ML18139B610

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Forwards VEP-FRD-45, VEPCO Nuclear Design Reliability Factors. Rept Describes Methods & Data Base Used to Derive Nuclear Reliability Factors for Application to Core Physics Input Parameters Used in Reload Safety Evaluation
ML18139B610
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Site: Surry, North Anna  Dominion icon.png
Issue date: 11/04/1981
From: Leasburg R
VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To: Harold Denton, Eisenhut D
Office of Nuclear Reactor Regulation
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ML18139B611 List:
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614, NUDOCS 8111100735
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'...

e VIRGINIA ELECTRIC.AND POWER COMPANY RICHMOND,. VIRGINIA 23261 November 4, 1981 R. H. LEASBURG VxoE PRESJDENT NUCLEAR OPERATIONS Mr. Harold R. Denton, Director Office of Nuclear Reactor Regulation Attn:

Mr. D. G. Eisenhut, Director Division of Licensing U. S. Nuclear Regulatory Commission Washington, DC 20555 Gentlemen:

Serial No. 614 FR/JGM:

plc Docket Nos.:

License Nos. :

VEPCO NUCLEAR DESIGN RELIABILITY FACTORS 50-280 50-281 50-338 50-339 DPR-32 DPR-37 NPF-4 NPF-7 Enclosed for your review are forty (40) copies of the Vepco Topical Report VEP-FRD-45, "Vepco Nuclear Design Reliability Factors".

This report is one of a series of topical reports supplying general information pertaining to the nuclear reload licensing and core follow support capabilities which have been developed at Vepco.

It describes the methods and data base used to derive Nuclear Reliability Factors for application to core physics input parameters used in the reload safety evaluation of Vepco nuclear units.

The Vepco topical report, which describes the methods in which these factors will be applied, has been previously submitted (VEP-FRD-42, "Vepco Reload Nuclear Design Methodology", transmitted by letter to you dated June 12, 1981, Serial No.

350).

It has been determined that the methodology and analysis capability described herein do not involve an unreviewed safety question as defined in 10CFR50.59.

We are aware that a fee will be required for the topical report review and will transmit the assessed fee upon completion of the review.

! 8111100735 811104 PDR ADOCK 05000280 P

PDR

e e

VIRGINIA ELECTRIC AND POWER COMPANY TO Mr. Harold R. Denton If you have any questions on the material in this topical report, please contact us.

cc:

Mr. Robert A. Clark, Chief Operating Reactors Branch No. 3 Division of Licensing Mr. Steven A. Varga, Chief Operating Reactors Branch No. 1 Division of Licensing

~- ___ :**.

Vepco NUCLEAR DESIGN RELIABILITY FACTORS VEP-FRD-45 SEPTEMBER 1981 FUEL RESOURCES DEPARTMEN-T VIRGINIA ELECTRIC AND PQ*WER COMPANY*

NOTICE.-

THE ATTACHED FILES ARE OFFICIAL RECORDS OF THE DIVISION OF DOCUMENT CONTROL. THEY HAVE BEEN CHARGED TO YOU FOR A LIMITED TIME PERIOD AND MUST BE RETURNED TO THE. RECORDS FACILITY BRANCH 016.

PLEASE DO NOT SEND DOCUMENTS CHARGED OUT THROUGH THE MAIL. REMOVAL OF ANY PAGE(S) FROM DOCUMENT FOR REPRODUCTION MUST BE REFERRED TO FILE PERSONNEL.

DEADLINE RETURN DATE RECORDS FACILITY BRANCH I

\\

I

VEP-FRD-45 VEPCO NUCLEAR DESIGN RELIABILITY FACTORS BY J. G. MILLER NUCLEAR FUEL ENGINEERING GROUP FUEL RESOURCES DEPARTMENT VIRGINIA ELECTRIC AHD POWER COMPANY RICHMOND, VIRGINIA SEPTEMBER, 1981 RECOMMENDED FOR APPROVAL:

M. L. Smith Supexvisox, Nucleax Fuel Engineexing APPROVED:

R. M. Bexxyman Dixectox, Nucleax Fuel Engineexing

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

PURPOSE, HOR SHALL ANY WARRANTY BE DEEMED TO'ARISE FROM COURSE OF DEALINQ OR USAGE OF TRADE, with respect to this report or any of the data, information, analytical techniques, or conclusions in it.

By making this report available, the Company does not authorize its use by others, and any such use is expressly forbidden except with the prior written approval of the Company. Any such written approval shall itself be deemed to incorporate the disclaimers of liability and disclaimers of warranties provided herein.

