Regulatory Guide 1.126

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

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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*nosi.*e*,idor 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 liIIdtfter*from 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

0 * In-reactor densification pellets affects fuel temperatures in ste..ral (shrinkage)','of oxide Iitel gap conductance may be reduced beca f6rthe de-

'0*ys: (1)

the initial density. i.e., the maximum density change, is assumed to be the same as the density change Asntr that would occur outside the reactor in the same pellet during resintering at I700°C for 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.

crease in pellet uiameter;.1t),) me linear neat generation rate is increased because,*\de decrease in pellet length;

and (3) the pellet-le' .d'teases may cause gaps in Where the ex-reactor resintering results in a negative the fuel colur id n, prMce local power spikes density change (i.e.. swelling), zero in-reactor densifi- and the pot ial c ing collapse. Dimensional cation should le assumed.

changes i Il11ets in lie reactor do not appear to be isotro,* , a radial pellet dimension changes 2. Densifieation Kinetics will b ted "clferently. Furthermore, items (1) and

(2) abo i;re single-pellet effects, whereas item (3) For pellets that have a resintering density change is the result of simultaneous changes in a large number Asntr of less than 4% of theoritical density (TD),

of pellets. These distinctions must be taken into account the in-reactor density change Ap -1%a function of in applying analytical models. burnup BU may be taken as**

The NRC staff has reviewed the available information *The model presented in this guide is applicahle only to U0 2 concerning fuel densification, and the technical basis fuel pellets.

for the Regulatory Position of this guide is given in *&Symbols are defined in the List of Symtols at the back of this Reference 1. The model presented in Sections C.I guide.

USNRC REGULATORY GUIDES Conmments should be ent 1o thi, Secretary of tI! Commist*,u,* US. Nucleiar Rf*u"

Reggulatory Guide%wte issuerd to desribe ant make available to the public methods latury Commitsion. Wsiir'nton, O.C. 70555, Attention- Dorcketrrg and Servly Branch.

acieptable to the NRC stail of implementing speeilic paris of the Commission's tegufations, to delineate techniqtur$ used by the %tsalIin evaluating poecifIic litottlern The guides are ss*uiri in ttte following ten htut*,t rlwvivions of rostulated accidents, or to provide guidance to applicants, Regulatory Guides awe not subltitutes lot regublions, arnd commlhince with them is tot required. t. Power Reactors 6. PelXjucls Methods and solutions dilferent from those set Out in the guides will be accept- 2. Research and Te'st Reactors 7. Ttantrurtatiun able If they provide a basis for the findings requisite to the issuance or continuance 3. Fuellsant Materials Facilities 8, Occupational IHealth of a permit or license by the Commission, 4. Environmental aontSiting 9. Antitrust tlevew.

S. Materials and Plant Protection t0. Geriryal Comments and suggestions for improvements in these guides rt- encouraged at all times, and guides wtil bit revised, A ,tprotriatle. to accommodate comments and RectueSts fat single covies Ol isisuo guides ferhich rmnay' tie eprodur.ced at tto;iace- to tretect new Information or experience. However. comments on this guideif ment on an automatic dititl)ution list for sing le copies of future f tidus in streciftc

1 Ieceived within about two months alter its i-.suanca. will fe tParticularly useful In divisions should be madte in writing to the US. Nuclear Regutlarnrv t Cnnmission, evaluating the neate for an early reviston. Washington, D.C. 70555, Attention: Ditector. Division o Document Crontfrol.

I . Ap=O0 (la) ating normally distributed data may be use

d. If the

"W" test (Ref. 2) demonstrates nonnormality at the -1%

(for BU < 20 NIWd/tU); level of significance. nonparametric statistical methods S *p=mlog(BU)+b (I b) should be used unless a different functional form can be (for 20 < BU < 2000 NtWd/tU); satisfactorily justified to describe the distribution of the LAsntr values. Thus 6sAnptr is tile upper one.sided and ,, = APsntr (Ic)

95/95 tolerance limit for the density changes and can (for BU > 2000 MWd/tU), be obtained from the sample values using one of the where tile coefficients m and b are given by methods outlined below.

