainties. An uncertainty in the ociculated DNBR at a statapoint exists due to randomness in the parameters which are being treated statistically in this analysis (i.e. those listed in Table 2.1.1). Those parameter uncertainties cro clearly independent of the model, code and correlation uncertainties; however, the effect of the parameters upon the DNBR cuot be considered more carefully. As defined below, the model and code uncertainties are independent of the parameter-induced DNBR uncertainty. However, though the actual DNBR is clearly independent of the correlation scatter, the DNBR as evaluated by the W-3 correlation is not. As a result, the correlation uncertainty was combined with the COBRA code output DNBR's as a cultiplicative factor upon each DNBR in Equation (2.4.1)., This cochined factor is independent of both the model and code uncertainties as defined herein and may therefore be combined with them statistically.

Code Uncertainty. This parameter accounts for any differences batueen Virginia Power's COBRA code and the Westinghouse THINC code with which the W-3 data were reduced, and any effects due to the codeling of a full core with a correlation based upon bundle test

2.0 - METHODOLOGY DESCRIPTION PAGE 44 data. These are clearly independent of the correlation, model and pcrameter-induced uncertainties as noted above. The code f uncertainty was quantified at SX, consistent with the factors OPocified for other thermal / hydraulic codes in References 6-7. A 5X code uncertainty is certainly conservative in light of the oxcellent COBRA /THIMCS7 and COBRA /datate comparisons. In fact, the COBRA code is not necessarily less accurate than THINC, and indeed ccy be more accurates the Reference 18 results suggested that the

{

COBRA /W-3 data scatter was less than the THINC/W-3 scatter.

Mcuever, the 5X penalty serves as a conservative factor which may bo shown to be wholly or partially unnecessary at a later time. A 95X confidence level on SIGMA (Code) will then be 3.04X (=5/1.645).

Model Uncertainty. The model standard deviation in matching the production model was evaluated at 1.83X at a 95X confidence lovel. This parameter is due solely to the effect of model mesh oise, and is independent of the other uncertainties. It may thus bo combined statistically with those uncertainties.

The terms may be combined in a " Square Root of the Sun of the Squares" calculation to obtain a sf.ngle DNBR standard deviation which accommodates all factors, each. at its 95X confidence level SIGMA (Total) = (SIGMA (P/C,95)*

+ SIGMA (Model) , SIGMA (Code): joes (2.5.1)

=

[0.20822 + 0.01831 + 0.030421**5 (2.5.2)

= 0.2112

2.0 - METHODOLOGY DESCRIPTION PAGE 45 i co that the combined DMBR uncertainty,. based uPon all the factors l

ocasidered herein, has a standard deviation of 21.1%.

____ _ - --- l

2.0 - METHODOLOGY DESCRIPTION PAGE 46 3

, 2.6 Calculation of DMBR Limit Any normally distributed variable Y can be rewritten as a

" Standard Moraal Random Variable" by means of the transformation l Y - Mu a = ----------- (2.6.1)

SIGMA in which Mu and SIGMA are the mean and standard deviation of Y, respectively. The Standard Mormal Randon Variable "z" has mean coro and standard deviation one. Equation (2.2.1) Was an example of an inverse standard Normal Randon Variable transformation. The characteristics of the 2-distribution may be used to set a DNBR limit so that DMB is avoided with 95X probability at a 95X Q

confidence level. The procedure is illustrated graphically in Figure 2.6.1 and explained in detail below.

Mu is the DMBR as calculated by a core thermal / hydraulics code at some statapoint. The actual DMBR in the core has a probability distribution with mean Mu and standard deviation SIGMA due to consurement and code / correlation uncertainty (as discussed in Scotion 2.5). By requiring that the probability of DMB actually cocurring (i. e. DMBRS1.0 or YS1.0) be small, "z" may be defined if the DNBR is normally distributed. Then, if SIGMA is known, Mu can bo set as a DNBR limit. When the calculated DNBR is greater than or equal to Mu, then the probability of DMB occurring is less than the specified value. To avoid DMB with 95X probability, a=-1.645 cust be selected. The Statistical DMBR Limit is then calculated

