U.S. NUCLEAR REGULATORY COMMISSION December 2008

OFFICE OF NUCLEAR REGULATORY RESEARCH Division 1

DRAFT REGULATORY GUIDE 

Contact: J. Voglewede

(301) 251-7555 

DRAFT REGULATORY GUIDE DG-1189 

(Proposed Revision 2 of Regulatory Guide 1.126, dated March 1978) 

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. 

The NRC issues regulatory guides to describe to the public methods that the staff considers 

This regulatory guide is being reissued in draft form to continue involvement of the public in discussions on this topic. This

version has not received final staff review or approval and does not represent an official NRC final staff position. 

Public comments are being solicited on this draft guide (including any implementation schedule) and its associated regulatory 

analysis or value/impact statement. Comments should be accompanied by appropriate supporting data. Written comments may 

be submitted to the Rulemaking, Directives, and Editing Branch, Office of Administration, U.S. Nuclear Regulatory 

Commission, Washington, DC 20555-0001; emailed to nrcrep.resource@nrc.gov; submitted through the NRC’s interactive 

rulemaking Web page at http://www.nrc.gov; faxed to (301) 415-5144; or hand-delivered to Rulemaking, Directives, and Editing 

Branch, Office of Administration, US NRC, 11555 Rockville Pike, Rockville, MD 20852, between 7:30 a.m. and 4:15 p.m. on 

Federal workdays. Copies of comments received may be examined at the NRC’s Public Document Room, 11555 Rockville Pike, 

Rockville, MD. Comments will be most helpful if received by February 9, 2009. 

Electronic copies of this draft regulatory guide are available through the NRC’s interactive rulemaking Web page (see above); the 

NRC’s public Web site under Draft Regulatory Guides in the Regulatory Guides document collection of the NRC’s Electronic 

Reading Room at http://www.nrc.gov/reading-rm/doc-collections/; and the NRC’s Agencywide Documents Access and 

Management System (ADAMS) at http://www.nrc.gov/reading-rm/adams.html, under Accession No. ML081700257. 
DG-1189, Page 2 

acceptable for use in implementing specific parts of the agency’s regulations, to explain techniques that 

the staff uses in evaluating specific problems or postulated accidents, and to provide guidance to 

applicants. Regulatory guides are not substitutes for regulations and conformity with them is not 

required. 

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 singlepellet 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. 

C. REGULATORY POSITION 

1. Maximum Densification 

The density of a fuel pellet† 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 (Δρsntr) at 1700 °C (3092 °F) for 24 hours:‡

. 

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

in-reactor densification should be assumed. 

 

†

 The model presented in this guide is applicable to UO2, UO2-PuO2, and UO2-Gd2O3 fuel pellets. 

‡

 The Terms of Equations at the back of this guide defines some of the terms and symbols used in this document. 
DG-1189, Page 3 

2. Densification Kinetics 

For pellets that have a resintering density change Δρ sntr of less than 4 percent of theoretical 

density (TD), the in-reactor density change Δρ as a function of burnup (BU) may be taken as the 

following: 

 Δρ = 0 

 (for BU < 20 MWd/t); 

 Δρ = m log (BU) + b 

 (for 20 < BU < 2000 MWd/t); 

and 

 Δρ = Δρ sntr

 (for BU > 2000 MWd/t), 

where the coefficients m and b are given by 

 0 = m log (20) + b 

and Δρ 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 burnup may be taken as the following: 

 Δρ = 0 

 (for BU < 5 MWd/t); 

 Δρ = m log (BU) + b 

 (for 5 < BU < 500 MWd/t); 

and 

 Δρ = Δρ sntr

 (for BU > 2000 MWd/t), 

where the coefficients m and b are given by 

 0 = m log (5) + b 

and Δρ sntr = m log (500) + b. 

In applications of these equations, Δρ sntr will have the value * Δρ sntr or ** Δρ 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). 
DG-1189, Page 4 

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 Δρ 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 ** Δρ sntr that conservatively bounds 95 percent of the population Δρ 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.§

If the distribution of Δρ 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 Δρ sntr values. Thus ** Δρ 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 below. 

