NUREG/CR-7001 

PNNL-17644

Predictive Bias and Sensitivity in 

NRC Fuel Performance Codes 

Office of Nuclear Regulatory Research 
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NUREG/CR-7001 

PNNL-17644 

Predictive Bias and Sensitivity in 

NRC Fuel Performance Codes 

Manuscript Completed: April 2009 

Date Published: October 2009 

Prepared by 

K.J. Geelhood, W.G. Luscher, C.E. Beyer, D.J. Senor, and 

M.E. Cunningham, D.D. Lanning, H.E. Adkins 

Pacific Northwest National Laboratory 

P.O. Box 999 

Richland, WA 99352 

NRC Job Code N6326

Office of Nuclear Regulatory Research 

iii 

ABSTRACT 

The latest versions of the fuel performance codes, FRAPCON-3 and FRAPTRAN were 

examined to ensure best estimate behavior of the codes and to ensure (to the extent possible 

that unintentional bias has been eliminated. Each individual model and type of code 

prediction was examined and compared to the data that was used to develop the model. In 

addition, a brief literature search was performed to determine if more recent data have 

become available since the original model development for model comparison. If new data 

were discovered, these data were compared to the models and code predictions in 

FRAPCON-3.3 and FRAPTRAN-1.3 in order to determine if the model is biased. Models 

or integral effect prediction found to be biased relative to the data were updated and 

corrected in the upcoming versions of the codes, FRAPCON-3.4 and FRAPTRAN 1.4. 

Areas where modeling may be lacking were noted for further model development. The 

details of the updated models are provided in this report. 

Subsequently, a sensitivity study was performed on the steady-state code, FRAPCON-3.3 

to determine the effects of uncertainty in model predictions, manufacturing parameters and 

power history on the code outputs of regulatory interest. 

v 

FOREWORD 

The purpose of this study was to re-examine the NRC fuel performance codes to ensure 

best estimate behavior of the codes and to ensure (to the extent possible) that unintentional 

bias has been eliminated. The tendency of these analytical tools to be (or to become) 

intrinsically conservative is understandable as the regulatory requirements themselves use 

conservatism to bound uncertainties. 

As an example of this regulatory approach, the required and acceptable features of 

evaluation models used in the calculation of stored energy of the fuel include: 

The steady-state temperature distribution and stored energy in the fuel before the 

hypothetical accident shall be calculated for the burn-up that yields the highest

calculation cladding temperature (or, optionally, the highest calculated stored 

energy.) 

10 CFR 50, Appendix K, Part (I)(A)(1) 

Thus, there is a motive for analytical tools used in the regulatory audit vendor safety 

analyses to incorporate conservatisms in an intrinsic or automated fashion. However, this 

may not be consistent with the need to compare code predictions with experimentallyderived information, such as fuel centerline thermocouple data. This current study seeks to 

identify and remove such conservatisms from the code (as opposed to removing them from 

the regulation). 

Further, in recognition of recent vendor efforts to combine uncertainties in fuel code input 

parameters, a sensitivity study was performed on the steady-state code, FRAPCON-3.3 to 

determine the effects of uncertainty in model predictions, manufacturing parameters, and 

power history on the code outputs of regulatory interest. This effort makes direct use of the 

first part of this study – the comparison of individual model or type of code prediction with 

the data that was used to develop that model. The results of these two complementary 

efforts both seek to improve the tools used by NRC in regulatory analysis. 

vii 

CONTENTS

ABSTRACT ......................................................................................................................... iii

FOREWORD..........................................................................................................................v

CONTENTS ........................................................................................................................ vii

LIST OF FIGURES................................................................................................................x

LIST OF TABLES ..............................................................................................................xvi

EXECUTIVE SUMMARY............................................................................................... xvii

ABBREVIATIONS.............................................................................................................xix

1.0 INTRODUCTION ...........................................................................................1.1

2.0 BIAS ASSESSMENT......................................................................................2.1

2.1 Thermal Modeling and Assessment.................................................................2.1

2.1.1 Code Solution Method, Fuel Rod Heat Transfer Solution Methods and 

Pellet Heat Generation Radial Profile..............................................................2.1

2.1.2 Fuel Thermal Conductivity..............................................................................2.5

2.1.2.1 UO2 .......................................................................................................2.5

2.1.2.2 MOX .....................................................................................................2.6

2.1.2.3 UO2-Gd2O3............................................................................................2.7

2.1.3 Gap Conductance.............................................................................................2.9

2.1.3.1 Conductance through the Gas ...............................................................2.9

2.1.3.2 Conductance through points of cladding-pellet contact......................2.10

2.1.3.3 Radiation heat transfer ........................................................................2.10

2.1.4 Fuel Thermal Expansion................................................................................2.10

2.1.5 Fuel Relocation..............................................................................................2.11

2.1.6 Other Models and Properties .........................................................................2.13

2.1.6.1 Cladding-Coolant Heat Transfer.........................................................2.14

2.1.6.2 Oxide Thermal Conductivity ..............................................................2.14

2.1.6.3 CRUD Thermal Conductivity .............................................................2.16

2.1.6.4 Cladding Thermal Conductivity..........................................................2.17

2.1.6.5 Gas Thermal Conductivity..................................................................2.18

2.1.6.6 Cladding Thermal Expansion..............................................................2.24

2.1.7 Integral Assessment .......................................................................................2.26

2.1.7.1 UO2 Temperature Comparisons ..........................................................2.26

2.1.7.2 UO2-Gd2O3 Temperature Comparisons ..............................................2.33

2.1.7.3 MOX Temperature Comparisons........................................................2.38

2.2 Fission Gas Release Model and Assessment .................................................2.43

2.2.1 Modeling........................................................................................................2.44

2.2.2 Assessment.....................................................................................................2.45

2.3 Cladding Corrosion and Hydriding Models...................................................2.49

2.3.1 Cladding Corrosion........................................................................................2.49

2.3.2 Hydrogen Pickup ...........................................................................................2.54

2.4 Fuel Densification and Swelling....................................................................2.57

2.4.1 Fuel Swelling .................................................................................................2.58

2.4.2 Fuel Densification..........................................................................................2.59

2.5 Assessment of Mechanical Modeling and Properties ....................................2.60

2.5.1 Modeling........................................................................................................2.60

2.5.2 Mechanical Properties....................................................................................2.61

2.5.2.1 Irradiation Creep .................................................................................2.61

2.5.2.2 Yield Strength .....................................................................................2.63

2.5.2.3 Young’s Modulus................................................................................2.65
viii 

2.5.3 Assessment of Power Ramped Rods..............................................................2.65

2.6 Void Volume Model and Assessment............................................................2.67

2.6.1 Rod Growth....................................................................................................2.67

2.6.2 Plenum Gas Temperature...............................................................................2.69

2.7 Time Dependent Models................................................................................2.70

2.7.1 Properties and Models without time dependence ..........................................2.71

2.7.2 Properties and models with time dependence that can change over short 

time intervals (e.g. < 10 minutes) and should be modeled in 

FRAPTRAN...................................................................................................2.72

2.7.3 Properties and models with time dependence much greater than the time 

period modeled in FRAPTRAN.....................................................................2.74

2.7.4 Summary........................................................................................................2.75

2.8 Conclusions....................................................................................................2.76

3.0 UPDATES TO MODELS................................................................................3.1

3.1 Corrosion and Hydrogen Pickup in Cladding Alloys ......................................3.1

3.1.1 Hydrogen pickup in Zircaloy-2........................................................................3.1

3.1.2 Corrosion in ZIRLOTM.....................................................................................3.2

3.1.3 Corrosion and Hydrogen Pickup in M5TM .......................................................3.5

3.2 Radial Power Profile in HWR..........................................................................3.8

3.3 Radial Power Profile in UO2-Gd2O3 ..............................................................3.10

3.4 Fuel Thermal Expansion at High Temperature..............................................3.15

3.5 Gas Thermal Conductivity at High Temperature...........................................3.16

3.6 Steam Conductivity........................................................................................3.20

3.7 Cladding Irradiation Creep ............................................................................3.22

4.0 Sensitivity Analysis .........................................................................................4.1

4.1 Outputs of Interest ...........................................................................................4.2

4.1.1 Rod Internal Gas Pressure................................................................................4.2

4.1.2 Peak Fuel Centerline Temperature...................................................................4.2

4.1.3 Cladding Permanent Hoop Strain ....................................................................4.2

4.1.4 Other Outputs of Interest .................................................................................4.3

4.2 Selection of Base Cases ...................................................................................4.3

4.3 Effects of Manufacturing Uncertainties...........................................................4.5

4.3.1 Cladding Inner Diameter................................................................................4.10

4.3.2 Cladding Thickness........................................................................................4.10

4.3.3 Cladding Roughness ......................................................................................4.11

4.3.4 Pellet Outer Diameter ....................................................................................4.11

4.3.5 Theoretical Pellet Density..............................................................................4.12

4.3.6 Pellet Re-Sinter Density.................................................................................4.13

4.3.7 Pellet Roughness............................................................................................4.13

4.3.8 Pellet Dish Diameter and Depth ....................................................................4.14

4.3.9 Rod Fill Pressure............................................................................................4.14

4.3.10 Rod Plenum Length .......................................................................................4.15

4.4 Effects of Model Uncertainties ......................................................................4.15

4.4.1 Fuel Thermal Conductivity............................................................................4.23

4.4.2 Fuel Thermal Expansion................................................................................4.24

4.4.3 Cladding Oxide Conductivity ........................................................................4.25

4.4.4 Cladding Conductivity...................................................................................4.27

4.4.5 Gas Conductance ...........................................................................................4.28

4.4.6 Fission Gas Release .......................................................................................4.29

4.4.7 Cladding Corrosion........................................................................................4.31

4.4.8 Fuel Swelling .................................................................................................4.33
ix 

4.4.9 Creep of Irradiated Cladding .........................................................................4.35

4.4.10 Cladding Yield Strength ................................................................................4.36

4.4.11 Young’s Modulus of Cladding.......................................................................4.38

4.4.12 Cladding Axial Growth..................................................................................4.39

4.4.13 Cladding Thermal Expansion ........................................................................4.41

4.5 Effects of Power Uncertainties ......................................................................4.42

4.5.1 Steady State....................................................................................................4.45

4.5.2 Height of AOO Pulse.....................................................................................4.45

4.5.3 Duration of AOO Pulse..................................................................................4.46

4.6 Conclusions....................................................................................................4.46

4.6.1 Rod Internal Pressure.....................................................................................4.47

4.6.2 Peak Fuel Centerline Temperature.................................................................4.47

4.6.3 Cladding Permanent Hoop Strain ..................................................................4.47

5.0 CONCLUSIONS .............................................................................................5.1

6.0 REFERENCES ................................................................................................6.1
x 

LIST OF FIGURES 

Figure 2.1 Radial burnup profile for BWR rod A3/6-4 at 55 GWd/MTU ......................... 2.2

Figure 2.2 Radial burnup profile for BWR rod H8/36-4 at 55 GWd/MTU ....................... 2.3

Figure 2.3 Radial burnup profile for PWR rod BK365 at 83 GWd/MTU ......................... 2.3

Figure 2.4 Radial burnup profile for PWR rod D200 at 25 GWd/MTU............................ 2.4

Figure 2.5 Radial burnup profile for PWR rod D226 at 45 GWd/MTU............................ 2.4

Figure 2.6 Predicted vs. measured thermal conductivity for unirradiated UO2. ................ 2.5

Figure 2.7 Predicted vs. measured thermal conductivity for irradiated UO2. .................... 2.6

Figure 2.8 Predicted vs. measured thermal conductivity for MOX fuel ............................ 2.7

Figure 2.9 Predicted vs. measured thermal conductivity for unirradiated UO2 Gd2O3. ..... 2.8

Figure 2.10 Predicted vs. measured thermal conductivity for irradiated UO2 Gd2O3. ..... 2.8

Figure 2.11 Thermal expansion data and model predictions for UO2 ........................... 2.11

Figure 2.12 Predicted and measured fuel centerline temperatures with argon and 

helium fill gases for a IFA-633 UO2 rod (as-fabricated radial gap is 105μm)........ 2.13

Figure 2.13 Comparison of MATPRO ZrO2 model to data used to develop the model 

and newer data......................................................................................................... 2.16

Figure 2.14 MATPRO model (CTHCON), the data on which it is based, newer data, 

and the Fink Model.................................................................................................. 2.18

Figure 2.15 Thermal conductivity data and model predictions for He .......................... 2.20

Figure 2.16 Thermal conductivity data and model predictions for Ar........................... 2.20

Figure 2.17 Thermal conductivity data and model predictions for Kr........................... 2.21

Figure 2.18 Thermal conductivity data and model predictions for Xe .......................... 2.21

Figure 2.19 Thermal conductivity data and model predictions for H2........................... 2.22

Figure 2.20 Thermal conductivity data and model predictions for N2........................... 2.22

Figure 2.21 Thermal conductivity data and model predictions for steam at 100 MPa .. 2.23

Figure 2.22 Predicted vs. measured thermal conductivity for various gas mixtures. .... 2.24

Figure 2.23 Axial thermal expansion model from FRAPCON-3.3 and FRAPTRAN 

1.3 compared to data ............................................................................................... 2.25

Figure 2.24 Circumferential thermal expansion model from FRAPCON-3.3 and 

FRAPTRAN 1.3 compared to data.......................................................................... 2.25

Figure 2.25 Predicted and measured temperature for BOL ramp to power................... 2.27

Figure 2.26 Measured and predicted centerline temperature for IFA-432r1 lower 

thermocouple (Burnup=45 GWd/MTU, as-fabricated radial gap=114μm)............. 2.28

Figure 2.27 Measured and predicted centerline temperature for IFA-432r3 lower 

thermocouple (Burnup=45 GWd/MTU, as-fabricated radial gap=38μm)............... 2.29

Figure 2.28 Measured and predicted centerline temperature for IFA-513r1 upper 

thermocouple (a) and lower thermocouple (b) (Burnup=10 GWd/MTU, asfabricated radial gap=108μm) ................................................................................. 2.30

Figure 2.29 Measured and predicted centerline temperature for IFA-513r6 upper 

thermocouple (a) and lower thermocouple (b) (Burnup=10 GWd/MTU, asfabricated radial gap=108μm) ................................................................................. 2.31

Figure 2.30 Measured and predicted rod-average centerline temperature for IFA562r18 (Burnup=76 GWd/MTU, as-fabricated radial gap=50μm) ......................... 2.32

Figure 2.31 Measured and predicted centerline temperature for IFA-597r8 (starting 

burnup=68 GWd/MTU, ending burnup=71 GWd/MTU, as-fabricated radial 

gap=105μm). ........................................................................................................... 2.33

Figure 2.32 Measured and predicted centerline temperature for IFA-515.10 rod A1 

(UO2) (a), and for IFA-515.10 rod A2 (UO2-8%Gd2O3) (b) (Burnup=80 

GWd/MTU, as-fabricated radial gap=25μm).......................................................... 2.34
xi 

Figure 2.33 Measured and predicted centerline temperature for IFA-515.10 rod B1 

(UO2) (a), and for IFA-515.10 rod B2 (UO2-8%Gd2O3) (b) (Burnup=80 

GWd/MTU, as-fabricated radial gap=25μm).......................................................... 2.35

Figure 2.34 Measured and predicted centerline temperature for IFA-636r2 (UO2-

8%Gd2O3) (Burnup=25 GWd/MTU, as-fabricated radial gap=77μm) ................... 2.36

Figure 2.35 Measured and predicted centerline temperature for IFA-636r4 (UO2-

8%Gd2O3) (Burnup=25 GWd/MTU, as-fabricated radial gap=77μm) ................... 2.36

Figure 2.36 Measured and predicted centerline temperature for IFA-681r1 (UO2) 

(Burnup=12 GWd/MTU, as-fabricated radial gap=85μm) ..................................... 2.37

Figure 2.37 Measured and predicted centerline temperature for IFA-681r2 (UO2

2%Gd2O3) (Burnup=10 GWd/MTU, as-fabricated radial gap=85μm) ................... 2.37

Figure 2.38 Measured and predicted centerline temperature for IFA-681r3 (UO2

8%Gd2O3) (Burnup=4 GWd/MTU, as-fabricated radial gap=85μm) ..................... 2.38

Figure 2.39 Predicted vs. measured centerline temperature for Halden MOX rods...... 2.39

Figure 2.40 Measured and predicted centerline temperature for IFA-629-1 rod 1 

(starting burnup=27 GWd/MTU, ending burnup=33 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.39

Figure 2.41 Measured and predicted centerline temperature for IFA-629-1 rod 2 

(starting burnup=29 GWd/MTU, ending burnup=40 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.40

Figure 2.42 Measured and predicted centerline temperature for IFA-610.2 (starting 

burnup=55 GWd/MTU, ending burnup=56 GWd/MTU, as-fabricated radial 

gap=84μm) .............................................................................................................. 2.40

Figure 2.43 Measured and predicted centerline temperature for IFA-610.4 (starting 

burnup=56, ending burnup=57 GWd/MTU, as-fabricated radial gap=84μm) ........ 2.41

Figure 2.44 Measured and predicted centerline temperature for IFA-648.1 rod 1 

(starting burnup=55 GWd/MTU, ending burnup=62 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.41

Figure 2.45 Measured and predicted centerline temperature for IFA-648.1 rod 2 

(starting burnup=55 GWd/MTU, ending burnup=62 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.42

Figure 2.46 Measured and predicted centerline temperature for IFA-629.3 rod 5 

(starting burnup=62 GWd/MTU, ending burnup=72 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.42

Figure 2.47 Measured and predicted centerline temperature for IFA-629.3 rod 6 

(starting burnup=62 GWd/MTU, ending burnup=68 GWd/MTU, as-fabricated 

radial gap=84μm) .................................................................................................... 2.43

Figure 2.48 Measured and predicted centerline temperature for IFA-606 Phase 2 

(starting burnup=50 GWd/MTU, as-fabricated radial gap=94μm) ......................... 2.43

Figure 2.49 Measured vs. predicted FGR for steady-state UO2 rods............................. 2.45

Figure 2.50 Measured vs. predicted FGR for power ramped UO2 rods......................... 2.46

Figure 2.51 Predicted minus measured FGR as a function of burnup for steady-state 

UO2 rods.................................................................................................................. 2.46

Figure 2.52 Predicted minus measured FGR as a function of burnup for power 

ramped UO2 rods (Rods with hold time less than 4 hours marked) ........................ 2.47

Figure 2.53 Measured vs. predicted FGR for steady-state and power ramped MOX 

rods .................................................................................................................... 2.48

Figure 2.54 Predicted minus measured FGR as a function of burnup for steady-state 

and power ramped MOX rods ................................................................................. 2.48
xii 

Figure 2.55 PWR Zircaloy-4 corrosion data and FRAPCON-3.3 PWR corrosion 

model (Smith et al., 1994, Pyecha, 1985, Newman, 1986, Balfour, 1982b, Dideon, 

1983, Garde, 1986).................................................................................................. 2.50

Figure 2.56 BWR Zircaloy-2 corrosion data and FRAPCON-3.3 BWR corrosion 

model (West et al., 1983, Barner et al., 1990)......................................................... 2.50

Figure 2.57 Zircaloy-2 BWR Corrosion Data for the Newer Cladding Types with 

Controlled SPP’s and composition (Yasuyuki et al., 2007, Sell et al., 2006, 

Hirano et al., 2005, Mutyala, 2004)......................................................................... 2.51

Figure 2.58 ZIRLOTM data and FRAPCON-3.3 predictions as a function of fuel duty 

index (FDI) (Knott et al., 2003) .............................................................................. 2.52

Figure 2.59 M5TM data and FRAPCON-3.3 predictions as a function of burnup 

(Mardon and Waeckel, 2003).................................................................................. 2.52

Figure 2.60 End of life oxide thickness and FRAPCON-3 predictions for Vandellos II 

rod A06, clad in ZIRLOTM and irradiated to 68 GWd/MTU (CSN, ENUSA, 

2002). .................................................................................................................... 2.53

Figure 2.61 End of life oxide thickness and FRAPCON-3 predictions for Vandellos II 

rod A12, clad in ZIRLOTM and irradiated to 68 GWd/MTU(CSN, ENUSA, 2002).

