ML20032C700

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VEPCO Nuclear Design Reliability Factors
ML20032C700
Person / Time
Site: Surry, North Anna  Dominion icon.png
Issue date: 09/30/1981
From: Berrryman R, Matthew Smith
VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:
Shared Package
ML18139B611 List:
References
VEP-FRD-45, NUDOCS 8111100754
Download: ML20032C700 (56)
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hTEBER981 Vepco NUCLEAR DESIGN RELIABILITY FACTORS oo

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lbi'1889"abbbyg FUEL RESOURCES DEPARTMENT VIRGINIA ELECTRIC AND POWER COMPANY

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VEP-FRD-45 VEPCO MUCLEAR DESIGN RELIABILITY FACTORS BY J.

G.

MILLER NUCLEAR FUEL ENGINEERING GROUP FUEL RESOURCES DEPARTMENT VIRGIN!\\ ELECTRIC AND POWER COMPANY RICHMOND, VIRGIMIA SEPTEMBER, 1981 RECOMMENDED FOR APPROVAL:

M. L '. Smith Supervisor, Nuclear Fuel Engineering APPROVED:

th.

m R.

M.

Berrym'an Director, Nuclear Fuel EngineerinJ

PAGE 2

CLASSIFICATION / DISCLAIMER The data, information, analytical techniques, and conclusions in this report have been prepared solely for use by the Virginia Electric and power Company (the Company), and they may not be appropriate for use in situations other than those for which they were specifically prepared. The company therefore makes no claim or warranty whatsoever, express or implied, as to their

accuracy, usefulness, or applicability.

In particular, THE COMPANY MAKES NO WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURp0S2,. HOR SHALL ANY WARRANTY BE DEEMED TO ARISE FROM COURSE 07 DEALING OR USAGE OF TRADE, uith respect to this report or any of the data, information, analytical techniques, or conclusions in it.

By making this report available, the a

Company does not authori=e its use by others, and any such use is expressly forbidden axcept uith the prior written approval of the company. Any such written approval shall itself be deemed to incorporate the disclaimers of liability and disclaimers of untranties provided herein.

In no event shall the Company be

liable, under any legal theory whatsoever (whether contract, t
tort, warranty, or strict or absolute liability),

for any Property damage, mental or physical injury or death, loss of use of

property, or other damage resulting from or arising out of the use, authorized or unauthori=ed, of this report or the data, g

information, and analytical techniques, or conclusions in it.

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PAGE 3

ABSTRACT This report Cescribes the methods and data base used to derive Nuclear Reliability Factors for application to tha reload safsty evaluation of Virginia Electric and power Company (Vepco) Operating nuclear units. Where possible the Muclear Reliability Factors are derived through a comparison of core physics measurements performed at the Vepco nuclear units and the corresponding design predictions of the Vepco physics design calculational models.

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PAGE 84 ACKNOWLEDGEMENTS The author would like to express his thanks to Messrs. David A.

Daniels.

C.

B.

Franklin and M.

L.

Smith for their 4

technical assistance in the development and preparation of this report.

The author would also like to express his j

appreciati n to a number of people who revLewed and provided comments on this report.

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4 TABLE OF CONTENTS Title Page 2

CLASSIFICATION / DISCLAIMER 3

ABSTRACT..............................................

4 ACKNOWLEDGEMENTS......................................

5 TABLE OF CONTENTS.....................................

7 LIST OF TABLES........................................

8 LIST OF FIGURES.......................................

SECTION 1 - INTRODUCTION 9

1.1 Purpose and Organi=ation of the Report 9

1.2 Definitions 11 13 1.3 Summary of Results SECTION 2 - MEASUREMENT AND CALCULATIONAL TECHNIQUES 17 17 2.1 Analytical Models 2.2 Reactivity Computer and Delayed Neutron Data 19 2.3 Temperature Coefficients 21 2.4 Power coefficients 23 2.5 Total Power Peaking Factors 25 SECTION 3 - STATISTICAL ANALYSIS METHODOLOGY 29 29 3.1 Introduction 31 3.2 Tests for Normality 3.3 Derivation of Nuclear Uncertainty Factors 32

... =

PAGE 6

i TABLE OF CONTENTS (cont.)

Title Page 1

33 SECTION 4 - RESULTS...................................

4.1 Reactivity and Kinetic Parameters 33 4.1.1 Doppler Temperature and Power a

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33 Coefficient..........................

j 4.1.2 Delayed Neutron Parameters 35 37 4.2 Power Peaking Factors f

4.2.1 Data Base Considerations 37.

i 47 4.2.2 Results..............................

55 OECTION 5 - REFERENCES................................

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J PAGE 7

LIST OF TABLES Table Title Page 3

1-1 Summary of Nuclear Reliability Factors 15 1

4-1 Total Peaking Factor Data Base 42 4-2 Axial Geometry for Power Distribuiton 44 Comparisons 4-3 Total Peaking Factor Results -- Morth Anna 1 48 Cycle 1.......................................

4-4 Total Peaking Factor Results -- Surry 1 49 Cycle 5.......................................

l 4-5 Total Peaking Factor Results -- Surry 2 50 Cycle 4 4-6 Summary of Total Peaking Factor Statistics 51 I

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'8 LIST OF FIGURES Figure Title Page 2-1 Moveable INCORE Detector Locations 28 4-1 Typical Measured / Predicted Axial Power 46 Distribution Comparison 4-2 Histogram of Total Peaking Factor Results --

52 North Anna 1 Cycle 1..........................

i 4-3 Histogram of Total Peaking Factor Results --

53 Surry 1 Cycle 5 i

4-4 Histogram of Total Peaking Factor Results --

54 Surry 2 Cycle 4...............................

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PAGE 9

SECTION 1 - INTRODUCTION 1.1 purpose and Organi=ation of the Report This report addresses the derivation of Nuclear Reliability Factors (NRFs) to be applied to safety related design predictions performed with the Vepco physics design models for Vepco reload cycles. When feasible, the value of the NRF for a

core physics parameter has been derived from a statistical comparison of core physics measurements with the corresponding predicted values.