3.1.1 Normal Distribution

In this case, ** Δρ sntr is given by the following: 

 ** Δρ sntr = Δρ sntr + c's, 

 

§

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

subsets. 
DG-1189, Page 5 

where Δρ 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 ** Δρ sntr

with Normal Distribution 

Number of 

Observations

c' 

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, ** Δρ sntr is given by the following: 

 ** Δρ sntr = (m) Δρ sntr , 

where (m) Δρ sntr is the mth largest Δρ sntr value in a ranking of the observed values of Δρ 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. 
DG-1189, Page 6 

Table 2 Values To Be Used for m To Determine ** Δρ 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 Δρ sntr values from the sample. The distribution of Δρ sntr 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 * Δρ sntr that bounds the selected material population mean with 

95-percent confidence. Thus, * Δρ sntr is the upper one-sided 95-percent confidence limit on the mean 

density change and can be obtained from the sample values using the following expression: 
DG-1189, Page 7 

 * Δρ sntr = sntr Δρ' + cs', 

where sntr Δρ' 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 * Δρ 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 Δρ 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 Δρ sntr / ρ = 3ΔDsntr / D , where ΔDsntr 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 
DG-1189, Page 8 

3092 °F for 24 hours in the model above) after temperature measurement errors have been taken into 

account. 

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., N2-H2) 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 ΔD/D = Δρ/3ρ. For changes in pellet or fuel 

column length L, anisotropic densification is assumed such that ΔL/L = Δρ/2ρ. For further discussion of 

the conservative nature of these assumptions, see Section III. D of NUREG-0085. 

D. IMPLEMENTATION 

The purpose of this section is to provide information to applicants and licensees regarding the 

NRC’s plans for using this draft regulatory guide. The NRC does not intend or approve any imposition or 

backfit in connection with its issuance. 

The NRC has issued this draft guide to encourage public participation in its development. The 

NRC will consider all public comments received in development of the final guidance document. In 

some cases, applicants or licensees may propose an alternative 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. 

REGULATORY ANALYSIS

1. Statement of the Problem 

In 1976, the NRC staff reviewed the available information concerning in-reactor densification of 

nuclear fuel. The current revision (Revision 1) of Regulatory Guide 1.126 (Ref. 6) reflected a refinement 

in NRC practice and superseded the previously accepted assumption that all fuels densify to a maximum 

density of 96.5 percent of their theoretical density as measured geometrically. The technical basis for the 

current regulatory position is contained in NUREG-0085. More recently, the following issues have 

emerged regarding continued implementation of this regulatory guide: 

• It is unclear whether the guidance on densification remains applicable to current fuel designs.

Comparison of more recent in-reactor densification and out-of-reactor resintering data has 

confirmed that densification in current fuel types is adequately represented by resintering data 

(particularly in MOX fuels) as described in Regulatory Guide 1.126. 

Recently, the NRC became aware that out-of-reactor densification of MOX may underestimate 

in-reactor densification for this fuel type. As a result, the NRC directed its contractor, Pacific 
DG-1189, Page 9 

Northwest National Laboratory (PNNL), to review in-reactor densification data on MOX fuel as 

well as data from the associated thermal resintering test. These two data sets were compared to 

determine if the standard resintering test specified in Regulatory Guide 1.126 is applicable to 

MOX fuel. 

In Reference 7, PNNL describes the data comparisons and results of its reexamination of the 

applicability of the standard resintering test to MOX fuel. The laboratory concludes that, “despite 

limited experimental data and opposing views regarding the mechanisms of in- and out-of-reactor 

densification of MOX, there is evidence that the values obtained from the out-of-reactor tests are 

equivalent to the maximum densification observed in reactor.” Consequently, the NRC staff is 

not proposing a change in the applicability of Regulatory Guide 1.126. 

• Since Regulatory Guide 1.126 deals more with statistical analysis than densification, it may be 

more appropriate to promulgate this guidance elsewhere than among Division 1 (Power Reactor) 

regulatory guides. 

While it is true that Regulatory Guide 1.126 deals more with statistical analysis than with 

densification, this is not the case within the technical basis for the regulatory position (Ref. 2). 

Regulatory Guide 1.126 deals with a process (densification) that occurs in fresh fuel during each 

core reload. Further, large populations (millions of fuel pellets) are involved for which statistical 

methods are highly appropriate. For these reasons, the NRC anticipates no change in the 

placement of this regulatory guide or its composition. 

• In considering single-pellet effects, Regulatory Guide 1.126 requires a density change that 

bounds 95 percent of the population with 95-percent confidence. In analysis of the LOCA, this 

may unfairly promote independent and simultaneous application of maximum uncertainties from 

other sources considered in the safety analysis. 