In no event shall the Company be

liable, under any legal theory whatsoever (whether contract,
tort, warranty, or strict or. absolute ~iability),

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 unauthorized, of this report or the data, information, and analytical techniques, or conclusions in it.

PAGE 3

ABSTRACT This report describes the methods and data base used to derive Nuclear Reliability Factors for application to the reload safety evaluation of Virginia Electric and Power Company CVepco) operating nuclear units. Where possible the Nuclear 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.

PAGE 4

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

Daniels, C.

B.

Franklin and M.

L.

Smith for their technical assistance in the development and preparation of this report.

The author would also like to express his appreciation to a number of people who reviewed and provided comments on this report.

PAGE 5

TABLE OF CONTENTS Title CLASSIFICATION/DISCLAIMER Page 2

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

3 ACKNOWLEDGEMENTS......................................

4 TABLE OF CONTENTS.....................................

5 LIST OF TABLES........................................

7 LIST OF FIGURES.......................................

8 SECTION 1 -

INTRODUCTION......................,.......

9 1.1 Purpose and Organization of the Report......

9

1. 2
1. 3 Definitions Summary of Results..........................

1 1 13 SECTION 2 -

MEASUREMENT AND CALCULATIONAL TECHNIQUES..

17

2. 1 2.2 2.3 2.4 Analytical Models Reactivity Computer and Delayed Neutron Data Temperature Coefficients....................

Power Coefficients..........................

17 1 9 21 23 2.5 Total Power Peaking Factors.................

25 SECTION 3 -

STATISTICAL ANALYSI~ METHODOLOGY..........

29

3. 1 Introdu*ction................................

2 9 3.2 Tests for Normality.........................

31 3.3 Derivation of Nuclear Uncertainty Factors...

32

PAGE 6

TABLE OF CONTENTS (cont.)

Title Page SECTION 4 -

RESULTS...................................

33 4.1 Reactivity and Kinetic Parameters......*....

33 4.1.1 Doppler Temperature and Power Coefficient............... ~..........

33 4.1.2 Delayed Neutron Pa~ameters.. ~........

35 4.2 Power.Peaking Factors.......................

37 4.2.1 D~ta Base Considerations.............

37 4.2.2 Results..............................

47 SECTION 5 -

REFERENCES................................

55

Table 1-1 4-1 PAGE 7

LIST OF TABLES Title Page Summary of Nuclear Reliability Factors........

15 Total Peaking Factor Data Base 42 4-2 Axial Geometry for Power Distribuiton Comparisons...................................

44 4-3 Total Peaking Factor Results -- North Anna 1 Cycle 1.......................................

48 4-4 Total Peaking Factor Results -- Surry 1 Cycle 5....................... *................

49 4-5 Total Peaking Factor Results -- Surry 2 I

Cycle 4 50 4-6 Summary of Total Peaking Factor Statistics....

51

PAGE 8

LIST OF FIGURES Figure Title Page 2-1 Moveable INCORE Detector Locations............

28 4-1 Typical Measured/Predicted Axial Power Distribution Comparison.......................

46 4-2 Histogram of Total Peaking Factor Results --

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

52 4-3 Histogram of Total Peaking Factor Results --

Surry 1 Cycle 5...............................

53 4-4 Histogram of Total Peaking Factor Results --

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

54

PA.GE 9

SECTION 1 -

INTRODUCTION 1.1 Purpose and Organization of the Report I

This report addresses the derivation of Nuclear Reliability Factors CHRFs) to be applied to safety related design predictions performed with the Vepco Jhysics design models for Vepco reload cycles. When feasible, the value of the HRF

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 HRF is derived from analytical engineering arguments.

The NRFi described in this study will be used in all reload safety evaluation calculations performed with the Vepco 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 re_ports 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. HRFs are to be applied,' as well as a

description of the models used to perform the-calculations. The present report summarizes the results from these previously published topicals as well as deriving the HRFs for parameters not previously reported.

The parameters not previously reported are the Doppler

PAGE 10 tempe:r:atu:re and powe:r:

coefficients, delayed neutron pa:ramete:r:s and the total peaking facto:r:.

\\

PAGE 11 1.2 Definitions The* Nuclear* Reliability Facto~ 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 F2, the value used in the safety analysis would be:

NRF x F2.

An

~xample of a parameter where the NRF is additive is the moderator temperature coefficient CMTC).