For those cases where the value of the parameter cannot be measured per se, the NRF is derived from analytical engineering arguments.

The NRFs described in this study will be used in all reload safety evaluation calculations performed with the Vepco l

physics design models as noted in Reference 1.

Values of the NRF for several of the core physics parameters have been previously reported in the topical reports describing the Vepco physics design models, (References 2,

3, and 4). These reports include a description of the cores of the Vepco nuclear units to which the NRFs are to be

applied, as well as a

description of the models used to perform the calculations. The present report summari=es the results from these previously published topicals as well as deriving the NRFs for parameters not previously reported.

The parameters not previously reported are the Doppler

PAGE 10 temperature and power coefficients, delayed neutron parameters and the total peaking factor.

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PAGE 11 1.2 Definitions The Nuclear Reliability Factor is defined as the allowance to be applied to a safety related physics design calculation to assure conservatism.

The application of the NRF to a predicted value can be either multiplicative or additive depending on the physics parameter under consideration. For

example, in the case of total peaking factor, the NRF is multiplicative.

If the predicted value of the total peaking factor is FS, the value used in the safety analysis would bes NRF x FS An example of a parameter where the NRF is additive is the moderator temperature coefficient (MTC).

The application of the NRF to the predicted value is always in the conservative direction from a

core safety consideration.

For the case of a multiplicative NRF such as i

that for the cumulative integral bank worth, the NRF of 1.1 would be used to either increase or decrease the bank worth by 10% so as to yield a conservative value depending on the use of the parameter in the safety analysis. Likewise, for an additive MRT such as that for the MTC, the value used in the safety analysis would be MTC 2 MRF, depending on whether addition or subtraction was in the conservative direction.

PAGE 12 The Nuclear Uncertainty Factor (HUF) is defined as the actual physics calculational uncertainty for a parameter derived from a

statistical analysis performed on a

comparison of measured and predicted results for the parameter.

When a

sufficiently large sample population is available for the comparison, the HUF is derived so that when it is applied to a predicted value, the result will be conservative compared to the corresponding measurement for 95%

of the sample population with a 95% confidence level.

Like the corresponding

HRF, the HUF will be either multiplicative or additive depending on the parameter it was derived from. For example, if F2 is the predicted value for the total peaking factor and M is the corresponding measured value, then l

HUF x F2 > M i

for 95% of the population with a 95% confidence level.

1 For those parameters for which a HUF has been derived, the i

corresponding HRF is chosen such that it is aluays more conservative then the HUF.

For

example, for the total peaking
factor, the value of the HRF uould be chosen such that:

[

HRF > HUF l

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PAGE 13 1.3 Summary of Results Table 1-1 presents a

summary of the Nuclear Reliability Factors derived for the Vepco physics design models.

Included in the table is the calculational model used to calculate each parameter and the topical report from which the HRF for the parameter was derived.

For the Doppler temperature coefficient, Doppler power coefficient, effective delayed neutron fraction, and prompt neutron lifetime no direct measurements are available from which to derive the NRFs.

Therefore, the NRFs for these parameters uere derived from analytical engineering arguments.

The NRFs for the moderator temperature coefficient, critical soluble boron concentration, differential boron

worth, individual integral bank
worth, cumulativ'e integral bank
worth, and differential bank worth were derived from comparison with measuremenets performed at beginning-of-cycle (BOC),

hot

=ero power (HZP) core conditions. It is to be noted that the moderator temperature coefficient results reflect measured and predicted values of the isothermal tempera +.ure coefficient since a

direct measurement of the moderator temperature coefficient is not possible.

The NRFs for the radial peaking factor (FDH), the core

PAGE 14 average axial peaking factor (Fn), and the total peaking factor (F2) are conservative with respect to a NUF uhich meets the 95%/95%

acceptance criteria based on the sample population.

The NUF3 for FDH, F= and F2 were derived from a comparison of the predicted power distributions with the measured power distributions calculated by the INCORE code (Reference 5).

The values of the NRFs which are preceded by a

multiplication

sign, "x",

are multiplicative in a

-conservative direction.

Otherwise the NRF is additive in a conservative direction.

PAGE 15 TABLE 1-1

SUMMARY

OF NUCLEAR RELIABILITY FACTORS Analytical Parameter Model Reference NRF Individual PD207 FRD-19A x 1.10 Integral discrete Bank Worth Cumulative PD207 FRD-19A x 1.10 Integral discrete Bank Worth Differential FLAME FRD-24A 2 pcm/ step Bank Worth Critical Boron PD207 FRD-19A 50 ppm concentration discrete Differential PD207 FRD-19A x 1.05 Boron Worth discrete Moderator PD207 FRD-20A 3 pcm/*F l

Temperature one-=one l

Coeffici,ent Doppler PD207 FRD-45 x 1.10 Temperature one-=one Coefficient l

Doppler Power PDQ07 FRD-45 x 1.10 Coefficient one-=one Effective PD207 FRD-45 x 1.05

(

Delayed discrete i

Neutron Fraction Prompt PD207 FRD-45 x 1.05 Neutron Lifetime discrete l

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PAGE 16 TABLE 1-1 (cont.)

Analytical Parameter Model Reference NRF FDH PD207 FRD-19A x 1.05 discrete F=

FLAME FRD-24A x 1.08 F2 FLAME FRD-45 i x 1.075 i

s Keys pcm = percent mille l

(1 pcm = change in reactivity of 10-5) f ppm = parts per million

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r PAGE g7 SECTION 2 - MEASUREMENT AND CALCULATIONAL TECHNIQUES 2.1 Analytical Models The major analytical models currently used in the design of a reload cycle ares 1.

the Vepco PDQ07 discrete model, 2.

the Vepco PD207 one-=one model, and 3.

the Vepco FLAME model.

