Regulatory Guide 1.126

an Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification

ML13350A271
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Issue date:	03/31/1977
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RG-1.126
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U.S. NUCLEAR REGULATORY

COMMISSION

March 1977REGULATORY

GUIDEOFFICE OF STANDARDS

DEVELOPMENT

REGULATORY

GUIDE 1.126AN ACCEPTABLE

MODEL AND RELATED STATISTICAL

METHODS FOR THEANALYSIS

OF FUEL DENSIFICATION

A. INTRODUCTION

and C.2 of this guide is not intended to supersede NRC-approved vendor models.Appendix K. "ECCS Evaluation Models,"

to 10 CFRPart 50, "Licensing of Production and Utilization The statistical methods (SectionC-.3).

measurement Facilities,"

requires that the steady-state temperature methods (Section C.4), and istarooy assumptions distribution and stored energy in the fuel before a hypo- (Section C.5) are compatible wtth models.thetical loss-of-coolant accident (LOCA) be calculated, Therefore Sections C.3. C-.;,aJid:`;c.5 co ild be appliedtaking fuel densification into consideration.

This to densitication models the one pre-guide provides an analytical model and related assump- sented in Sect ins.Q.-i

'nd C2;, "tions and procedures that are acceptable to the NRCstaff for predicting thle effects of fuel densification inlight-water-cooled nuclear power reactors.

The guide C REGU.iATORY

POSITIONalso describes statistical methods related to productsampling that will provide assurance that this and li.-Maximum iDisification other approved analytical models will adequately de-scribe the effects of densification for each initial core" -:-, .The; density of a fuel pellet* in the reactor increases and reload fuel quantity produced.

,.... witA. burnup and achieves a maximum value at a rela--tively low burntip (generally

< 10,000 M\Yd/t U). For

B. DISCUSSION

analytical purposes, this maximum density minusthe initial density.

i.e., the maximum density change,* In-reactor densification (shrinkage)','of oxide Iitel is assumed to be the same as the density change Asntrpellets affects fuel temperatures in ste..ral

'0*ys: (1) that would occur outside the reactor in the samegap conductance may be reduced beca f6rthe de- pellet during resintering at I 700°C for 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.0crease in pellet uiameter;.

1t),) me linear neat generation rate is increased decrease in pellet length;and (3) the pellet-le'

.d'teases may cause gaps inthe fuel colur id n, prMce local power spikesand the pot ial c ing collapse.

Dimensional changes i Il11ets in lie reactor do not appear to be

, a radial pellet dimension changeswill b ted "clferently.

Furthermore, items (1) and(2) abo i;re single-pellet effects, whereas item (3)is the result of simultaneous changes in a large numberof pellets.

These distinctions must be taken into accountin applying analytical models.The NRC staff has reviewed the available information concerning fuel densification, and the technical basisfor the Regulatory Position of this guide is given inReference

1. The model presented in Sections C.IWhere the ex-reactor resintering results in a negativedensity change (i.e.. swelling),

zero in-reactor densifi-cation should le assumed.2. Densifieation KineticsFor pellets that have a resintering density changeAsntr of less than 4% of theoritical density (TD),the in-reactor density change Ap -1% a function ofburnup BU may be taken as***The model presented in this guide is applicahle only to U02fuel pellets.*&Symbols are defined in the List of Symtols at the back of thisguid

e. USNRC REGULATORY

GUIDESReggulatory Guide% wte issuerd to desribe ant make available to the public methodsacieptable to the NRC stail of implementing speeilic paris of the Commission's tegufations, to delineate techniqtur$

used by the %tsalI in evaluating poecifIic litottlern of rostulated accidents, or to provide guidance to applicants, Regulatory Guidesawe not subltitutes lot regublions, arnd commlhince with them is tot required.

Methods and solutions dilferent from those set Out in the guides will be accept-able If they provide a basis for the findings requisite to the issuance or continuance of a permit or license by the Commission, Comments and suggestions for improvements in these guides rt- encouraged at alltimes, and guides wtil bit revised, A ,tprotriatle.

to accommodate comments andto tretect new Information or experience.

However.

comments on this guideifI eceived within about two months alter its i-.suanca.

will fe tParticularly useful Inevaluating the neate for an early reviston.

Conmments should be ent 1o thi, Secretary of tI!

US. Nucleiar latury Commitsion.