The application of the NRF to the predicted value is always in the conservative di~ection

  • from a

co~e safety consideration.

For the case of a multiplicative NRF such as 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 NRF such as that for the MTC, the value used in the safety analysis would be MTC +/- HRF, depending on whether addition or subtraction was in the conservative direction.

PAGE 12 The Nuclear Uncertainty Factor (NUF) 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 NUF 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 NUF will be either multiplicative or additive depending on the parameter it was derived from. For example, if FQ is the predicted value for the total peaking factor and Mis the corresponding measured value, then HUF K FQ > M for 95% of the population with a 95% *confidence level.

For those parameters for which a HUF has been derived, the corresponding HRF is chosen such that it is always more conservative then the HUF.

For

example, for the total peaking
factor, that:

the value of the NRF would be chosen such NRF > HUF.

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

summary of the Nuclear Reliability 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 HRFs for these parameters were analytical epgineering arguments.

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

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

hot zero power CHZP) core conditions. It is to be noted that the moderator temperature coefficient results r~flect measured and predicted values of the isothermal temperature coefficient since a

direct measurement of the moderator temperature coefficient is not possible.

The HRFs for the radial peaking factor CFDH), the core

PAGE 14 average axial peaking factor (Fz), and the total peaking factor CFQ) are conservative with respect to a NUF which meets the 95%/95%

acceptance criteria based on the sample population.

The NUFs for FDH, Fz and FQ 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 multiplication

sign, conservative direction.

conservative direction.

NRFs which are preceded by a

"x"

  • are multiplicative in a

Otherwise the NRF is additive in a

TABLE 1-1

SUMMARY

OF NUCLEAR RELIABILITY FACTORS Analytical Par:amete:c Model Refer:ence NRF Individual PDQ07 FRD-19A H 1. 10 Integr:al discr:ete Bank Wo:cth Cumulative PD207 FRD-19A H 1. 10 Integr:al disc:cete Bank t.Jo:cth Diffe:centiaJ.

FLAME FRD-24A 2 pcm/step Bank Wo:cth Cr:itical Boron PDQ07 FRD-19A 50 ppm Concentr:ation disc:cete Differ:entiaJ.

PD207 FRD-19A H 1. 05 Bor:on Worth disc:cete Mode:cato:c PDQ07 FRD-20A 3 pcm/°F Temper:atu:re one-zone Coefficient DoppJ.e:c PD207 FRD-45 K 1. 1 0 Tempe:catu:ce one-zone Coefficient Doppler Power PDQ07 FRD-45 X 1. 10 Coefficient one-zone Effective PD207 FRD-45 H 1. 05 Delayed discr:ete Neutr:on Fraction Pr:ompt PD207 FRD-45 H 1. 05 Neut:con Lifetime discrete

TABLE 1-1 (cont.)

Analytical Parameter Model FDH PDQ07 Fz FQ Key:

discrete FLAME FLAME pcm= percent mille PAGE 16 Reference NRF FRD-19A x 1.05 FRD-24A FRD-45 K 1.08 K 1. 07 5 (1 pcm= change in reactivity of 10- 5 )

ppm= parts per million

PAGE 17 SECTIOH 2 -

MEASUREMENT AND CALCULATIOHAL TECHNIQUES 2.1 Analytical Models The major analytical models currently used in the, design of a reload cycle are:

1.

the Vepco PDQ07 discrete model,

2.

the Vepco PDQ07 one-zone model, and

3.

the Vepco FLAME model.

The Vepco PDQ07 models perform two-dimensional Cx-y) geometry diffusion-depletion 'calculations for two neutron energy groups.

These models utilize the HULIF code (Reference

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 two models are differentiated according to their mesh size, (i.e.,

either a

discrete mesh or a one-zone mesh.) The discrete mesh model generally has one mesh line per fuel pin, while the one-zone mesh model has a mesh size of 6K6 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-zone models respectively.

PAGE 18 The Vepco FLAME model is used to perform three-dimensional Cx-y-z) geometry nodal power density and core reactivity calculations using a

one energy group, modified diffusion theory.

The model utilizes the NULIF code and several auxiliary codes t-0 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 quarter core symmetric three-dimensional geometry or a full core three-dimensional geometry may be specified. As with the PDQ07

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.

i

PAGE 19 2.2 Reactivity Computer and Delayed Neutron Data Reactivity measurements for the Surry and North Anna nuclear power stations are ohtain8d using a Westinghouse reactivity computer.

neutron detectors.