2.0 - METHODOLOGY DESCRIPTION PAGE 47 from Equation (2.6.1) as Mu = Y - z* SIGMA (Total) (2.6.2)

= 1.0 + 1.64555IGMA(Total) (2.6.3)

= SDL (2.6.4)

Or SDL = 1.0 + 1.645* SIGMA (Total). (2.6.5)

The limit is defined so that, for a DNBR equal to the SDL, DNB uill be avoided with 95X probability at a 95X confidence level. The Probability was determined by setting z=-1.645, and the confidence i

lovel was obtained by deriving each component of SIGMA at that lovel.

An important aspect of the statistical methodology should be noted here. Traditionally, the deterministic DNBR limit (DDL) has boon set by the expression 1.0 DDL = ------------- . (2.6.6)

M - k*5IGMA in which M is the mean of the measured-to-predicted CHF data ratio (o value very near to 1.0) and k is a probability multiplier which 10 near 1.645. The use of equation (2.6.5) rather than (2.6.6) will yield a slightly different result. Either method is valid, but the basis of using equation (2.6.5) is more strongly supported by current state-of-the-art statistical techniques. Equation (2.6.5) provides protection from DNB with 95X probability at a 95X confidence levels (2.6.6) provides protection at greater than 95X

s 2.0 - METHODOLOGY DESCRIPTION PAGE 48 s

probability at a 95% confidence level. The difference in the terms any be quantified by noting that (2.6.5) is in fact a truncated binomial expansion of equation (2.6.6) for the case of M= 1, with tha second and higher order terms neglected. However, Equation

, (2.6.5) was not developed in a binomial expansion, but rather by tha independent method of the Standard Normal Randon Variable L

trcnsformation as noted above. The use of 0.2112 as the total DNBR l

i otendard deviation in equation (2.6.5) yields SDL = 1.0 + 1.645*0.2112 (2.6.7)

= 1.35. (2.6.8)

A Statistical DNBR Limit of 1.35 thus provides peak fuel rod DMB protection at greater than 95% probability at a 95% confidence lovel. However, the full core DMB probability remains to be ovoluated.

i

( The derivation of the SDL may be developed further for illustrative purposes. To protect the hot fuel rod from DMB (i.e.

DMER$1.0), Equation (2.6.5) is rewritten as

, 1.0 = 3DL - 1.64585IGMACTotal) *

(2.6.9) l l

1.0 SIGMA (Total)

--- = 1.0 - 1.645 * -------------- (2.6.10)

SDL SDL

= 1.0 - 1.645

• CV (2.6.11) whara CV is the DNBR coefficient of variation, the ratio of its

2.0 - METHODOLOGY DESCRIPTION PAGE 49 otendard deviation to its mean at the SDL. Then, 1.0 SDL = ---------------- (2.6.12) 1.0 - 1.645*cv cnd the most conservative SDL is obtained by maximizing the DNBR ccofficient of variation at the SDL. Notably, Equation (2.6.10) is vory similar in form to equation (2.6.6). As may be seen in Table 2.4.1, the nominal statapoint with the highest DNBR standard doviation also had the highest DNBR coefficient of variation, i

)

2.0 - METHODOLOGY DESCRIPTION PAGE 50 2,5 l

Statistical DNBR 7 Limit 2 , o .'

D <

s 3

/ 1.5.

F R

< 3 A

3 I

L I

T T 1. 0 .

D s

S I

T Y

0.5. -

DN8 occurs; lower 5% tail 1.645a o.o ,

04 c.s i.: ,, **0 t.4 MINIMUn QNg gggl0 (110NBRI Figure 2.6.1 - pg,3,3f l

3.0 - CORE-WIDE DMB PROBABILITY ANALYSIS PAGE 51 i

i

, 3.0 Core-wide DMB Probability Analysis l An accurate method of calculating core-wide DMB probabilities han been developed. The evaluation methodology compares the DNBR l

of each fuel rod in the core to the DNBR limit. Given the DMBR l standard deviation, the probability of DMB is calculated for each L

red and summed over the entire core. This step is accomplished by unking the assumption that the normally distributed DNBR standard a

j doviation is bounding for every rod in the reactor core.