 .................................................................................................................... 2.53

Figure 2.62 End of life oxide thickness and FRAPCON-3 predictions for Gravelines 

5 rod N05, clad in M5TM and irradiated to 70 GWd/MTU (Segura et al., 2002). ... 2.54

Figure 2.63 Measured and predicted hydrogen pickup for PWR rods with Zircaloy-4 

cladding (Smith et al., 1994, Pyecha, 1985, Newman, 1986, Balfour, 1982b, 

Dideon, 1983, Garde, 1986) .................................................................................... 2.55

Figure 2.64 Measured and predicted hydrogen pickup for BWR rods with Zircaloy-2 

cladding (Itagaki, 2003.) ......................................................................................... 2.56

Figure 2.65 Measured and predicted hydrogen pickup from recent literature search 

for BWR rods with Zircaloy-2 cladding (Hayashi et al., 2003, Sell et al., 2006, 

Hirano et al., 2005, Ledberger et al., 2005)............................................................. 2.56

Figure 2.66 Measured and predicted hydrogen pickup for PWR rods with ZIRLOTM 

(Tsukuda et al., 2003, Kitaguawa et al., 2005)........................................................ 2.57

Figure 2.67 Measured and predicted hydrogen pickup for PWR rods with M5TM 

(Mardon and Waeckel, 2003).................................................................................. 2.57

Figure 2.68 FRAPCON-3.3 swelling model prediction and data as a function of 

burnup .................................................................................................................... 2.58

Figure 2.69 FRAPCON-3.3 swelling rate and observed swelling rates from Halden 

instrumented fuel assemblies (EOL burnups shown for each point)....................... 2.59

Figure 2.70 Comparison of FUDENS fuel densification predictions to the 

experimental data from which the fit coefficients were determined and to more 

recent published data............................................................................................... 2.60

Figure 2.71 Predicted and measured cladding creepdown from the 2nd and 3rd cycle 

rods in the ANO-2 PWR assembly, TSQ002. ......................................................... 2.62

Figure 2.72 Predicted and measured cladding creepdown from the 3rd, 4th, and 5th

cycle rods in the Oconee PWR assembly, 15309. ................................................... 2.62

Figure 2.73 Predicted vs. measured yield stress from irradiated and unirradiated 

Zircaloy-2 and Zircaloy-4 ....................................................................................... 2.64

Figure 2.74 Measured and predicted yield stress for high burnup cladding from the 

PROMETRA database. ........................................................................................... 2.64

Figure 2.75 Measured vs. predicted Young’s modulus for model development data 

and recent data......................................................................................................... 2.65

Figure 2.76 Predicted and measured permanent hoop strain from Cabri and NSRR 

RIA tests.................................................................................................................. 2.66
xiii 

Figure 2.77 Predicted and measured permanent axial strain from Cabri and NSRR 

RIA tests.................................................................................................................. 2.67

Figure 2.78 FRAPCON-3.3 model for axial growth in PWR cladding compared to 

data used for model development and recent data................................................... 2.68

Figure 2.79 FRAPCON-3.3 model for axial growth in BWR cladding compared to 

data used for model development and recent data................................................... 2.69

Figure 3.1 Comparison of recent Zircaloy-2 hydrogen pickup data to new correlations 

for old and new Zircaloy-2 cladding ......................................................................... 3.2

Figure 3.2 ZIRLOTM data vs. burnup and (a) FRAPCON-3.3 and (b) FRAPCON-3.4 

model predictions for several sample PWR rods ...................................................... 3.3

Figure 3.3. Old and New ZIRLOTM model predictions for end of life oxide thickness 

for rod A06 ................................................................................................................ 3.4

Figure 3.4 Old and New ZIRLOTM model predictions for end of life oxide thickness 

for rod A12 ................................................................................................................ 3.5

Figure 3.5 M5TM data vs. burnup and (a) FRAPCON-3.3 and (b) FRAPCON-3.4 

model predictions for several sample PWR rods ...................................................... 3.6

Figure 3.6 Old and New M5TM model predictions for end of life oxide thickness for 

rod N05...................................................................................................................... 3.7

Figure 3.7 Hydrogen concentration data for M5TM and FRAPCON-3.4 predictions of 

hydrogen for typical PWR cases ............................................................................... 3.8

Figure 3.8 Burnup distribution in rod section F9-3-44 with U-235 enrichment of 5%, 

irradiated to 39 GWd/MTU in the Halden reactor .................................................... 3.9

Figure 3.9 Burnup distribution in rod section AF21-2-8 with U-235 enrichment of 

1.5%, irradiated to 72.2 GWd/MTU in the DR3 reactor ........................................... 3.9

Figure 3.10 Radial power profile in IFA-558 as predicted by FTEMP and TUBRNP 

with U-235 enrichment of 7%, irradiated in the Halden reactor ............................. 3.10

Figure 3.11 Centerline temperature measurements and predictions for IFA-636 Rod 2 

with hollow pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses the 

new table of radial power profiles........................................................................... 3.12

Figure 3.12 Centerline temperature measurements and predictions for IFA-636 Rod 4 

with solid pellets and 8 wt% Gd2O3 (Solid pellet temperatures are estimated from 

measurements made on hollow pellets in IFA-636 Rod 2.) The FRAPCON-3.3 

prediction uses the Halden table of radial power profiles. The FRAPCON-3.4 

prediction uses the new table of radial power profiles ............................................ 3.12

Figure 3.13 Centerline temperature measurements and predictions for IFA-681 Rod 2 

with solid pellets and 2 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses the 

new table of radial power profiles........................................................................... 3.13

Figure 3.14 Centerline temperature measurements and predictions for IFA-681 Rod 3 

with solid pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses the 

new table of radial power profiles........................................................................... 3.13

Figure 3.15 Centerline temperature measurements and predictions for IFA-681 Rod 4 

with hollow pellets and 2 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses the 

new table of radial power profiles........................................................................... 3.14

Figure 3.16 Centerline temperature measurements and predictions for IFA-681 Rod 6 

with hollow pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses the 

new table of radial power profiles........................................................................... 3.14
xiv 

Figure 3.17 Original and modified UO2 thermal expansion model with available data 

as a function of temperature. ................................................................................... 3.16

Figure 3.18 Original and modified model for He thermal conductivity (σ=0.00899)... 3.17

Figure 3.19 Original and modified model for Ar thermal conductivity (σ=0.000966) . 3.18

Figure 3.20 Original and modified model for Kr thermal conductivity (σ=0.000886) . 3.18

Figure 3.21 Original and modified model for Xe thermal conductivity (σ=0.000534). 3.19

Figure 3.22 Original and modified model for H2 thermal conductivity (σ=0.0167) ..... 3.19

Figure 3.23 Original and modified model for N2 thermal conductivity (σ=0.000197) . 3.20

Figure 3.24 Comparison of low temperature steam conductivity models from 

MATPRO, FRAPTRAN-1.3, and FRAPCON-3.3 with adopted values of 

experimental data from ASME................................................................................ 3.21

Figure 3.25 Predicted and measured cladding creepdown using the original and new 

creep models from the 2nd and 3rd cycle rods in the AN0-2 PWR assembly, 

TSQ002 ................................................................................................................... 3.24

Figure 3.26 Predicted and measured cladding creepdown using the original and new 

creep models from the 3rd, 4th, and 5th cycle rods in the Oconee PWR assembly, 

15309 .................................................................................................................... 3.25

Figure 3.27 Predicted vs. measured cladding creepdown using the new creep model 

from creepdown data from irradiated SRA tubes.................................................... 3.26

Figure 3.28 Predicted vs. measured cladding creepdown using the new creep model 

from creepdown data from irradiated RXA tubes ................................................... 3.26

Figure 4.1 Power histories for PWR and BWR base cases without AOO ......................... 4.4

Figure 4.2 Predicted and measured thermal conductivity data with ±0.5 W/m-K as 

upper and lower bounds .......................................................................................... 4.23

Figure 4.3 UO2 thermal conductivity model and available data with ±15% as upper and 

lower bounds ........................................................................................................... 4.24

Figure 4.4 ZrO2 thermal conductivity model and available data with ±0.5 W/m-K as 

upper and lower bounds .......................................................................................... 4.26

Figure 4.5 Zircaloy thermal conductivity model and available data with +5/-3 W/m-K 

as upper and lower bounds ...................................................................................... 4.27

Figure 4.6 Helium thermal conductivity model and available data with ±5% as upper 

and lower bounds..................................................................................................... 4.28

Figure 4.7 Nominal predicted vs. measured fission gas release....................................... 4.29

Figure 4.8 Predicted vs. measured fission gas release for upper bound model 

with D*2.................................................................................................................. 4.30

Figure 4.9 Predicted vs. measured fission gas release for lower bound model 

with D/2................................................................................................................... 4.30

Figure 4.10 Nominal predicted vs. measured oxide thickness....................................... 4.31

Figure 4.11 Predicted vs. measured oxide thickness for upper bound model with 

+40% .................................................................................................................... 4.32

Figure 4.12 Predicted vs. measured oxide thickness for lower bound model with 

-40% .................................................................................................................... 4.32

Figure 4.13 Fuel swelling model and available data with ±0.3% ΔV/V per 10 

GWd/MTU as upper and lower bounds on the swelling rate .................................. 4.34

Figure 4.14 Cladding creep model and available data with +10%/-40% upper and 

lower bound on creep rate. ...................................................................................... 4.35

Figure 4.15 Nominal predicted vs. measured yield stress ............................................. 4.36

Figure 4.16 Predicted vs. measured yield stress for upper bound model with K*1.3.... 4.37

Figure 4.17 Predicted vs. measured yield stress for lower bound model with K/1.3 .... 4.37
xv 

Figure 4.18 Predicted and measured cladding Young’s Modulus data with +5/-10 

GPa as upper and lower bounds .............................................................................. 4.38

Figure 4.19 Cladding axial growth model for PWR cladding with ±50% as upper and 

lower bounds ........................................................................................................... 4.39

Figure 4.20 Cladding axial growth model for BWR cladding with ±50% as upper and 

lower bounds ........................................................................................................... 4.40

Figure 4.21 Cladding diametral thermal expansion model with ±30% as upper and 

lower bounds ........................................................................................................... 4.41

Figure 4.22 Cladding axial thermal expansion model with +30%/-10% as upper and 

lower bounds ........................................................................................................... 4.41
xvi 

LIST OF TABLES 

Table 2.1 Properties and models without time dependence...................................................2.70

Table 2.2 Properties and models with time dependence that can change over short time 

intervals (e.g. < 10 minutes) and should be modeled in FRAPTRAN ................2.70

Table 2.3 Properties and models with time dependence much greater than the time 

period modeled in FRAPTRAN ...........................................................................2.71

Table 3.1 Original A and B coefficients used in FRAPCON-3.3 and FRAPTRAN 1.3 .......3.16

Table 3.2 Modified A and B coefficients ..............................................................................3.17

Table 3.3 Parameters for FRAPCON-3.4 creep equation for SRA and RXA cladding.........3.23

Table 4.1 Typical fuel design parameters used for base case code input (NUREG-1754)......4.3

Table 4.2 Axial power profile used for PWR and BWR base case input ................................4.5

Table 4.3 Comparison between unbiased output and output biased by manufacturing 

uncertainty for a 17x17 PWR .................................................................................4.6 

Table 4.4 Comparison between unbiased output and output biased by manufacturing 

uncertainty for a 10x10 BWR·················································································4.8 

Table 4.5 Comparison between unbiased output and output biased by model 

uncertainties for a 17x17 PWR·············································································4.17 

Table 4.6 Comparison between unbiased output and output biased by model 

uncertainties for a 10x10 BWR ············································································4.20 

Table 4.7 Comparison between unbiased output and output biased by power 

uncertainties for a 17x17 PWR·············································································4.43 

Table 4.8 Comparison between unbiased output and output biased by power 

uncertainties for a 10x10 BWR ············································································4.44 

 
xvii 

EXECUTIVE SUMMARY 

FRAPCON-3 (Lanning et al., 1997a, Lanning et al, 1997b, Berna et al., 1997, Lanning et 

al., 2005a) is the steady state fuel performance code maintained by Pacific Northwest 

National Laboratory (PNNL) for the United States Nuclear Regulatory Commission 

(USNRC). FRAPCON-3 predicts fuel rod performance in pressurized water reactors 

(PWRs) and boiling water reactors (BWRs) by modeling the material responses of both the 

fuel and the cladding under normal operating conditions and anticipated operational 

occurrences (AOOs) with a duration of several minutes or greater. FRAPTRAN 

(Cunningham et al., 2001a, Cunningham et al., 2001b) is the corresponding transient fuel 

performance code maintained by PNNL for the USNRC. FRAPTRAN predicts fuel rod 

performance in PWRs and BWRs by modeling the material responses of both the fuel and 

the cladding under fast transient and accident conditions. 

Material properties modeled by FRAPCON-3 and FRAPTRAN include fuel thermal 

conductivity, fuel thermal expansion, cladding oxide thermal conductivity, cladding 

thermal conductivity, gas conductance, fission gas release, cladding corrosion, fuel 

swelling, creep of irradiated cladding, cladding yield strength, Young’s modulus of 

cladding, cladding axial irradiation growth, and cladding thermal expansion. By modeling 

material properties, important fuel rod performance parameters, such as rod internal gas 

pressure, peak fuel centerline temperature, and cladding permanent (i.e. plastic) hoop strain, 

can be predicted up to high burnup levels (65 GWd/MTU). 

It has been noted that the original fuel performance codes used by the USNRC, the 

predecessors of FRAPCON-3 and FRAPTRAN were intrinsically conservative. In fact, the 

current version of FRAPCON-3 continues to provide conservative options (although these 

options are no longer used or recommended by PNNL). Despite efforts to update the codes 

and the models over the past 15 years, the codes are still considered by some to be not just 

optionally but intrinsically conservative. In order to quantitatively determine if these codes 

are biased, the latest versions of FRAPCON-3 and FRAPTRAN were examined to 

determine if the individual material property models or code outputs are biased relative to 

the available data. 

Each material property model was examined and compared to the data that was used to 

develop the model. In addition, a brief literature search was performed to determine if 

more recent data has become available, since the original model development, to further 

validate each model. If new data were discovered, these data were compared to the models 

in FRAPCON-3.3 and FRAPTRAN 1.3 in order to determine if the model is biased relative 

to the data. In addition to examining each model individually, code predictions that are a 

combination of multiple model predictions such as fuel centerline temperature, and fission 

gas release were compared to data from rods where these parameters were measured to 

determine if these integral effect predictions are biased. Although several individual 

models were found to be biased, the overall integral predictions of FRAPCON-3.3 and 

FRAPTRAN 1.3 compare well with integral effects data. 

For models or integral effect predictions that was found to be biased relative to the data, a 

new correlation was developed that provides a best-estimate fit to the available data. New 

correlations have been developed for cladding corrosion and hydrogen pickup, radial power 

profile for heavy water reactor conditions, radial power profile for UO2-Gd2O3 fuel, fuel 

thermal expansion at high temperature, gas thermal conductivity at high temperature, and 
xviii 

cladding creep. These new correlations are discussed in this report and will be included in 

the upcoming versions of the codes, FRAPCON-3.4 and FRAPTRAN 1.4. Areas where 

modeling may be lacking were noted for further model development. 

Fuel performance codes similar to FRAPCON-3 and FRAPTRAN are developed by the 

fuel vendors and are used to demonstrate safe performance of the fuel rods for each core 

reload analysis. The fuel vendors must demonstrate that uncertainty in model predictions, 

fabrication parameters and power history are accounted for in this analysis. In order to do 

this, fuel vendors have used methodologies where the uncertainty in key critical parameters 

are included and others that have little effect on the outputs of regulatory interest are not 

included. 

In order to determine the effect of each key parameter on the outputs of regulatory interest, 

a sensitivity study was performed using FRAPCON-3 where each fabrication parameter, 

model, and power history parameter was individually biased to a high and low value to 

determine the sensitivity of the uncertainty in these parameters to the outputs of regulatory 

interest. The results of this study are summarized in this document. This report shows the 

sensitivity of selected model uncertainties, manufacturing uncertainties, and power 

uncertainties on the code prediction of rod internal gas pressure, fuel centerline temperature, 

and cladding strain for sample BWR and PWR cases. It should be noted that the sensitivity 

to these parameters could change based on differences in power history or fuel rod design. 

The results from this study can be used to select parameters to vary in an analysis to 

determine upper bound output values from a statistical combination of uncertainties. 
xix 

ABBREVIATIONS 

ASME American Society of Mechanical Engineers 

AOO Anticipated Operational Occurrence 

BOL Beginning of Life 

BWR Boiling Water Reactor 

CE Combustion Engineering 

CHF Critical Heat Flux 

CRUD Chalk River Unknown Deposit (generic term for various residues 

deposited on fuel rod surfaces, originally coined by Atomic Energy 

of Canada, Ltd. (AECL) to describe deposits observed on fuel from 

the test reactor at Chalk River.) 

DNB Departure from Nucleate Boiling 

EBWR Experimental Boiling Water Reactor 

EPMA Electron Probe Micro-Analysis 

FDI Fuel Duty Index 

FGR Fission Gas Release 

HTC Heat Transfer Correlation 

HWR Heavy Water Reactor 

ID Inner Diameter 

INEL Idaho National Engineering Laboratory 

LGHR Linear Heat Generation Rate 

LOCA Loss of Coolant Accident 

MOX Mixed Oxide 

NSRR Nuclear Safety Research Reactor 

OECD Organization for Economic Co-operation and Development 

OD Outer Diameter 

PBF Power Burst Facility 

PCMI Pellet/Cladding Mechanical Interaction 

PIE Post Irradiation Examination 

PNNL Pacific Northwest National Laboratory 

PWR Pressurized Water Reactor 

RIA Reactivity Initiated Accident 

RXA Recrystallized Annealed 

SNF Spent Nuclear Fuel 

SPP Second Phase Precipitates 

SRA Stress Relief Annealed 

TD Theoretical Density 

USNRC United States Nuclear Regulatory Commission 

W Westinghouse 

1.1 

1.0 INTRODUCTION 

FRAPCON-3 (Lanning et al., 1997a, Lanning et al, 1997b, Berna et al., 1997, Lanning et al., 

2005a) is the steady state fuel performance code maintained by Pacific Northwest National 

Laboratory (PNNL) for the United States Nuclear Regulatory Commission (USNRC). 

FRAPCON-3 predicts fuel rod performance in pressurized water reactors (PWRs) and boiling 

water reactors (BWRs) by modeling the material responses of both the fuel and the cladding 

under normal operating conditions and anticipated operational occurrences (AOOs) with a 

duration of several minutes or greater. FRAPTRAN (Cunningham et al., 2001a, Cunningham et 

al., 2001b) is the corresponding transient fuel performance code maintained by PNNL for the 

USNRC. FRAPTRAN predicts fuel rod performance in PWRs and BWRs by modeling the 

material responses of both the fuel and the cladding under fast transient and accident conditions. 

Material properties modeled by FRAPCON-3 and FRAPTRAN include fuel thermal conductivity, 

fuel thermal expansion, cladding oxide thermal conductivity, cladding thermal conductivity, gas 

conductance, fission gas release, cladding corrosion, fuel swelling, creep of irradiated cladding, 

cladding yield strength, Young’s modulus of cladding, cladding axial irradiation growth, and 

cladding thermal expansion. By modeling material properties, important fuel rod performance 

parameters, such as rod internal gas pressure, peak fuel centerline temperature, and cladding 

permanent (i.e. plastic) hoop strain, can be predicted up to high burnup levels (65 GWd/MTU). 

It has been noted that the original fuel performance codes used by the USNRC, the predecessors 

of FRAPCON-3 and FRAPTRAN were intrinsically conservative. In fact, the current version of 

FRAPCON-3 continues to provide conservative options (although these options are no longer 

used or recommended by PNNL). Despite efforts to update the codes and the models over the 

past 15 years, the codes are still considered by some to be not just optionally but intrinsically 

conservative. In order to quantitatively determine if these codes are biased, the latest versions of 

FRAPCON-3 and FRAPTRAN were examined to determine if the individual material property 

models or code outputs are biased relative to the available data. 

This document describes the work that was done to evaluate the USNRC fuel performance codes 

FRAPCON-3.3 (Lanning et al., 1997a, Lanning et al, 1997b, Berna et al., 1997, Lanning et al., 

2005a) and FRAPTRAN 1.3 (Cunningham et al., 2001a, Cunningham et al., 2001b) for any 

predictive bias and to determine the sensitivity of model, manufacturing, and power history 

uncertainties on predictions of fuel centerline temperature, cladding strain, and rod internal 

pressure. The intent of this report is not to ensure the conservatism in predicted fuel behavior. 

The intent is to ensure best-estimate behavior of the codes and to ensure (to the extent possible) 

that unintentional bias has been eliminated. 

Section 2.0 provides the results of the bias study. In this section, each individual material 

property model is compared to the data that was used to develop the model as well as new data 

that has become available since the original model development. In addition, code predictions 

that rely on the integral effects of multiple material property models, such as fission gas release 

and fuel centerline temperature, are compared to data that have been taken from fuel rods where 

these properties were measured. 

For individual material properties or code predictions that were found to be biased or otherwise in 

error, a new correlation was developed to provide a best estimate fit to the data that had been used 

in the original model development and the new data that was available. Section 3.0 describes the 
1.2 

new models that have been developed as a result of this study. For each new model, a detailed 

description is provided as well as a plot showing its comparison to data. Each of these models 

will be included in the upcoming versions of the codes, FRAPCON-3.4 and FRAPTRAN 1.4. 

Areas where modeling may be lacking were noted for further model development. 

Section 4.0 provides the result of the sensitivity study that was performed using FRAPCON-3.3. 

This study documents the effect of uncertainty in various models, manufacturing parameters, and 

power histories on the code predictions of rod internal pressure, centerline temperature, and 

cladding hoop strain. 