The reactivity computer periodically samples flux level signals from one of.*four ex-core 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 monoenergetic point reactor kinetics Cinhour) equations with siK de~ayed neutron groups. _ The resulting calculated

\\

reacti~ity 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 core 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 he used for all startup physics measurements at hot zero power CHZP) since sensitivity. studies performed with the PDQ07 discrete model have indicated that the rodded configuration of the plant ha~

minimal effect on the delayed neturon data,* (typically less than 0.2%.)

J

PAGE 20 The delayed neutxon paxametexs of beta-effective (Beff) and pxompt neutron lifetime Clp) are required for input to the re.load 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 0.97. 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.

I.

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-zone model. The change in core reactivity is calculated for changes in both the fuel and moderator temperatures of

+/-5°F about the HZP core average temperature of 547°F. This change in core reactivity divided

~y the t~tal change in the fuel and moderator temperatures, (i.e.,

10°F),

yields the vaiue of the ITC in units of pcm/°F. Calculation of the moderator temperature coefficient CnTC) is similar, but with the fuel temperature being frozen 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 Dopple~ temperature coefficient (DTC) is defined as the change in core reactivity per degree change in fuel tempe~ature and is calculated by taking the difference between the p~edicted values of the ITC and MTC.

PA.GE 23 2.4 Power Coefficients The total power coefficient is defined as the change in reactivity due to the combined effect of the moderator and fuel temperature change due to a change in core power level.

The Doppler "only" power coefficient CDPC) 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 few measurements which have been made are highly unreliable.

Furthermore.

coefficient comparisons incorporating a

design tolerance of

+/-30%.

direct measurement of the Doppler "only" power is not between possible.

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

Power coefficient predictions are performed with the PDQ07 one-zone model.

The DPC is found by subtracting the reactivity change with power due to a

change* in the moderator temperature o~ly, (i.e.,

the moderator power coefficient), from the total power coefficient. To calculate the total power coefficient, PDQ07 one-zone 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 frozen 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 predi~ted total power coefficient to find the moderator power coefficient.

PAGE 25 2.5 Total Power Peaking Factozs The* total peaking factor FQ is defined as the ratio of the pea~

power density in a

fuel pellet to the core average power density.

The maximum total peaking factor for the

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 location z

in the

core, FQ(z), are calculated using the PDQ07 discrete and FLAME models.

If FQ(x,y,z) is the nodewise three-dimensional power distribution for ~he node located at Cx,y,z) calculated by the FLAME model, then the value of FQ at axial location z for radial location Cx,y) is given by FQ(z) = FQ(x,y,z) x FDH(x,y) / RPD(x,y) where FDHCx,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 FDH(x,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 inst~umentation system.

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

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

-I

PAGE 26 thimbles.

Input to the IHCORE program consists of:

1.

a description of the reactor conditions when 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 d~screte model.

IHCORE corrects raw pointwise flux measurements for leakage

current, changes in power level between measurements, and relative detector sensitivities to determine the pointwise reaction rate in the flux thimbles. The measured reaction I

rates are then compared with expected values.

IHCORE computes the relative local power produced by each fuel

assembly, Pm, and the power in th~ peak fuel rod for each assembly.

For the assemblies with monitored thimble locations, the assemblywise 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 PDQ07 discrete model, and Rp is the reaction rate for the thimble calculated by the PDQ07 model. The values for Pm for all 157

PAGE 27 assemblies in the coie axe noxmalized so that theix sum equals unity.

INCORE calculates the peak FQCz) fox each assembly fox 61 axial nodes.

PAGE 28 FIGURE 2-1 MOVABLE INCORE DETECTOR LOCATIONS R

p H

M L

K J

  • H G

F E

D C

B A

I l**I I

1 I_I_I_I I

I I

I l**I I

2

_I_I_I_I_I_

I I

I 3

I I

I**

    • I I

4

_I_I_I _______ I ___ I_

l**I I**

I** *~

I** I 5

_I_I_I ______ I ___ I_

    • I I

I 6

_I ______

. I ___ I_I_

I I

l**I I

I l**I I

7 1_1_1_1_1 ______ 1 ___ 1_1_1

. I** I l**I I**

    • l**I I

8 1_1_1_1_1 _________ 1_1_1 I

I I

I I**

t::t: **

I

  • I** I 9

1_1_1_1_1 _________ 1_1_1

    • I I

I**

l**I 1 0

_I_I _______ I_

I I**

I I**

    • **I I

I I

1 1

_1_1 __ 1_1 ____ 1_

    • I I

l**I I

  • 1 :t::i: I** I 12

_1_1 __ 1_1_1 ___ 1_

I I

I l**I I

I 13 1_1 __ 1_1_1 ___ 1_

I**

I I

I**

I 14 1 __ 1_1_1 ___ 1 l**I I

15 I_I_I_

Inco~e Movable Detecto~ Location

PAGE 29 SECTION 3 -

STATISTICAL ANALYSIS METHODOLOGY 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.,

