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 1977 REGULATORY

GUIDE OFFICE OF STANDARDS

DEVELOPMENT

REGULATORY

GUIDE 1.126 AN ACCEPTABLE

MODEL AND RELATED STATISTICAL

METHODS FOR THE ANALYSIS 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 CFR Part 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 applied taking 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 NRC staff for predicting thle effects of fuel densification in light-water-cooled nuclear power reactors.

The guide C REGU.iATORY

POSITION also describes statistical methods related to product sampling 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 minus the 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 Asntr pellets affects fuel temperatures in ste..ral '0*ys: (1) that would occur outside the reactor in the same gap 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 />.0 crease in pellet uiameter;.

1 t),) me linear neat generation rate is increased decrease in pellet length;and (3) the pellet-le' .d'teases may cause gaps in the fuel colur id n, prMce local power spikes and the pot ial c ing collapse.

Dimensional changes i Il11ets in lie reactor do not appear to be, a radial pellet dimension changes will 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 number of pellets. These distinctions must be taken into account in applying analytical models.The NRC staff has reviewed the available information concerning fuel densification, and the technical basis for the Regulatory Position of this guide is given in Reference

1. The model presented in Sections C.I Where the ex-reactor resintering results in a negative density change (i.e.. swelling), zero in-reactor densifi-cation should le assumed.2. Densifieation Kinetics For pellets that have a resintering density change Asntr of less than 4% of theoritical density (TD), the in-reactor density change Ap -1% a function of burnup BU may be taken as***The model presented in this guide is applicahle only to U0 2 fuel pellets.*&Symbols are defined in the List of Symtols at the back of this guid

e. USNRC REGULATORY

GUIDES Reggulatory Guide% wte issuerd to desribe ant make available to the public methods acieptable 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 Guides awe 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 all times, and guides wtil bit revised, A ,tprotriatle.

to accommodate comments and to tretect new Information or experience.

However. comments on this guideif I eceived within about two months alter its i-.suanca.

will fe tParticularly useful In evaluating 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 Servly Branch.The guides are in ttte following ten rlwvivions t. Power Reactors 6. PelXjucls 2. Research and Te'st Reactors

7. Ttantrurtatiun

3. Fuellsant Materials Facilities

8, Occupational IHealth 4. Environmental aontSiting

9. Antitrust tlevew.S. Materials and Plant Protection t0. Geriryal RectueSts fat single covies Ol isisuo guides ferhich rmnay' tie eprodur.ced at tto* ;iace-ment on an automatic dititl)ution list for sing 1 le 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 o t Document 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 by 0 = m log(20) + b and'Psntr = i log(2000)

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

nonparametric statistical methods should be used unless a different functional form can be satisfactorily justified to describe the distribution of the LAsntr values. Thus 6sAnptr is tile upper one.sided 95/95 tolerance limit for the density changes and can be obtained from the sample values using one of the methods outlined below.(1) NormalDistribution.

In this case, Ps*nr is given by ASiltr = Epsnir + C's.wherce -'Nsntr is tile mean of the sample data, s is the standard deviation of tile sample data, and c' is given in 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 by 0 = m log(S) + b and ,Psntr = m log(500) + b.(2a)(21b )GOc TABLE I VALUES TO BE USED FOR c'TO DETERMINE

64lr WITH NORMAL DISTRIBUTION

Number of Observations c In applications of Equations I and 2, ,Psntr will have tile value st**r or tmntr. which will be described in Section C.3. The burnup unit MWd/tU in the above expressions is megawatt days per metric ton of heavy metal (uranium).

3. Statistical Methods To apply tile above model or any densification model that depends on an ex-reactor resintering density change, a random sample of the pellet population of interest must be resintered.

Resintering the pellets in the sample will result in a set of density changes 6Psntr. Several characteristics of these values are needed to complete the densification analysis.a. Single-Pellet Effects Analyses of the effect of densification on stored energy and linear heat generation rate must account for pellets that have the greatest propensity for densifica.

tion. To accomplish this with a resintering-based model such 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 with 95% confidence should be used. The population of interest is the initial core loading or. reload quantity of 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.4 5 6 7 8 9 10 11 12 is 20 25 30 40 60 100 200 500 00 5.15 4.20 3.71 3.40 3.19 3.03 2.91 2.82 2.74 2.57:.40 2.29 2.2 2 2.13 2.02 1.93 1.84 1.76 1.64 (2)given by NonnormalDistribution.