Overall conclusions from these studies are given in Section 5.0. References are given in Section 

6.0. 
2.1 

2.0 BIAS ASSESSMENT 

The latest code versions, FRAPCON-3.3 and FRAPTRAN 1.3, were examined to determine if the 

codes are intrinsically conservative. Each model was examined and compared to the data that 

were used to develop the model. In addition, a brief literature search was performed to determine 

if more recent data has become available, after release of the three code versions, to compare to 

each model. If new data were discovered, these data were compared to the models in 

FRAPCON-3.3 and FRAPTRAN-1.3 in order to determine if the model is biased relative to the 

data. This section will not validate the current models, as this work has already been performed 

(Lanning et al, 1997a, Lanning et al, 1997b, Lanning et al, 2005a, Cunningham et al, 2001b). 

Rather this section will just examine the models and integral effect predictions to determine if 

they are biased relative to the data. 

Most of the material properties used in these come from the library of nuclear material properties 

found in MATPRO (Hagrman et al., 1981). Some of these properties have been updated in 

FRAPCON-3.3 and FRATPRAN 1.3 as a result of new data at higher burnup becoming available. 

The result of this study is a list given in section 2.8 of models in FRAPCON-3.3 and FRAPTRAN 

1.3 that are considered to be best-estimate relative to the most up-to-date data and a list of models 

that are biased relative to the data. In addition, the integral effects calculations such as 

temperature and cladding strain are compared to data to determine if these predictions are biased. 

Models or integral effect predictions found to be biased relative to the data will be updated and 

corrected in the upcoming versions of the codes, FRAPCON-3.4 and FRAPTRAN 1.4. Areas 

where modeling may be lacking were noted for further model development. 

2.1 Thermal Modeling and Assessment 

This section describes the thermal modeling in FRAPCON-3.3 and FRAPTRAN-1.3. Section 

2.1.1 describes the code solution method. Sections 2.1.2-2.1.6 describe the property models that 

are used in determining the temperature distribution radially from the cladding outer surface to 

the fuel center. Section 2.1.7 describes the assessment of the code predictions to measured 

temperature data from instrumented fuel rods. 

2.1.1 Code Solution Method, Fuel Rod Heat Transfer Solution Methods and 

Pellet Heat Generation Radial Profile 

The FRAPCON-3.3 and FRAPTRAN-1.3 codes iteratively calculate the interrelated effects of 

fuel and cladding temperature, rod internal gas pressure, fuel and cladding deformation, release of 

fission product gases, fuel swelling and densification, cladding thermal expansion and the 

irradiation-induced growth, cladding corrosion, and CRUD (Chalk River Unknown Deposit) 

deposition as functions of time and fuel rod specific power. The solution methods are described 

in detail in Berna et al. (1997) and Cunningham et al. (2001a). 

For both codes, the models assume a cylindrical fuel pellet located symmetrically within a 

cylindrical fuel rod cladding surrounded by coolant. The local linear heat generation rate is used 

to calculate the coolant bulk temperature. Using this temperature as a boundary condition, 

FRAPCON-3.3 uses a one-dimensional (1-D) steady-state solution method to determine the 

temperature distribution in the cladding, gap, and fuel from the outside in, while FRAPTRAN-1.3 

uses a 1-D transient solution method to determine the temperature distribution in the cladding, 

gap, and fuel from the outside in. 
2.2 

FRAPCON-3.3 uses the TUBRNP subcode (Lassman et al., 1994) to calculate the radial power 

profile as a function of U-235 enrichment and burnup. FRAPCON is also capable of calculating 

radial power profiles for mixed oxide (MOX) fuel as a function of plutonium isotope 

concentration and burnup. FRAPCON-3.3 has the capability of calculating a radial power profile 

for fuel in a heavy water reactor (HWR), but it does not appear to give adequate predictions of 

these radial power profiles. FRAPCON-3.3 does not have the capability to model the radial 

power profile for UO2-Gd2O3 fuel. The capability to model fuel in HWR conditions and to 

model UO2-Gd2O3 will be added to the upcoming version of FRAPCON-3 and is described in 

Section 3. 

Because the radial power profile is burnup dependent, FRAPTRAN-1.3 does not have a radial 

power profile model, but rather has an option for user input of radial power profile or for 

initialization from FRAPCON-3.3. Since FRAPTRAN-1.3 models events that take place over a 

very short period of time (<10 min), there will be minimal burnup accumulation so it is 

acceptable to use the same radial power profile throughout the duration of the event. For an event 

that occurs after some period of irradiation, the base irradiation is modeled in FRAPCON-3, and 

the burnup dependent information including the radial burnup profile is passed to FRAPTRAN 

for the calculation of the fast transient event. It is acknowledged that for a fast transient such as a 

reactivity initiated accident (RIA) the radial power profile in the fuel rod closest to the control rod 

will be somewhat asymmetric. However, in a two-dimensional code (axial and radial) such as 

FRAPTRAN, it is acceptable to use the same radial power profile calculated for steady-state. The 

overall shape will not significantly change during the transient. 

The burnup profiles calculated by TUBRNP are compared to radial burnup measurements made 

by electron probe microanalysis (EPMA) of the non-mobile fission product, Nd, at various 

burnup levels for BWR and PWR rods. These comparisons are reported in Lanning et al. (1997a) 

and can be seen in Figures 2.1 through 2.5. There have been no comparisons made to HWR rods 

such as those from the Halden reactor. 

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1 1.2

Radius, Normalized

Local Burnup, GWd/MTU

TUBRNP EPMA/Nd Data

Figure 2.1 Radial burnup profile for BWR rod A3/6-4 at 55 GWd/MTU 
2.3 

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1 1.2

Radius, Normalized

Local Burnup, GWd/MTU

TUBRNP EPMA/Nd Data

Figure 2.2 Radial burnup profile for BWR rod H8/36-4 at 55 GWd/MTU 

0

20

40

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1 1.2

Radius, Normalized

Local Burnup, GWd/MTU

TUBRNP EPMA/Nd Data

Figure 2.3 Radial burnup profile for PWR rod BK365 at 83 GWd/MTU 
2.4 

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1 1.2

Radius, Normalized

Local Burnup, GWd/MTU

TUBRNP EPMA/Nd Data

Figure 2.4 Radial burnup profile for PWR rod D200 at 25 GWd/MTU 

0

20

40

60

80

100

120

0 0.2 0.4 0.6 0.8 1 1.2

Radius, Normalized

Local Burnup, GWd/MTU

TUBRNP EPMA/Nd Data

Figure 2.5 Radial burnup profile for PWR rod D226 at 45 GWd/MTU 

These comparisons demonstrate that the TUBRNP model in FRAPCON-3.3 predicts the EPMA 

data well. It appears that the TUBRNP model may overpredict the edge burnup. The reason for 

this is because the actual power profile is very edge peaked, but the EPMA data does not always 
2.5 

capture this on the very edge of the pellet. This is demonstrated by examining the data in Figures 

2.1 and 2.2 where for BWR rods with the same burnup, significantly different edge peaking can 

be seen. It can be concluded that the radial power profile model predicts radial power and burnup 

well within the accuracy of the data. 

2.1.2 Fuel Thermal Conductivity 

The FRAPCON-3.3 and FRAPTRAN-1.3 codes have two fuel thermal conductivity models. One 

model is for urania (UO2) and the other model is for mixed-oxide fuel (MOX). In addition, each 

model has the same correction for gadolinia (Gd2O3) additions. Section 2.1.2.1 describes the 

assessment of the UO2 model. Section 2.1.2.2 describes the assessment of the MOX model. 

Section 2.1.2.3 describes the assessment of the correction for Gd2O3 additions. 

2.1.2.1 UO2

The UO2 thermal conductivity model is the same in both FRAPCON-3.3 and FRAPTRAN-1.3. 

This model is described in Lanning et al. (2005a). This model is a function of burnup and 

temperature. Unirradiated (Ronchi, 1999, Lucuta, 1996, Christensen et al., 1964, Godfrey et al., 

1094, Bates, 1970, Gibby, 1971, Weilbacker, 1972, Goldsmith and Douglas, 1973, and Hobson et 

al., 1974) and irradiated (Carrol, 1994, Ronchi, 2004) data was collected to compare to model 

predictions. Figures 2.6 and 2.7 show the predicted minus measured values for thermal 

conductivity for unirradiated and irradiated disks, respectively. It can be seen from these figures 

that the model provides a best-estimate calculation of UO2 thermal conductivity. There is a slight 

code underprediction for thermal conductivity values greater than 5 W/m-K. These values are 

measured at and around room temperature and will not impact fuel temperature calculations at 

normal reactor conditions. The UO2 model is acceptable based on good comparison to thermal 

conductivity data and measured centerline temperatures. 

0

1

2

3

4

5

6

7

8

9

0369

Measured Thermal Conductivity, W/m-K

Predicted Thermal 

Conductivity, W/m-K

Ronchi Lucuta Christensen Godfrey Bates

Gibby Weilbacker Goldsmith Hobson

Figure 2.6 Predicted vs. measured thermal conductivity for unirradiated UO2. 
2.6 

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Measured Thermal Conductivity, W/m-K

Predicted Thermal Conductivity, 

W/m-K

Ronchi Data Carrol Data

Figure 2.7 Predicted vs. measured thermal conductivity for irradiated UO2. 

2.1.2.2 MOX 

The MOX thermal conductivity model in FRAPCON-3.3 is described in Lanning et al (2005a). 

This model is a function of burnup, oxygen to metal ratio and temperature. Lanning et al. (2005a) 

provides no model to data comparisons. A literature search was performed and several sources of 

unirradiated MOX thermal conductivity were found (Duriez, 2000, Philipponneau, 1992). Figure 

2.8 shows the predicted vs. measured values for thermal conductivity for unirradiated disks. It 

can be seen from this figure that the current MOX model provides a best-estimate prediction of 

MOX thermal conductivity. No data was found on irradiated MOX, but the burnup dependence 

in this model is the same as the burnup dependence in the UO2 model and is judged to be 

acceptable based on comparisons to fuel temperatures measured in-reactor as a function of 

burnup. 
2.7 

1

1.5

2

2.5

3

3.5

4

4.5

5

12345

Measured Thermal Conductivity, W/m-K

Predicted Thermal Conductivity, W/m-K

Duriez Data Philipponneau Data

Figure 2.8 Predicted vs. measured thermal conductivity for MOX fuel 

2.1.2.3 UO2-Gd2O3

The Massih adjustment (Massih, 1992) for thermal conductivity of UO2 – Gd2O3 fuel is used in 

FRAPCON-3.3 as described in Lanning et al. (2005a). No adjustment for thermal conductivity of 

UO2 – Gd2O3 fuel is used in FRAPTRAN-1.3, but this will be added in FRAPTRAN-1.4 to be 

consistent with FRAPCON-3.4. There was no assessment of this model adjustment in Lanning 

(2005a), however, recently, a database of gadolinia thermal conductivity measurements has been 

collected on irradiated (Minato, 2001, Amaya, 1997, Newman, 1982, and Hirai, 1991) and 

unirradiated disks (Minato, 2001, Amaya, 2002). Based on good comparisons to these data and 

centerline temperature data from Halden tests on gadolinia rods, it was determined that the 

Massih adjustment is acceptable. Figures 2.9 and 2.10 show the predicted vs. measured values 

for thermal conductivity for unirradiated and irradiated disks, respectively. It should be noted 

that thermal conductivity measurements on irradiated disks are only valid at the irradiation 

temperature (Beyer, 1998) and this is why there is significantly less data for irradiated disks than 

unirradiated disks. The largest overprediction shown in Figure 2.9 is for samples measured at 

room temperature. This overprediction will not affect the in-reactor temperature predictions (For 

temperature greater than 400°C, thermal conductivity is less than 3.5 W/m-K). Comparisons to 

temperature measurements will be shown in Section 2.1.7. 
2.8 

0

1

2

3

4

5

6

7

01234567

Measured Thermal Conductivity, W/m-K

Predicted Thermal Conductivity, W/m-K

Data

Figure 2.9 Predicted vs. measured thermal conductivity for unirradiated UO2 Gd2O3. 

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Measured Thermal Conductivity (W/m-K)

Predicted Thermal Conductivity (W/m-K)

Data

Figure 2.10 Predicted vs. measured thermal conductivity for irradiated UO2 Gd2O3. 
2.9 

2.1.3 Gap Conductance 

The gap conductance model in FRAPCON-3.3 and FRAPTRAN-1.3 is based upon the 

assumption of a symmetric radial gap between the fuel pellet and the cladding, which has finite 

size even when strong pellet-cladding mechanical interaction (“hard contact”) occurs due to 

surface roughness effects. Effects of pellet eccentricity upon effective gap conductance are 

deemed to be overshadowed by the effects of pellet cracking and fragment outward relocation, 

which for any normal irradiation will occur upon the first rise to full power (see Section 2.1.5). 

Hence, three parallel paths of heat conduction are envisioned across the pellet-cladding gap: 

a. Conduction (bulk diffusion) through the gas (modified by thermal accommodation at the 

bounding surfaces, in the Knudsen regime). 

b. Conduction through points of contact (when pellet-cladding contact has occurred). 

c. Radiation heat transfer (for pellet outer surface temperatures during normal operation, 

this is a minor contribution). 

These three paths will be discussed in the sections below. 

2.1.3.1 Conductance through the Gas 

The conductivity of the pure gases and gas mixtures encountered in fuel rods is described in 

Section 2.1.6.5. This includes the mixing rules for calculating mixed-gas conductivity and 

conductivity of fill gas (normally helium) that has become significantly diluted by released 

fission gases. The conductance contribution from this pathway is described by Berna et al. 

(1997). 

 

The physical gap separation is calculated from the as-fabricated input gap size, modified by fuel 

and cladding displacements due to thermal expansion, fuel relocation, fuel densification and 

swelling, and cladding creep. Fuel creep in the FRAPCON-3.3 and FRAPTRAN-1.3 codes is not 

calculated, as it is not a large source of pellet outer surface displacement during normal operation. 

This assumption of a “rigid pellet” is discussed in greater detail in Section 2.5. 

The “temperature jump distance” is an increment added to the physical gap separation to account 

for imperfect thermal accommodation (i.e., energy transfer) of the gas molecules impinging on 

the bounding surfaces of the gap. That is, the gas molecule kinetic energy is incompletely 

transferred to thermal energy in the cladding, and the thermal energy of the atoms on the fuel 

pellet surface is incompletely transferred to the gas molecules in the gap. Both of these 

incomplete energy transfers result in higher fuel temperatures, and they are represented by 

“accommodation coefficients” (with values of <1.0) for both surfaces. The relationship between 

temperature jump distance and accommodation coefficient is described by Berna et al. (1997). 

The development of this model, and its selection from among other possibilities, is explained in 

(Lanning, 1975). Both ex-reactor gap conductance experiments at PNNL (Garnier and Begej, 

1979a, Garnier and Begej, 1979b) and in-reactor experiments at Halden Reactor Project in 

Norway (Miller, 1980) have confirmed the magnitude of the jump distance that is calculated by 

FRAPCON-3.3. 

It should be noted that, for modern PWR and even BWR fuel rods, the pressurization of the 

helium fill gas leads to in-reactor rod internal pressures that make absolute values of temperature 

jump distance very insignificant relative to the total gap size. This is even true when the gap has 
2.10 

closed because the temperature jump distances are still small relative to the combined fuel pellet 

and cladding surface roughnesses. 

It should further be noted that, when pellet-cladding contact first occurs, the gap size reduces to 

the sum of the roughness values. However, as hard contact occurs, this gap size is further 

reduced slightly as a function of the interface pressure. This is explained in (Lanning et al., 

1997a). 

2.1.3.2 Conductance through points of cladding-pellet contact 

When the net fuel pellet and cladding deformations result in pellet-cladding contact and 

mechanical interaction, direct solid-to-solid heat transfer will occur across the roughness asperity 

points where, on a microscopic level, contact is actually occurring. Initially, the contact pressure 

is very small, because the cracked and relocated pellet fragments will be partially pushed back 

into place by the ongoing differential displacements of fuel and cladding (so-called “soft 

contact”). In FRAPCON-3.3, this period of soft contact is assigned zero interfacial pressure, and 

hence no credit is taken for solid-solid contact conductance. When 50% of the fuel pellet 

outward relocation is consumed by differential deformations, the mechanical model is permitted 

to calculate interfacial pressure from the increasing differential displacements, and the solid-solid 

contact conductance is calculated as a function of interface pressure and cladding and fuel 

conditions. This model is described by Berna et al. (1997). 

In FRAPTRAN-1.3 as opposed to FRAPCON-3.3, the relocation is not allowed to recover due to 

the rapid nature of transients and the pellet-cladding contact conduction described above is used 

immediately upon gap closure. 

2.1.3.3 Radiation heat transfer 

Due to the high axial aspect ratio for the fuel-to-cladding gap, the radiation heat transfer from the 

fuel pellet surface to the cladding is calculated assuming the fuel and cladding are infinite 

concentric cylinders, gray body derived by Kreith (1964). This model is described by Berna et al. 

(1997). 

This model appears to provide an adequate approximation of the radiation heat transfer between 

the two bodies. Typically, this pathway constitutes a very small fraction of the total conductance. 

2.1.4 Fuel Thermal Expansion 

The fuel thermal expansion model in both FRAPCON-3.3 and FRAPTRAN-1.3 is the FTHEXP 

model documented in MATPRO 11, Rev. 2 (Hagrman et al. 1981). The actual coding in terms of 

comments and formatting varies somewhat, however the effective coding is the same. 

The model is based on both measurements of the lattice constant by x-ray diffraction, which were 

applied for model development at temperatures below 800K only, and data from bulk thermal 

expansion measurements. The same model form is used for both UO2 and PuO2 fuels, with the 

constants changed depending on the fuel type. Fuel thermal expansion for mixed oxide is 

determined based on weight fraction. 

The model in FRAPCON-3.3 and FRAPTRAN-1.3 was compared to data provided in the original 

MATPRO reference (Grønvold, 1955, Baldock et al., 1966, Christensen, 1963, Kempter and 

Elliott, 1959, Burdick and Parker, 1956, and Tokar and Nutt, 1972). In, addition, a literature 

search was performed to find any further thermal expansion data since the publication of the 

MATPRO model. This search yielded a review of thermal expansion data by Martin (1988) and 
2.11 

Momin et al (1991) and a model that fits the data well. In addition, two other sources (Fink, 

2000b and Carbajo, 2001) recommend the Martin model. The data used in the development of 

the MATPRO model and the Martin model are shown in Figure 2.11. It can be seen from this 

figure that the MATPRO model and the Martin model are highly similar up to 2200K. Beyond 

this, the MATRPO model provides lower thermal expansion than the Martin model. 

Based on the latest thermal expansion data, the thermal expansion model in FRAPCON-3.3 and 

FRAPTRAN-1.3 may underpredict fuel thermal expansion above 2200K. The magnitude of 

under prediction could be as high as 10% by 3000K. 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Expansion, 

ΔL/L

MATPRO Gronvold Baldock

Burdick Other MATPRO References Martin References

Martin Equation

Figure 2.11 Thermal expansion data and model predictions for UO2

The impact of underpredicting the fuel thermal expansion for temperatures greater than 2200K is 

as follows. 

• less radial/axial thermal expansion for temperatures greater than 2200K 

• less gap closure at higher temperature 

• less cladding strain at higher temperature 

• less increase in gas pressure at higher temperature 

Based on these data comparisons it is concluded that the fuel thermal expansion model in 

FRAPCON-3.3 and FRAPTRAN-1.3 provides a best estimate prediction for fuel thermal 

expansion up to 2200K. Beyond this temperature, the model may underpredict fuel thermal 

expansion. This model will be updated in both FRAPCON-3.4 and FRAPTRAN 1.4 as described 

in Section 3.4. 

2.1.5 Fuel Relocation 

When fresh fuel rods first rise to operating power level, the pellets begin to crack radially, due to 

the thermal hoop stresses generated by the temperature gradient from center to surface and the 
2.12 

differential thermal expansion of central region material compared to peripheral region material. 

A full diametral crack has been observed to develop at linear heat generation rates (LHGRs) as 

low as 3 kW/ft (Lanning and Cunningham, 1981). Higher LHGR levels typically experienced at 

beginning of cycle result in multiple radial cracks. The resulting roughly pie-shaped pellet 

fragments quickly relocate outwards toward the cladding, due to thermal ratcheting (increasing 

and decreasing temperature rearranging pellet fragments). This results in significant gap closure 

and reduction in the effective thermal gap, and hence increase in the gap conductance. 

A best-estimate pellet relocation model was developed for GAPCON-THERMAL-2 Rev. 2 

(GT2R2) (Beyer and Cunningham, 1984) and was recommended for use in FRAPCON-3 in 

conjunction with the FRACAS-1 mechanical model. This GT2R2 model is a function of LHGR 

and burnup. The gap closure due to relocation as a fraction of the as-fabricated pellet-cladding 

gap is given for FRAPCON-3.3 by Lanning et al. (1997a). 