The Vepco PDQ07 models perform two-dimensional (x-y) geometry diffusion-depletion calculations for tuo neutron energy groups.

These models utili=e the NULIF code (Refrrence 6) and several auxiliary codes to generate and format the cross section input and to perform fuel assembly shuffles and other data management functions. The tuo models are differentiated according to thei=

mesh si=e, (i.e.,

either a

discrete mesh or a one-=one mesh.) The discrete mesh model generally has one mesh line per fuel pin, while the ona-=one mesh model has a mesh si=e of 6x6 per fuel assembly.

Either a

quarter core symmetric two-dimensional geometry or a

full core two-dimensional geometry may be specified.

Effects of nonuniform moderator density and fuel temperatures are accounted for by thermal-hydraulic feedback.

More complete descriptions of these models and their associated auxiliary codes are presented in References 3 and 4 for the discrete and one-=one models respectively.

PAGE 13 The Vepco FLAME model is used to perform three-dimensional (x-y-=)

geometry nodal power density and core reactivity calculations using a

one energy group, modified diffusion theory.

The model utili=es the NULIF code and several auxiliary codes to generate and format cross section input and to perform fuel assembly shuffles and other data management tasks.

Each fuel assembly in the core is represented by one radial node and 32 axial nodes. Either a 7

quarter core symmetric three-dimensional geometry or a full core three-dimensional geometry may be specified. As with the pp207

models, the effects of nonuniform moderator density and fuel temperature are accounted for by thermal hydraulic feedback. A more complete description of the model and the auxiliary codes used with it will be found in Reference 2.

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PAGE 19 2.2 Reactivity Computer and Delayed Neutron Data Reactivity measurements for the Surry and North Anna nuclear power stations are obtained using a Mastinghouse reactivity computer.

The reactivity computer periodically sarples neutron flux level signals from one of four ex-core detectors.

Each ex-core detector consists of two five-foot ion chambers stacked one on top of the other. These signals are then converted to overall core reactivity by solving the moneenergetic point reactor kinetics (inhour) equations with six delayed neutron groups.

The resulting calculated reactivity and flux level for the core are then displayed on a strip chart recorder.

The delayed neutron data for input to the reactivity computer are calculated by the PD207 discrete model. The delayed neutron fraction and decay constant for each of the six delayed neutron groups at a given cere condition are calculated by weighting the delayed neutron fraction for each fissionable isotope for each group by the core integrated fission rate of that isotope. Normally, a single set of delayed neutron predictions will be used for all startup physics measurements at hot =ero power (HZp) since sensitivity studies performed with the pDQ07 discrete model have indicated that the radded configuration of the plant has minimal-effect on the delayed neturon data, (typically less than 0.2%.)

PAGE 20 The delayed neutron parameters of beta-effective (Beff) and prompt neutron lifetime (lp) are required for input to the reload cycle safety analysis. Beff is defined as the product of the core average delayed neturon fraction and the importance factor.

The importance factor accounts for the decrease in effectiveness of the delayed neutrons when compared to prompt neutrons in causing fission and is set equal to 7.97. The prompt neutron lifetime is the time from neutron generation to absorption.

It is a core average parameter calculated with the cross section generating code.

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PAGE 21 2.3 Temperature Coefficients The isothermal temperature coefficient (ITC) is defined as the change in reactivity per degree change in the moderator, clad and fuel temperatures of the core. ITCs are measured at HZP for various core rodded configurations during the startup physics testing of each cycle.

For each rodded configuration, reactivity measurements are made during a reactor coolant system (RCS) cooldown of approximately 5'F.

a RCS heatup of approximately 10'F, and another RCS cooldown of approximately 5'F.

The slopes of the change in core reactivity versus the change in the RCS temperature as plotted by the reactivity computer is then used to derive an average value for the ITC for the core configuration.

prediction of the isothermal temperature coefficient is performed using the PD207 one-=one model. The change in core reactivity is calculsted for changes in both the fuel and moderator temperatures of 15'T about the HZp core average temperature of 547'F. This change in core reactivity divided by the total change in the fuel and moderator temperatures, (i.e.,

10*F),

yields the value of the ITC in units of pcm/'F. Calculation of thu moderator temperature coefficient (MTC) is similar, but with the fuel temperature being fro =en at the HZp value for both calculations. Therefore, the moderator temperature coefficient is defined as the change in core reactivity per change in *F of the core moderator

PAGE 22 temperature only. The Doppler temperature coefficient (DTC) is defined as the change in core reactivity per degree change in fuel temperature and is calculated by taking the difference between the predicted values of the ITC and MTC.

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pAGE 23 2.4 pouer Coefficient.

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The totsI power coefficient is defined as the change in due to the combined effect of the moderator and reactivity, fuel temperature change due to a change in core power level.

The Doppler "only" power coefficient (DpC) relates to the change in power which produces a change in the fuel and clad temperature, power coefficient measurements are not routinely performed during the startup physics testing of Vepco nuclear units.

The feu measurements which have been made are highly unreliable, incorporating a

design tolerance of 230%.

Furthermore, direct measurement of the Doppler "only" power coefficient is not possible.

For these reasons no comparisons between measured and predicted power coefficients have been performed for the derivation of calculational uncertainties.

power coefficient predictions are performed with the pD207 one-=one model.

The DpC is found by subtracting the reactivity change uith power due to a

change in the moderator temperature

only, (i.e.,

the moderator power coefficient), from the total power coefficient. To calculate the total power coefficient, pD207 one-=one model calculations are performed at !10% power levels about the target power

level, all other core conditions being held constant. Thermal hydraulic feedback effects are included in

PAGE 24 the calculation.