0 = m log(20) + b and (1) NormalDistribution. In this case, Ps*nr is

'Psntr = i log(2000) + b. given by ASiltr = Epsnir + C's.

For pellets exhiibiting a resintering density change in excess of 4% TD. the in-reactor density change as wherce -'Nsntr is tile mean of the sample data, s is the a function burnup may be taken as standard deviation of tile sample data, and c' is given Lp =0 (2a) in Table I (from Ref. 3).

(forhBU *<5 MWd/tU):

Ap = m log(BU) + b (21b )

(for 5 < BU < 500 MWd/tU): TABLE I

VALUES TO BE USED FOR c'

and -P - APsntr GOc TO DETERMINE 64lr (for BU > 500 MWd/tU), WITH NORMAL DISTRIBUTION

where the coefficients m and b are given by Number of

0 = m log(S) + b Observations c and ,Psntr = m log(500) + b.

4 5.15 In applications of Equations I and 2, ,Psntr will 5 4.20

have tile value st**r or tmntr. which will be described

6 3.71 in Section C.3. The burnup unit MWd/tU in the above

7 3.40

expressions is megawatt days per metric ton of heavy

8 3.19 metal (uranium).

9 3.03

10 2.91

3. Statistical Methods 11 2.82

12 2.74 To apply tile above model or any densification model is 2.57 that depends on an ex-reactor resintering density change, 20  :.40

a random sample of the pellet population of interest 25 2.29 must be resintered. Resintering the pellets in the sample 30 2.2 2 will result in a set of density changes 6Psntr. Several 40 2.13 characteristics of these values are needed to complete 60 2.02 the densification analysis. 100 1.93

200 1.84 a. Single-Pellet Effects 500 1.76

00 1.64 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- (2) NonnormalDistribution. In this case Apntis sintering density change value Apjn*tr that conservative- given by Ap~t t 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 where P is the mth largest 5Psntr value in a ranking of fuel for which the safety analysis, and hence the den- ot the observed values o0 6Psntr from the sample.

sification analysis, is being performed. If the distri- The integer m depends on tile sample size according to bution of *Asnlr values is normal, methods of evalu. Table 2 (from Ref. 4).

1.126-2

TABLE 2 where 'P;sntr is the mean of t(ie sample data from the VALUES TO BE USED FOR m TO DETERMINE selected lot, s' is the standard deviation of the sample tA*rrn*tr WITH NONNORMAL DISTRIBUTION data from the selected lot, and c is given in Table 3 (from Ref. 3).

Number of Observations m TABLE 3 VALUES TO BE USED FOR c

50

TO DETERMNINE i.snir

55

60

Number of

65 Observations C

70

75

4 1.18

80 0.95

85

6 0.82

90

7 0.73

95 2 (0.67

100 8

9 0.62

110

10 0.58

120

II 0.55

130 3 12 0.52

140 3 0.45

15o 3

20 0.39

170 4 25 0.34

200 5

30 0.31

300 9 0.27

13 40

400 0.-2

60

500 17 0.17

100

600 21 0.12

200

700 26

500 0.07

800 30 0

900 35

1000 39 4. Measurement Methods Note that a minimum of 60 observations is required to To measure the density change A,sntr during resin- produce a meaningful result by this method. tering, either geometric or true densities may he used, so long as the same method is used before and after resin.

b. Multiple-Pellet Effects tering. Techniques such as vacuum impregnation/

water immersion, mercury immersion, gamnta.r-ay ab- Fuel-column.length changes, which can result in sorption. and mensuration ate acceptable. It is also axial gaps in the pellet stack, are determined by average acceptable to infer the density change from a diameter pellet behavior. In this case, however, the population change. using the isotropic relation "Psnir/o =

to be considered is not the core or reload quantity 3LDsntr/D. where ADsntr is the diameter change exper- characterized above, but rather the pellet lot within ienced during resintering.