Regulatory Guide 1.126 provides statistically appropriate guidance for single- and multiple-pellet 

effects. It does not (correctly) provide guidance on how these uncertainties must be combined or 

convoluted with uncertainties from other portions of the LOCA analysis. This issue is subject to 

review in the staff’s evaluation of LOCA analysis methods rather than in the evaluation of 

conformity with the provisions of Regulatory Guide 1.126. 

 

• Modern fuel types are less prone to densification, and the problems associated with densification, 

than those used at the time of the first publication of Regulatory Guide 1.126. The guidelines 

provided in the guide may no longer be necessary. 

The model and methods described in Regulatory Guide 1.126 are applicable to fuel materials 

exhibiting low in-reactor density change. Conformity with the guidance does not justify 

elimination of the guidance. 

• The technical references used in Regulatory Guide 1.126 are old and difficult to obtain. This 

suggests that the guidance itself may be obsolete. 

The statistical guidance provided in Regulatory Guide 1.126 is not obsolete. To minimize the 

need for external sources, the tables in the guide incorporate pertinent information. The same 

information is available from more current sources. 
DG-1189, Page 10 

2. Objective 

The objective of this regulatory action is to confirm that existing guidance on in-reactor 

densification remains applicable to current fuel designs. 

3. Alternative Approaches 

 In conducting this review, the NRC staff considered the following alternative approaches: 

• Do not reissue Regulatory Guide 1.126. 

• Reissue unmodified Regulatory Guide 1.126. 

• Update Regulatory Guide 1.126. 

3.1 Alternative 1: Do Not Reissue Regulatory Guide 1.126 

Under this alternative, the NRC would not revise this guidance, and the original version 

(Revision 1) of this regulatory guide would continue to be used. This alternative is considered the 

baseline or Ano action@ alternative and, as such, involves no value/impact considerations. 

3.2 Alternative 2: Reissue Unmodified Regulatory Guide 1.126

Under this alternative, the NRC would reissue Regulatory Guide 1.126, with consideration of 

more recent information on in-reactor densification but without substantive changes in the existing 

technical guidance. This alternative would reformat the regulatory guide document and reconfirm the 

existing regulatory approach to this issue. The cost of reissuing a reformatted document is expected to be 

relatively small. Applicants and existing licensees would incur little or no additional cost because the 

technical requirements would remain unchanged. 

3.3 Alternative 3: Update Regulatory Guide 1.126

Under this alternative, the NRC would update and reissue Regulatory Guide 1.126, with 

consideration of recent information, particularly about the manner in which other parts of the safety 

analysis use resintering data. One benefit of this action is that it would enhance reactor safety by ensuring 

regulatory consistency. However, the cost to licensees would be significant because it would involve 

reanalysis using revised methods. The impact to the NRC would be the significant costs associated with 

preparing and issuing the revised regulatory guide. The impact to the public would be the voluntary costs 

associated with reviewing and providing comments to NRC during the public comment period. 

4. Conclusion 

Based on the review described previously, the staff recommends Alternative 2, the NRC reissue 

of the reformatted but technically unmodified Regulatory Guide 1.126. The staff concludes that the 

proposed action would maintain the existing level of reactor safety. This alternative would result in no 

additional costs to the industry because the technical requirements would remain unchanged. 
DG-1189, Page 11 

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/cm3

) 

ΔD in-reactor pellet diameter change (function of burnup), cm 

ΔDsntr measured diameter change of a pellet resulting from ex-reactor resintering, cm 

ΔL in-reactor fuel column length change (function of burnup), cm 

Δρ in-reactor pellet density change (function of burnup), g/cm3

Δρ sntr measured density change of a pellet resulting from ex-reactor resintering, g/cm3

Δρ sntr mean of the measured density change data, Δρ sntr , g/cm3

sntr Δρ' mean of a selected material population of the measured density data, Δρ sntr , g/cm3

* Δρ sntr one-sided 95-percent upper confidence limit on the mean of the Δρ sntr values from the selected 

material population, g/cm3

** Δρ sntr one-sided 95/95 upper tolerance limit for the total population of Δρ sntr values, g/cm3

ρ nominal initial pellet density, g/cm3
DG-1189, Page 12 

REFERENCES 

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. 

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. 

6. U.S. Nuclear Regulatory Commission, Regulatory Guide 1.126, “An Acceptable Model and 

Related Statistical Methods for the Analysis of Fuel Densification,” Washington, DC. 

7. W.G. Luscher (PNNL) letter to J.C. Voglewede (NRC) on “Densification in MOX Fuel,” 

January 7, 2008.