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

WITH NONNORMAL

DISTRIBUTION

Number of Observations

50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 15o 170 200 300 400 500 600 700 800 900 1000 m 2 3 3 3 4 5 9 13 17 21 26 30 35 39 where 'P;sntr is the mean of t(ie sample data from the selected lot, s' is the standard deviation of the sample data from the selected lot, and c is given in Table 3 (from Ref. 3).TABLE 3 VALUES TO BE USED FOR c TO DETERMNINE

i.snir Number of Observations C 4 6 7 8 9 10 I I 12 20 25 30 40 60 100 200 500 1.18 0.95 0.82 0.73 (0.67 0.62 0.58 0.55 0.52 0.45 0.39 0.34 0.31 0.27 0.-2 0.17 0.12 0.07 0 4. Measurement Methods Note that a minimum of 60 observations is required to produce a meaningful result by this method.b. Multiple-Pellet Effects Fuel-column.length changes, which can result in axial gaps in the pellet stack, are determined by average pellet behavior.

In this case, however, the population to be considered is not the core or reload quantity characterized above, but rather the pellet lot within that quantity that exhibits the largest mean of the 6,sntr values from the sample. A pellet lot is defined as a group of pellets made from a single UOi powder source that has been processed under the same condi-tions. The distribution of 6Psntr values for the selected pellet lot is assumed to be normal. To analyze effects related to column-length changes. resintering-based densification models should use a density change valuethat bbunds the selected pellet lot mean with 95% confidence, Thus ,'s'ntr is the upper one-sided 95% confidence limit on the mean density change and can be obtained from the sample values using the expres-sion: APs 4 ntr ="Psntr + cs'To measure the density change A, sntr during resin-tering, either geometric or true densities may he used, so long 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 also acceptable to infer the density change from a diameter change. 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 or calibrated optical methods with established black-body conditions.

Furnace temperatures should be so maintained that true specimen temperatures are no lower than the desired test temperature

(1700'C in the model above) after temperature measurement errors have 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.0 1.126-3

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

For ch: ages in pellet diameter D. isotropic densilication may be assumed, so that ,:I)/D = .Ap/3p. For changes in pellet or fuel column leigth L. anisolropic densification is assumed such that -./L =Ar.1 2,o.

D. IMPLEMENTATION

The purpose of this section is to provide information to applicants and licensees regarding the NRC" staft's plans for using this regulatory guide.This guide reflects a relinement in NRC( practice and supersedes the previously accepted assumption that all fuels densify to a maximum density of 9thi.5'; of tineir theoretical density as measured geometrically.

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

the method described herein will be used in the evaluation of sub.mittals for construction permit, operating license, and reload applications docketed after November I. 1977.unless this guide is revised as a result of suggestions from the public or additional staff review. If for any reason the effects of' fuel densification are reanalyzed for fuel covered in an applicalion docketed on tir before No-vember 1. 1977. the method described in this guide would not be necessary and previously approved assunmp-tions would he allowed for that fuel.If an applicant wishes to use this regulatory guide in developing submittals for applications docketed on or before November 1. 1977. the pertinent portions of the application 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' the Assumnption 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 SYMBOLS T'he major symbols used in Sections C.I through C.5 are identified below: BU iHurnup. %IWdjtU.D Nominal initial pellet diameter, cni.I, Nominal initial pellet length, cm.TI) Theoretical density, g/cm 3.A 1) In-reactor pellet diameter change (function of burnup). cm.ADsntr Measured diameter change of a pellet due to ex-reactor resintering, cm.A t. In-reactor pellet length change (function of hurnup), cm.A, In-reactor pellet density change (function of burnup), g/cm 3.APsntr Measured density change of a pellet due to ex-reactor resintering, g/cm 3.s.ntr One-sided

95% upper confidence limit on, the mean of tile A0sntr values from the selected lot. g/cm 3.A 0 *n*r One-sided

95/95 upper tolerance limit for the total population of tLsntr values, g/cm 3.P Nominal initial pellet density, g/cm 3.1,126-4