Xi= (Mi - Pi) K 100% / Mi Here Mi is the measured value for observation i, Pi is the predicted value for observation i

and Xi is the percent difference between th~

measurement and prediction for the ith observation. Xi is assumed to be a normally distributed random variable whose mean X and standard deviation Sare defined as:

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

S 2 =

SUM (Xi -

X) 2 /

(n -

1*)

CS-Z) 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 includes the statistical uncertainties due to both measurement. and calculation. That is, the variance of Xi is given as:

where Sm 2 is the variance due only to measurement

PAGE 30 unce~tainty and is the va~iance due only to calculational uncertainty. Therefore, any standard deviation for calculational uncertainty derived using equation (5-2) is conservative since an additional ma~gin for measurement uncertainty is included.

/

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 referred to as the D-test) is 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 used to derive the reliability factors.

The assumption of normality is rejected when the computed values of Dare less than the test D value which corresponds to a

95% confidence level with a.05 level of significance for the indicated sample size,n. These results are summarized 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 sample is considered to be nonnormal.

) '

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

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

.TL= X + CK x S)

(5-7) where 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 size n

used* to derive TL, (Reference 8). In cases where the value of the mean (or bias) reduces the value of TL in a non-conservative direction, Ci.e., a negative bias for total peaking factor),

the value 0£ the mean is set equal to zero to insure conservatism.

The value of the Nuclear Uncertainty ~actor HUF is derived from the one sided upper tolerance limit as HUF= 1 + CTL/100)

(5-8)

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

PAGE 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 changes in the core's fuel temperature and the core's moderator properties.

Mqst 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 of -2 pcm/°F for Vepco nuclear units and shows little variation over the lifetime of a

cycle.

)

Therefore, a

Nuclear Reliability Factor of L 1 Ci.e., 10%)

will be assumed for the Doppler temperature coefficient.

Measurements of the total power coefficient have been performed during the start~p 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 from the startup physics testing program for Vepco nuclear units.

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

Due to the difficulty 0£ obtaining accurate

~easurements of the total power coefficient, the design tolerance for the above Vepco measurements was set at

PAGE 34

+/-307o.

This large measurement uncertainty along with the small size of the available data base makes a derivation of an uncertainty factor for the Doppler component of the power coefficient based on compa:z:ison of measurement and of questionable value.

Therefore, a

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

PAGE 35 4.1.2 Delayed Neutron Parameters The delayed neutron parameters input to the reload cycle safety analysis are the effective delayed neutron fraction Be££ and the prompt neutron lifetime lp. Be££ is the more important factox in dete~mining the r~liability 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 Be££ are the experimental values of the delayed neutron fractions and the percursor decay constants for each delayed neutron group input to the PD207 discrete

model, the predicted core nuclide concentrations Cin particular uz 35,

uz3s and PuZ 3 9), the calculation of the fission sharing of I

each fissionable isotope 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 a:re on the I

o:i:der of 47.,

(Reference 9).

The low uncertainty factor associated with the prediction of the radial peaking factors over cycle lifetime by the PDQ-07 discrete model (less than 5%) implies a simi~ar accuracy in the prediction of the core nuclide concentrations of

uz3s, uz3s and Pu 239 and the fission sharing for the isotopes.

Finally*,

Be££ is relatively insensitive to uncertainty in the importance I

PAGE 36 factor since a

typical value for the importance factor, Ce. 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 lp of 5% appears to be a reasonably conservative estimate.

PAGE 37 4.2 Power Peaking Factors 4.2.1 Data Base Considerations.

Uncertainty factors* for the total power peaking factors FQ 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 proble~

experienc~d during the initial operation 0£ the cycre, it was excluded from* the data base. The two Surry cycles are 18-month cycles with large lum.ped burnable poison loadings.

Surry 2

Cycle 4 employed an out/in fuel loading strategy.

Surry 1 Cycle 5 employed an*in/out fuel lQ~ding strategy and is representative 0£ the future fuel loading strategy being planned £or Vepco nuclear units. Horth Anna 1 Cycle 1 was an initial core 18 month cycle with a large loading of lumped burnable poison.