This relocation model is not applied in FRAPTRAN-1.3 because relocation has a small burnup 

dependence and there is no significant burnup accumulation over the time periods of the events 

that are modeled in FRAPTRAN-1.3. However, FRAPTRAN-1.3 does assume some initial 

relocation prior to the start of a transient based on the FRAPCON-3.3 model (Cunningham et al., 

2001a). For fresh fuel, the relocation is assumed to be 30% of the gap size. For irradiated fuel, 

the relocation is assumed to be 45% of the gap size. If FRAPCON-3.3 is used to initialize a 

FRAPTRAN-1.3 evaluation, then the relocation calculated by FRAPCON-3.3 is used. 

The assumption is made in FRAPCON-3.3 that 50% of the relocation displacement must be 

consumed by differential pellet-cladding displacements, before “hard” contact (pellet-cladding 

mechanical interaction) occurs. This is derived from beginning-of-life (BOL) measurements of 

the onset of cladding axial elongation, and from Halden squeeze tests that show approximately 

half the assigned relocation must be taken up before fuel pellet compliance changes back towards 

that of a solid pellet. In FRAPTRAN-1.3, no recovery of the relocation is allowed due to the 

rapid nature of transients and “hard” contact is assumed to occur as soon as the fuel and cladding 

come into contact. 

Fuel pellet center temperatures measured at BOL in instrumented test rods have repeatedly been 

found to be lower than values predicted assuming that the as-fabricated fuel-cladding gap size is 

reduced solely by differential fuel and cladding thermal expansion (Lanning, 1981; Kjaerheim 

and Rolstad, 1967). It has long been concluded, on the basis of microscopic examination of fuel 

cross sections (Galbraith, 1973, and Dutt, et al., 1974), that fuel pellet cracking promotes an 

outward relocation of the pellet fragments that causes additional gap closure, and hence increases 

the gap conductance and lowers the fuel temperatures. This process begins at beginning-of-life 

(BOL) and quickly reaches equilibrium. Oguma (1983) characterized this approach to 

equilibrium based on his analysis of BOL test fuel rod elongation data from Halden instrumented 

test assemblies. 

In a series of tests in the PBF reactor at Idaho National Engineering Laboratory (INEL) (Garner, 

1978), titled the Gap Conductance (GC) series, GC-1,2, and 3, test rods of varying gap size and 

fill gas compositions were instrumented with both centerline thermocouples and multiple 

coplanar off-center thermocouples, in an attempt to quantify this transfer of thermal resistance 

from gap to fuel. The results indicated a major effect; according to INEL's analysis, the BOL gap 

size is reduced to much less than 50% of its unrelocated value on average. However, this does 

not agree with the extensive Halden data at BOL that suggests that the relocated gap size is 

approximately 50% of the un-relocated value. 
2.13 

“Soft" pellet cladding mechanical interaction (PCMI) occurs when the cracked (and highly 

deformable) pellet interacts mechanically with the cladding, producing fuel-cladding contact and 

limited enhanced axial rod elongation, but not the steep elongation vs. LHGR and bamboo 

ridging associated with "hard" PCMI. A rod displaying soft PCMI in operation also displays 

pellet deformability in rod radial compression tests. The occurrence of "soft" PCMI is consistent 

with the results of several experiments in the Halden Reactor, including NRC-sponsored tests, in 

which fuel temperature and rod elongation were simultaneously measured as a function of burnup 

and LHGR (Williford, 1980). 

Verification of the resulting gap closure functions have been done primarily with instrumented 

fuel tests in which fill gasses have been alternated at constant LHGR between helium and argon, 

and the change in pellet center temperature noted. These are indirect verifications of gap size, but 

they do have the advantage of yielding an “effective thermal gap” under varying conditions of 

LHGR level and burnup, which is the essential parameter that a fuel performance code needs to 

perform fuel temperature calculations. 

Figure 2.12 shows the temperature changes that occurred in a UO2 rod from IFA-633 near BOL 

when the helium fill gas was exchanged for argon fill gas at LHGRs steps up to 17 kW/m (Wright, 

2004). The close agreement between predicted temperature change by FRAPCON-3.3 and that 

measured is qualitative verification that, for this open-gap situation, the thermal gap is closely 

predicted by the current relocation model. 

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25

LHGR, kW/m

Centerline Temperature, °C

Helium Prediction Helium Top TC Helium Bottom TC

Argon Prediction Argon Top TC Argon Bottom TC

Figure 2.12 Predicted and measured fuel centerline temperatures with argon and helium 

fill gases for a IFA-633 UO2 rod (as-fabricated radial gap is 105μm) 

2.1.6 Other Models and Properties 

This section will describe the following models and properties and provide data comparisons for 

each one. 

• Clad-coolant heat transfer 
2.14 

• Oxide thermal conductivity 

• CRUD thermal conductivity 

• Cladding thermal conductivity 

• Gas conductance 

• Cladding thermal expansion 

The following subsections provide an assessment of each of these models 

2.1.6.1 Cladding-Coolant Heat Transfer 

The coolant bulk temperature in FRAPCON-3.3 is calculated for each axial node assuming a 

single, closed coolant channel as described in Berna (1997). The calculation of the fuel rod 

surface temperature is performed assuming forced convection and/or nucleate boiling depending 

on the conditions. The model selection and a description of each model are described in Berna 

(1997). 

In FRAPTRAN-1.3 there are several ways for the user to specify the coolant conditions. The first 

is for the user to specify the coolant temperature, pressure, and surface heat transfer coefficient. 

In this case, the code uses these values to calculate the cladding surface temperature using the 

coolant temperature. The second is for the user to specify the coolant as water and specify the 

enthalpy, pressure, mass flux, and select a heat transfer correlation (HTC) and critical heat flux 

(CHF) correlation. The HTC and CHF correlations have been updated in FRAPTRAN 1.4. User 

guidelines will be provided for selecting the appropriate correlations. Work has been performed 

to assess the correlations and demonstrate that these correlations provide best-estimate 

predictions of cladding surface temperature over a wide range of coolant conditions (Cuta, 2007). 

It is concluded that the clad-coolant heat transfer models in FRAPCON-3.3 are acceptable and 

provide best-estimate values of cladding surface temperature based on good comparisons to fuel 

centerline temperature and general acceptance of the correlations used. The correlations used in 

FRAPTRAN-1.3 were satisfactory 25 years ago, but based on new data and information, they 

needed to be updated. The new correlations have been added to FRAPTRAN-1.4 and provide a 

best-estimate prediction of cladding surface temperature over a wide range of coolant conditions 

but are not documented in this report. 

2.1.6.2 Oxide Thermal Conductivity 

The zirconium oxide (ZrO2) thermal conductivity model used in both FRAPCON-3.3 (Lanning et 

al., 2005a) and FRAPTRAN-1.3 (Cunningham et al., 2001a) is the ZOTCON model documented 

in MATPRO 11, Rev. 2 (Hagrman et al. 1981). 

The model is based on the data of Kingery et al. (1954). Data from Maki (1973) and Lapshov 

and Bashkatov (1973) were reviewed during the development of the ZOTCON model, but not 

used in the model because it was concluded that those data were not applicable. The model is 

stated to be applicable for the temperature range 100-1400 ̊C. 

The MATPRO description provides data source references and a plot of the Kingery et al. data 

compared to the ZOTCON model. This data-model comparison is provided in Figure 2.13. The 

Kingery et al. reference used two sample types for data generation: a bulk ZrO2 that was 100% 

dense and used for the model, and a sample that had approximately 13% porosity, but was not 

used for model development. 
2.15 

A search was performed for ZrO2 thermal conductivity data published since the development of 

the ZOTCON model. The only openly-published source of oxide thermal conductivity versus 

temperature data that was found was Gilchrist (1979). Gilchrist measured the thermal 

conductivity of oxide grown on Zry-2 tubes rather than bulk ZrO2. The oxides were generated 

under different oxidation conditions and to different thicknesses. 

Two room-temperature values of ZrO2 thermal conductivity were found. Accuractus.com 

(Accuractus, 2007) listed the thermal conductivity as 2 W/m-K for bulk Y2O3 stabilized ZrO2. 

Matweb.com (Matweb, 2007) listed the thermal conductivity as 1.675 W/m-K for material that 

was 100% dense. 

A comparison of the MATPRO ZrO2 thermal conductivity model to the Kingery et al. (1954) data 

is presented in Figure 2.13. There is an excellent model-data comparison for the 100% dense 

material. However, the model is approximately 20% high compared to the data from the porous 

ZrO2. This is important because the porous material, with the lower thermal conductivity is 

believed to be more representative of the actual oxide on cladding. 

The ZrO2 data by Gilchrist (1979) are also shown in Figure 2.13. The Gilchrist samples are oxide 

actually grown on Zry-2 tubes and are, therefore, more representative of the oxide observed inreactor. These data are considerably lower than the MATPRO model and the Kingery et al. 

porous data. This figure demonstrates that the model in FRAPCON and FRAPTRAN predicts 

100% dense oxide well, but overpredicts less dense oxide that is seen in-reactor by approximately 

100%. 

The two room-temperature data points are also included in Figure 2.13 (“bulk data” points). 

These two data points are in general agreement with the MATPRO model and the data presented 

by Kingery et al. As with the Kingery et al. data, the oxide source is apparently high-density bulk 

oxide rather than porous oxide. High-density bulk oxide apparently has a higher thermal 

conductivity than porous oxide and does not appear to be an appropriate material for generating 

thermal conductivity data for the purpose of modeling fuel rod thermal performance. 

The impact of overpredicting oxide thermal conductivity (i.e., overpredicting heat flow through 

the oxide) would be: 

• underprediction of the temperature at the oxide-metal interface; 

• underprediction of oxide growth because of underpredicting the oxide-metal interface 

temperature; and 

• underprediction of the bulk cladding temperature, gap gas temperature, and fuel 

temperature. 

It is recommended that the MATPRO ZrO2 thermal conductivity model be further evaluated with 

an expectation of reducing the predicted thermal conductivity. An Organization for Economic 

Cooperation and Development (OECD) document (OECD 1995) from 1995 also concluded that 

“thermal conductivity of oxide needs further clarification.” Based on the Gilchrist data, a simple 

“fix” might be to reduce the predicted oxide thermal conductivity by 50%. Debate on this issue is 

ongoing. The difference in centerline temperature that the cladding thermal conductivity model 

being biased high would have is only about 10°C. 
2.16 

0

0.5

1

1.5

2

2.5

3

0 500 1000 1500 2000

Temperature (K)

Thermal Conductivity (W/m-K)

MATPRO Model Kingery w/porosity Kingery 100% dense

Gilchrist #1 Gilchrist #3 Gilchrist #4

Gilchrist #5 Gilchrist #6 Gilchrist #7

bulk data

Figure 2.13 Comparison of MATPRO ZrO2 model to data used to develop the model and 

newer data 

2.1.6.3 CRUD Thermal Conductivity 

CRUD is commonly defined as the deposition of oxidation products, formed in the primary 

coolant circuit, on the surface of the fuel rods. There are two types of CRUD that accumulate, a 

light fluffy CRUD and a more tenacious CRUD. The light fluffy CRUD is mainly an iron oxide 

(hematite) and is usually not a significant barrier to heat flow. The tenacious CRUD can differ 

depending on if it is in a BWR or a PWR with the former being a zinc-iron oxide with nickel and 

the later consisting of a nickel ferrite oxide, but can also consist of other oxides or compounds. 

The tenacious CRUD deposition is important in fuel rod modeling from the standpoint of 

affecting the zirconium oxide/metal interface temperature, and thus the rate of formation of 

additional zirconium oxide (Cheng et al., 2000). 

The CRUD thermal conductivity model used in FRAPCON-3.3 (Lanning et al., 2005a) is a 

constant value of 0.87 W/m-K (0.5 BTU/hr-ft-F). 

The FRAPCON-3.3 documentation does not state where the CRUD thermal conductivity value 

originates. There is no CRUD thermal conductivity model used in FRAPTRAN-1.3 

(Cunningham et al., 2001a) nor is there a CRUD thermal conductivity model defined in 

MATPRO 11, Rev. 2 (Hagrman et al. 1981). 

A search was performed for published CRUD thermal conductivity data. There was very little 

information found. Leyse (2003) stated a value of 0.8 W/m-K for hydrated alumina in the 

Experimental Boiling Water Reactor (EBWR). This is close to the value used in FRAPCON-3.3. 
2.17 

The effects of an uncertain value for CRUD conductivity are mitigated by the fact that the growth 

of CRUD is reactor specific, and FRAPCON-3.3 does not have a CRUD growth model. Rather 

the user must either input a constant CRUD thickness or a rate of CRUD growth. Currently, no 

data in the open literature exists to verify a value used for the GRUD growth rate. 

2.1.6.4 Cladding Thermal Conductivity 

The cladding thermal conductivity model in both FRAPCON-3.3 (Lanning et al. 2005a) and 

FRAPTRAN-1.3 (Cunningham et al. 2001a) is the CTHCON model documented in MATPRO 

(Hagrman et al. 1981). FRAPTRAN-1.3 includes an optional cladding thermal conductivity 

model appropriate for Zr-1Nb type alloys such as ZIRLO that are not included in FRAPCON-3.3. 

This model was included at the request of the Russian Research Center, Kurchatov Institute (the 

Russion E110 cladding alloy is Zr-1Nb) and has not been validated by PNNL. Therefore it will 

not be included in this assessment. 

The CTHCON model is based on thermal conductivity data for both Zircaloy-2 and Zircaloy-4. 

This model draws no distinction between these two alloys. CTHCON is a function of 

temperature only. No thermal diffusivity data were used to develop the CTHCON model. 

Hagrman et al. (1981) provides data source references, plots of data compared to the model, and 

tables of the thermal conductivity data used to develop the model, including data for Zircaloy-2 

(Anderson et al., 1962, Lucks and Deem, 1958, and Powers, 1961) and Zircaloy-4 (Chirigos et al., 

1961, Feith, 1966, and Scott, 1965). 

A search was performed for Zircaloy thermal conductivity and diffusivity data published since 

the last modification of the CTHCON model in June 1978. Multiple data sources were found 

containing data from both Zircaloy-2 and Zircaloy-4 (Murabayashi et al., 1975, Gilchrist, 1976, 

Peggs et al., 1976, Bunnell et al., 1983, Maglic et al., 1994, Krett and Cleveland, 1997). 

In addition, Fink (2000a) provides a summary of the data used to develop the CTHCON model in 

MATPRO, thermal diffusivity data not used in development of the CTHCON model, thermal 

conductivity data reported in the literature since the CTHCON model was produced, and a new 

second-order polynomial correlation that takes into account some of the newer thermal 

conductivity data. 

Figure 2.14 provides a comparison of the CTHCON model as incorporated in MATPRO, 

FRAPCON-3.3, and FRAPTRAN-1.3 with the data on which it is based, extrapolated to the 

melting point of Zircaloy (2098K). In addition, this figure shows the more recent data and the 

Fink model. The scatter in the data due to differences in alloy, form, or measurement direction is 

comparable to the variation between individual data sets. The scatter in the data is distributed 

relatively uniformly around the curve representing the CTHCON model, except for the Bunnell et 

al. (1983) data above 1300K. However, these data are anomalously lower than all other data 

reported in the literature. It can be seen that below 1600K, the MATPRO model and the Fink 

model are relatively consistent with each other. The largest difference comes above 1600K, 

where the MATPRO model predicts higher conductivity than the Fink model. However, there is 

little data at these temperatures and the MATPRO model predicts the few high temperature data 

points better than the Fink model. 
2.18 

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Recent Data (Bunnell) Fink Model

Figure 2.14 MATPRO model (CTHCON), the data on which it is based, newer data, and 

the Fink Model. 

Based on this comparison, it can be concluded that the model used in FRAPCON-3.3 and 

FRAPTRAN-1.3 for cladding thermal conductivity provides a best-estimate prediction for 

Zircaloy-2 and Zircaloy-4. 

2.1.6.5 Gas Thermal Conductivity 

The gas thermal conductivity models included in the GTHCON subroutines and those for 

FRAPCON-3.3 (Lanning et al. 2005a) and FRAPTRAN-1.3 (Cunningham et al. 2001a) exhibit 

some differences. The thermal conductivity models for the gases helium (He), argon (Ar), 

krypton (Kr), xenon (Xe), hydrogen (H2), and nitrogen (N2) are the same in both codes (with the 

exception of one difference in the fourth significant digit of the “bb” parameter for Xe). The 

individual gas thermal conductivity models and fit coefficients in both codes agree with those 

listed in MATPRO (Hagrman et al. 1981). The methodology for calculating the thermal 

conductivity of gas mixtures is identical in both codes (with the exception of one difference in the 

fourth and fifth significant digits of the “a” parameter for steam (H2O)) and agrees with that 

described in Hagrman et al. The gas thermal conductivity model for steam is different in 

FRAPCON-3.3 and FRAPTRAN-1.3, and neither code agrees with the steam conductivity model 

in Hagrman et al. This discrepancy, and what will be done regarding this will be discussed below. 

The mixing model included in FRAPCON-3.3 is identical to that employeed in FRAPTRAN-1.3. 

This mixing model is identical to the mixing model described by Hagrman et al. (1981). 

The data source references for the gas thermal conductivity models are provided by Hagrman et 

al. (1981) as follows. The He model is based on data from Johnston and Grilly (1946), Kannuluik 

and Carman (1952), von Ubisch (1959), Zaitseva (1959), Cheung et al. (1962), Timrot and 

Totskii (1965), Timrot and Umanskii (1965), Gambhir et al. (1967), and Saxena and Saxena 

(1968a). The Ar model is based on data from Kannuluik and Carman (1952), von Ubisch (1959), 
2.19 

Zaitseva (1959), Cheung et al. (1962), Gambhir et al. (1967), and Brokaw (1969). The Kr model 

is based on data from Kannuluik and Carman (1952), von Ubisch (1959), Zaitseva (1959), and 

Gambhir et al. (1967). The Xe model is based on data from Kannuluik and Carman (1952), 

Zaitseva (1959), and Gambhir et al. (1967). The H2 model is based on data from Johnston and 

Grilly (1946) and Timrot and Umanskii (1966). The N2 model is based on data from Keyes 

(1952), Cheung et al. (1962), and Brokaw (1969). The low temperature steam thermal 

conductivity model is taken from the American Society of Mechanical Engineers (ASME) 

(ASME, 1968), and the high temperature steam conductivity model is taken from Tsederberg 

(1965). The methodology for calculating the thermal conductivity of gas mixtures was taken 

from Brokaw (1969). 

A literature search was performed to obtain more gas thermal conductivity data. The following 

sources of data were found for each type of gas 

• Three new references were selected for comparison with the Hagrman et al. He thermal 

conductivity model over the temperature range 400-2500K. These were Faubert and 

Springer (1973), Jain and Saxena (1975), and Jody et al. (1977). 

• Five new references were selected for comparison with the Hagrman et al. Ar thermal 

conductivity model over the temperature range 350-2500K. These were Timrot and 

Umanskii (1966), Saxena and Saxena (1968b), Faubert and Springer (1972), Springer and 

Wingeier (1973), and Stefanov et al. (1976). 

• Three new references were selected for comparison with the Hagrman et al. Kr thermal 

conductivity model over the temperature range 318-2300K. These were Saxena and 

Saxena (1969), Vargaftik and Yakush (1971), and Stefanov et al. (1976). 

• Three new references were selected for comparison with the Hagrman et al. Xe thermal 

conductivity model over the temperature range 298-2200K. These were Saxena and 

Saxena (1969), Springer and Wingeier (1973), and Stefanov et al. (1976). 

• One new reference was selected for comparison with the Hagrman et al. H2 thermal 

conductivity model over the temperature range 373-1273K. This was Saxena and Saxena 

(1970). 

• Three new references were selected for comparison with the Hagrman et al. N2 thermal 

conductivity model over the temperature range 304-2473K. These were Vargaftik and 

Zimina (1964), Faubert and Springer (1972), and Chen and Saxena (1973). 

Figures 2.15 to 2.20 show the predicted and measured thermal conductivity for He, Ar, Kr, Xe, 

H2, and N2, respectively. Each of these figures show the MATPRO model, the data used in 

developing the MATPRO model, and recent data that has been collected as part of this 

assessment. It can be seen from these figures that the He model fits the data well up to 2500K. 

The Ar, Kr, Xe, and H2 models predict the data well up to 1200K, and overpredict the data at 

higher temperature. The N2 models predict the data well up to 1200K and underpredict the data 

at higher temperature. The poor performance of these rods at high temperature is due to a lack of 

available data when these correlations were developed. This will not affect any of the current 

predictions, because the steady-state gas temperature never gets above the temperature where the 

models deviate from the measurements. This may impact high temperature transient and accident 

analyses. These correlations will be updated to fit recent data in FRAPCON-3.4 and 

FRAPTRAN 1.4. The updates are discussed in Section 3.5. 
2.20 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.15 Thermal conductivity data and model predictions for He 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.16 Thermal conductivity data and model predictions for Ar 
2.21 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.17 Thermal conductivity data and model predictions for Kr 

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.18 Thermal conductivity data and model predictions for Xe 
2.22 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.19 Thermal conductivity data and model predictions for H2

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Figure 2.20 Thermal conductivity data and model predictions for N2

As discussed earlier, there is a difference in the models for steam conductivity between what is in 

MATPRO, FRAPCON-3.3, and FRAPTRAN-1.3. These three models are plotted in Figure 2.21 

for a pressure of 100 MPa. Also shown in this figure is the ASME model that is essentially the 

same as the MATPRO model, and some data. 
2.23 

It can be seen from this figure that the MATPRO and ASME models predict the data well. The 

FRAPCON-3.3 model underpredicts the data by 10-30%, because it is only valid up to 0.1 MPa. 

