Regulatory Guide 1.126

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

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DG-1189 RG-1.126, Rev. 2
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U.S. NUCLEAR REGULATORY COMMISSION

March 2010

Revision 2 REGULATORY GUIDE

OFFICE OF NUCLEAR REGULATORY RESEARCH

The NRC issues regulatory guides to describe and make available to the public methods that the NRC staff considers acceptable for use in implementing specific parts of the agency

=s regulations, techniques that the staff uses in evaluating specific problems or postulated accidents, and data that the staff needs in reviewing applications for permits and licenses. Regulatory guides are not substitutes for regulations, and compliance with them is not required. Methods and solutions that differ from those set forth in regulatory guides will be deemed acceptable if they provide a basis for the findings required for the issuance or continuance of a permit or license by the Commission.

This guide was issued after consideration of comments received from the public.

Regulatory guides are issued in 10 broad divisions C1, Power Reactors; 2, Research and Test Reactors; 3, Fuels and Materials Facilities; 4, Environmental and Siting; 5, Materials and Plant Protection; 6, Products; 7, Transportation; 8, Occupational Hea lth; 9, Antitrust and Financial Review; and 10, General.

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8. REGULATORY GUIDE

1.126 (Draft was issued as DG-1189, dated December 2008) AN ACCEPTABLE MODEL AND RELATED STATISTICAL METHODS FOR THE ANALYSIS OF FUEL DENSIFICATION

A. INTRODUCTION

This guide describes an analytical model and related assumptions and procedures that the staff of the U.S. Nuclear Regulatory Commission (NRC) considers acceptable for predicting the effects of fuel densification in light-water-cooled nuclear power reactors. To meet these objectives, the guide describes statistical methods related to product sampling that will ensure that this and other approved analytical models will adequately describe the effects of densification for each initial core and reload fuel quantity produced.

The regulatory framework that the NRC has established for nuclear power plants consists of a number of regulations and supporting guidelines, including General Design Criterion 10, "Reactor Design," as set forth in Appendix A, "General Design Criteria for Nuclear Power Plants," to Title 10, Part 50, "Domestic Licensing of Production and Utilization Facilities," of the Code of Federal Regulations (10 CFR Part 50) (Ref. 1). Specifically, Appendix K, "ECCS Evaluation Models," to 10 CFR Part 50 requires that the steady-state temperature distribution and stored energy in the fuel before a hypothetical loss-of-coolant accident (LOCA) be calculated, taking fuel densification into consideration.

Rev. 2 of RG 1.126, Page 2 This regulatory guide contains information collection requirements covered by 10 CFR Part 50 that the Office of Management and Budget (OMB) approved under OMB control number 3150-0011. The NRC may neither conduct nor sponsor, and a person is not required to respond to, an information collection request or requirement unless the requesting document displays a currently valid OMB control number.

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 decrease in pellet diameter, (2) the linear heat generation rate is increased because of the decrease in pellet length, and (3) the decrease in pellet length may cause gaps in the fuel column and may produce local power spikes and the potential for cladding collapse. Dimensional changes in pellets in the reactor do not appear to be isotropic, so axial and radial pellet dimension changes will be treated differently. Furthermore, 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 distinctions must be considered in applying analytical models.

The NRC staff has reviewed the available information concerning fuel densification. NUREG-0085, "The Analysis of Fuel Densification," issued July 1976, contains the technical basis for the regulatory position of this guide (Ref. 2). The model presented in Sections C.1 and C.2 of this guide is not intended to supersede NRC-approved vendor models.

The statistical methods (Section C.3), measurement methods (Section C.4), and isotropy assumptions (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.

Rev. 2 of RG 1.126, Page 3

C. REGULATORY POSITION

1. Maximum Densification The density of a fuel pellet

1 in the reactor increases with burnup and achieves a maximum value at a relatively low burnup (generally less than 10,000 megawatt days per metric ton (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 density change that would occur outside the reactor in the same pellet during resintering (sntr) at 1700 °C (3092 °F) for 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />s:

2. Where the ex-reactor resintering results in a negative density change (i.e., swelling), zero in-reactor densification should be assumed.

2. Densification Kinetics For pellets that have a resintering density change sntr of less than 4 percent of theoretical density (TD), the in-reactor density change as a function of burnup (BU) may be taken as the following:

= 0 (for BU 20 MWd/t);

= m log (BU) + b (for 20 < BU < 2000 MWd/t); and = sntr (for BU 2000 MWd/t), where the coefficients m and b are given by

0 = m log (20) + b and sntr = m log (2000) + b.