2 The calculational procedura may be summarized as follows. The l

outremely conservative bounding rod power census in Table 3.0.1 was

first developed from a review of all the Morth Anna cycle-specific l data available to date. Using this census, the peak power rods are than set at the SDL. The DNBR's of the remaining rods in the core cro calculated by the use of a conservative DNBR sensitivity to rod power. Each rod will be "z" standard deviations from the DNBR limit of 1.0, where 1.0 - DNBR z = -------------- (3.0.1)

SIGMA (Total) which is Equation (2.6.1) in modified form. The rod will then have l

O DMB probability equal to F(z), where F(z) is the integral of the

]

, Standard Moraal Distribution from negative infinity to z. F(z) is calculated for each rod and summed over the whole core to obtain an oxpocted number of rods in DMB for the entire core. This procedure is illustrated in Figure 3.0.1.

t

3.0 - CORE-WIDE DMB PROBABILITY ANALYSIS PAGE 52 1

This analysis uns performed with the DNBR standard deviation of 0.2112 from Chapter 2 and from the generic rod power census. It l l

uno Virginia Power's objective to find a SDL which resulted in an oxpected number of rods in DMB uhich was less than 0.1% of the total in the core. The initial analysis with a SDL of 1.35, based upon the peak rod DMB probability of 0.05, found that the 0.1%

criterion was exceeded the analysis was thus repeated with a higher SDL. Clearly, the higher Statistical DNBR Limit, for a fixed DNBR standard deviation, will yield a lower number of rods which are expected to be in DNB. The analysis was performed itoratively, until the 0.1% criterion was met. That level was obtained for a SDL of 1.44, at which point peak pin DMB protection ,

una provided with 98% probability rather than 95%. A summary of tho probability iteration is presented in Table 3.0.2. For the occple calculation of this report, the Statistical DNBR Limit of 1.44 which is based upon core-wide DMB probability, being more rostrictive than the peak rod DMB probability limit, is the final rocult of this methodology analysis.

I i

I i

3.0 - CORE-WIDE DMB PROBABILITY ANALYSIS PAGE 53 1

t L

TABLE 3.0.1 GENERIC R0D POWER CENSUS FOR MORTH ANNA Rod Power Level Percent of Rods in Core with (Fdhn) Same or Greater Power 1.5500 0.0C0 1.5457 0.135 1.5438 0.2 1.5412 0.3 1.5388 0.4 1.5373 0.5 1.5358 0.6 1.5343 0.7 1.5324 0.8 1.5300 0.9 1.5269 1.0 1.5087 1.5 1.5024 2.0 1.4965 2.5 1.4912 3.0 1.4838 4.0 1.4758 E.0 1.4663 6.0 1.4550 7.0 1.4460 8.0 1.4404 9.0 1.4356 10.0 1.3966 20.0 1.3451 30.0 1.3100 40.0 1.2528 50.0 1.1588 60.0 1.0111 70.0 0.8314 80.0 0.3861 90.0 0.0000 100.0 l

3.0 - CORE-WIDE DNB PROBABILITY ANALYSIS PAGE 54 25 .

DNB A occurs high-power rod mid-power rod 20 low-power rod e

4 e

a n

15-

! F j a

? O s

A s '

I L

I l t Y 10 s

S I

T Y

05-i high-power rod DNB probability 0,0 Y 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 f .1 2.3 2.5 MINIMUM ON6 RATIO (MONBRI Figure 3.0.1 - Cora-uide DNB Probability Analysis e

-- ---,--...--.w.w-- -,---,.--,,,n-- .-,...a , - - , -.pn -.4 - y an,e- - - -- . , - . ---

3.0 - CORE-WIDE DMB PROBABILITY ANALYSIS PAGE 55 i

TABLE 3.0.2 CORE-WIDE DMB PROBABILITY ITERATION

SUMMARY

Iteration SDL Porcentage Peak Rod Number of Tuel DMB Probability Rods in DMB*

1 1.35 0.32% 0.049 2 1.37 0.25% 0.040 3 1.40 0.17% 0.029 4 1.42 0.13% 0.023 5 1.43 0.11% 0.021 6 1.44 0.10% 0.019

• These numbers are conservative overestimates, bedause of 1) the Parameters which have been deterministically treated, and 2) the conservative methods used to determine the DNBR standard deviation uPon which they are based.