The change in reactivity between the two calculations as a

function of the change in power level yields the value of the total power coefficient in units of pcm/%

power. The Doppler component of the power coefficient is predicted by performing a calculation at the +10% power level, but with the core inlet enthalpy value of the thermal hydraulic feedback part of the calculation adjusted so that the value of the moderator temperature is fro =en to the value used in the

-10%

power level calculation.

The resulting change in core reactivity as a function of power level between this calculation and the -10% power level calculation yields the value of the Doppler "only" power coefficient.

The Doppler "only" power coefficient is then substracted from the predicted total power coefficient to find the moderator power coefficient.

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PAGE 25 2.5 Total Power Penking Factars The total peaking factor F2 is defined as the ratio of the peak power density in a

fuel pellet to the core average power density.

The maximum total peaking factor for th,e

core, also referred to as the heat flux hot channel factor, is defined as the peak power density in the core divided by the core average power density. Values of F2 for an axial locati7n

=

in the

core, F2(=), are calculated using the PD207 discrete and FLAME models.

If F2(x,y,=)

is the nodeuise three-dimensional power distribution for the node located at (x,y,=) calculated by the FLAME model, then the value of F2 at axial location = for radial location (x,y) is given by F2(x,y,=) x FDH(x,y) / RPD(x,y)

F2(=)

=

where FDH(x,y) is the peak radial power for the assembly and RPD(x,y) is the corresponding average assembly power calculated by the two-dimensional PD207 discrete model. The ratio FDHCx,y)/RPD(x,y) is referred to as the PD207 pin-to-box ratio.

Measured power distributions are calculated by the INCORE code based on detector readings obtained from the movable incore instrumentation system.

This system consists of 50 movable detector locations as shown in Figure 2-1.

Three-dimensional flux distributions are provided by the axial movement of the detectors in the instrumentation

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PAGE 26 thimbles.

Input to the INCORE program consists of 1.

a description of the reactor conditions when f

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measurements were made (such as power level, control rod positions, etc.)

2.

incore detector readings including which flux thimbles were used and neutron cross sections of the sensor, and 3.

fast and thermal fluxes, radial assembly average powers and radial pin powers calculated by the PD207 discrete model.

INCORE corrects raw pointuise flux measurements for leakage

current, changes in power level between measurements, and relative detector sensitivities to determine the pointuise reaction rate in the flux thimbles. The measured reaction rates are then compared with expected values.

INCORE computes the relative local power produced by each fuel. assembly, Pm, and the power in the peak-fuel rod for each assembly.

For the assemblies with monitored thimble locations, the assemblyuise power is'given by the equation Pm = Rm x PP / RP where Rm is the measured reaction rate for the thimble, pp is the power calculated for the thimble by the PD207 discrete model, and RP is the reaction rate for the thimble calculated by the PD207 model. The values for pm for all 157

PAGE 27 assemblien in the core are normali=ed so that their sum equals unity.

INCORE calculates the peak F2(=) for each assembly for 61 axial nodes.

PAGE 28 FIGURE 2-1 MOVABLE INCORE DETECTOR LOCATIONS R

P H

M L

M J

11 G

F E

D C

B A

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I PAGE 29 SECTION 3 - STATISTICAL AHALYSIS METi!0DOLOGY 3.1 Introduction In order to derive the calculational uncertainty for the total peaking factor F2, a

statistical analysis was performed on the percent difference between the measured and predicted values for each core location; i.e.,

(Mi - Pi) x 100% / Mi Xi

=

Here Mi is the measured value for observation i. Pi is the predicted value for observation i

and Xi is the percent difference between the measurement and prediction for the ith observation. Xi is assumed to be a normally distributed 4

I random variable whose mean X and standard deviation S are defined as:

A X = SUM (Xi) /n (5-1)

=

SUM (Xi - X)2/ (n - 1)

(5-2)

St a

where the notation SUM indicates a summation over values of i

from 1

to n

of the quantity in parentheses which immediately follows.

In

general, the standard deviation as calculated above includec the statistical uncertainties due to both 4 -

measurement and calculation. That is, the variance of Xi is i

given as St = Sm2+ Sp2 where Sm2 is the variance due only to measurement

PAGE 30 uncertainty and Sp2 is the variance due only to calculatinnal uncertainty. Therefore, any standard deviation for calculational uncertainty derived using equation (5-2) is conservative since an additional margin for measurement tincertainty is included.

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PAGE 31 3.2 Tests for Normality The distribution of the differences, Xi, for the total peaking factor was tested for normality using the method outlined in Reference 7.

This method, the Kolmogorov-Smirnov test (hereafter scierred to as the D-test) in valid for distributions containing over 50 observations. All tests were performed for a 95% confidence level with a.05 level of -significance being considered as adequate for rejection of the assumption of normality for the data The D-test compares the value of a test statistic, D,

for the sample distribution with the value of the test statistic for a

normal distribution of the same size. Tables 4-3 through 4-6 provide the normality test results for the.

' difference ~ distributions ust4 to derive the 2eliability factors.

The assumption of normality is rejected when the computed values of D are less than the test D value which cor:esponds to a

95% confidence level with a.05 level of significance for the indicated sample si=e n.

These results are summari=ed under the columns labeled PROB >D.

A value in the column of less than.05 indicates a rejection of the null hypothesis--i.e.,

the sar.ple is considered to be nonnormal.

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i PAGE 32 3.3 Derivation of Nuclear Uncertainty Factors For the total peaking factor, nuclear reliability factors were derived using one sided upper tolerance limit methodology, (Reference 8).