The FRAPTRAN-1.3 model predicts negative values for the thermal conductivity which indicates 

a coding error in this model. The ASME model will be included in both FRAPCON-3.4 and 

FRAPTRAN-1.4 since it predicts the data best and is valid over the largest pressure range. This 

discrepancy has not affected any of the assessment cases to date since none of them used steam as 

a fill gas. In FRAPTRAN 1.3, the code uses steam in the fuel/cladding gap after the rods bursts, 

but at this point, temperature predictions are not of great concern. 

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

600 650 700 750 800 850 900 950 1000

Temperature, K

Thermal Conductivity, W/m-K

Data ASME (1968) MATPRO FRAPTRAN-1.3 FRAPCON-3.3

Figure 2.21 Thermal conductivity data and model predictions for steam at 100 MPa 

The mixing model in FRAPCON-3.3 and FRAPTRAN-1.3 was used to compare against thermal 

conductivity data taken on various gas mixtures (Ibbs and Hirst, 1929, Mason and von Ubisch, 

1960, and Gray and Wright, 1961). It can be seen from Figure 2.22 that the gas mixing model in 

FRAPCON-3.3 and FRAPTRAN-1.3 predicts these data well. Some biases in the predictions at 

higher temperatures may be due to over- or under-prediction in the individual conductivities of 

the gases at high temperature. 
2.24 

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.02 0.04 0.06 0.08 0.1 0.12

Measured Thermal Conductivity, W/m-K

Predicted Thermal Conductivity,

 W/m-K

MATPRO Measured = Predicted

Figure 2.22 Predicted vs. measured thermal conductivity for various gas mixtures. 

Based on this assessment, it is concluded that the He model for thermal conductivity and the 

mixing model are acceptable. The models for Ar, Kr, Xe, H2, and N2 thermal conductivity will be 

fit to the new high temperature data that had not been available during the original model 

development. However, these changes are not expected to significantly change code predictions 

because the gap temperature is significantly less than 1200K. The models for steam conductivity 

in FRAPCON-3.3 and FRAPTRAN-1.3 will be replaced by the ASME model. 

2.1.6.6 Cladding Thermal Expansion 

The cladding thermal expansion model in both FRAPCON-3.3 (Lanning et al. 2005a) and 

FRAPTRAN 1.3 (Cunningham et al. 2001a) is not the same as that in the CTHEXP model 

documented in MATPRO 11 Rev. 2 (Hagrman et al. 1981). Rather, the fuel codes use a look up 

table that contains thermal expansion in the axial and circumferential directions based on several 

data sources (Kearns 1965, Scott 1965, and Mehan and Wiesinger 1961). 

The model in FRAPCON-3.3 and FRAPTRAN 1.3 was compared to these data and a litereature 

search was performed to determine if any other data are available. The search yielded one new 

data source (Bunnell et al. 1977). The data used in the development of the model in FRAPCON3.3 and FRAPTRAN 1.3 as well as the new data are shown in Figures 2.23 and 2.24 for the axial 

and circumferential directions, respectively. It can be seen that the original data agree well with 

these models in both directions. The new data is slightly greater than the model in the 

circumferential direction, and significantly greater than the model in the axial direction. The 

original data were taken on as received cladding specimens with a room temperature reference. 

The data from Bunnell et al has been adjusted so the strain is zero at 300K, but the actual 

reference temperature for the experiment was not stated. Because of this uncertainty in the new 

data, the original data is assumed to better represent the thermal expansion of Zircaloy. 
2.25 

Based on the original thermal expansion data, the cladding thermal expansion model in 

FRAPCON-3.3 and FRAPTRAN 1.3 provides a best-estimate fit to data up to 1100K. Very little 

data exists above this temperature such that the model cannot be validated above 1100K. 

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

0 200 400 600 800 1000 1200 1400

Temperature, K

Axial Thermal Expansion, in/in

FRAPCON-3 Data used by FRAPCON-3 Bunnell Data

Figure 2.23 Axial thermal expansion model from FRAPCON-3.3 and FRAPTRAN 1.3 

compared to data 

0

0.001

0.002

0.003

0.004

0.005

0.006

0 200 400 600 800 1000 1200 1400

Temperature, K

Circumferential Thermal Expansion, 

in/in

FRAPCON-3 Data used by FRAPCON-3 Bunnell Data

Figure 2.24 Circumferential thermal expansion model from FRAPCON-3.3 and 

FRAPTRAN 1.3 compared to data 
2.26 

2.1.7 Integral Assessment 

Instrument fuel rods irradiated in Halden have been used to assess the predicted temperatures 

from FRAPCON-3.3, by comparing the predictions to measurements taken in-reactor using 

centerline thermocouples, and expansion thermometers. The following sections show the results 

of temperature comparisons for UO2 rods, UO2-Gd2O3 rods and MOX rods. 

In a search of the literature, PNNL has been unable to find any reported tests that have collected 

centerline temperature during fast transients. Therefore, FRAPTRAN-1.3 was not assessed 

relative to its prediction of centerline temperature. However, since it uses the same models as 

FRAPCON-3.3, it is expected to provide centerline temperature predictions that are as accurate as 

those of FRAPCON-3.3. 

2.1.7.1 UO2 Temperature Comparisons 

FRAPCON-3 was initially assessed against BOL temperature measurements taken during the first 

ramp to power and against temperature measurements made throughout the life of the rod. Five 

rods are used to assess the performance of FRAPCON-3 at beginning of life. These rods are IFA432 rod 1, IFA-432 rod 2, IFA-432 rod 3, IFA-513 rod 1, and IFA-513 rod 6. Four additional 

rods, IFA-681r1, IFA-633r1, IFA-633r3, and IFA-633r5 were recently added to the beginning of 

life temperature assessment. The rods, IFA-432 rod 1, IFA-432 rod 2, IFA-432 rod 3, IFA-513 

rod 1, IFA-513 rod 6, and IFA-562 rod 18 were also initially used to assess the performance of 

FRAPCON-3 as a function of burnup with a seventh rod being recently added. The seventh rod is 

IFA-597 rod 8. IFA-432 rod 2 has been removed as an assessment of FRAPCON-3 as a function 

of burnup, as the test is not prototypic of current fuel designs due to its large gap, and a small 

overprediction in fission gas release can result in a large temperature overprediction. 

Figure 2.25 shows the predicted vs. measured temperature for the BOL ramp up to power for the 

five assessment cases. It can be seen from this figure that FRAPCON-3.3 predicts these 

temperatures within ±50K for all these rods except IFA-513r6. This rod is slightly 

underpredicted at high temperatures. However, this prediction is still within the uncertainty of 

the data. A ±50K uncertainty on temperature predictions is reasonable given the uncertainty in 

the thermocouple data and the calculated rod power. 
2.27 

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

Measured Temperature, K

Predicted Temperature, K

IFA-432r1 IFA-432r2 IFA-432r3 IFA-513r1 IFA513r6

IFA-681r1 IFA-633r1 IFA-633r3 IFA-633r5

Figure 2.25 Predicted and measured temperature for BOL ramp to power. 

The following figures show measured and predicted fuel centerline temperatures from rods with 

centerline temperature measurements. Individual rod predictions may demonstrate a systematic 

error (bias) that may be due to thermocouple decalibration or a systematic error in the power 

history provided due to decalibration in the neutron detectors. However, when all the 

comparisons are examined, it is found that there is no overall systematic error (bias) in the 

prediction of UO2 fuel temperature throughout life similar to what was seen in Figure 2.25 for 

UO2 at BOL. 

Figure 2.26 shows the measured and predicted centerline temperature for IFA-432r1. This figure 

contains data from the lower thermocouple. This rod also contained an upper thermocouple, but 

it failed after 150 days. The comparisons to the upper thermocouple data are similar to the lower 

thermocouple. This figure shows excellent agreement between the FRAPCON-3.3 predictions 

and the data. 
2.28 

1000

1100

1200

1300

1400

1500

1600

1700

1800

0 100 200 300 400 500 600 700 800

Time, Days

Centerline Temperature, K

Lower TC Data FRAPCON-3.3

Figure 2.26 Measured and predicted centerline temperature for IFA-432r1 lower 

thermocouple (Burnup=45 GWd/MTU, as-fabricated radial gap=114μm) 

Figure 2.27 shows the measured and predicted centerline temperature for IFA-432r3. This figure 

contains data from the lower thermocouple. This rod also contained an upper thermocouple, but 

it failed after 550 days. The comparisons to the upper thermocouple data are similar to the lower 

thermocouple. This figure shows excellent agreement between the FRAPCON-3.3 predictions 

and the data at beginning of life, and overprediction of about 100K at end of life. This 

overprediction may be due to FRAPCON-3.3 overpredicting the gas release, leading to higher 

predicted temperatures. As noted earlier, overprediction of gas release leads to lower gap 

conductivity and results in higher fuel temperature predictions. 
2.29 

800

900

1000

1100

1200

1300

1400

1500

0 200 400 600 800 1000 1200

Time, Days

Centerline Temperature, K

Lower TC Data FRAPCON-3.3

Figure 2.27 Measured and predicted centerline temperature for IFA-432r3 lower 

thermocouple (Burnup=45 GWd/MTU, as-fabricated radial gap=38μm) 

Figure 2.28 shows the measured and predicted centerline temperature for IFA-513r1. This figure 

contains data from the upper and lower thermocouples. This figure shows reasonable agreement 

between the FRAPCON-3.3 predictions and the data. 
2.30 

500

700

900

1100

1300

1500

1700

1900

2100

0 50 100 150 200

Time, days

Temperature, K

Upper TC Data FRAPCON-3.3 (Upper TC)

 (a) 

500

700

900

1100

1300

1500

1700

0 50 100 150 200

Time, days

Temperature, K

Lower TC Data FRAPCON-3.3 (Lower TC)

(b) 

Figure 2.28 Measured and predicted centerline temperature for IFA-513r1 upper 

thermocouple (a) and lower thermocouple (b) (Burnup=10 GWd/MTU, asfabricated radial gap=108μm) 

Figure 2.29 shows the measured and predicted centerline temperature for IFA-513r6. This figure 

contains data from the upper and lower thermocouples. This figure shows reasonable agreement 

between the FRAPCON-3.3 predictions and the data. 
2.31 

500

700

900

1100

1300

1500

1700

1900

2100

2300

0 50 100 150 200

Time, days

Temperature, K

Upper TC Data FRAPCON-3.3 (Upper TC)

 (a) 

500

700

900

1100

1300

1500

1700

1900

0 50 100 150 200

Time, days

Temperature, K

Lower TC Data FRAPCON-3.3 (Lower TC)

 (b) 

Figure 2.29 Measured and predicted centerline temperature for IFA-513r6 upper 

thermocouple (a) and lower thermocouple (b) (Burnup=10 GWd/MTU, asfabricated radial gap=108μm) 

Figure 2.30 shows the measured and predicted centerline temperature for IFA-562r18. This 

figure contains rod-average data from the expansion thermometer. This figure shows excellent 

agreement between the FRAPCON-3.3 predictions and the data. 
2.32 

700

800

900

1000

1100

1200

1300

1400

0 200 400 600 800 1000

Time, days

Centerline Temperature, K

Rod-Average Data FRAPCON-3.3

Figure 2.30 Measured and predicted rod-average centerline temperature for IFA-562r18 

(Burnup=76 GWd/MTU, as-fabricated radial gap=50μm) 

Figure 2.31 shows the measured and predicted centerline temperature for IFA-597r8. This rod 

was refabricated from a commercial rod that was irradiated to 68 GWd/MTU. This figure 

contains upper thermocouple data. This figure shows reasonable agreement between the 

FRAPCON-3.3 predictions and the data (±75K). 
2.33 

800

900

1000

1100

1200

1300

1400

0 20 40 60 80 100

Time, days

Centerline Temperature, K

Upper TC Data FRAPCON-3.3

Figure 2.31 Measured and predicted centerline temperature for IFA-597r8 (starting 

burnup=68 GWd/MTU, ending burnup=71 GWd/MTU, as-fabricated radial 

gap=105μm). 

This section demonstrates that FRAPCON-3.3 continues to provide a best-estimate prediction of 

centerline temperature for UO2 rods to within ±70K for recent experimental data. 

2.1.7.2 UO2-Gd2O3 Temperature Comparisons 

The adjustment for gadolinia in the thermal conductivity model has recently been assessed 

against centerline temperature predictions from three instrumented fuel assemblies irradiated at 

the Halden Reactor. The results of these comparisons are provided in this section. 

Figures 2.32 and 2.33 show the measured and predicted centerline temperature for IFA-515.10. 

Rods A1 and B1 are UO2 rods and rods A2 and B2 are UO2-Gd2O3 rods with depleted Gd. These 

rods were meant to show the difference only due to the thermal conductivity degradation from 

Gd2O3, not due to the difference in radial power profile. It can be seen from these figures that 

FRAPCON-3.3 predicts the centerline temperatures for UO2-Gd2O3 rods as well as for UO2 rods. 

In these figures the vertical line denotes where the thermocouple failed. Although data was 

reported after this point, it is not valid. 
2.34 

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Burnup, GWd/MTU

Temperature, °C

A1 Data FRAPCON-3.3 TC failed

(a)

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Burnup, GWd/MTU

Temperature, °C

A2 Data FRAPCON-3.3 TC Failed

(b) 

Figure 2.32 Measured and predicted centerline temperature for IFA-515.10 rod A1 (UO2) 

(a), and for IFA-515.10 rod A2 (UO2-8%Gd2O3) (b) (Burnup=80 GWd/MTU, 

as-fabricated radial gap=25μm) 
2.35 

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Burnup, GWd/MTU

Temperature, °C

B1 Data FRAPCON-3.3

(a) 

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Burnup, GWd/MTU

Temperature, °C

B2 Data FRAPCON-3.3 TC Failed

(b) 

Figure 2.33 Measured and predicted centerline temperature for IFA-515.10 rod B1 (UO2) 

(a), and for IFA-515.10 rod B2 (UO2-8%Gd2O3) (b) (Burnup=80 GWd/MTU, 

as-fabricated radial gap=25μm) 

Figures 2.34 and 2.35 show the measured and predicted centerline temperature for IFA-636 rod 2 

and rod 4. These rods contain standard Gd. Because of this, it was necessary to modify 

FRAPCON-3 to use the radial power profiles provided by Halden for these rods. Rod 2 was 

equipped with a centerline thermocouple and the data from this thermocouple is shown in Figure 

2.32. Rod 4 contains solid pellets, and the data shown in Figure 2.34 is estimated from Rod 2. 

Because of this, there is more uncertainty in the data from rod 4. In addition, during the first rise 

to power, as the Gd is burning out, there is a high level of uncertainty on the rod power. Because 

of this, FRAPCON-3.3 may not predict the centerline temperature well during this period. These 
2.36 

figures show excellent agreement between the FRAPCON-3.3 predictions and the data for rod 2 

and reasonable agreement for rod 4 that has greater uncertainty. 

0

200

400

600

800

1000

1200

0 200 400 600 800

Time, Days

Temperature, °C

636 Rod 2 Data FRAPCON-3.3

Figure 2.34 Measured and predicted centerline temperature for IFA-636r2 (UO2-

8%Gd2O3) (Burnup=25 GWd/MTU, as-fabricated radial gap=77μm) 

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

Rod Average Burnup, GWd/MTU

Temperature, °C

636 Rod 4 Data FRAPCON-3.3

Figure 2.35 Measured and predicted centerline temperature for IFA-636r4 (UO2-

8%Gd2O3) (Burnup=25 GWd/MTU, as-fabricated radial gap=77μm) 

Figures 2.36 through 2.38 show the measured and predicted centerline temperature for IFA-681 

rod 1, rod 2 and rod 3. Rods 4-6 are not shown here, because there are still some issues in regards 

to calibrating the data from these rods. Rod 1 is a UO2 rod. Rods 2 and 3 contain standard Gd 

with 2 wt% and 8 wt% Gd2O3. Because of this, it was necessary to use the modified FRAPCON3 discussed above to use the radial power profiles provided by Halden for these rods. During the 
2.37 

first rise to power, as the Gd is burning out, there is a high level of uncertainty on the rod power. 

Because of this, FRAPCON-3.3 may not predict the centerline temperature well during this 

period. These figures show excellent agreement between the FRAPCON-3.3 predictions and the 

data for all three rods, particularly after the Gd has burned out (~100 days for Figure 2.37, >175 

days for Figure 2.38) and there is less uncertainty in the rod power. 

0

200

400

600

800

1000

1200

1400

0 50 100 150

Time Days

Temperature, °C

Rod 1 Data FRAPCON-3.3

Figure 2.36 Measured and predicted centerline temperature for IFA-681r1 (UO2) 

(Burnup=12 GWd/MTU, as-fabricated radial gap=85μm) 

0

200

400

600

800

1000

1200

1400

0 50 100 150

Time Days

Temperature, °C

Rod 2 Data FRAPCON-3.3

Figure 2.37 Measured and predicted centerline temperature for IFA-681r2 (UO2

2%Gd2O3) (Burnup=10 GWd/MTU, as-fabricated radial gap=85μm) 
2.38 

0

200

400

600

800

1000

1200

0 50 100 150

Time Days

Temperature, °C

Rod 3 Data FRAPCON-3.3

Figure 2.38 Measured and predicted centerline temperature for IFA-681r3 (UO2

8%Gd2O3) (Burnup=4 GWd/MTU, as-fabricated radial gap=85μm) 

2.1.7.3 MOX Temperature Comparisons 

FRAPCON-3.3 predictions have been benchmarked against centerline temperatures taken from 

five Halden tests with instrumented fuel assemblies containing 9 rods. The results of these 

comparisons are provided in this section. 

Figure 2.39 shows the results of all nine rods as predicted centerline temperature vs. measured 

centerline temperature. It can be seen from this figure that although predictions of individual rods 

may be biased high or low, the overall predictions are in excellent agreement with the 

measurements (±10%). 
2.39 

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400

Measured Centerline Temperature, °C

Predicted Centerline 

Temperature, °C

629-1r1 629-1r2 610.2

610.4 648.1r1 648r2

IFA-629.3r5 IFA-629.3r6 IFA-606

Predicted = Measured Pred.=Meas.*1.1 Pred.=Meas.*0.9

Figure 2.39 Predicted vs. measured centerline temperature for Halden MOX rods. 

Figures 2.40 and 2.41 show the measured and predicted centerline temperatures for IFA-629-1 

rods 1 and 2. These figures show good agreement between the FRAPCON-3.3 predictions and 

the data. The slight offset during parts of the irradiation could be due to power or thermocouple 

calibration changes at the end of each cycle. 

0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80 100 120

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.40 Measured and predicted centerline temperature for IFA-629-1 rod 1 (starting 

burnup=27 GWd/MTU, ending burnup=33 GWd/MTU, as-fabricated radial 

gap=84μm) 
2.40 

0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80 100 120

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.41 Measured and predicted centerline temperature for IFA-629-1 rod 2 (starting 

burnup=29 GWd/MTU, ending burnup=40 GWd/MTU, as-fabricated radial 

gap=84μm) 

Figures 2.42 and 2.43 show the measured and predicted centerline temperature for IFA-610.2 and 

IFA-610.4. These figures show excellent agreement between the FRAPCON-3.3 predictions and 

the data. 

0

100

200

300

400

500

600

700

800

900

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.42 Measured and predicted centerline temperature for IFA-610.2 (starting 

burnup=55 GWd/MTU, ending burnup=56 GWd/MTU, as-fabricated radial 

gap=84μm) 
2.41 

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.43 Measured and predicted centerline temperature for IFA-610.4 (starting 

burnup=56, ending burnup=57 GWd/MTU, as-fabricated radial gap=84μm) 

Figures 2.44 and 2.45 show the measured and predicted centerline temperature for IFA-648.1 

rods 1 and 2. These figures show excellent agreement between the FRAPCON-3.3 predictions 

and the data. 

0

100

200

300

400

500

600

700

0 50 100 150 200 250 300 350

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.44 Measured and predicted centerline temperature for IFA-648.1 rod 1 (starting 

burnup=55 GWd/MTU, ending burnup=62 GWd/MTU, as-fabricated radial 

gap=84μm) 
2.42 

0

100

200

300

400

500

600

700

0 50 100 150 200 250 300 350

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.45 Measured and predicted centerline temperature for IFA-648.1 rod 2 (starting 

burnup=55 GWd/MTU, ending burnup=62 GWd/MTU, as-fabricated radial 

gap=84μm) 

Figures 2.46 and 2.47 show the measured and predicted centerline temperature for IFA-629.3 

rods 5 and 6. These figures show excellent agreement between the FRAPCON-3.3 predictions 

and the data. 