4.0 - APPLICATION TO REACTOR PROTECTIOM PAGE 56 4.0 Application to Reactor Protection Because the statistically-treated uncertainties have been accounted for, it is no longer necessary to incorporate them deterministically into DNBR analysis. Transient DNBR analyses may thus be performed by using best estimate pressure, inlet temperature, core power and vessel flow rate

• as initial conditions. The best estimate flow fraction may be used in datermining core flow. The assumed radial factor may be reduced by the 4% which uns previously added to the best estimate values a nuclear enthalpy-rise factor of 1.49 may thus be used in the COBRA model. This value deterministically treats the calculational uncertainty component. Finally, no engineering hot-channel anthalpy-rise uncertainty needs to be applied to the DNBR calculation. These treatments are summari=ed in Table 4.0.1.

Most DMBR transients are terminated by the overtemperature dolta-T trip function (OTDT) ', which is based upon the DNBR limit and vessel-exit boiling considerations (i.e., the core thermal linits). Eight of the nine nominal statapoints in Table 2.2.1 were chosen at the core thermal limits because of their importance in Protecting the core from DNB. The OTDT trip function continuously a Mote: As a contingency factor for future steam generator tube plugging, a thermal design flow which is slightly less than best estimate flow will be assumed. Inlet temperature will be adjusted accordingly to maintain the same vessel-average temperature.

4.0 . APPLICATION TO REACTOR PROTECTION PAGE 57 l nonitors average temperature, temperature rise and pressure in the reactor vessel in order to terminate reactor operation when the core thermal limits are reached. For this reason, formal Technical Spocifications changes which incorporate Virginia Power's statistical DNBR methodology must include core thermal limits which are based upon the statistical DNBR limit. Then, the OTDT trip system will ensure that no DNBR violations occur for any OTDT-terminated transient.

The Loss of Flou Accident (LOTA) is the DNBR-limiting accident which is not terminated by the OTDT trip function. The 3-pump LOFA in terminated on reactor coolant pump under-frequency. The current docketed LOTA analysis found that the LOFA did not violate the DNBR limit. When Virginia Power's Statistical DNBR Evaluation Mathodology is used, the Operating Margin in the LOFA analysis will increase, due to the more realistic treatment of the parameter uncertainties. Protection against DNBR transients which are not terminated by the OTDT trip system is thus maintained. Nominal statepoint I in Table 2.2.1 is known to bound the LOTA transient DMBR, and was for that reason selected for statistical analysis, s

3 i

s Table 4.0.1 Treatment of Parameters in Statistical Methodology Parameter Treatment in Treatment in Deterministic Statistical Methodology Methodology

) Tamparature Add uncertainty Use best actimate j to best estimate value Prossure Subtract uncertainty Use best estimate from best estimate value Power Add uncertainty Use best estimate to best estimate value Flow Use conservatively Use best estimate low value Effective Flou Use conservatively Use best estimate Fraction low value Engineering Use conservatively Not applied Enthalpy-rise high value (Fdha)

Muclear Add uncertainty to Use Fdhn=1.49*

Enthalpy-rise best estimate value (Fdhn) (i.e. use Fdhn=1.55)

• The 1.49 value is obtained by the deterministic addition of the 4% calculational uncertainty to the 1.435 limit. The measurement uncertainty, having been incorporated into the development of the SDL, does not need to be treated again here.

5.0 - COHCLUSIONS PAGE 59 5.0 conclusions The sample North Anna calculations described herein yielded a Statistical DNBR Limit of 1.44. The use of the statistical nothodology provides a DNBR margin gain of about 13%. Depending upon the uncertainty magnitudes in the plant-specific analysis, the actual SDL may well be different from the value calculated here.

