Regulatory Guide 1.126
| ML003739385 | |
| Person / Time | |
|---|---|
| Issue date: | 03/31/1978 |
| From: | Office of Nuclear Regulatory Research |
| To: | |
| References | |
| RG-1.126 Rev 1 | |
| Download: ML003739385 (5) | |
U.S. NUCLEAR REGULATORY COMMISSION
Revision 1 March 1978 REGULATORY GUIDE
Is OFFICE OF STANDARDS DEVELOPMENT
REGULATORY GUIDE 1.126 AN ACCEPTABLE MODEL AND RELATED STATISTICAL METHODS FOR THE
ANALYSIS OF FUEL DENSIFICATION
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. 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.
B. DISCUSSION
In-reactor densification (shrinkage) of oxide fuel pellets affects fuel temperatures in several ways: (1)
gap conductance may be reduced because of the de crease in pellet diameter; (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. 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 pellet
s. 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 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 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 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
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-Gd2 O3 fuel pellets.
USNRC REGULATORY GUIDES
Comments should be sent to the Secretary of the Commission. US. Nuclear Regu latory Commission. Washington, D.C.
20555, Attention: 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. Regulatory Guides are not substitutes for regulations, and compliance with them is not required.
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
3. Fuels and Materials Facilities
8. Occupational Health of a permit or license by the Commi~sion.
4. Environmental and Siting
9. Antitrust Review
5. Materials and Plant Protection
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:
Director, Division of Document Conitrol.
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) + 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.
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. 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. 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.
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. 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. 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. 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 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
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
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 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. 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.
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 (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 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 ý 2.00) should be main tained. This may be accomplished by using dry tank hydrogen or dry gas mixtures (e.g., N2-H2) 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. 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.
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:
Burnup, MWd/t.
D
Nominal initial pellet diameter, cm.
L
Nominal initial pellet length, cm.
TD
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.
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 95% upper confidence limit on the mean of the Apsntr values from the selected material population, g/cm 3.
APsntr 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