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.46 Measured and predicted centerline temperature for IFA-629.3 rod 5 (starting 

burnup=62 GWd/MTU, ending burnup=72 GWd/MTU, as-fabricated radial 

gap=84μm) 
2.43 

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.47 Measured and predicted centerline temperature for IFA-629.3 rod 6 (starting 

burnup=62 GWd/MTU, ending burnup=68 GWd/MTU, as-fabricated radial 

gap=84μm) 

Figure 2.48 shows the measured and predicted centerline temperature for IFA-606 Phase 2. This 

figure shows reasonable agreement between the FRAPCON-3.3 predictions and the data (within 

±75K). 

0

200

400

600

800

1000

1200

1400

49.5 49.7 49.9 50.1 50.3 50.5

Time, days

Centerline Temperature, °C

Data FRAPCON-3.3

Figure 2.48 Measured and predicted centerline temperature for IFA-606 Phase 2 (starting 

burnup=50 GWd/MTU, as-fabricated radial gap=94μm) 

2.2 Fission Gas Release Model and Assessment 

The following section describes the fission gas release model in FRAPCON-3.3 and provides an 

assessment of the prediction. It is important to be able to predict fission gas release; especially at 
2.44 

high release levels as fission gas increases the rod internal pressure and degrades the gap thermal 

conductivity, increasing the fuel temperature. 

2.2.1 Modeling 

The fission gas release (FGR) model in FRAPCON-3.3 is a two-stage diffusion model. Gas is 

produced inside spherical grains at a rate proportional to power generation. Gas is allowed to 

diffuse from these grains to the grain boundaries that are considered to be an infinite sink for gas 

atoms. The diffusion of gas from the grains is controlled by a diffusion coefficient that is a 

function of temperature and burnup. 

When the gas atoms arrive at the grain boundaries a fraction of these atoms are considered to be 

re-solved back into the grain. However, since the resolution depth is very small, these atoms are 

not added back into the atoms still in the grain, but are stored separately as resolved gas. The 

remaining gas accumulates on the grain boundary until the grain boundary saturation is exceeded. 

This saturation value is a function of temperature, external pressure, and grain size. When the 

saturation value is exceeded, both the gas on the grain boundary and the resolved gas are released 

to the rod void volume. The concentration of gas on the grain boundaries must then exceed the 

saturation value for further release to occur. 

In addition to this thermally driven gas release, an athermal contribution is also determined that 

models the release of an additional 1% gas for every 10 GWd/MTU of rod average burnup above 

40 GWd/MTU. 

In order to accurately model MOX fuel, the diffusion coefficient is increased by an empirical 

constant factor to account for the observation of greater gas release from MOX than UO2. 

Many of the parameters in this model are difficult to measure in-reactor. In order to develop this 

model, values are selected such that the model gives a best-estimate prediction of gas release for a 

wide variety of rod types and conditions. 

In this model, the following parameters were selected to best predict measured FGR data from 

rods in the assessment database. 

• Pre-exponential diffusion coefficient 

• Activation energy for diffusion coefficient 

• Burnup dependence of the diffusion coefficient 

• Coefficient that defined the fraction of gas arriving on the grain boundaries that is 

resolved 

There is no FGR model in FRAPTRAN-1.3 because it was thought that the time periods over 

which events are modeled in FRAPTRAN are too short for gas to diffuse and release to occur. 

However, in experimental programs performed in the Cabri reactor (Papin et al., 2003) large 

amounts of fission gas have been released during RIA events (5-33%). This is believed to be due 

to grain boundary cracking and separation during the fast transient. Because of this, it is 

important that a transient FGR model be developed for FRAPTRAN-1.3 and that the steady-state 

FGR in FRAPCON-3.3 be assessed and modified if necessary to initialize FRAPTRAN. 

The following section will show the fit of the FGR model in FRAPCON-3.3 to the data from rods 

in the assessment database. 
2.45 

2.2.2 Assessment 

The assessment of the UO2 model for fission gas release is documented in Lanning et al. (2005a). 

Figures 2.49 and 2.50 show the predicted fission gas release as a function of measured fission gas 

release for the steady-state rods and power ramped rods, respectively. Figures 2.51 and 2.52 

show the predicted minus measured fission gas release as a function of burnup for the steady-state 

rods and power ramped rods, respectively. The standard deviation for the steady state predictions 

is 2.8 % FGR. The standard deviation for the power ramped cases is 5.3% FGR. These figures 

demonstrate that FRAPCON-3.3 provides a best-estimate calculation of fission gas over a wide 

range of burnup and gas release levels. 

It has been observed that FRAPCON-3.3 seems to slightly underpredict power ramped rods with 

short hold times (<4 hours). In Figure 2.52 the rods with short hold times are noted. Although 

two of these rods are within the standard error of the predictions, the fact that all three rods with 

short hold time are underpredicted, leads to the conclusion that FRAPCON-3.3 may underpredict 

power ramped rods with short (<4 hours) hold times. In future versions of FRAPCON-3, this 

underprediction will be addressed. Until this time, PNNL has recommended that the hold time 

for power ramps less than 4 hours be increased by a factor of 3 to conservatively bound the 

expected fission gas release (Beyer, 2007). 

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Measured FGR, %

Predicted FGR, %

FRAPCON-3.3 Predicted = Measured

Figure 2.49 Measured vs. predicted FGR for steady-state UO2 rods 
2.46 

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50

Measured FGR, %

Predicted FGR, %

FRAPCON-3.3 Predicted = Measured

Figure 2.50 Measured vs. predicted FGR for power ramped UO2 rods 

-6

-4

-2

0

2

4

6

8

0 10 20 30 40 50 60 70 80 90 100

Burnup, GWd/MTU

Predicted-Measured FGR, %

Figure 2.51 Predicted minus measured FGR as a function of burnup for steady-state UO2

rods 
2.47 

-10

-5

0

5

10

0 20 40 60 80

Burnup, GWd/MTU

Predicted-Measured FGR, %

4hr hold

1.5hr hold

Figure 2.52 Predicted minus measured FGR as a function of burnup for power ramped 

UO2 rods (Rods with hold time less than 4 hours marked) 

A limited assessment of the MOX fission gas release model was performed by Lanning et al. 

(2005a). Since then, more MOX rods were added to the database and a more comprehensive 

assessment was performed and is documented in Lanning et al. (2005b) and Geelhood and Beyer 

(2008). Figure 2.53 shows the predicted fission gas release as a function of measured fission gas 

release for the steady-state and power ramped rods. Figure 2.54 shows the predicted minus 

measured fission gas release as a function of burnup. It can be seen that there is a large degree of 

scatter in the predictions. However, for the rods with the large overprediction, (ATR phase I and 

II and M504) there are no measured temperatures available to verify that this overprediction is 

due solely to a deviation in the FGR model. In addition, these rods were irradiated in test reactors 

with small cores and consequently there could be considerable uncertainty in the reported power 

levels. However, for the cases with measured temperature below 62 GWd/MTU (IFA-651.1, 

IFA-629.1, IFA-606 phase 2, IFA-597.4,.5,.6,.7 and IFA-633.1 Rod 6) FRAPCON-3.3 provides a 

much better prediction of fission gas over a wide range of gas release levels up to a burnup of 58 

GWd/MTU with a standard error of 4.2% FGR. For example, those rods that demonstrated a 

small underpredicition in fuel temperature also resulted in a small underprediction in FGR and for 

those rods with a small overprediction in FGR were similarly overpredicted. Figure 2.54 

indicates that the model may underpredict FGR from MOX at high burnups (>60 GWd/MTU) 

based on the two rods from IFA-629.3 where fuel temperatures were predicted well (Rod 5 in 

Figure 2.46) or overpredicted (Rod 6 in Figure 2.47) and FGR was underpredicted. It is 

recommended that more high burnup FGR data be obtained as it becomes available and attempt 

to verify or refute behavior with MOX. 
2.48 

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Measured FGR, %

Predicted FGR, %

Gravelines MOX IFA 629.1 IFA 606 phase 2 IFA 633.1 rod 6

IFA-651.1 M504 Rods M501 Rods M308 Rod

IFA-629.3 IFA-597.4,5,6,7 E09 Rods ATR Phase II

ATR Phase III ATR Phase IV

Figure 2.53 Measured vs. predicted FGR for steady-state and power ramped MOX rods 

-20

-15

-10

-5

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80

Burnup, GWd/MTM

Predicted minus Measured FGR, 

%

Gravelines MOX IFA 629.1 IFA 606 phase 2 IFA 633.1 rod 6

IFA-651.1 M504 Rods M501 Rods M308 Rod

IFA-629.3 IFA-597.4,5,6,7 E09 Rods ATR Phase II

ATR Phase III ATR Phase IV

Figure 2.54 Predicted minus measured FGR as a function of burnup for steady-state and 

power ramped MOX rods 

Rods with possible 

power uncertainty 
2.49 

Based on the above assessment, it can be concluded that FRAPCON-3.3 provides a best-estimate 

prediction of FGR for UO2 rods and MOX rods up to 60 GWd/MTU. At higher burnup, more 

data is needed to assess if the MOX model still provides a best-estimate prediction of FGR. 

A transient fission gas release model is being developed and implemented in FRAPTRAN-1.4. 

This model will be initialized with the new model in FRAPCON-3.4 that accurately predicts the 

concentration of gas in the grains and on the grain boundaries. This model is not presented in this 

report. 

2.3 Cladding Corrosion and Hydriding Models 

The following sections discuss the assessment of the cladding corrosion and hydriding models in 

FRAPCON-3.3 and FRAPTRAN-1.3. It is important to accurately predict oxidation to determine 

the temperature drop across the cladding. It is also important to accurately predict hydrogen 

pickup so cladding ductility can be calculated. 

2.3.1 Cladding Corrosion 

The corrosion model in MATPRO has been developed to model cladding corrosion in BWR rods. 

The cladding corrosion model in FRAPCON-3.3 has been modified from that of the MATPRO 

model, CORROS, because the MATPRO model underpredicted cladding corrosion by a factor of 

4 to 5 for PWR rods. The new model is described in Lanning et al. (1997a) and is applicable for 

Zircaloy-2 and Zircaloy-4 in BWR and PWR environments. In addition, this model has recently 

been modified to account for the reduced corrosion seen in ZIRLOTM and M5TM. These 

modifications are described in Lanning, et al., (2005a) 

FRAPTRAN-1.3 does not model low temperature corrosion because the time periods of the 

events that FRAPTRAN-1.3 is used for are are not long enough for a significant amount to occur. 

FRAPTRAN-1.3 does model high temperature corrosion such as occurs during a loss-of-coolant 

accident (LOCA). In FRAPTRAN-1.3, the user can select to model high temperature corrosion 

with either the Cathcart/Pawel (Cathcart et al., 1977) or the more conservative Baker/Just (Baker 

et al., 1962) model. 

Figure 2.55 shows the comparisons of the FRAPCON-3.3 prediction to data for PWR Zircaloy 4 

cladding and coolant conditions. Figure 2.56 shows the comparisons of the FRAPCON-3.3 

prediction to data for BWR Zircaloy-2 cladding and coolant conditions from the original model 

assessment (Lanning et al., 1997b). Since this time, BWR vendors have switched to using 

cladding with controlled second phase precipitate (SPP) sizes and more tightly defined chemical 

compositions. Data on these newer Zircaloy-2 cladding types has been collected and compared to 

the model for Zircaloy-2 BWR corrosion (Yasuyuki et al., 2007, Sell et al., 2006, Hirano et al., 

2005, Mutyala, 2004). Figure 2.57 shows the comparisons of the FRAPCON-3.3 prediction to 

data from newer Zircaloy-2 BWR cladding. It can be seen from these figures that FRAPCON-3.3 

provides good predictions of oxide thickness for older and new Zircaloy-2 and Zircaloy-4 in both 

BWR and PWR conditions. 
2.50 

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Measured Oxide Thickness, microns

Predicted Oxide Thickness

PWR Data Measured=Predicted

Figure 2.55 PWR Zircaloy-4 corrosion data and FRAPCON-3.3 PWR corrosion model 

(Smith et al., 1994, Pyecha, 1985, Newman, 1986, Balfour, 1982b, Dideon, 

1983, Garde, 1986). 

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70

Rod Average Burnup, GWd/MTU

Oxide Thickness, microns

BWR Data FRAPCON-3.3

Figure 2.56 BWR Zircaloy-2 corrosion data and FRAPCON-3.3 BWR corrosion model 

(West et al., 1983, Barner et al., 1990) 
2.51 

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Full Power Days

Oxide Thickness, microns

Type B 9x9 Seimens LTP 9x9 GNF Step III

Westinghouse LK3 FRAPCON-3.3

Figure 2.57 Zircaloy-2 BWR Corrosion Data for the Newer Cladding Types with 

Controlled SPP’s and composition (Yasuyuki et al., 2007, Sell et al., 2006, 

Hirano et al., 2005, Mutyala, 2004) 

As mentioned above, the corrosion model in FRAPCON-3.3 has recently been updated to include 

adjustments for the lower corrosion rates seen in the advanced cladding alloys ZIRLOTM and 

M5TM. This adjustment is simply a reduction of the current PWR model that fits the available 

data for ZIRLOTM (Knott et al., 2003) and M5TM (Mardon and Waeckel, 2003). Figures 2.58 and 

2.59 show the corrosion data and model predictions for standard PWR cases using the ZIRLOTM 

and M5TM correlations, respectively. The ZIRLO data is plotted as a function of Fuel Duty Index 

(FDI) which is a function of power and time at power. Based on these comparisons FRAPCON3.3 predicts the oxide thickness from ZIRLOTM and M5TM well. 
2.52 

0

20

40

60

80

100

120

0 200 400 600 800 1000

FDI

Oxide Thickness, microns

ZIRLO Data FRAPCON-3.3

Figure 2.58 ZIRLOTM data and FRAPCON-3.3 predictions as a function of fuel duty 

index (FDI) (Knott et al., 2003) 

0

5

10

15

20

25

30

35

40

0 20 40 60 80

Burnup, GWd/tU

Oxide Thickness, microns

FRAPCON-3.3 M5 Data

Figure 2.59 M5TM data and FRAPCON-3.3 predictions as a function of burnup (Mardon 

and Waeckel, 2003) 

However, recent data from high burnup Spanish and French rods clad in ZIRLOTM (CSN, 

ENUSA, 2002) and M5TM (Segura et al., 2002) indicate that the corrosion adjustments that have 

been recently made for these alloys underpredict the oxide thickness for ZIRLOTM at high burnup 

and overpredict the oxide thickness for M5TM. Figures 2.60 and 2.61 show the end of life oxide 

profile for two Spanish rods clad in ZIRLOTM irradiated to a rod average burnup of 68 

GWd/MTU. Figure 2.62 shows the end of life oxide profile for a French rod clad in M5TM 

irradiated to 70 GWd/MTU. Also shown on these figures for reference is the FRAPCON-3.3 

correlation for Zircaloy-4. These figures support the conclusions given above and emphasize the 

need to develop new correlations specifically for ZIRLOTM and M5TM, rather than just adding a 

multiplicative factor to the current correlation for Zircaloy. A new correlation will be developed 
2.53 

for M5TM and ZIRLOTM in FRAPCON-3.4 that will provide better predictions of the high burnup 

corrosion data. These new correlations are discussed in Section 3.1. 

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, microns

Data Lower Bound Data Median Data Upper Bound

ZIRLO Correlation Zircaloy-4 Correlation

Figure 2.60 End of life oxide thickness and FRAPCON-3 predictions for Vandellos II rod 

A06, clad in ZIRLOTM and irradiated to 68 GWd/MTU (CSN, ENUSA, 

2002). 

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, microns

Data Lower Bound Data Median Data Upper Bound

ZIRLO Correlation Zircaloy-4 Correlation

Figure 2.61 End of life oxide thickness and FRAPCON-3 predictions for Vandellos II rod 

A12, clad in ZIRLOTM and irradiated to 68 GWd/MTU(CSN, ENUSA, 2002). 
2.54 

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, microns

Data Lower Bound Data Median Data Upper Bound

M5 Correlation Zircaloy-4 Correlation

Figure 2.62 End of life oxide thickness and FRAPCON-3 predictions for Gravelines 5 

rod N05, clad in M5TM and irradiated to 70 GWd/MTU (Segura et al., 2002). 

Cunningham et al, (2001b) has assessed the Cathcart-Pawel and Baker-Just models in 

FRAPTRAN-1.3. The conclusion of this assessment is that the Cathcart-Pawel model is more 

accurate below 1800K, and the Baker-Just model is more accurate above 1800K. Experimental 

work is currently ongoing to determine the high temperature oxidation behavior for zirconium 

alloys as a function of burnup. It has been determined that fabrication and heat treatment as well 

as level of hydrides can drastically affect the high temperature oxidation performance. For 

example, it has been determined that M5 shows good oxidation performance, while E-110, which 

is nominally the same composition, shows very poor oxidation performance at high temperature 

in steam. 

As more data become available, the high temperature oxidation models in FRAPTRAN-1.3 can 

be re-evaluated to determine if they provide a best-estimate calculation for high temperature 

corrosion. However, using the models currently in FRAPTRAN-1.3 with the above 

recommendations should provide close to a best-estimate prediction of high temperature 

oxidation behavior. 

2.3.2 Hydrogen Pickup 

FRAPCON-3.3 uses a hydrogen pickup fraction of 29% for BWR corrosion and 15% for PWR 

corrosion. These pickup fractions are valid for Zircaloy-2 and Zircaloy-4. The code has recently 

been changed to model the improved hydrogen pickup performance of ZIRLOTM and M5TM. The 

hydrogen pickup fraction for ZIRLOTM in a PWR is 12.5% while the hydrogen pickup fraction 

for M5TM in a PWR is 7.5%. No correlations for ZIRLOTM or M5TM in a BWR were developed 

since all the vendors currently use Zircaloy-2 cladding in BWRs. 

FRAPTRAN does not model hydrogen pickup from low temperature corrosion, since it does not 

model low temperature corrosion. There has not been any data that indicated what the hydrogen 
2.55 

pickup would be during high temperature oxidation. Because of this, there is no hydrogen pickup 

model in FRAPTRAN. 

Figure 2.63 shows the measured and predicted hydrogen data for PWR Zircaloy-4 rods. It can be 

seen from this figure that the model predicts the data well. Figure 2.64 shows the measured and 

predicted hydrogen pickup fraction for BWR Zircaloy-2 rods. Because there was such a limited 

number of BWR hydrogen pickup data, a literature search was performed to find more hydrogen 

pickup data for Zircaloy-2 in BWR conditions. A more recent data comparison of older Zircaloy2 without controlled SPP sizes and controlled compositions (Hayashi et al., 2003) and of newer 

Zircaloy-2 with controlled SPP sizes and compositions (Hayashi et al., 2003, Sell et al., 2006, 

Hirano et al., 2005, Ledberger et al., 2005) found that a constant hydrogen pickup fraction is not 

appropriate for hydrogen pickup in Zircaloy-2. Figure 2.65 shows the new data plotted as a 

function of local axial burnup along with the 29% hydrogen pickup fraction used in FRAPCON3.3. In addition, it was found that the hydrogen pickup in new Zircaloy-2 where the vendors have 

better control over the alloy composition and second-phase precipitate (SPP) size is different 

from older Zircaloy. New correlations have been developed and will be included in FRAPCON3.4 that provide a better prediction of the hydrogen pickup in older and new Zircaloy-2 as a 

function of burnup. These correlations are described in Section 3.1. 

Figure 2.66 shows the measured and predicted hydrogen data for PWR ZIRLOTM rods (Tsukuda 

et al., 2003, Kitaguawa et al., 2005). It can be seen from this figure that the model predicts the 

data well. Figure 2.67 shows the measured and predicted hydrogen pickup fraction for PWR 

M5TM. Also shown on this figure are hydrogen concentration values predicted by FRAPCON-3.3 

for standard PWR rods. It can be seen from this figure that although there is significant scatter in 

the hydrogen content when plotted as a function of burnup, the model predicts the data well. This 

scatter is due to overprediction of oxide thickness and will be less for the new model described in 

Section 3.1 

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 800

Measured Hydrogen, ppm

Predicted Hydrogen, ppm

Figure 2.63 Measured and predicted hydrogen pickup for PWR rods with Zircaloy-4 

cladding (Smith et al., 1994, Pyecha, 1985, Newman, 1986, Balfour, 1982b, 

Dideon, 1983, Garde, 1986) 
2.56 

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Rod-Average Burnup, GWd/MTU

Hydrogen Pickup 

Fraction, %

Data FRAPCON-3.3

Figure 2.64 Measured and predicted hydrogen pickup for BWR rods with Zircaloy-2 

cladding (Itagaki, 2003.) 

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80

Local Axial Burnup [MWd/kgU]

Hydrogen Content [ppm] 

Old Zircaloy-2 New Zircaloy-2 FRAPCON-3.3

Figure 2.65 Measured and predicted hydrogen pickup from recent literature search for 

BWR rods with Zircaloy-2 cladding (Hayashi et al., 2003, Sell et al., 2006, 

Hirano et al., 2005, Ledberger et al., 2005) 
2.57 

0

100

200

300

400

500

0 10 20 30 40 50 60 70

Oxide Thickness, microns

Hydrogen Pickup, ppm.