Measured total peaking factors were calculated by the IHCORE code.

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

PAGE 38

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

map in the mid ~ower range for an essentially unrodded core conditio~

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.

Measured peaking factors are compared only for monitored thimble lo<;ations in order to avoid the additional uncertainty introduced by the INCORE code in interpolating peaking factors for the non-monitored assembly locations.

Thimble readings for a flux map are normally discarded if the readings are incomplete or if the thimble suffered severe misalignment during the measurement. Such thimble locations have been deleted from the data base used to derive the peaking factor calculational uncertainties.

In order to generate total peaking factor predictions, concentration files for FLAME were created at each cycle burnup at whi-0h a

flux map was taken. Normally the FLAME depletion was performed at an

ARO, HFP core condition.

Howe.ve:c, unlike

a.

two-dimensional calculation, a

th:cee-dimensional modeling of the core is sensitive to the 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

PAGE 39 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 was on the order of 3% or greater a more accurate modeling of the core 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 of the flux map. The total relative power distribution in each three-dimensional node of the FLAME calculatioµ is converted to a

total peaking factor by multiplying by the two-dimensional PDQ07 pin-to-box ratio at the appropriate core conditions for the axial region.

Total peaking factor comparisons are performed for 6 axial planes for a North Anna unit and 5 axial plans for a Surry Unit.

These axial planes have been selected at locations

~pproximately halfway between neighboring assembly grid stra~s 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 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 the core.

The planes selected f~r the measurement/prediction comparisons correspond to the INCORE nodes listed in Table 4-2.

  • The FLAME model contains 32 axial nodes numbered from

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 FQ value 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 ~HCORE plane. These axial FLAME nodes are listed, in Table 4-2.

Axial locations approximately halfway between t~e grids were chosen for the comparisons in order to add conservatism to the derivation of the total peaking factors calculational uncertainty. Since the FLAME model does not model the grids, 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 FQ to occur about halfway between the grid locations where the measured value usually'exceeds the predicted. Hence, using these locations for the data base results 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 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 peaiing factors whose relative power distributions CRPDs) 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

~1.0 have been included in the data base. This approach excludes large pe~cent difference values which often result 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.

PAGE 42 TABLE 4-1 TOTAL PEAKING FACTOR DATA BASE Cycle Humbe:c of Flux Powe:c Bu:cnup Rodded Monito:ced Cycle Map i Level MWD/MTU Condition Thimbles M1C1 1

4 0

D/228 48 H1C1 2

4 0

D/0 46 H1C1 5

30 50 D/195 48 N1C1 6

30 50 Ejected Rod 48 N1C1 1 0 49 50 D:copped Rod 48 N1C1 15 73 150 D/215 38 N1C1 37 96 3047 D/213 39 N1C1 50 96 7340 D/205 38 N1C1 53 97 9135 D/220 39 N1C1 58 100 11003 D/228 38 N1C1 64 100 12960 D/227 46 N1C1 75 97 1s*142 D/224 49 S1C5 1

0 0

D/218 40 S1C5 3

4 0

D/0,C/219 43 S1C5 4

50 0

D/200 43 S1C5 12 100 2123

.D/218 42 S1C5 17 100 4072 D/223 43 S1C5 19 100 5270 D/224 43 S1C5 23 100 7411 D/224 43 S1C5 26 100 8973 D/226 42 S1C5 30 100 10125 D/226 43 S1C5 32 100 11580 D/216 42

\\

PAGE 43 TABLE 4-1 (cont.)

Cycle Number of Flux Power Burnup Rodded Monitored Cycle Map

ff:

Level MWD/MTU Condition Thimbles S2C4 1

4 0

D/218 47 S2C4 2

7 0

D/0 47 S2C4 5

6 1 8

D/155 47 S2C4 11 100 1800 D/225 45 S2C4 18 100 5266 D/224 45 S2C4 22 100 6968 D/210 43 S2C4 27 100 9250 D/202 42 S2C4 30 100 110 0 6 D/223 49 S2C4 36 100 13200 D/222 49

PAGE 44 TABLE 4-2 A~IAL GEOMETRY FOR POWER DISTRIBUTION COMPARISONS Noxth Anna Units 1 and 2 Suxxy Units 1 and 2

% Coxe*

% Coxe Height Descxiption Height Descxiption 103.5 G:i::id

ff: 1 104.0 G:i::id
ff: 1 89.2 G:i::id
ff:

2 90.8 G:i::id

ff: 2 85.9 FLAME Node 28 85.9 FLAME Node 28 82.8 FLAME Node 27 83.3 INCORE Node 1 1
81. 7 INCORE Node 1 2 82.8 FLAME Node 27 79.7 FLAME Node 26 79.7 FLAME Node 26 74.9 G:rid :ff: 3 72.6 G:rid :ff: 3 70.3 FLAME Node 23 67.2 FLAME Node 22 68.3 INCORE Node 20
64. 1 FLAME Node 21 67.2 FLAME Node 22 63.3 INCORE Node 23 6 4. 1 FLAME Node 2 1 60.9 FLAME Node 20 60.6 G:rid i 4*

54.4 G:rid :ff: 4 57.8 FLAME Node 19 48.4 FLAME Node 16 54.7 FLAME Node 18 45.3 FLAME Node 15 53.3 INCORE Node 29 45.0 INCORE Node 34

51. 6 FLAME Node 17 42.2 FLAME Node 14 46.4 G:rid i 5

36.2 G:rid :ff: 5 42.2 FLAME Node 14 29.7 FLAME Node 1 0

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 Gxid :ff: 6 18.0 G:rid
  • 6 29.7 FLAME Node 10 17.2 FLAME Node 6 26.6 FLAME Node 9
14. 1 FLAME Node 5 25.0 INCORE Node 46 13.3 INCORE Node 53 23.4 FLAME Node 8 1 0. 9 FLAME Node 4
17. 8 G:rid :ff: 7 1. 3 G:i::id
ff: 7

PAGE 45 TABLE 4-2 (cont.)

North Anna Units 1 and 2

% Core :t:

Height Description 17.2 FLAME Mode 6

15. 0 INCORE Node 52 1 4. 1 FLAME Node 5
10. 9 FLAME Node 4 0.8 Grid :ff: 8

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

T 0

T A

L p

E A

K I

N G

F A

C T

0 R

PAGE 46 FIGURE 4-1 TYPICAL MEASURED/PREDICTED AXIAL POWER DISTRIBUTION COMPARISON NORTH ANNA l CYCLE l FLUX MAP 37 --

THIMBLE LOCATION Hl3 l. 6 l. 5 l. 4 l. 3 l. 2 l. l l.o 0.9 0.8 o.7 0.6 o.5 0.4 0.3 0.2

0. l o.o 0

l 0 20 30 LEGEND: POWER 40 50 60 PERCENT OF CORE HEIGHT

~*

~*

  • I** MEASURED 70 60 90 100 o o.o
  • P R E D I C T E D

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 I predicted axial offsets CA.O) 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 m~y 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.

Ho 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 on 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 TOT~L PEAKING FACTOR RESULTS -- HORTH ANNA 1 CYCLE 1 For Measured and Predicted FQ

~ 1. 0

\\

X s

Min.

Max.

Map Mean Std. Dev.

Meas. Pred. A.O.

i n

(%)

(%)

PROB>D Diff. Diff.

A.O.

A.O. Diff.

1 232 1. 19 3.62

>O. 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

>O. 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 1 0 252

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. 7 6

-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 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 summary statistics for Horth Anna 1 Cycle 1 FQ data base:

Yo Diff. = (Measured -

Predicted) x 100% / Measured n = 2822 Mean= 0.49%

standard Deviation= 3.81%

PROB>D = >0.15

PAGE 49 TABLE 4-4 TOTAL PI;:AKING FACTOR RESULTS --

SURRY 1 CYCLE 5 For Measured and Predicted FQ

~ 1. 0 X

s Min.

Max.

Map Mean Std. Dev.

Meas. Pred. A.O.

ff

n

(%)

(%)

PROB>D Diff. Diff.

A

  • 0
  • A.0. Diff.

1 129 0.76 4.47

>O. 15 -12.11 15.30 27.4 24.8 2.6 3

138

1. 22 2.99

>O. 15

-4.77

9. 51 22.7 22.4 0.3 4

166

1. 18 3.66

>O. 15

-7.99 9.98 6.3 8.2

-1.9 12 170 0.88

3. 9 1

>O. 15

-8.60 11. 2 5

-1. 6

-3.8

2. 2 17 173 0.93 4.44

>O. 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

>O. 15

-6.24 8.61

-3.5

-2.5

-1. 0 Summary statistics for Surry 1 Cycle 5 F2 data base:

% Diff.* = C Measured -

Predicted) x 10 0% / Measm:ed n

Mean standa:rd Deviation PROB>D

=

=

=

=

1647

1. 0 9%

3.59%

>O. 15

PAGE 50 TABLE 4-5 TOTAL PEAKING FACTOR P.ESULTS --

SU TI.RY 2 CYCLE 4 Foz: Measuz:ed and Pz:edicted FQ

~ 1. 0 X

s Min.