The SDL was developed by statistically treating measurement uncertainties in selected operating parameters. The limit is based upon a minimum probability of 95% that the hot fuel rod will not experience DNB, as well as an expected number of rods in DNB of no more than 0.1% of the total in the core. Measurement uncertainties were quoted from the North Anna UFSAR and Technical Specifications; a typical value of effective flow fraction was selected. Upon NRC cyproval of forthcoming Technical Specification change submittals which will be based upon this methodology and rigorously justified uncertainties, transient analyses for DNBR evaluation will be performed With best-estimate or near best-estimate initial conditions for the statistically-treated parameters. The Virginia power methodology is similar to those which have been developed by the fuel vendors.

This report will serve as the basis to develop future Technical Specification change submittals for both the North Anna and Surry power Stations. Those submittals will be based upon analyses which are consistent with those described herein, and will include justifications of the parameter probability distributions

5.0 - CONCLUSIONS PAGE 60 based upon a plant hardware / procedures analysis. Each submittal will include:

1) A justification of parameter uncertainties.

2) A summary of the Monte Carlo DNBR calculations.

3) A summary of the core-wide probability analysis.

4) A new Statistical DNBR Limit and related Technical Specifications.

5) New core thermal limit-related Technical Specifications.

6) A revised table of retained DNBR margin (see Appendix A).

REFERENCES PAGE 61 l

1. Sliz, F. W. and K. L. Basehore: "Vepco Reactor Core Thermal-Hydraulic Analysis Using the COBRA IIIC/MIT Computer Code," VEP-FRD-33-A (October 1983).

2. Heller, A. S.,' Jones, J. H. and D. A. Farnsworth: " Statistical Core Design Applied to the Babcock-205 Core," BAW-10145 (October 1980).

3. Chelemer, H., Boman, L. H. and D. R. Sharps " Improved Thermal Design Procedure," WCAP-8567 (July 1975).

4. " Statistical Combination of Uncertainties," CEM-139(A)-NP (November 1980).

5. Letter from C. O. Thomas (NRC) to J. H. Taylor (BCW),

" Acceptance for Referencing

• of Licensing Topical Report BAW-10145P, ' Statistical Core Design Applied to the Babcock-205 Core,'" dated June 20, 1985.

6. Letter from J. F. Stolz (NRC) to C. Eicheldinger (Wes'inghouse),

" Staff Evaluation of WCAP-7956, WCAP-8054. WCAP-d567, and WCAP-8762," dated April 19, 1978.

7. Letter from R. A. Clark (NRC) to W. Cavanaugh, III (Arkansas Power C Light Co.), " Operation of ANO-2 During Cycle 2," dated July 21, 1981.

8. Cadek, T. F., et al.: "Effect of Local Heat Flux Spikes on DNB in Non-uniformly Heated Rod Bundles," WCAP-8174-P-A (February 1975).

9. Updated Final Safety Analysis Report, North Anna Power Station Units 1 & 2, Virginia Electric and Power Company.

10. Letter from R. H. Leasburg (Virginia Power) to H. R. Denton (NRC), " Supplementary Information for Amendment to Operating Licenses NPT-4 and NPT-7 North Anna Power Station Unit Mos. 1 and 2 Proposed Technical Specification Change," Ser. No. 80, dated February 10, 1982.

11. McFarlane, A. F.: " Topical Report Peaking Factors," WCAP-7912-L (March 1972). '

12. Ray, A. A., Ed. "SAS User's Guides Basics, 1982 Edition," SAS Institute, Inc., Raleigh, M. C. (1982).

REFERENCES PAGE 62 l 13. " Assessment of the Assumption of Normality (Employing Individual Observed Values),"'AMSI N15.15 (1974).

14. Salvatori, R., et al.: " Reference Core Report - 17 x 17,"

WCAP-8185 Amendment 1, Westinghouse Electric Corporation (December 1973).