Tsukuda ZIRLO Data Kitaguawa ZIRLO Data 12.5% Pickup

Figure 2.66 Measured and predicted hydrogen pickup for PWR rods with ZIRLOTM 

(Tsukuda et al., 2003, Kitaguawa et al., 2005) 

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80

Burnup, GWd/MTU

Hydrogen, ppm

FRAPCON-3.3 M5 Data

Figure 2.67 Measured and predicted hydrogen pickup for PWR rods with M5TM (Mardon 

and Waeckel, 2003) 

2.4 Fuel Densification and Swelling 

The following sections describe the fuel swelling and densification models in FRAPCON-3.3 and 

provides data comparisons for these models. 
2.58 

FRAPTRAN-1.3 does not contain a fuel densification or swelling model. This is acceptable 

because fuel densification and swelling are burnup-related phenomena and no significant burnup 

accumulates over the time periods of the events that are modeled in FRAPTRAN-1.3. 

2.4.1 Fuel Swelling 

The fuel swelling model in FRAPCON-3.3 has been modified from the model documented in 

MATPRO (Hagrman et al. 1981). This model is accurately described in Lanning et al (1997a). 

The swelling model in FRAPCON-3.3 is a function of pellet-average burnup only. 

The swelling model is based on dimensional data obtained on UO2 pellets and pellet stacks 

irradiated within cladding (i.e., constrained) in PWRs. Data obtained from ex-reactor, thermallyheated, unconstrained pellet swelling experiments were not included. Lanning et al. (1997a) 

provided data source references and plots of data compared to the modified FSWELL model. 

The PWR data of Dideon and Bain (1983), Garde (1986), Newman (1986), and Smith et al. 

(1994) were used to develop the swelling model in FRAPCON-3.3. A search was performed for 

recent fuel swelling data. Two references were found that included data for constrained UO2

pellets irradiated in light water reactors (Zacharie et al., 1998, Lafchiev and Tverberg, 2005). 

Figure 2.68 provides a comparison of the swelling model in FRAPCON-3.3, compared to the data 

on which it is based, up to the 70 GWd/MTU burnup limit specified by Lanning et al. (1997a). It 

can be seen from this figure that while there is considerable scatter in the swelling data, the 

FRAPCON-3.3 model seems to provide a best-estimate prediction of fuel swelling. A fuel 

swelling rate has been deduced from a number of Halden fuel assemblies (Lafchiev and Tverberg, 

2005). These rates are shown in Figure 2.69 along with the FRAPCON-3.3 swelling rate of 

0.77% ΔV/V per 10 GWd/MTU. This figure shows that the swelling rate used on FRAPCON-3.3 

is within the scatter of the swelling rates that have been observed at Halden, but slightly higher 

than the average rate from these data. 

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120

Pellet Average Burnup, GWd/MTU

ΔV/V, %

FRAPCON-3.3 Model Data for Model Development Recent Data

Figure 2.68 FRAPCON-3.3 swelling model prediction and data as a function of burnup 
2.59 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

IFA-655

Rods 1

&3

IFA-655

Rods 2

&4

IFA-633 IFA-610 IFA629.3IFA629.4IFA534.14IFA597.3

Swelling Rate, %

ΔV/V per 10 GWd/MTM

FRAPCON-3.3 Swelling Rate, 

0.77% ΔV/V per 10 GWd/MTU

99 GWd/MTU99 GWd/MTU17 GWd/MTU62 GWd/MTU68 GWd/MTU65 GWd/MTU62 GWd/MTU70 GWd/MTU

Figure 2.69 FRAPCON-3.3 swelling rate and observed swelling rates from Halden 

instrumented fuel assemblies (EOL burnups shown for each point) 

2.4.2 Fuel Densification 

FRAPCON-3.3 uses the MATPRO model, FUDENS, to calculate fuel densification as a function 

of burnup and maximum densification. The code contains several methods for calculating 

maximum densification. The first and most commonly used method is to use the user-input value 

for maximum densification and simply convert this to a linear strain. The maximum densification 

can be estimated using a standard densification test (1700°C for 24 hours). This is the method 

recommended in US NRC Regulatory Guide 1.126 (1978) and has been shown to correlate well 

with observed maximum in-reactor densification. If the maximum densification is not input, 

FRAPCON-3.3 uses the equations given in the MATPRO subroutine FUDENS that are a function 

of fuel temperature, fuel density, and fuel sintering temperature. 

The FUDENS model in FRAPCON-3.3 has been fit to provide the best fit to the data of Freshley 

et al. (1976). A search was performed for recent fuel densification data. Three new sources of 

data (Banks, 1974, Freshley et al., 1978, and Small, 1987) were obtained. 

Figure 2.70 compares the predicted densification values to the experimental values from the data 

used to tune the model and from more recent data. In general, the model predicts the correct 

densification trends. However, there is a considerable amount of scatter in the densification data. 

In addition, FRAPCON-3.3 is not typically used to calculate the densification, but rather the 

maximum densification is often provided as an input variable to the code. 
2.60 

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Measured Densification (% TD)

Predicted Densification (% TD)

Data used to tune model Recent Data

Figure 2.70 Comparison of FUDENS fuel densification predictions to the experimental 

data from which the fit coefficients were determined and to more recent 

published data. 

Based on this comparison and the fact that maximum densification is typically provided as a code 

input as recommended by NRC (US NRC Regulatory Guide 1.126, 1978), it can be concluded 

that FRAPCON-3.3 provides a reasonable estimate of fuel densification. 

2.5 Assessment of Mechanical Modeling and Properties 

This section will discuss the modeling approach that is used in FRAPCON-3.3 and FRAPTRAN 

1.3 to model the mechanical responses of the fuel and the cladding. In addition, each model for 

the mechanical properties of the fuel and cladding will be described and compared to applicable 

data. 

2.5.1 Modeling 

Both FRAPCON-3.3 and FRAPTRAN-1.3 use the FRACAS-I finite difference model to calculate 

the stress and strain in the cladding due to fill gas pressure and pellet-cladding mechanical 

interaction. In this model, the stress induced deformation in the fuel is neglected and a rigid 

pellet assumption is used. 

The code must account for two different loading conditions. The first occurs when the pelletcladding gap is open. During this time, the rod internal gas pressure and coolant pressure exert 

forces on the cladding causing a stress in the cladding. The resultant strain in the cladding due to 

this stress is calculated by the FRACAS-I model. The second loading condition occurs after the 

pellet cladding gap is closed due to a combination of fuel swelling, thermal expansion, and 

cladding creepdown. During this time, the rigid pellet strains the cladding, and the resultant 

stress in the cladding is calculated by the FRACAS-I model. The FRACAS-I model in 
2.61 

FRAPCON-3.3 and FRAPTRAN-1.3 are described in greater detail by Berna et al. (1997) and by 

Cunningham et al (2001a). 

2.5.2 Mechanical Properties 

The mechanical properties of primary concern for modeling the stress and strain response of the 

cladding are irradiation creep, yield stress, and Young’s modulus. These properties are discussed 

in detail and compared to data in the following section. 

2.5.2.1 Irradiation Creep 

The irradiation creep model in FRAPCON-3.3 is the same model that was in FRAPCON-2. This 

model is not discussed in the documentation for FRAPCON-3. The model has, however, been 

documented for FRAPCON-2. This model is summarized below. 

( ) 3600 1.1547 2 1* 2* 3 2

= ⋅ ⋅ ε

ε

A A A &

Where 

ε& = creep strain rate, in/in/hr 

φ 29 1 5.129 10− A = ×

φ = fast neutron flux, n/m2/s 

⎟

⎠

⎞ ⎜

⎝

⎛

⋅

− = T

A

1.987

10000 2 exp

T = temperature, K 

3 725.2exp(4.967 10 ) 8 = σ + × ⋅σ − A

σ = hoop stress, Pa 

ε = creep strain from previous time step, in/in (if ε <0.0001, use ε =0.0001) 

This model is a function of time, stress, fast neutron flux, and temperature. The time and stress 

dependence is based on Ibrahin (1973). The flux dependence is based on Ross-Ross and Hunt 

(1968). The temperature dependence is based on a value of q = 10000 cal/mole near 573K from 

Fidleris (1974). 

Lanning et al. (1997b) compared the creep model to measurements from two PWR rod sets 

(Smith et al., 1994 and Newman, 1986). The results of these comparisons have changed due to 

the discovery of an error in the code with the calculation of fast neutron fluence. The results of 

these comparisons for end-of-life creepdown with FRAPCON-3.3 can be seen in Figures 2.71 and 

2.72. 
2.62 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2E+25 4E+25 6E+25 8E+25 1E+26 1.2E+26

Rod Average Fluence, n/m2

Average Hoop Strain, %

FRAPCON-3.3 Data

Figure 2.71 Predicted and measured cladding creepdown from the 2nd and 3rd cycle rods 

in the ANO-2 PWR assembly, TSQ002. 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2E+25 4E+25 6E+25 8E+25 1E+26

Rod Average Fluence, n/m2

Average Hoop Strain, %

FRAPCON-3.3 Data

Figure 2.72 Predicted and measured cladding creepdown from the 3rd, 4th, and 5th cycle 

rods in the Oconee PWR assembly, 15309. 

It can be seen from these comparisons that the current creep model may predict too high of a 

creep rate. Several organizations have stated that they believe the cladding creep model in 

FRAPCON-3.3 predicts creep to occur more rapidly than that normally exhibited. This causes 

FRAPCON-3.3 to predict gap closure before it might actually occur. A new cladding creep 

model has been developed to provide a best estimate model for cladding creepdown in 

FRAPCON-3.4. This model is described in Section 3.7. 
2.63 

There currently is no thermal creep model in FRAPCON-3.3 or FRAPTRAN 1.3. The impact of 

this lack of thermal creep is that stress relaxation due to thermal creep strain is not calculated. 

The new model described in Section 3.7 contains a thermal term. The impact of this inclusion 

will be discussed more in Section 3.7. 

It should be acknowledged that many fabrication parameters can affect the irradiation creep in 

Zircaloy cladding. Because of this, different cladding vendors should have an irradiation creep 

model that accurately predicts cladding irradiation creep in cladding manufactured by their 

supplier. 

FRAPTRAN-1.3 does not contain an irradiation creep model. This is acceptable because 

irradiation creep is a fast neutron fluence-related phenomena and no significant fluence 

accumulates over the time periods of the events that are modeled in FRAPTRAN-1.3. 

2.5.2.2 Yield Strength 

The plastic stress/strain relationship in FRAPTRAN and FRAPCON-3 is given by a power law 

relationship. The yield stress is the point where the plastic curve, represented by a power law 

relationship, intersects with the elastic curve, represented by a linear relationship. The 

coefficients used in the power law are a function of temperature, fast neutron fluence, cladding 

cold work, strain rate, and cladding type. These coefficients have been modified from those 

provided in MATPRO to provide a best-estimate prediction of yield stress and ultimate tensile 

strength from axial tube tensile tests and burst tests taken on irradiated cladding. The model used 

in FRAPCON-3.3 and FRAPTRAN-1.3 assumes the cladding behaves isotropically and is 

described in the release document for FRAPTRAN-1.3 (Geelhood, 2005a). 

PNNL has compiled a large database of mechanical properties for irradiated and unirradiated 

Zircaloy-2 and Zircaloy-4 with fast neutron fluence levels up to 12x1025 n/m2

. Figure 2.73 shows 

the predicted yield stress as a function of the measured yield stress for these data. It can be seen 

from this figure that the model provides a best-estimate prediction of the cladding yield stress for 

Zircaloy-2 and Zircaloy-4. 
2.64 

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Measured Yield Stress, MPa

Predicted Yield Stress, MPa

Axial Tests Burst Tests Ring Tests

Figure 2.73 Predicted vs. measured yield stress from irradiated and unirradiated Zircaloy2 and Zircaloy-4 

In addition to these data, there has been data from the PROMETRA program that has been 

irradiated up to about 8x1025 n/m2. These data, and the model predictions for three different 

strain rates are shown in Figure 2.74. It can be seen from this figure that the model accurately 

predicts the strain rate dependence as well as the yield stress at very high temperature. 

0

200

400

600

800

1000

1200

200 500 800 1100 1400

Temperature, K

Yield Stress, MPa

0.01 /s Hoop

0.01 /s Axial

0.01 /s Ax_Joule

0.2 /s Hoop

0.2 /s Axial

0.2 /s Ax_Joule

5 /s Hoop

5 /s Axial

5 /s Ax_Joule

FRAPTRAN 0.001 /s

FRAPTRAN 1 /s

FRAPTRAN 10 /s

Figure 2.74 Measured and predicted yield stress for high burnup cladding from the 

PROMETRA database. 

Based on these comparisons, it can be seen that the cladding yield stress model in FRAPCON and 

FRAPTRAN provides a best-estimate prediction of yield stress over a wide range of temperature, 

fluence, cold work, and strain rate. 
2.65 

2.5.2.3 Young’s Modulus 

The model for Young’s modulus of cladding material in FRAPCON-3.3 and FRAPTRAN-1.3 is 

the CELMOD model from MATPRO. This model is a function of temperature, cladding cold 

work, fluence and oxygen concentration and assumed the Zircaloy cladding behaves isotropically. 

This model is based on data taken using the dynamic method from several different sources on 

unirradiated cladding (Bunnell, 1977, Armstrong and Brown, 1964, Padel and Groff, 1976, Busby, 

1966, Spasic, 1968, Mehan, 1958, and Northwood, 1975). No Young’s modulus data was 

available for irradiated cladding, so data from the Saxton Core II Fuel Performance Evaluation 

(Smalley, 1971) was used to estimate the effects of fast neutron fluence. 

A search was performed to find more recent Young’s modulus data. No data was found for 

irradiated Zicaloy, but one data source (Bolmaro, 1988) was found for unirradiated Zircaloy. 

Figure 2.75 shows the predicted vs. measured values of Young’s modulus for the data used for 

model development and the more recent data. It can be seen from this figure that the model in 

FRAPCON-3.3 and FRAPTRAN-1.3 continues to provide a best-estimate prediction of Young’s 

modulus for Zircaloy cladding. The model may slightly underpredict Young’s modulus for 

measured modulus of greater than 90 MPa. These measurements are taken at room temperature 

and are not relevant for fuel performance modeling. 

0

40

80

120

0 40 80 120

Measured Young's Modulus, GPa

Predicted Young's Modulus, GPa

Model Development Data Recent Data

Figure 2.75 Measured vs. predicted Young’s modulus for model development data and 

recent data 

2.5.3 Assessment of Power Ramped Rods 

Power ramps that can be modeled in FRAPCON-3.3 are typically not severe enough to induce 

any permanent deformation due to plastic slip. Typically in FRAPCON-3.3, permanent 

deformation is due to cladding creep. However, the models for the elastic and plastic stress and 

strain relationships in FRAPCON-3.3 are identical to those in FRAPTRAN-1.3. Because of this, 
2.66 

the plastic deformation models in both FRAPCON-3.3 and FRAPTRAN-1.3 can be assessed 

based on the results from fast transients modeled in FRAPTRAN-1.3. 

During a reactivity initiated accident (RIA), the fuel is heated at a rapid rate and expands against 

the cladding. During this type of accident, the fuel causes plastic deformation in the cladding in 

both the hoop direction and the axial direction. RIA accidents have been simulated in the Cabri 

reactor (Papin, et al, 2003) and in the NSRR reactor (Fuketa et al., 1997, Fuketa et al., 2001, 

Nakamura et al, 2002). Many have been simulated with FRAPTRAN-1.3, and the permanent 

strain predictions have been compared to the measured permanent strain. Figure 2.76 shows the 

predicted and measured hoop strain for the non-failed rods that have been modeled with 

FRAPTRAN-1.3. It can be seen that FRAPTRAN-1.3 does a good job of predicting the hoop 

strain when the permanent strain is below about 1.5%. However, at higher strain values, 

FRAPTRAN-1.3 underpredicts the measured permanent hoop strain. Some of this 

underprediction may be due to an underprediction of cladding temperature due to departure from 

nucleate boiling (DNB) occurring in the NSRR tests with stagnant water that cannot be modeled 

in FRAPTRAN-1.3 due to geometric complexities of the test capsule. 

0

1

2

3

4

5

012345

Measured Permanent Hoop Strain, %

Predicted Permanent Hoop Strain, %

Cabri FRAPTRAN1.3 NSRR FRAPTRAN1.3

Figure 2.76 Predicted and measured permanent hoop strain from Cabri and NSRR RIA 

tests. 

Figure 2.77 shows the predicted and measured axial strain for the non-failed rods that have been 

modeled with FRAPTRAN-1.3. It can be seen that FRAPTRAN-1.3 overpredicts the axial strain 

for these rods. This is because in FRAPTRAN-1.3, when the fuel and cladding come in contact, 

they are assumed to be locked up radially and axially with each other. In reality, the fuel and 

cladding may slip axially in reference to one-another as the pellets expand. A finite element 

analysis (FEA) model that allows axial slip has been developed and included in FRAPTRAN 1.4 

based on the recommendations of several assessment studies (Geelhood, 2005b, Geelhood, 2006). 

In addition, a representative friction coefficient between the pellet and the cladding will be 

developed to improved these predictions of axial strain. The final assessment and 

recommendations will be included in the FRAPCON-3.4/FRAPTRAN 1.4 release documents. 
2.67 

0

1

2

3

4

01234

Measured Permanent Axial Strain, %

Predicted Permanent Axial Strain, 

%

Cabri FRAPTRAN1.3 NSRR FRAPTRAN1.3

Figure 2.77 Predicted and measured permanent axial strain from Cabri and NSRR RIA 

tests. 

2.6 Void Volume Model and Assessment 

The rod void volume is primarily affected by the rod growth model and the fuel swelling model. 

This model and the plenum gas temperature model affect the gas pressure calculation. The rod 

growth model and plenum gas temperature models will be discussed in the sections below and 

compared to applicable data. 

2.6.1 Rod Growth 

The cladding axial growth model in FRAPCON-3.3 has been updated from the CAGROW model 

documented in MATPRO. The updated model is documented in Lanning et al. (1997a). This 

model is a modified version of a model developed by Franklin (Franklin 1982). There is no axial 

growth model in FRAPTRAN-1.3 because cladding axial growth is a fluence (burnup) dependant 

phenomenon and there is no significant fluence accumulation over the time periods of the events 

that are modeled in FRAPTRAN-1.3. The model is reduced by a factor of 2 (half its size) for 

modeling BWR cladding, as the data shows a reduction of growth in BWR cladding. This is most 

likely due to the fact that most BWR cladding is recrystallized Zircaloy-2, while most PWR 

cladding is stress relieved Zircaloy-4. This model is valid for these two alloys. No comparison 

has been made for ZIRLOTM and M5TM. To model these two newer alloys, PNNL recommends 

using the PWR model for ZIRLOTM (stress-relief annealed) and the BWR model for M5TM 

(recrystallized). 

The axial growth model in FRAPCON-3.3 is based on data obtained from post-irradiation 

examination (PIE) data resulting from experiments conducted by Combustion Engineering (CE) 

and Westinghouse (W) in five different PWRs (Franklin, 1982). The cladding material was coldworked stress relieved Zircaloy-4. Lanning et al. (1997a) compared the FRAPCON-3.3 model to 

PWR cladding growth data from six different irradiation experiments (Newman, 1986, Balfour, 

1982a, Dideon, 1983, Smith, 1986, Smally, 1974, and Smith, 1983) and BWR cladding growth 

data (West et al., 1983 and Barner, 1990) from two irradiation experiments. 
2.68 

A search was performed for cladding axial growth data published recently. One data source was 

found (Gilbon, 2000), and more data was found in a Franklin paper (Franklin, 1982). 

Figure 2.78 provides a comparison of the FRAPCON-3.3 model for PWR cladding to the data on 

which it is based and to the more recent PWR data. Figure 2.79 provides a comparison of the 

FRAPCON-3.3 model for BWR cladding to the data on which it is based and to the more recent 

BWR data. 

0

0.2

0.4

0.6

0.8

1

1.2

0 2E+21 4E+21 6E+21 8E+21 1E+22 1.2E+22 1.4E+22

Fast Fluence (n/cm2

, E > 1 MeV)

∆L/Lo (%)

FRAPCON-3.3 Data for FRAPCON Assessment Recent Data

Figure 2.78 FRAPCON-3.3 model for axial growth in PWR cladding compared to data 

used for model development and recent data 
2.69 

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2E+21 4E+21 6E+21 8E+21 1E+22 1.2E+22 1.4E+22

Fast Fluence (n/cm2

, E > 1 MeV)

∆L/Lo (%)

FRAPCON-3.3 Data for FRAPCON Assessment Recent Data

Figure 2.79 FRAPCON-3.3 model for axial growth in BWR cladding compared to data 

used for model development and recent data 

It can be seen from these figures that the FRAPCON-3.3 model for cladding axial growth 

continues to provide a best-estimate prediction of cladding axial growth for PWR (stress relief 

annealed (SRA) Zircaloy-4) and BWR (recrystallized annealed RXA Zircaloy-2) cladding. 

