Regulatory Guide 1.126: Difference between revisions

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{{Adams
{{Adams
| number = ML003739385
| number = ML13350A271
| issue date = 03/31/1978
| issue date = 03/31/1977
| title = Acceptable Model & Related Statistical Methods for Analysis of Fuel Densification
| title = an Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification
| author name =  
| author name =  
| author affiliation = NRC/RES
| author affiliation = NRC/OSD
| addressee name =  
| addressee name =  
| addressee affiliation =  
| addressee affiliation =  
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| license number =  
| license number =  
| contact person =  
| contact person =  
| document report number = RG-1.126 Rev 1
| document report number = RG-1.126
| document type = Regulatory Guide
| document type = Regulatory Guide
| page count = 5
| page count = 4
}}
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{{#Wiki_filter:U.S. NUCLEAR REGULATORY  
{{#Wiki_filter:U.S. NUCLEAR REGULATORY  
COMMISSION
COMMISSION
Revision 1 March 1978 REGULATORY  
March 1977 REGULATORY  
GUIDE Is OFFICE OF STANDARDS  
GUIDE OFFICE OF STANDARDS  
DEVELOPMENT  
DEVELOPMENT
REGULATORY  
REGULATORY  
GUIDE 1.126 AN ACCEPTABLE  
GUIDE 1.126 AN ACCEPTABLE  
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==A. INTRODUCTION==
==A. INTRODUCTION==
Appendix K, "ECCS Evaluation Models," to 10 CFR Part 50, "Licensing of Production and Utiliza tion Facilities," requires that the steady-state tem perature distribution and stored energy in the fuel be fore a hypothetical loss-of-coolant accident (LOCA) be calculated, taking fuel densification into consid eration. This guide provides an analytical model and related assumptions and procedures that are accept able to the NRC staff for predicting the effects of fuel densification in light-water-cooled nuclear power reactors.
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.


The guide also describes statistical methods related to product sampling that will provide assur ance that this and other approved analytical models will adequately describe the effects of densification for each initial core and reload fuel quantity pro duced. The Advisory Committee on Reactor Safeguards has been consulted concerning this guide and has concurred in the regulatory position.
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==
==B. DISCUSSION==
In-reactor densification (shrinkage)  
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 f''6rthe de- pellet during resintering at I 700&deg;C for 24 hours.0 crease in pellet uiameter;.
of oxide fuel pellets affects fuel temperatures in several ways: (1) gap conductance may be reduced because of the de crease in pellet diameter;  
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.
(2) the linear heat genera tion rate is increased because of the decrease in pellet length; and (3) the pellet-length decreases may cause gaps in the fuel column and may produce local power spikes and the potential for cladding collapse.


Di mensional changes in pellets in the reactor do not ap pear to be isotropic, so axial and radial pellet dimen sion changes will be treated differently.
Dimensional changes i Il11ets in lie reactor do not appear to be, a radial pellet dimension changes will b ted "clferently.


Fur thermore, items (1) and (2) above are single-pellet effects, whereas item (3) is the result of simultaneous changes in a large number of pellets. These distinc* Lines indicate substantive changes from previous issue.tions must be taken into account in applying analyt ical models. The NRC staff has reviewed the available informa tion concerning fuel densification, and the technical basis for the regulatory position of this guide is given in Reference  
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 Sec tions C.A and C.2 of this guide is not intended to supersede NRC-approved vendor models.  The statistical methods (Section C.3), measure ment methods (Section C.4), and isotropy assump tions (Section C.5) are compatible with most vendor models. Therefore Sections C.3, C.4, and C.5 could be applied to densification models that differ from the one presented in Sections C. 1 and C.2.  C. REGULATORY
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
POSITION 1. Maximum Densification The density of a fuel pellett in the reactor in creases with burnup and achieves a maximum value at a relatively low burnup (generally
<10,000 MWd/t). For analytical purposes, this maximum density minus the initial density, i.e., the maximum density change, is assumed to be the same as the den sity change APsntr that would occur outside the reac tor in the same pellet during resintering at 1700'C for 24 hours.  Where the ex-reactor resintering results in a nega tive density-change (i.e., swelling), zero in-reactor densification should be assumed.


t The model presented in this guide is applicable to U02, UO PuO 2 , and U02-Gd 2 O 3 fuel pellet
====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.