that quantity that exhibits the largest mean of the

6,sntr values from the sample. A pellet lot is defined Resintering should be performed in a laboratory- as a group of pellets made from a single UOi powder quality furnace with a known temperature distribution, source that has been processed under the same condi- in the working region. Temperatures during resintering tions. The distribution of 6Psntr values for the selected should be measured using either thermocouples or pellet lot is assumed to be normal. To analyze effects calibrated optical methods with established black- related to column-length changes. resintering-based body conditions. Furnace temperatures should be so densification models should use a density change value maintained that true specimen temperatures are no Ap*sntr that bbunds the selected pellet lot mean with lower than the desired test temperature (1700'C in

95% confidence, Thus ,'s'ntr is the upper one-sided the model above) after temperature measurement errors

95% confidence limit on the mean density change and have been taken into account.

can be obtained from the sample values using the expres- sion: Fuel stoichiometry (O/M ,; 2.00) should be main- tained by using dry tank hydrogen or dry gas mixtures

0

(e.g.. N2-H2) and avoiding temperatures in excess of

4 - 1800°eC.

APs ntr ="Psntr + cs'

1.126-3

5. Isotropy Assumptions theoretical density as measured geometrically. Except iim those cases in which the applicant proposes an accept- In order to use predicted density changes in a cal- able alternative method for complying with specified culation of the effects of inTreactor densification, it is portions of the Commission's regulations,. the method necessary to make some assumlplion about tile isotropy described herein will be used in the evaluation of sub.

of' fuel densification. For ch: ages in pellet diameter mittals for construction permit, operating license, and D. isotropic densilication may be assumed, so that reload applications docketed after November I. 1977.

,:I)/D = .Ap/3p. For changes in pellet or fuel column unless this guide is revised as a result of suggestions from leigth L. anisolropic densification is assumed such the public or additional staff revie

w. If for any reason

1 that -. /L =Ar. 2,o. the effects of' fuel densification are reanalyzed for fuel covered in an applicalion docketed on tir before No-

D. IMPLEMENTATION

vember 1. 1977. the method described in this guide would not be necessary and previously approved assunmp- The purpose of this section is to provide information tions would he allowed for that fuel.

to applicants and licensees regarding the NRC" staft's plans for using this regulatory guide.

If an applicant wishes to use this regulatory guide in This guide reflects a relinement in NRC( practice and developing submittals for applications docketed on or supersedes the previously accepted assumption that all before November 1. 1977. the pertinent portions of the fuels densify to a maximum density of 9thi.5'; of tineir application will be evaluated on ihe basis of1 this guide.

REFERENCES

1. R. 0. Meyer. ""rhe Anakysis of Fuel Densi- 3. G. J. Hahn. "Statistical Intervals for a Normal Pop- fication." USNRC Report NURIFG-005. July 1976. ulation. Part I. Tables, Examples and Applications,"

J. Quality Technol. 115 (1970),

2. "American National Standard Assessment of' the 4, P. N. Somerville. "Tables for Obtaining Non.Para- Assumnption of' Normnality (Emploving Ind ividu;,I Ob- metric Tolerance Limits." Ann. Math. Stat. 29, 559 served Values)'" ANSI Standard NI 5.15-19 74. (1958).

LIST OF SYMBOLS

T'he major symbols used in Sections C.I through C.5 At. In-reactor pellet length change (function of are identified below: hurnup), cm.

BU iHurnup. %IWdjtU. A, In-reactor pellet density change (function of burnup), g/cm 3 .

D Nominal initial pellet diameter, cni.

APsntr Measured density change of a pellet due to ex- I, Nominal initial pellet length, cm. reactor resintering, g/cm 3 .

TI) Theoretical density, g/cm 3 . s.ntr One-sided 95% upper confidence limit on, the mean of tile A0sntr values from the selected A1) In-reactor pellet diameter change (function of lot. g/cm 3 .

burnup). cm. A0 *n*r One-sided 95/95 upper tolerance limit for the total population of tLsntr values, g/cm 3 .

ADsntr Measured diameter change of a pellet due to ex-reactor resintering, cm. P Nominal initial pellet density, g/cm 3 .

1,126-4