Wsiir'nton, O.C. 70555, Attention- Dorcketrrg and ServlyBranch.The guides are in ttte following ten rlwvivions

6. PelXjucls

2. Research and Te'st Reactors

7. Ttantrurtatiun

3. Fuellsant Materials Facilities

8, Occupational IHealth4. Environmental aontSiting

9. Antitrust tlevew.S. Materials and Plant Protection t0. GeriryalRectueSts fat single covies Ol isisuo guides ferhich rmnay' tie eprodur.ced at tto* ;iace-ment on an automatic dititl)ution list for sing1le copies of future f tidus in streciftc divisions should be madte in writing to the US. Nuclear Regutlarnrv Cnnmission, Washington, D.C. 70555, Attention:

Ditector.

Division otDocument Crontfrol.

I .Ap=O0(for BU < 20 NIWd/tU);

S

(for 20 < BU < 2000 NtWd/tU);

(la)(I b)(Ic)and,, = APsntr(for BU > 2000 MWd/tU),where tile coefficients m and b are given by0 = m log(20) + b and'Psntr = i log(2000)

+ b.For pellets exhiibiting a resintering density changein excess of 4% TD. the in-reactor density change asa function burnup may be taken asating normally distributed data may be used. If the"W" test (Ref. 2) demonstrates nonnormality at the -1%level of significance.

nonparametric statistical methodsshould be used unless a different functional form can besatisfactorily justified to describe the distribution ofthe LAsntr values. Thus 6sAnptr is tile upper on

e. sided

95/95 tolerance limit for the density changes and canbe obtained from the sample values using one of themethods outlined below.(1) NormalDistribution.

In this case, Ps*nr isgiven byASiltr = Epsnir + C's.wherce -'Nsntr is tile mean of the sample data, s is thestandard deviation of tile sample data, and c' is givenin Table I (from Ref. 3).Lp =0(forhBU 5 MWd/tU):Ap = m log(BU) + b(for 5 < BU < 500 MWd/tU):and -P -APsntr(for BU > 500 MWd/tU),where the coefficients m and b are given by0 = m log(S) + band ,Psntr = m log(500)

+ b.(2a)(21b )GOcTABLE IVALUES TO BE USED FOR c'TO DETERMINE

64lrWITH NORMAL DISTRIBUTION

Number ofObservations cIn applications of Equations I and 2, ,Psntr willhave tile value st**r or tmntr. which will be described in Section C.3. The burnup unit MWd/tU in the aboveexpressions is megawatt days per metric ton of heavymetal (uranium).

3. Statistical MethodsTo apply tile above model or any densification modelthat depends on an ex-reactor resintering density change,a random sample of the pellet population of interestmust be resintered.

Resintering the pellets in the samplewill result in a set of density changes 6Psntr. Severalcharacteristics of these values are needed to completethe densification analysis.

a. Single-Pellet EffectsAnalyses of the effect of densification on storedenergy and linear heat generation rate must account forpellets that have the greatest propensity for densifica.

tion. To accomplish this with a resintering-based modelsuch as that described in Sections C.1 and C.2, a re-sintering density change value Apjn*tr that conservative- ly bounds 95% of the population APsntr values with95% confidence should be used. The population ofinterest is the initial core loading or. reload quantityof fuel for which the safety analysis, and hence the den-sification analysis, is being performed.

If the distri-bution of values is normal, methods of evalu.456789101112is2025304060100200500005.154.203.713.403.193.032.912.822.742.57:.402.292.2 22.132.021.931.841.761.64(2)given byNonnormalDistribution.

In this case ApntisAp~t twhere P is the mth largest 5Psntr value in a rankingot the observed values o0 6Psntr from the sample.The integer m depends on tile sample size according toTable 2 (from Ref. 4).1.126-2 TABLE 2VALUES TO BE USED FOR m TO DETERMINE

WITH NONNORMAL

DISTRIBUTION

Number ofObservations

5055606570758085909510011012013014015o1702003004005006007008009001000m233345913172126303539where 'P;sntr is the mean of t(ie sample data from theselected lot, s' is the standard deviation of the sampledata from the selected lot, and c is given in Table 3(from Ref. 3).TABLE 3VALUES TO BE USED FOR cTO DETERMNINE

i.snirNumber ofObservations C4678910I I1220253040601002005001.180.950.820.73(0.670.620.580.550.520.450.390.340.310.270.-20.170.120.0704. Measurement MethodsNote that a minimum of 60 observations is required toproduce a meaningful result by this method.b. Multiple-Pellet EffectsFuel-column.length changes, which can result inaxial gaps in the pellet stack, are determined by averagepellet behavior.