For pellets exhibiting a resintering density change in excess of 4-percent TD, the in-reactor density change as a function of burnup may be taken as the following:

= 0 (for BU 5 MWd/t);

= m log (BU) + b (for 5 < BU < 500 MWd/t); and = sntr (for BU 500 MWd/t),

1 The model presented in this guide is applicable to UO

2, UO 2-PuO 2, and UO 2-Gd 2 O 3 fuel pellets.

2 The Terms of Equations at the back of this guide defines some of the terms and symbols used in this document.

Rev. 2 of RG 1.126, Page 4 where the coefficients m and b are given by

0 = m log (5) + b and sntr = m log (500) + b.

In applications of these equations, sntr will have the value

• sntror **sntr, which will be described 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 (MOX) 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 sntr. Several characteristics of these values are needed to complete the densification analysis.

The population of analytical interest may be composed of subsets of pellets from either a single material population or a group of material populations. A "material population" is defined as a group of pellets manufactured 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.

3.1 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 densification. To accomplish this with a resintering-based model such as that described in Sections C. 1 and C.2, a resintering density change value **sntrthat conservatively bounds 95 percent of the population sntr values with 95-percent confidence should be used. The population of analytical interest is the initial core loading or reload quantity 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 resulting population is not feasible, a conservative characterization may be obtained by using the largest of the characterizations of the contributing subsets.

1 If the distribution of sntr 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. 3) demonstrates nonnormality at the 1-percent level of significance, nonparametric statistical methods should be used unless a different functional form can be satisfactorily justified to describe the distribution of the sntr value

s. Thus

• • sntr is the 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 belo

w.

1 It is incorrect to prorate the characterizations of the contributing subsets by computing weighted averages over the subsets.

Rev. 2 of RG 1.126, Page 5 3.1.1 Normal Distribution In this case, **sntris given by the following:

• • sntr = sntr + c's, where sntr 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. 4).

Table 1 Values To Be Used for c' To Determine

• • sntr with Normal Distribution Number of Observationsc' 4 5.15 5 4.20 6 3.71 7 3.40 8 3.19 9 3.03 10 2.91 11 2.82 12 2.74 15 2.57 20 2.40 25 2.29 30 2.22 40 2.13 60 2.02 100 1.93 200 1.84 500 1.76 1.64 3.1.2 Nonnormal Distribution In this case, **sntris given by the following:

• • sntr = )(m sntr, where )(m sntr is the m th largest sntr value in a ranking of the observed values of sntr from the sample. The integer m depends on the sample size according to Table 2 (from Ref. 5).

This method requires a minimum of 60 observations to produce a meaningful result.

Rev. 2 of RG 1.126, Page 6 Table 2 Values To Be Used for m To Determine

• • sntr with Nonnormal Distribution Number of Observations m 50 - 55 - 60 1 65 1 70 1 75 1 80 1 85 1 90 1 95 2 100 2 110 2 120 2 130 3 140 3 150 3 170 4 200 5 300 9 400 13 500 17 600 21 700 26 800 30 900 35 1000 39 3.2 Multiple-Pellet Effects Average pellet behavior determines changes in fuel column length, which can result in axial gaps in the pellet stack. In this case, however, the population to be considered is not the core or reload quantity characterized above, but rather the material population (or subset thereof) within that quantity that exhibits the largest mean of the sntrvalues from the sample. The distribution of sntrvalues 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

• sntrthat bounds the selected material population mean with 95-percent confidence. Thus, *sntris the upper one-sided 95-percent confidence limit on the mean

Rev. 2 of RG 1.126, Page 7 density change and can be obtained from the sample values using the following expression:

• sntr = sntr'+ cs', where sntr'is the mean of the sample data from the selected material population, s' is the standard deviation of the sample data from the selected material population, and c is given in Table 3 (from Ref. 4). Table 3 Values To Be Used for c To Determine

• sntr Number of Observations c 4 1.18 5 0.95 6 0.82 7 0.73 8 0.67 9 0.62 10 0.58 11 0.55 12 0.52 15 0.45 20 0.39 25 0.34 30 0.31 40 0.27 60 0.22 100 0.17 200 0.12 500 0.07 0 4. Measurement Methods To measure the density change sntr during resintering, 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 acceptable. It is also acceptable to infer the density change from a diameter change, using the isotropic relation /sntr = 3 D D sntr/, where sntr D is the diameter change experienced during resintering.