Assuming that the sample distribution, Xi, is normal, the one sided upper tolerance limit TL is defined as:

TL = X+

(K x S)

(5-7) uhere K is the one-sided tolerance factor. K is chosen such that 95% of the population is less than the value of TL with a

95%

confidence level. The value of K is dependent on the sample si=e n

used to derive TL, (Reference 8). In cases uhere the value of the mean (or bias) reduces the value of TL in a non-conservative direction, (i.e.,

a negative bias for total peaking factor),

the value of the mean is set equal to =ero to insure conservatism.

l The value of the Nuclear Uncertainty Factor MUF is derived from the one sided upper tolerance limit as 1 + (TL/100)

(5-8)

NUF =

For example if the value of TL is 10%, the NUF is 1.1.

.pAGS 33 SECTION 4 - RESULTS 4.1 Reactivity and Kinetic parameters 4.1.1 Doppler Temperature and power Coefficient Direct measurement:of Doppler reactivity effects in the core is not feasible due to the coupling between change-in the core's fuel temperature and the core's moderator properties.

Most of the measurement / prediction uncertainty in the isothermal. temperature coefficient can be attributed to the moderator component since the value of the Doppler component is of the order oi -2 pcm/*F for Vepco nuclear units and shows little variation over the lifetime of a

cycle.

Therefore, a

Muclear Reliability Factor of 1.1 Ci.e.,

10%)

uill be assumed for the Doppler temperature coefficient.

Measurements of the total power coefficient have. been performed during the startup physics testing of Surry 1 Cycle 4,

Surry 2 Cycle 4,

Surry 1 Cycle 5 and North Anna 1 Cycle 1 for a total of 14 measurements. Since the startup of Surry 1

Cycle 5 the power coefficient measurement has been discontinued frcm the startup physics testing program for Vepco nuclear units.

The Doppler component of the power coefficient cannot be measured directly.

Due to the difficulty of obtaining accurate measurements of the total power coe fficient, the design tolerance for the chove Vepco measurements was set at

PAGE 34 230%.

This large measurement uncertainty. along with the 1

small si=e of the available data base makes a derivation of an uncertainty factor for the Doppler component of the power coefficient based on comparison of measurement and l-prediction of questionable value.

Therefore, a

Muclear i

Reliability Factor for the Doppler "only" power coefficient is conservatively chosen to be 10%.

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PAGE 35 4.1.2 Delayed Heutron parameters The delayed neutron parameters input to the reload cycle safety analysis are the effective delayed neutron fraction Beff and the prompt neutron lifetime lp. Beff is the more important factor in determining the reliability of core physics design predictions; however, measurements of this parameter are not available for comparing with predictions in order to derive an uncertainty factor.

The major uncertainties associated with the prediction of Beff are the experimental values of the delayed neutron fractions and the percursor decay constants for each delayed neutron group input to the PDS07 discrete

model, the predicted core nuclide concentrations (in particular U 23s, Uzas and pu23'), the calculation of the fission sharing of each fissionable isotopo for the weighting of the delayed neutron fraction of the isotopes, and the estimate of the importance factor.

The experimental uncertainty for the delayed neutron fractions and decay constants are on the order of 4%,

(Reference 9).

The lou uncertainty factor associated with the prediction of the radial peaking factors over cycle lifetime by the PDS07 discrete model (less than E T. e implits a similar accuracy in the prediction of the core nuclide concentrations of

U23s, Uzas and pu23' and the fission sharing for the isotopes.
Finally, Beff is relatively insensitive to uncertainty in the impwrtance

~ - _ -

PAGE 36 factor since a

typical v'lue for the importance factor, (e.g.,

0.97),

indicates a

reduction in the core average delayed neutron fraction of only 3%.

From these considerations a Nuclear Reliability Factor for-Beff and 1p of 5% appears to be a reasonably conservative

]

estimate.

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)

i J

t 4

I J

l 4

t f

PAGE 37 4.2 power peaking Factors 4.2.1 Data Base Considerations Uncertainty factors for the total power peaking factors F2 were derived from a

comparison of measurements and predictions based on a

one-sided 95%/95% upper tolerance limit.

The data base consisted of three Vepco nuclear cycles: North Anna 1

Cycle 1,

Surry 2 Cycle 4 and Surry 1 Cycle 5.

These cycles were the latest Vepco cycles to have completed operation at the time this report was in preparation. One additional

cycle, North Anna 1 Cycle 2, had also completed operation, but due to the radial flux tilt problem l

experienced during the initial operation of the~ cycle, it was excluded from the data base. The two Surry cycles are 18-month cycles with large lumped burnable poison loadings.

Surry 2

Cycle 4 employed an out/in fuel loading strategy.

Surry 1 Cycle 5 etsployed an in/out fuel loading strategy and l

is representative of the future fuel loading strategy being l

Planned for Vepco nuclear units. North Anna 1 Cycle 1 was an initial core 18 month cycle with a large loading of lumped l

burnable poison, Measured total peaking factors were calculated by the INCORE i

l code.

Table 4-1 presents a listing of the INCORE flux maps included in the data base. Each cycle includes flux maps at l

PAGE 38

HZp, BOC for both a rodded and unrodded core configuration, a

map in the mid power range for an essentially unrodded core condition near BOC and a selection of HFp flux maps throughout the remaining cycle lifetime. In addition two mid power range maps near BOC for a pseudo-ejected rod test and a

dropped rod test are included for North Anna 1 Cycle 1.

I Measured peaking factors are compared only for monitored I

thimble locations in order to avoid the additional i

uncertainty introduced by the INCORE code in interpolating peaking factors for the non-monitored assembly locations.

j Thimble readings for a flux map are normally discarded if the readings are incomplete or if the thimble suffered 1

severe misalignment during the measurement. Such thimble i

l locations have been deleted from the data base used to l

l derive the peaking factor calculational uncertainties.