====s. USNRC REGULATORY ====
to accommodate comments and to tretect new Information or experience.
GUIDES Comments should be sent to the Secretary of the Commission.


US. Nuclear Regu latory Commission.
However. comments on this guideif I eceived within about two months alter its i-.suanca.


Washington, D.C. 20555, Attention:
will fe tParticularly useful In evaluating the neate for an early reviston.Conmments should be ent 1o thi, Secretary of tI!
Docketing and Service Regulatory Guides are issued to describe and make available to the public methods Branch.  acceptable to the NRC staff of implementing specific parts of the Commission's regulations, to delineate techniques used by the staff in evaluating specific problems The guides are issued in the following ten broad divisions or postulated accidents, or to provide guidance to applicants.
US. Nucleiar latury Commitsion.


Regulatory Guides are not substitutes for regulations, and compliance with them is not required.
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


1. Power Reactors 6. Products Methods and solutions different from those set out in the guides will be accept- 2. Research and Test Reactors 7. Transportation able if they provide a basis for the findings requisite to the issuance or continuance
===7. Ttantrurtatiun===
3. Fuels and Materials Facilities  
3. Fuellsant Materials Facilities  
8. Occupational Health of a permit or license by the Commi~sion.
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.


4. Environmental and Siting 9. Antitrust Review 5. Materials and Plant Protection
Division o t Document Crontfrol.
10t General Comments and suggestions for improvements in these guides are encouraged at all Requests for single copies of issued guides lwhich may be reproduced)
or for place.  times, and guides will *be revised, as appropriate, to accommodate comments and ment on an automatic distribution list for single copies of future guides in specific to reflect new information or experience.


This guide was revised as a result of divisions should be made in writing to the U.S- Nuclear Regulatory Commission, substantive comments received from the public and additional staff review. Washington, D.C. 20555, Attention:
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)
Director, Division of Document Conitrol.
+ 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.


2. Densification Kinetics For pellets that have a resintering density change APsntr of less than 4% of theoretical density (TD), the in-reactor density change Ap as a function of burnup BU may be taken as t Ap =0 (la) (for BU < 20 MWd/t); Ap= m log (BU) + b (lb) (for 20 < BU < 2000 MWd/t);and Ap =APsntr (for BU > 2000 MWd/t), where the coefficients m and b are given by 0 = m log(20) + b and APsntr = m log(2000)
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.
+ b.  For pellets exhibiting a resintering density change in excess of 4% TD, the in-reactor density change as a function burnup may be taken as Ap= 0 (2a) (for BU < 5 MWd/t); Ap = m log(BU) + b -(2b) (for 5 < BU < 500 MWd/t); and Ap = APsntr (2c) (for BU 500 MWd/t), where the coefficients m and b are given by 0 = m log(5) + b and Apsntr = m log(500) + b.In applications of Equations
1 and 2, Apsntr will have the value Ap*s*t or APs'ntr, which will be de scribed in Section C.3. The burnup unit MWd/t in the above expressions is megawatt days per metric ton of heavy metal (uranium or uranium plus plutonium in mixed-oxide fuels).  3. Statistical Methods To apply the above model or any densification model that depends on an ex-reactor resintering density change, a random sample of the pellet population of interest should be resintered.


Resintering the pellets in the sample will result in a set of density changes APsntr.  Several characteristics of these values are needed to complete the densification analysis.
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.


The population of analytical interest may be com posed of subsets of pellets from either a single material f Symbols are defined in the List of Symbols at the back of this guide.population or a group of material populations.
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.