Resintering should be performed in a 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 blackbody conditions. Furnace temperatures should be maintained so that specimen temperatures are no lower than the desired test temperature (1700 °C or 3092 °F for 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> in the model above) after temperature measurement errors have been taken into account.

Rev. 2 of RG 1.126, Page 8 In considering fuel stoichiometry, an oxygen-to-metal ratio of approximately 2.00 should be maintained. 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 about 1800 °C (3272 °F).

5. Isotropy Assumptions To use predicted density changes in a calculation of the effects of in-reactor densification, it is necessary to make some assumption about the isotropy of fuel densification. For changes in pellet diameter D, isotropic densification may be assumed, so that D/D = /3. For changes in pellet or fuel column length L, anisotropic densification is assumed such that L/L = /2. For further discussion of the conservative nature of these assumptions, see Section III. D of NUREG-008

D. IMPLEMENTATION

The purpose of this section is to provide information to applicants and licensees regarding the NRC's plans for using this regulatory guide. The NRC does not intend or approve any imposition or backfit in connection with its issuance.

In some cases, applicants or licensees may propose or use a previously established acceptable alternative method for complying with specified portions of the NRC's regulations. Otherwise, the methods described in this guide will be used in evaluating compliance with the applicable regulations for license applications, license amendment applications, and amendment requests.

Rev. 2 of RG 1.126, Page 9 TERMS USED IN EQUATIONS

The following identifies the major symbols used in Section C:

BU burn up unit expressed in megawatt days per metric ton of heavy metal (MWd/t)

c, c' population parameters in Tables 1 and 3

D nominal initial pellet diameter, centimeters (cm)

L nominal fuel column length, cm m population parameter from Table 2

s standard deviation of the sample data s' standard deviation of the sample data from the selected material population

TD theoretical density, grams per cubic centimeter (g/cm

3) D in-reactor pellet diameter change (function of burnup), cm sntr D measured diameter change of a pellet resulting from ex-reactor resintering, cm L in-reactor fuel column length change (function of burnup), cm in-reactor pellet density change (function of burnup), g/cm

3 sntr measured density change of a pellet resulting from ex-reactor resintering, g/cm

3 sntr mean of the measured density change data, sntr, g/cm 3 sntr' mean of a selected material population of the measured density data, sntr, g/cm 3 *sntr one-sided 95-percent upper confidence limit on the mean of the sntr values from the selected material population, g/cm

3 **sntr one-sided 95/95 upper tolerance limit for the total population of sntrvalues, g/cm

3 nominal initial pellet density, g/cm

3 Rev. 2 of RG 1.126, Page 10

REFERENCES

1 1. 10 CFR Part 50, "Domestic Licensing of Production and Utilization Facilities," U.S. Nuclear Regulatory Commission, Washington, DC.

2. NUREG-0085, "The Analysis of Fuel Densification," R.0. Meyer, U.S. Nuclear Regulatory Commission, Washington, DC, July 1976.

3. ANSI Standard N15.15-1974, "Assessment of the Assumption of Normality (Employing Individual Observed Values)," American National Standards Institute.

2 4. G.J. Hahn, "Statistical Intervals for a Normal Population, Part I. Tables, Examples and Applications," J. Quality Technol. 2, 115, 1970.

5. P.N. Somerville, "Tables for Obtaining Non-Parametric Tolerance Limits," Ann. Math. Stat. 29, pp. 599-601, 1958.

1 Publicly available NRC published documents such as Regulations, Regulatory Guides, NUREGs, and Generic Letters listed herein are available electronically through the Electronic Reading Room on the NRC's public Web site at:

http://www.nrc.gov/reading-rm/doc-collections/. Copies are also available for inspection or copying for a fee from the NRC's Public Document Room (PDR) at 11555 Rockville Pike, Rockville, MD; the mailing address is USNRC PDR, Washington, DC 20555; telephone 301-415-4737 or (800) 397-4209; fax (301) 415-3548; and e-mail

PDR.Resource@nrc.gov. 2 Copies of the non-NRC documents included in these references may be obtained directly from the publishing organization.