In order to generate total peaking factor predictions, concentration files for FLAME uere created at each cycle burnup at which a

flux map was taken. Normally the FLAME l

l depletion was performed at an

ARD, HFp core condition.

l

However, unlike a

tuo-dimensional calculation.

a three-dimensional modeling of the core is sensitive to the f

actual changes in core conditions which occurred during the burnup depletion.

This sensitivity can be monitored by comparing the measured and predicted axial offset (A.O.) for a

given flux map core condition. A large difference between the axial offsets is indicative of oversimplified modeling L

l

PAGE 39 I

of the core history prior to the time the flux map was taken.

The severity of this problem was quantified by comparing the predicted and measured axial offsets for each flux map.

If the measured / predicted difference uns on the order of 3% or greater a more accurate modeling of the core i

history was performed by depleting the previous burnup step with the D

bank partially inserted. The FLAME calculation for each flux map was then performed at the core condition r

of the flux map. The total relative power distribution in each three-dimensional node of the FLAME calculation is converted to a

total peaking factor by multiplying by the two-dimensional PD207 pin-to-box ratio at the appropriate core conditions for the axial region.

Total peaking factor comparisons are performed for 6 axial s

planes for a North Anna unit and 5 axial plans for a surry l

i Unit.

These axial planes have been selected at locations approximately halfway between neighboring assembly grid st:6ps as shown in Table 4-2.

Table 4-2 gives the axial locations of the center of the grids and the locations of the center of the INCORE or FLAME axial nodes used in the i

analysis in terms of the percent of active core height as measured from the bottom of the active core. INCORE nodes are number from 1 to 61 with node 1 being at the top of thct core.

The planes selected for the measurement / prediction i

comparisons correspond to the INCORE nodes listed in Table 1

4-2.

The FLAME model contains 32 axial nodes numbered from i

~,,.

i pAGE 40 the bottom to the top of-the core with axial node 1 being at the bottom of the core. In order to derive a predicted F9 talue for the percent of core height corresponding to the selected INCORE plane a Lagrange interpolation was performed on the predicted total peaking factors for the 3 axial FLAME nodes which most closely bracketed each selected INCORE plane. These axial FLAME nodes are listed in Table 4-2.

Axial locations approximately halfway between the grids were

'he comparisons in order to add conservatism to chosen for t

L i

the derivation of the total peaking factors calculational l

uncertainty. Since the FLAME model does not model the grids, l

l the ' predicted axial power distribution is not depressed at the grid locations.

This results in a tendency for the maximum difference between measured and predicted FS to occur about halfway between the grid locations where the measured value usually exceeds the predicted. Hence, using these locations for the data base rasults in an additional conservatism to be added to the uncertainty factor and removes the necessity of having to apply a special-grid correction factor to a predicted value at a between-the-grid location to allow for the unmodeled grid depression effect.

Figure 4-1 provides an example of this phenomena in plotting the measured and predicted axial power distribution for a I

specific monitored thimble location for a North Anna 1 Cycle 1 flux map.

PAGE 41 Only radial core locations corresponding to accepted monitored thimble locations were included in the data base.

Since only peaking factors whose relative power distributions (RpDs) are greater than the core average are of interest in the safety analysis of-a reload core, only pairs of observations where both the predicted and measured RpDs are 21.0 have been included in the data base. This approach excludes large percent difference values which often r,.sult from comparing the relatively low RPDs that tend to occur near the radial core periphery and at the top and bottom of the core due to the steeper power distribution slopes in these areas.

f i

1

l l

l

.PAGE 42 4

i

~

TABLE 4-1 TOTAL PEAMING FACTOR DATA' BASE Cycle Number of Flux Power Burnup Rodded Monitored Cycle Map 4 Level MWD /MTU Condition Thimbles MIC1 1

4 0

D/228 48 4-N1C1 2

4 0

D/0 46 l

N1C1 5

30 50 D/195 48 N1C1 6

30 50 Ejected Rod

'43 l

MIC1 10 49 50 Dropped Rod 48 N1C1 15 73 150 D/215 38' HIC 1 37

~96 3047 D/213 39 NIC1 50 96 7340 D/205 38 N1C1 53 97 9135 D/220 39 i

l N1C1 58 100 11003 D/228 38 NIC1 64 100 12960 D/227 46 NIC1 75 97 15142 D/224 49 l

51C5 1

0 0

D/213 40 l-51C5 3

4 0

D/0,C/219 L. 3 51C5 4

50 0

D/200 43 f

SICS 12 100 2123 D/218 42 51C5 17 100 4072 D/223 43 f

S1CS 19 100 5270 D/224 43 I

51C5 23 100 7411 D/224 43 S1C5 26 100 8973 D/226 42 SIC 5 30 100 10125 D/226 43 S1CS 32 100 11580 D/216 42 f

l l

m..

ma i

PAGE 43 TABLE 4-1 (cont.)

Cycle Number of Flux Power Burnup Rodded Monitored Cycle Map #

Level MWD /MTU Condition Thimbles S2C4 1

4 0

D/218 47 S2C4 2

7 0

D/0 47 S2C4 5

61 8

D/155 47 r

S2C4 11 100 1800 D/225 45 S2C4 18 100 5266 D/224 45 i

S2C4 22 100 6968 D/210 43 S2C4 27 100 9250 D/202 42 S2C4 30 100 11006 D/223 49 52C4 36 100 13200 D/222 49 i

l i

E i

l l

l I

l i.- -

PAGE 44 TABLE 4-2 AXIAL GEOMETRY FOR POWER DISTRIBUTION COMPARISONS North Anna Units 1 and 2 Surry Units 1 and 2