A "ma terial population" is defined as a group of pellets man ufactured from a single powder source under the same range of fabricating conditions in such a manner that the pellets exhibit consistent resintering behavior.
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.


For those subsets taken from material populations that exhibit consistent resintering behavior, the sample data from the material population taken as a whole may be used to characterize the densification behavior of the subsets.
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.


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 den sification.
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.


To accomplish this with a resintering-based model such as that described in Sections C. 1 and C.2, a resintering density change value Ap** that conserva tively bounds 95% of the population APsntr values with 95% confidence should be used. The population of ana lytical interest is the initial core loading or reload quan tity of fuel for which the safety analysis, and hence the densification analysis, is being performed, and this population may be composed of subsets from a number of material populations.
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.


Once the material populations and their respective contributions (i.e., subsets) to the population of analytical interest are determined, random sampling procedures may be used to characterize the resulting population.
and mensuration ate acceptable.


When random sampling of the re sulting population is not feasible, a conservative charac terization may be obtained by using the largest of the characterizations of the contributing subsets.tt If the distribution of APsntr values of a population is normal, methods of evaluating normally distributed data may be used, If the "W" test or D' test (when 50 or more data points are used) (Ref. 2) demon strates nonnormality at the 1% level of significance, nonparametric statistical methods should be used un less a different functional form can be satisfactorily justified to describe the distribution of the Apsntr val ues. Thus Ap,*tr is the upper one-sided
It is also acceptable to infer the density change from a diameter change. using the isotropic relation "Psnir/o =3LDsntr/D.
95/95 toler ance limit for the density changes and can be ob tained from the sample values using one of the methods outlined below.  (1) Normal Distribution.


In this case, AP~str is given by Aps*tr -APsntr + C'S, where Apsntr is the mean of the sample data, s is the standard deviation of the sample data, and c' is given in Table 1 (from Ref. 3).  tt It is incorrect to prorate the characterizations of the con tributing subsets by computing weighted averages over the sub sets.1.126-2 I
where ADsntr is the diameter change exper-ienced during resintering.
TABLE 1 VALUES TO BE USED FOR c' TO DETERMINE
Apsntr WITH NORMAL DISTRIBUTION
Number of Observations
4 5 6 7 8 9 10 11 12 15 20 25 30 40 60 100 200 500 00 (2) Nonnormal Distribution.


AP~sr is given by AP*ntr TABLE 2 VALUES TO BE USED FOR m TO DETERMINE
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.
Apmsntr WITH NONNORMAL
DISTRIBUTION
Number of Observations m C, 5.15 4.20 3.71 3.40 3.19 3.03 2.91 2.82 2.74 2.57 2.40 2.29 2.22 2.13 2.02 1.93 1.84 1.76 1.64 In this case where Aps nt is the mth largest Apsntr value in a rank ing of the observed values of Apsntr from the sample.  The integer m depends on the sample size according to Table 2 (from Ref. 4).  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 aver age pellet behavior.


In this case, however, the popu lation to be considered is not the core or reload quan tity characterized above, but rather the material popu lation (or subset thereof) within that quantity that exhibits the largest mean of the APsntr values from the sample. The distribution of Apsntr values for the selected material population may be assumed to be normal. To analyze effects related to column-length changes, resintering-based densification models should use a density change value AP*sntr that bounds the selected material population mean with 95% con fidence. Thus Ap,*sntr is the upper one-sided
Furnace temperatures should be so maintained that true specimen temperatures are no lower than the desired test temperature
95% confidence limit on the mean density change and can be obtained from the sample values using the expres sion: Ap~sntr = AP'sntr + cs', 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 170 200 300 400 500 600 700 800 900 1000 where Ap'sntr is the mean of the sample data from the selected material population, s' is the standard devia tion of the sample data from the selected material population, and c is given in Table 3 (from Ref. 3).  4. Measurement Methods To measure the density change Apsntr during resin tering, either geometric or true densities may be used, so long as the same method is used before and after resintering.
(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&deg;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.