Max.

Map Mean Std. Dev.

Meas. P:ced. A.O.

ff:

n

( % )

(%)

PROB>D Diff. Diff.

A.0.

A.O. Diff.

1 157

1. 35 4.00

>O. 15

-9.45 10.57

21. 9 23.5

-1. 6 2

163

1. 06 4.53

>O. 15 -11. 47 12.93

17. 6 20.3

-2.7 5

178 -0.33 3.54

>O. 15

-7.47

7. 8 1 -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

>O. 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. 5 2 2.58 0.145

-4.81 8.56

-1. 7

-2.8 1. 1 36 213

1. 30 2'. 98

<0.01

-5.91 7.92

-1. 4

-3.3 1. 9 Summaz:y statistics foz: Suz:z:y 2 Cycle 4 FQ data base:

% Diff. = (Measuz:ed -

P:cedicted) x 100% / Measu:ced n

Mean Standa:rd Deviation PROB>D

=

=

=

=

1724 1. 11 %

3.58%

>O. 15

PAGE TABLE 4-6

SUMMARY

OF TOTAL PEAKING FACTOR STATISTICS Cycle N1C1 S1C5 S2C4 n

2822 1647 1724 X

Mean

(%)

0.49

1. 09 1. 11 s

Std. Dev.

(%)

3.81 3.59 3.58 No:rmality Test PROB>D

>O. 15

>O. 15

>O. 15 95%/95%

Unce:rtainty Facto:r 1. 0 6 9

1. 072
1. 07 2 51

PAGE 52 FIGURE 4-2 HJSTOGRAM OF TOTAL PEAKJNG FACTOR RESULTS NORTH ANNA l CYCLE l PERCENT DIFFERENCE DISTRIBUTION FOR MEASURED/PREDICTED FO

> l.G FREQUENCY 600 500 400 300 200 100

-10

-6

-6

-4

-2 0

2 4*

6 8

10 l 2 PERCENT DIFFERENCE

PAGE 53 FIGURE 4-3 HISTOGRAM OF TOTAL PEAKING FACTOR RESULTS --

SURRY l CYCLE 5 PERCENT DIFFERENCE DISTRIBUTION ~OR MEASURED/PREDICTED FQ > l.O FREQUENCY 390 360 330 300 270 240 210 180 150 120 90 60 30 10

-8

-6

-4

-2 0

2 4

6 8

10 12 14 15 PERCENT DIFFERENCE

PAGE 54 FIGURE 4-4 HISTOGRAM OF TOTAL PEAKING FACTOR RESULTS --

SURRY 2 CYCLE 4 PERCENT DIFFERENCE DISTRIBUTION FOR MEBSURED/PREDJCTED FQ

> l.G FREQUENCY 390 360 330 300 270 2 40 210 160 150 120 90 60 30 10

-B

-6

-4

-2 0

2 4

6 6

10 12 13

\\

PERCENT DIFFERENCE

~ --

SECTION 5 -

REFERENCES

1.
s. A. Ahmed, et al., "Reload Nuclear Design Methodology," VEP-FRD-42, April 1981, (Virginia Electric and Power Company).

PAGE

2.

W. C. Beck, "The Vepco FLAME Model", VEP-FRD-24A, July 1981, (Virginia Electric and Power Company).

3.

M. L. S~ith, "The PD207 Discrete Model," VEP-FRD-19A, July 1981, (Virginia Electric and Power Company).

4.

J. R. Rodes, "The PDQ07 One Zone Model," VEP-FRD-20A, July 1981, (Virginia Electric and Power Company).

5.

W. D. Leggett III and L. D. Eisenhart, "The INCORE Code", WCAP-7149, December 1967, (Westinghouse).

6.

W. A.Wittkop£, et al., "NULIF-Neutron Spectrum Generator, Few Group Constant Calculator and Fuel tiepletion Code," BAW-10115, June 1976, (Babcock and Wilcox).

55

7.

M. A. Stephens, "Use of the Kolmogorov-Smirnov, Cra~er-Von Mises and related statistics without extensive 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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