% Core *

% Core Neight Description Height Description 103.5 Grid # 1 104.0 Grid # 1 89.2 Grid # 2 90.8 Grid # 2 85.9 FLAME Hode 28 85.9 FLAME Mode 28 82.8 FLAME Node 27 83.3 INCORE Node 11 81.7 INCORE Node 12 82.8 FLAME Node 27 79.7 FLAME Node 26 79.7 FL;.ME Node 26 74.9 Grid # 3 72.6 Grid # 3 70.3 FLAME Node 23 67.2 FLAME Node 22 68.3 INCORE Hode 20 64.1 FLAME Node 21 67.2 FLAME Node 22 63.3 INCORE Node 23 64.1 FLAME Node 21 60.9 FLAME Node 20 60.6 Grid # 4 54.4 Grid

  • 4 57.8 FLAME Node 19 48.4 FLAME Node 16 54.7 FLAME Node 18 45.3 FLAME Hode 15 53.3 INCORE Node 29 45.0 INCORE Node 34 51.6 FLAME Node 17 42.2 FLAME Node 14 46.4 Grid # 5 36.2 Grid # 5 42.2 FLAME Hode 14 29.7 FLAME Node 10 39.1 FLAME Node 13 26.7 INCORE Node 45 38.3 INCORE Node 38 26.6 FLAME Node 9 35.9 FLAME Node 12 23.4 FLAME Node 8 32.1 Grid # 6 18.0 Grid # 6 29.7 FLAME Node 10 17.2 FLAME Node 6 26.6 FLAME Node 9 14.1 FLAME Mode 5 25.0 INCORE Node 46 13.3 INCORE Node 53 23.4 FLAME Node 8 10.9 FLAME Node 4 17.8 Grid # 7 1.3 Grid # 7

PAGE 45 TABLE 4-2 (cont.)

j North Anna Units 1 and 2 4

1 1

% Core

  • Height Description 17.2 FLAME Node 6 l

15.0 INCORE Node 52 14.1 FLAME Node 5 I

10.9 FLAME Hode 4 0.8 Grid 9 8 i

a

% core Height is measured from the bottom of the core.

1 f

r t

=

t t

i t

j l

t

.,n-,

4 l

PAGE 46 FIGURE 4-1 TYPICAL MEASURED / PREDICTED AXIAL POWER 0!STRIBUTION COMPARISON NORTH ANNA 1 CYCLE-1 FLUX MRP37 -- THIMBLE LOCATION H13.

l.G-

/_ c l

1.5-l.4-i~

1.3-3 1.2-T 1.1-1 0

u T

A 10-L P

0.9-E R

K 0.8-I N

G 0.7-F A

0.6-C i

T O

0.5-

.l R

j 0. 4.-

i 0.3-0.2.

i

(

0.1-i i

0.0 0

10 20 30 40 50 60 70 80 90 100.

i i

PERCENT OF CORE HEIGHT I

LEGEND: POWER m. MEASURED e-e-e. P RE01 C TE D 1

PAGE 47 4.2.2 Results Tables 4-3 through 4-5 present a

summary of the total peaking factor comparisons for each cycle on a flux map by flux map basis. Included in the tables is a listing of the measured and predicted axial offsets (A.0) and the arithmetic difference between the two for each map.

Figures 4-2 through 4-4 present histograms of the comparison results for the total peaking factors for each cycle. The histograms may be used as a visual check on the normality of each percent difference distribution.

Table 4-6 presents a summary of the peaking factor data base statistics.

No problem in the normality testing of any of the cycles for the total peaking factor was found although results for individual maps for a particular cycle often failed the normality test.

Based en the 95%/95% uncertainty factors listed in Table 4-6 it is concluded that an acceptable Reliability Factor for the total peaking factor is 1.075.

PAGE 48 TABLE 4-3 TOTAL PEAKING FACTOR RESULTS -- NORTH ANNA 1 CYCLE 1 l

For Measured and Predicted F2 2 1.0 X

S Min.

Max.

Map Mean Std. Dev.

Meas. Pred.

A.O.

4 n

(%)

(%)

PROB >D Diff. Diff.

A.O.

A.O.

Diff.

1 232 1.19 3.62

>0.15

-6.75 8.89 0.6

-0.2 0.8 2

231 0.70 5.06

>0.15 -10.53 12.18

-0.1

-0.5 0.4 5

241 1.29 3.97

>0.15

-7.24 11.43 8.3 7.3 1.0 6

241 0.94 3.62 0.037

-7.20 8.98 6.1 7.7

-1.6 10 252 0.97 3.86 0.072

-8.70 10.59

-4.4

-3.8

-0.6 15 213 -0.03 4.43

>0.15 -10.24 11.76

-3.3

-5.3 2.0 37 215 0.67 3.67

<0.01

-8.06 9.21

-5.6

-7.4 1.8 50 218 0.68 2.45 0.031

-8.00 5.91

-7.4

-6.9

-0.5 53 224 0.37 2.09 0.093

-5.06 5.34

-2.7

-3.2 0.5 l

58 216 -0.35 4.38

<0.01

-9.30 9.25 0.4

-3.3 3.7 64 261 -0.14 2.89

<0.01

-6.44 7.78

-2.4

-3.5 1.1 75 278 -0.35 4.21

>0.15 -10.06 11.02 0.5

-2.3 2.8 l

Summary statistics for North Anna 1 Cycle 1 F2 data base:

(Measured - Predicted) x 100% / Measured

% Diff.

=

2822 n =

0.49%

Mean

=

Standard Deviation = 3.81%

>0.15 PROB >D

=

l l

PAGE 49 TABLE 4-4 TOTAL PEAKING FACTOR RESULTS -- SURRY 1 CYCLE 5 For Measured and Predicted FQ 2 1.0

.(

3 Min.

Max.

map Mean Std. Dev.

Meas. Pred.

A.O.

n

(%)

(X)

PROB >D Diff. Diff.

A.O.

A.O.

Diff.