Techniques such as vacuum impregnation/water immersion, mercury immersion, gamma-ray absorption, and mensuration are accept able. It is also acceptable to infer the density change from a diameter change, using the isotropic relation Apsntr/p = 3ADsntrD, where ADsnt, is the diameter change experienced during resintering.
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.


Resintering should be performed in a furnace with a known temperature distribution in the working re gion. Temperatures during resintering should be measured using either thermocouples or calibrated optical methods with established blackbody condi tions. Furnace temperatures should be so maintained that specimen temperatures are no lower than the de sired test temperature
==D. IMPLEMENTATION==
(1700'C in the model above) after temperature measurement errors have been taken into account.1.126-3 1 1 1 1 I 1 1 2 2 2 2 3 3 3 4 5 9 13 17 21 26 30 35 3,9 TABLE 3 VALUES TO BE USED FOR c TO DETERMINE
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.
Aps*ntr Number of Observations
4 5 6 7 8 9 10 11 12 15 20 25 30 40 60 100 200 500 c 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 0.22 0.17 0.12 0.07 0 Fuel stoichiometry (O/M &#xfd; 2.00) should be main tained. This may be accomplished by using dry tank hydrogen or dry gas mixtures (e.g., N 2-H 2) and avoiding temperatures in excess of -1-800'C.


5. Isotrophy Assumptions In order to use predicted density changes in a cal culation of the effects of in-reactor densification, it is necessary to make some assumption about the iso tropy of fuel densification.
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


For changes in pellet diameter D, isotropic densification may be assumed, so that AD/D = Ap/3p. For changes in pellet or fuel column length L, anisotropic densification is assumed such that AL/L = Ap/2p.
====e. REFERENCES====
 
1. R. 0. Meyer. ""rhe Anakysis of Fuel Densi-fication." USNRC Report NURIFG-005.
==D. IMPLEMENTATION==
The purpose of this section is to provide informa tion to applicants and licensees regarding the NRC staff's plans for using this regulatory guide.  This guide reflects a refinement in NRC practice and supersedes the previously accepted assumption that all fuels densify to a maximum density of 96.5% of their theoretical density as measured geometri cally. Except in those cases in which the applicant proposes an acceptable alternative method for com plying with specified portions of the Commission's regulations, the method described herein should be used in submittals for construction permit, operating license, and reload applications until this guide is revised as a result of suggestions from the public or additional staff review.L 1.126-4 REFERENCES
1. R. 0. Meyer, "The Analysis of Fuel Densifica tion," USNRC Report NUREG-0085, July 1976.  2. "American National Standard Assessment of the Assumption of Normality (Employing Individual Ob served Values)," ANSI Standard N15.15-1974.


3. G. J. Hahn, "Statistical Intervals for a Normal Population, Part I. Tables, Examples and Applica tions." J. Quality Technol. 2, 115 (1970).  4. P. N. Somerville, "Tables for Obtaining Non Parametric Tolerance Limits," Ann. Math., Stat. 29, 599 (1958).LIST OF SYMBOLS The major symbols used in Sections C. I through C.5 are identified below: BU Burnup, MWd/t. D Nominal initial pellet diameter, cm. L Nominal initial pellet length, cm.TD AD Theoretical density, g/cm 3. In-reactor pellet diameter change (function of burnup), cm.ADsntr Measured diameter change of a pellet due to ex-reactor resintering, cm.AL In-reactor pellet length change (function of burnup), cm. Ap 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. AP*ntr One-sided  
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 the Apsntr values from the selected material population, g/cm 3. APsntr 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 Apsntr values, g/cm' p Nominal initial pellet density, g/cm 3.1.126-5}}
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}}


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Revision as of 20:53, 12 October 2018

an Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification
ML13350A271
Person / Time
Issue date: 03/31/1977
From:
NRC/OSD
To:
References
RG-1.126
Download: ML13350A271 (4)
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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


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