In this case, however, the population to be considered is not the core or reload quantitycharacterized above, but rather the pellet lot withinthat quantity that exhibits the largest mean of the6,sntr values from the sample. A pellet lot is definedas a group of pellets made from a single UOi powdersource that has been processed under the same condi-tions. The distribution of 6Psntr values for the selectedpellet lot is assumed to be normal. To analyze effectsrelated to column-length changes.

resintering-based densification models should use a density change valuethat bbunds the selected pellet lot mean with95% confidence, Thus ,'s'ntr is the upper one-sided

95% confidence limit on the mean density change andcan be obtained from the sample values using the expres-sion:APs4ntr ="Psntr + cs'To measure the density change A, sntr during resin-tering, either geometric or true densities may he used, solong as the same method is used before and after resin.tering. Techniques such as vacuum impregnation/

water immersion, mercury immersion, gamnta.r-ay ab-sorption.

and mensuration ate acceptable.

It is alsoacceptable to infer the density change from a diameterchange. using the isotropic relation

"Psnir/o

=3LDsntr/D.

where ADsntr is the diameter change exper-ienced during resintering.

Resintering should be performed in a laboratory- quality furnace with a known temperature distribution, in the working region. Temperatures during resintering should be measured using either thermocouples orcalibrated optical methods with established black-body conditions.

Furnace temperatures should be somaintained that true specimen temperatures are nolower than the desired test temperature

(1700'C inthe model above) after temperature measurement errorshave been taken into account.Fuel stoichiometry (O/M ,; 2.00) should be main-tained by using dry tank hydrogen or dry gas mixtures(e.g.. N2-H2) and avoiding temperatures in excess of-1800°eC.01.126-3

5. Isotropy Assumptions In order to use predicted density changes in a cal-culation of the effects of inTreactor densification, it isnecessary to make some assumlplion about tile isotropyof' fuel densification.

For ch: ages in pellet diameterD. isotropic densilication may be assumed, so that,:I)/D = .Ap/3p. For changes in pellet or fuel columnleigth L. anisolropic densification is assumed suchthat -./L =Ar.12,o.

D. IMPLEMENTATION

The purpose of this section is to provide information to applicants and licensees regarding the NRC" staft'splans for using this regulatory guide.This guide reflects a relinement in NRC( practice andsupersedes the previously accepted assumption that allfuels densify to a maximum density of 9thi.5';

of tineirtheoretical density as measured geometrically.

Exceptiim those cases in which the applicant proposes an accept-able alternative method for complying with specified portions of the Commission's regulations,.

the methoddescribed herein will be used in the evaluation of sub.mittals for construction permit, operating license, andreload applications docketed after November I. 1977.unless this guide is revised as a result of suggestions fromthe public or additional staff review. If for any reasonthe effects of' fuel densification are reanalyzed for fuelcovered in an applicalion docketed on tir before No-vember 1. 1977. the method described in this guidewould not be necessary and previously approved assunmp-tions would he allowed for that fuel.If an applicant wishes to use this regulatory guide indeveloping submittals for applications docketed on orbefore November

1. 1977. the pertinent portions of theapplication will be evaluated on ihe basis of1 this guid

e. REFERENCES

1. R. 0. Meyer. ""rhe Anakysis of Fuel Densi-fication."

USNRC Report NURIFG-005.

July 1976.2. "American National Standard Assessment of' theAssumnption of' Normnality (Emploving Ind ividu;,I

Ob-served Values)'"

ANSI Standard NI 5.15-19 74.3. G. J. Hahn. "Statistical Intervals for a Normal Pop-ulation.

Part I. Tables, Examples and Applications,"

J. Quality Technol.

115 (1970),4, P. N. Somerville.

"Tables for Obtaining Non.Para- metric Tolerance Limits."

Ann. Math. Stat. 29, 559(1958).LIST OF SYMBOLST'he major symbols used in Sections C.I through C.5are identified below:BU iHurnup.

%IWdjtU.D Nominal initial pellet diameter, cni.I, Nominal initial pellet length, cm.TI) Theoretical density, g/cm3.A 1) In-reactor pellet diameter change (function ofburnup).

cm.ADsntr Measured diameter change of a pellet due toex-reactor resintering, cm.A t. In-reactor pellet length change (function ofhurnup),

cm.A, In-reactor pellet density change (function ofburnup),

g/cm3.APsntr Measured density change of a pellet due to ex-reactor resintering, g/cm3.s.ntr One-sided

95% upper confidence limit on, themean of tile A0sntr values from the selectedlot. g/cm3.A 0 *n*r One-sided

95/95 upper tolerance limit for thetotal population of tLsntr values, g/cm3.P Nominal initial pellet density, g/cm3.1,126-4