1 129 0.76 4.47

>0.15 -12.11 15.30 27.4 24.8 2.6 3

138 1.22 2.99

>0.15

-4.77 9.51 22.7 22.4 0.3 4

166 1.18 3.66

>0.15

-7.99 9.98 6.3 8.2

-1.9 12 170 0.88 3.91

>0.15

-8.60 11.25

-1.6

-3.8 2.2 17 173 0.93 4.44

>0.15

-8.91 10.26

-1.6

-4.7 3.1 19 171 1.28 3.98

<0.01

-5.58 10.98

-2.5

-5.2 2.7 23 175 0.99 2.96 0.018

-5.95 7.99

-3.2

-3.7 0.5 26 175 0.89 2.27 0.047

-4.41 7.25

-2.9

-3.3 0.4 30 175 1.54 3.73 0.105

-7.80 8.97

-3.7

-1.6

-2.1 32 175 1.17 3.10

>0.15

-6.24 8.61

-3.5

-2.5

-1.0 Summary statistics for Surry 1 Cycle 5 FS data baset (Measured - Predicted) x 100% / Measured

% Diff.

=

n=

1647 1.09%

Mean =

Standard Deviation = 3.59%

>0.15 PROB >D

=

I i

l I

i PAGE 50 TABLE 4-5 TOTAL PEAKING FACTOR P.ESULTS -- SUPRY 2 CYCLE 4 For Measured and Predicted FC 2 1.0 X

S Min.

Max.

Map Mean Std. Dev.

Meas. Pred.

A.O.

n

(%)

(%)

PROB >D Diff. Diff.

A.O.

A.O.

Diff.

1 157 1.35 4.00

>0.15

-9.45 10.57 21.9 23.5

-1.6 2

163 1.06 4.53

>0.15 -11.47 12.93 17.6 20.3

-2.7 5

178 -0.33 3.54

>0.15

-7.47 7.81 -10.4

-8.1

-2.3 11 203 0.30 4.19 0.092 -11.02 11.14

-2.9

-5.2 2.3 18 205 1.11 3.28 0.130

-7.39 9.55

-2.6

-4.2 1.6 22 203 1.51 3.33

>0.15

-6.65 9.76

-4.0

-5.4 1.4 27 185 2.09 3.24 0.078

-5.55 9.92

-5.8

-5.3

-0.5 30 217 1.52 2.58 0.145

-4.81 8.56

-1.7

-2.8 1.1 36 213 1.30 2.98

<d.01

-5.91 7.92

-1.4

-3.3 1.9 Summary statistics for Surry 2 Cycle 4 F2 data base:

(Measured - Predicted) x 100% / Measured

% Diff. =

n= '1724 Mean = 1.11%

Standard Deviation = 3.58%

>0.15 PROB >D =

I t

PAGE 51 TABLE 4-6

SUMMARY

OF TOTAL PEAKING FACTOR STATISTICS l

X S

Normality 95%/95%

Mean Std. Dev.

Test Uncertainty Cycle n

(%)

(X)

PROB >D Factor MIC1 2822 0.49 3.81

>0.15 1.069 51C5 1647 1.09 3.59

>0.15 1.072 S2C4 1724-1.11 3.58

>0.15 1.072 i

I l

i I

I

PACE 52 FIGURE 4-2 R

0 FE E JCE BU 0 4 Fh Abuk0 REDI E

FC >

0 FREQUENCY 600 -

500 -

400 -

300 -

rm

-10

-8

-6

-4

-2 0

2 4

6 8

10 12 PERCENT O!FFERENCE l

PAGE 53 FIGURE 4-3 PERCENIDIFFERENCED!STRIBUTICNFORMERSURED[PRED!CTEDF0>

1.0 FREQUENCY 390 -

360 -

330 --

300 270 -

240 -

210 -

180 -

150 -

120 -

90 -

6 0 --

30 -

- 93 9 3

- 10

-8

-6

-4

-2 0

2 4

6 8

10 12 14 15 PERCENT O!FFERENCE

PAGE 54 FIGURE 4-4 PERCENT GI FERENCE DISTPIBUTION FOR 11EASURED[PREb! TED i 0 > 1.0

"'l'"'!

)

e0 360 -

330 -

300 -

270 -

240 -

210 -

180 -

150 -

I 120 -

90 -

60 -

30 -

Y Y

e,

- 10

-8

-6

-4

-2 0

2 4

6 8

10 12 13 PERCENT DIFFERENCE

+

PAGE 55 SECTION 5 - REFERENCES 1.

S.

A.

Ahmed, et al.,

" Reload Nuclear Design Methodology," VEP-FRD-42, April 1981, CVirginia Electric and Power Company).

2.

?J.

C.

Beck, "The Vepco FL%ME Model", VEP-FRD-24A, July i

1981, (Virginia Electric and Power Company).

3.

M.

L.

Smith, "The PD207 Discrete Model," VEP-FRD-19A, July 1981, (Virginia Electric and Power Company).

4.

G.

R.

Rodes, "The PD207 One Zone Model," VEP-FRD-20A, July 1981, (Virginia Electric and Power Company).

5.

W.

D.

Leggttt III and L.

D.

Eisenhart, "The IHCORE Code", WCAP-7149, December 1967, (Westinghouse).

6.

W.

4.Wittkopf, et al.,

"NULIF-Neutron Spectrum Generator, Feu Group Constant Calculator and Fuel Depletion Code," BAW-10115, June 1976, (Babcock and Wilcox).

7.

M.

A.

Stephens, "Use of the Kolmogorev-Smirnov, Cramer-Von Mises and related statistics without ex tensive tables,"

J.

American Statistical Association, 69:730, 1974 8.

"An Acceptance Model and Related Statistical Methods for the Analysis of Fuel Densification," U.S.N.R.C.

Regulatory Guide 1.126, Revision 1,

March 1978.

{

9.

G.

R.

Keepin, " Physics of Nuclear Kinetics,"

Addison-Wesley, 1965.

_ _.

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