15. Bourne and Green, " Reliability Technology," Wiley-Interscience, John Wiley C Sons, pp.336-337.

16. Selby, S., Ed. " Standard Mathematical Tables," chemical Rubber Company, 19th Ed., p. 611 (1971).

17. Letter from R. H. Leasburg (Virginia Power) to H. R. Denton (MRC), " Topical Report VEP-FRD-33 Vepco Reactor Core Thermal-Hydraulic Analyses Using the COBRA.IIIc/MIT Computer Code," Ser. No. 384, dated May 27, 1982.

18. Letter from W. N. Thomas (Virginia Power) to H. R. Denton (NRC),

" Topical Report VEP-FRD-33 Vapco Reactor Core Thermal-dydraulic Analyses Using the COBRA IIIC/MIT Computer Code," Ser. No. 359, dated June 12, 1981.

19. Ellenberger, S. L., et al.: " Design Bases for the Thermal Overpower delta-T and Thermal overtemperature delta-T Trip Functions," WCAP-8745 (March 1977).

20. Letter from W. L. Stewart (Virginia Power) to H. R. Denton (NRC), " Amendment to operating Licenses NPF-4 and MPT-7 North Anna Power Station Unit Mos. 1 and 2 Proposed Technical Specification Change," Ser. No. 731, dated February 14, 1985.

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i APPENDIX A - ADJUSTMENTS TO RETAINED DNBR MARGIN PAGE 63 l

APPENDIX A Adjustments to Retained DNBR Margin l

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APPENDIX A - ADJUSTMENTS TO RETAINED DNBR MARGIN PAGE 64 Virginia Power's deterministic DNBR evaluation methodology has savoral conservative factors built in which are not a part of the COBRA licensing basis. These conservative factors are known as retained DNBR margin, and by their application penali=e DNBR ..& ;

t ta']

calculations to such a degree that no separate steps must be taken to accommodate the rod how penalty. For the North Anna example the retained DMBR margin consists of a conservative factor in the deterministic DNBR limit of 1.30, a conservative W-3 correlation coefficient, a conservatively low Thermal Diffusion coefficient, a hot channel pitch reduction and the absence of a mixing vane grid in the models. Each parameter reduces the calculated DNBR from the best estimate value except for the conservatively large DMBR limit.-

, Each parameter reduces operating margin. Two of the factors are affected by the statistical DNBR evaluation methodology as notal below.

The elimination of the pitch reduction from the core T/H models Provided a benefit in terms of DNBR, and permitted the development of a core model which was not call type-specific. However, the pitch roduction was part of the retained DNBR margin for North Anna. Its use contributed some of Morth Anna's retained DNBR margin to offset tho rod bou penalty and provide some additional margin as a contingency factor. The retained margin must be reduced accordingly, as noted in Table A.1.

Reference 14 also notes that the actual deterministic W-3 DNBR limit is 1.28, rather than 1.30, for 17x17 fuel. The use of a 1.30

APPENDIX A - ADJUSTMENTS TO RETAINED DNBR MARGIN PAGE 65 limit has been accepted as both t'raditional and conservative. Its uso has provided 1.6X retained DMBR margin for North Anna as a contingency factor, and has served to help offset the rod bou penalty. However, the use of the actual W-3 data standard deviation in developing the SDL, rather than one based upon a 1.30, means that this factor no longer contributes to the retained DNBR margin and cannot be used as such. The appropriately modified retained DNBR margin is listed in Table A.1.

APPEMDIX A - ADJUSTMENTS TO RETAIMED DMBR MARGIN PAGE 66 Table A.1 Retained DMBR Margin for Westinghouse Standard 17x17 Fuel Deterministic Statistical Retained DMBR Margin Component Methodology Methodology 1.28 vs. 1.30 DMBR Limit 1.6% -

DMB Correlation Coefficient 1.7% 1.7%

(0.865 vs. 0.88 actual)

TDC: 0.038 vs. 0.051 1.2% 1.2%

Best Estimate Pitch Reduction 1.7% -

Extra Grid 2.9% 2.9%

Total Retained DMBR Margin 9.1% 5.8%

Source: Reference 20

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