2.6.2 Plenum Gas Temperature 

Since about 50-80% of the free volume of a fuel rod is contained in the upper plenum region, it is 

important for the gas pressure calculation to provide an accurate prediction of plenum gas 

temperature. 

In FRAPCON-3.3, the gas temperature is calculated by calculating the heat transfer to the plenum 

gas from the end pellet, the hold-down spring, and the coolant. Gamma heating in the spring is 

considered in this calculation, but gamma heating in the cladding is not. 

In FRAPTRAN-1.3 there are two options available for calculating plenum gas temperature. The 

first option is to assume that the plenum gas temperature is 10K greater than the coolant 

temperature at the top axial node based on the results of more detailed calculations. The second 

option is to employ a detailed calculation similar to the calculation performed in FRAPCON-3.3. 

However, in FRAPTRAN-1.3, the calculation accounts for gamma heating in the cladding. 

All of these methods have provided reasonable and not widely disparate estimates of the plenum 

gas temperature in the past, and are judged to be acceptable for providing a best-estimate 

calculation of plenum gas temperature. 
2.70 

2.7 Time Dependent Models 

In order to be consistent with each other, the two fuel performance codes, FRAPCON-3.3 and 

FRAPTRAN 1.3 use the same set of material properties and models when appropriate. Since 

FRAPCON-3 is a steady state code, changes that occur over the time period of milliseconds to 

minutes are not considered. However, FRAPTRAN is specifically designed to calculate changes 

in temperature and other parameters over such short intervals of time. 

Because of this, there is some concern that the material properties or other models used to 

calculate the behavior of the fuel and cladding may not change instantly when the temperature of 

the material changes. An example of this would be a material property that requires some atom 

diffusion to occur when the temperature changes such as the cladding annealing or hydrogen 

solubility models. 

The material properties of the fuel and cladding can be divided into 3 categories. (1) Those 

without time dependence that can be included in FRAPTRAN as given, (2) those with time 

dependence that can change over short time intervals (e.g. < 10 minutes) and should include a 

time dependence term in FRAPTRAN, and (3) those with a time dependence much greater than 

the time interval that is typically modeled in FRAPTRAN and can be ignored completely in 

FRAPTRAN. Tables 2.1-2.3 list the properties of fuel and cladding in their appropriate 

categories. 

Table 2.1 Properties and models without time dependence 

Property Use 

Young’s modulus Calculate stress/strain behavior 

Thermal conductivity Calculate flow of heat through fuel, gas, 

cladding and oxide 

Thermal expansion Calculate size of fuel and cladding at various 

temperature 

k, m, and n Coefficients used to calculate plastic 

stress/strain behavior 

Table 2.2 Properties and models with time dependence that can change over short time 

intervals (e.g. < 10 minutes) and should be modeled in FRAPTRAN 

Property Use 

Zircaloy annealing Calculate effective fluence and cold work as a 

function of time and temperature for 

mechanical properties, E, k, m, and n. 

Power law for plastic stress/strain behavior and 

thermal creep 

Calculates yield stress and plastic stress/strain 

behavior as a function of E, k, m, n, and strain 

rate. Thermal creep not currently modeled in 

FRAPCON-3.3 

Release of fission gas from grain boundary due 

to cracking 

Calculate amount of fission gas residing on the 

grain boundary to be released to the rod void 

volume 

Hydrogen dissolution and precipitation Used to calculate the excess hydrogen content 

that is used to calculate failure strain 

Fuel melting Calculates volume change due to melting 
2.71 

Table 2.3 Properties and models with time dependence much greater than the time 

period modeled in FRAPTRAN 

Property Use 

Fuel Relocation Calculates size of irradiated pellet due to 

relocation 

Recovery of fuel relocation Percentage of fuel relocation to be recovered 

upon gap closure 

Release of fission gas from grains to grain 

boundaries 

Calculates amount of fission gas inside the 

grains that is released to the grain boundaries 

Fuel swelling and densification Calculates size of fuel pellet as a function of 

burnup 

Cladding irradiation creep Calculates creep induced in the cladding due to 

irradiation and external stress 

Cladding irradiation growth Calculates axial growth induced by irradiation 

in the cladding 

The following section will examine each of these three types of properties and explain why each 

property is in this category and how the property is treated or should be treated in FRAPTRAN. 

2.7.1 Properties and Models without time dependence 

Young’s Modulus

The Young’s modulus is governed by the strength of inter-atomic forces. These forces are a 

function of the lattice temperature and are not expected to have any time dependence. Of course, 

during a transient, the local temperature will not immediately reach the steady-state temperature, 

but FRAPTRAN divides the fuel and the cladding into many radial nodes, and uses a transient 

temperature calculator to calculate the local temperature at each radial node. Given the local 

temperature as calculated by FRAPTRAN, it is not expected that the Young’s modulus will have 

any time dependence. 

There is the possibility of annealing changing the crystal structure by removing the effect of cold 

work and irradiation defects. The model for Young’s modulus in FRAPTRAN is a function of 

cold work and fast neutron fluence. A separate annealing model calculates effective values of 

cold work and fast neutron fluence that are used as input to this model. 

Thermal Conductivity

The fuel thermal conductivity of the fuel in FRAPTRAN is composed of two terms. The first is a 

phonon term that describes the heat transfer in the solid by lattice vibration. The ability of a 

lattice to transfer heat is not a function of time at temperature unless a phase change is expected. 

The extent of irradiation damage is a function of fluence and temperature, and impacts phonon 

heat transfer. FRAPCON-3.3 and FRAPTRAN 1.3 assume instantaneous change in the 

irradiation damage when the temperature changes such as a temperature transient but this is most 

likely not correct because the higher temperature will anneal the damage. In reality, the 

annealing of damage is most likely time dependent. There are some thermal diffusivity data that 

are measured above the irradiation temperature that may provide some information on how to 

model this damage as a function of time. The second term is an electronic term that describes 
2.72 

heat transfer by electrons. This term is not expected to have any time dependence of a rapid 

change with temperature. 

Thermal Expansion

Thermal expansion in both the fuel and the cladding is a function of the crystal lattice constant 

increasing due to increased temperature changing the inter-atomic bond energies. This change in 

lattice constant manifests itself as a macroscopic swelling of the material. There is no delay 

between the increase in temperature and the macroscopic swelling in the fuel or the cladding. 

k, m, and n

The strength coefficient, k, strain rate exponent, m, and strain hardening exponent, n are used to 

determine the stress, strain behavior of the cladding. These coefficients are a function of 

temperature, cold work, fast neutron fluence, and alloy type. Although the effective cold work 

and fluence effects (due to irradiation damage) can change, this is modeled in the annealing 

model, and the stress strain correlation has strain rate dependence in it, the equations for k, m, and 

n should not change with time for a given set of temperature, cold work and fast neutron fluence. 

2.7.2 Properties and models with time dependence that can change over short 

time intervals (e.g. < 10 minutes) and should be modeled in FRAPTRAN 

Zircaloy annealing

The current versions of both FRAPCON-3 and FRAPTRAN contain a Zircaloy annealing model. 

The mechanical properties in FRAPCON-3 and FRAPTRAN are a function of both cold work 

and fast neutron fluence. The effects that these parameters have on the mechanical properties of 

Zircaloy are reduced when the cladding temperature increases during a transient. In addition, the 

time at temperature affects the degree to which these effects are reduced. The annealing model in 

FRAPCON-3 and FRAPTRAN is the ‘CANEAL’ model from MATPRO-11. This model 

calculates effective values for the cladding cold work and fast neutron fluence based on the 

temperature history that the cladding has seen. In this way, the time dependence of temperature 

on cladding mechanical properties is accounted for. 

The current annealing model is based on limited data. However, there is not currently 

significantly more data on cladding annealing. If more data become available, this model will be 

re-examined. 

Power law for plastic stress/strain behavior

The stress strain behavior of zirconium alloy cladding is affected by the strain rate as well as the 

cold work and neutron fluence. For example, it has been observed that the yield stress and 

ultimate tensile strength of irradiated Zircaloy is about 15% greater during tests at high strain 

rates such as 1-10 in/in/s than during tests at lows strain rates such as 10-5 in/in/s. 

FRAPTRAN calculates the strain rate in the cladding based on the strain rate from the previous 

time step. The power law that relates plastic stress and strain is a function of strain rate. In this 

way, the strain rate is accounted for in the cladding stress/strain behavior. 
2.73 

Release of fission gas from grain boundary

Fission gas that is accumulated on the grain boundary can be released to the rod void volume if 

the fuel temperature were to increase rapidly. This is of particular concern for RIA accidents, 

where it has been observed that fission gas release on the order of 5-20% is observed over a time 

period of less than 1 second. 

Currently, FRAPTRAN 1.3 has no transient fission gas release model. However, a new model 

has been developed for FRAPCON-3 that can be used to predict how much gas is on the grain 

boundaries, in addition to how much gas has been released during normal operation. A transient 

gas release model is under development that can use the gas on the grain boundary to predict how 

much gas will be released during a power transient. The release of grain boundary gas is 

expected to be nearly instantaneous with the temperature increase due to cracking and/or grain 

boundary separation. Additional diffusion of gas to the grain boundary is not expected over the 

time periods (< 10 minutes) modeled in FRAPTRAN. 

Hydrogen dissolution and precipitation

FRAPTRAN-1.3 contains a strain based failure model that is used for cladding failure due to 

PMCI at temperatures below 700K. This model is used to predict failure during RIA-type 

accidents. This model is a function of temperature and excess hydrogen in the cladding. During 

a RIA, the cladding temperature is rapidly heated up within less than a second. The rate of 

change in excess hydrogen is such that the level of hydrogen in the cladding does not change 

appreciably over such a short time period. Because of this the steady state (equilibrium) value of 

hydrogen solubility that increases as the cladding temperature increases should not be used to 

predict the excess hydrogen in the cladding for this transient. A rate dependent dissolution 

(Kearns 1968) and precipitation (Une et al. 2003) model of hydrogen in Zircaloy is included in 

FRAPTRAN-1.3, so that the excess hydrogen content can be determined as a function of time and 

temperature during heat-up of the cladding on the order of several seconds or minutes. 

Fuel melting

As energy increases in the fuel and the temperature reaches the fuel melting point, the heat of 

fusion must be absorbed by the fuel before the fuel temperature will continue to increase. This 

will cause a delay in the fuel temperature as a function of energy deposited that must be modeled 

in FRAPTRAN. In FRAPTRAN-1.3, when the fuel reaches the fuel melting temperature, the fuel 

temperature is held at the melting temperature until the fuel absorbs the heat of fusion. During 

the period of time that the fuel is absorbing the heat of fusion, the code calculates the volume 

fraction of fuel that is molten and the volume fraction that is solid. This volume fraction is used 

to determine the fuel thermal expansion of the pellet given the two phase composition and the 

volume change associated with fuel melting. 
2.74 

2.7.3 Properties and models with time dependence much greater than the time 

period modeled in FRAPTRAN 

Fuel Relocation

Fuel relocation is the term used to describe the cracking that occurs in a pellet as it expands and 

cracks and becomes larger than the solid pellet had been. This process is modeled in FRAPCON3 as a power and burnup dependent phenomenon for the first 5 GWd/MTU of operation and 

remains constant for higher burnup. This model is based on beginning of life fuel temperature 

measurements taken in the Halden reactor. 

Because burnup accumulation is not modeled in FRAPTRAN the evolution of relocation is not 

modeled in FRAPTRAN. FRAPTRAN uses a simplification of the FRAPCON-3 model. For 

unirradiated fuel, the relocation is assumed to be 30% of the gap size. For irradiated fuel, the 

relocation is assumed to be 45% of the gap size. If FRAPCON-3 is used to initialize 

FRAPTRAN, the relocation calculated in FRAPCON-3 for a burnup dependent case is passed to 

FRAPTRAN as a pellet strain and the simplified model discussed above is ignored. 

Recovery of fuel relocation

In FRAPCON-3 when the pellet and cladding come in contact, 50% of the calculated relocation is 

accommodated back into the pellet, to account for the repacking of some of the fuel fragments. 

This assumption is based on beginning of life measurements of the onset of cladding axial 

elongation and Halden squeeze tests on fuel pellets. This accommodation process occurs over 

some length of time that is assumed to be greater than the time modeled in FRAPTRAN. In 

FRAPTRAN, hard contact is assumed to occur when the pellet and cladding first come into 

contact. This assumption was made so that the predicted hoop strains in FRAPTRAN compare 

well with measured hoop strains from RIA tests. 

Release of fission gas from grains to grain boundaries

Fission gas is produced within the fuel grains and diffuses out of the grains to the grain 

boundaries. Once these grain boundaries are saturated, the gas on the grain boundaries is released 

to the rod void. The rate of diffusion of Xe and Kr in UO2 is such that over the period of < 10 

minutes significant diffusion will not occur. Because of this, the transient fission gas release 

model that will be developed for FRAPTRAN will not consider gas diffusion from the grains. 

The only source of fission gas for this transient model will be gas that has previously accumulated 

on the grain boundaries. 

Fuel swelling and densification

Solid fission product swelling and fuel densification happen over a long period of time. These 

changes are typically on the order of ± 1 % ΔV/V per 10 GWd/MTU (>100 days). Since the 

period of time that is typically modeled in FRAPTRAN (< 10 minutes) is significantly shorter 

than this period of time, no fuel swelling or densification is modeled in FRAPTRAN. For a case 

with burnup dependent properties from FRAPCON-3, the deformed pellet radius from the final 

time step that includes changes due to densification and solid swelling is input to FRAPTRAN. 

No further swelling or densification is calculated in FRATPRAN for this case. 
2.75 

Gaseous swelling is not modeled in FRAPCON-3.3 or FRAPTRAN 1.3. Gaseous swelling may 

be important at high burnups (> 40 GWd/MTU) for high power increases on the order of several 

minutes at power. Gaseous swelling is diffusion dependent. 

Cladding irradiation and thermal creep 

Irradiation creep in the cladding is a process that causes strain in the cladding as a function of fast 

neutron flux, time, and temperature. The period of time that is typically modeling in 

FRAPTRAN (< 10 minutes) is significantly shorter than the time required to get significant 

irradiation creep. As with the swelling and densification, FRAPTRAN assumes that no 

irradiation creep occurs. For a case with burnup dependent properties from FRAPCON-3, the 

deformed cladding radius from the final time step is input to FRAPTRAN. No further cladding 

creep is calculated in FRAPTRAN for this case. 

Thermal creep is not modeled in either FRAPCON-3.3 or FRAPTRAN 1.3 with the exception of 

cladding ballooning at very high temperature (>750°C) that is modeled in FRAPTRAN 1.3. 

Cladding ballooning can occur during a LOCA event. Thermal creep is diffusion dependent such 

that it takes several seconds to hours depending on cladding temperature to be significant. The 

new creep model that has been developed and implemented in FRAPCON-3.4 contains a thermal 

creep term. This model is described in Section 3.7. 

Cladding irradiation growth

Irradiation growth in the cladding is a process that causes axial strain in the cladding as a function 

of fast neutron fluence. The period of time that is typically modeled in FRAPTRAN (< 10 

minutes) is significantly shorter than the time required to get significant growth. As with the 

cladding creep, FRAPTRAN assumes that no irradiation growth occurs. For a case with burnup 

dependent properties from FRAPCON-3, the cladding elongation from the final time step is input 

to FRAPTRAN. No further cladding growth is calculated in FRAPTRAN for this case. 

2.7.4 Summary 

The material properties and models for the fuel and cladding can be divided into three categories. 

These categories are; those with out time dependence, those with time dependence that can 

change over short time intervals (e.g. < 10 minutes) and should include a time dependence term 

in FRAPTRAN, and those with a time dependence much greater than the time interval that is 

typically modeled in FRAPTRAN that can be ignored completely in FRAPTRAN. The material 

properties and models of the fuel and cladding are divided up into each of these categories, and 

those in the second category have been examined to ensure that they are adequately modeled in 

FRAPTRAN. 

For those material properties and models with time dependence that can change over short time 

intervals (e.g. < 10 minutes), all are assumed to be correctly modeled in FRAPTRAN, except for 

grain boundary release of fission gas. A model is currently under development to simulate this 

behavior. In addition, there are not much data to support the cladding annealing model, but no 

more is currently available. As more data become available, this model will be re-examined. No 

gaseous swelling model or thermal creep model exists in FRAPTRAN-1.3 or FRAPCON-3.3. A 

gaseous swelling model is currently under development. A thermal term has been included in the 

new creep model described in Section 3.7. 
2.76 

2.8 Conclusions 

The conclusion of this assessment is that both FRAPCON-3.3 and FRAPTRAN 1.3 provide bestestimate predictions of fuel temperature (see Section 2.1.7), fission gas release (see Section 2.2.2) 

and cladding stress and strain (see Section 2.5.3). Several individual models have been identified 

as being biased over certain ranges, but the integral predictions of fuel and cladding temperature 

and cladding stress and strain in FRAPCON-3.3 and FRAPTRAN 1.3 are best-estimate. The 

following list includes individual models that have been re-examined, to improve the model’s 

predictive capability in FRAPCON-3.4 and FRAPTRAN 1.4. These model improvements are 

discussed in Section 3. 

• Cladding corrosion: Recent adjustments have been made to simulate corrosion on ZIRLOTM 

and M5TM. Some comparisons have shown that this adjustment may not be valid at high 

burnup for ZIRLOTM. This model has been reassessed and made to provide a better fit to 

ZIRLOTM corrosion data. 

• BWR cladding hydrogen content: New data show the need for a new model for predicting 

BWR cladding hydrogen content. A model has been developed to calculate this. 

• Radial power profile: The radial power profile should be assessed relative to the expected 

radial power profile in a HWR and a radial power model has been developed for UO2-Gd2O3

fuel. 

• Fuel thermal expansion at high temperature: A new model has been developed to better fit 

the data at high temperature. 

• Gas thermal conductivity: The gas conductivity models are not valid for most gasses beyond 

1100K and new data are available for new model development. This will not affect most of 

the temperature predictions since the gas does not typically exceed 1000K. New models have 

been developed that better predict these data. 

• Steam thermal conductivity: The models in both codes have been changed to match the 

ASME model. This is most important in FRAPTRAN 1.3 where the gap may be filled with 

steam after cladding rupture. 

• Cladding irradiation creepdown: Some evidence indicates that the cladding irradiation 

creepdown model in FRAPCON-3.3 may predict creepdown to occur too rapidly. This has 

been assessed and a new irradiation creepdown model has been developed. 

• Thermal creep impacts calculation of permanent strains below the yield stress for transients 

on the order of several minutes to hours. The new creep model contains a thermal creep term. 

• Clad-coolant heat transfer models – The models for clad-coolant heat transfer in FRAPTRAN 

were updated. These models are discussed elsewhere (Cuta, 2007). 

The following list contains areas where modeling has not been done, but where new modeling 

capabilities could be added and possibly improve the codes’ predictive capabilities. 

• Fission gas release: There is no fission gas release model in FRAPTRAN 1.3. Significant 

gas release has been observed during RIAs. A model should be developed to simulate this 

release in FRAPTRAN 1.3, and if necessary, the model in FRAPCON-3.3 should be modified 

to provide initial conditions to this new model. 

• Fission gas release: The fission gas release model in FRAPCON-3.3 underpredicts FGR for 

power ramped rods with hold times less than 4 hours. The model should be modified to 

account for this. Until this time, PNNL recommends that the hold time be increased by a 

factor of 3 for power ramp hold times less than 4 hours to conservatively bound the expected 

fission gas release behavior. 
2.77 

• Gaseous swelling is not modeled and may be important for transient in high burnup fuel 

lasting several minutes to hours. 

• Time dependent change in thermal conductivity due to thermal annealing of irradiation 

defects during a slow temperature transient. 

• Hydrogen pickup from high temperature oxidation not modeled in FRAPTRAN 1.3 

• Axial and radial strain predictions in FRAPTRAN 1.3 

3.1 

3.0 UPDATES TO MODELS 

This section discusses the models that have been found to be biased in Section 2.0 and have been 

updated to provide a best-estimate fit to the available data. Since these models are new, they will 

be validated relative to the available data and standard deviation will be calculated relative to the 

available data. All of these models will be included in the new code versions, FRAPCON-3.4 

and FRATPRAN 1.4, when they are released. The release of FRAPCON-3.4 and FRAPTRAN 

1.4 will each be accompanied by a document that describes the changes that have been made 

since the previous version as well as providing the results of the integral assessment comparisons 

for integral effects such as centerline temperature and rod internal pressure. The integral effects 

may be impacted by the changes made to models described in this section as well as other 

changes made since the previous code release. The overall code validation will be performed in 

the documents accompanying the release of each code. 

3.1 Corrosion and Hydrogen Pickup in Cladding Alloys 

Section 2.3 identified that the corrosion and hydrogen pickup models in FRAPCON-3.3 are 

deficient in the areas of hydrogen pickup in Zircaloy-2 in BWR conditions, corrosion of 

ZIRLOTM at high burnup, and corrosion of M5TM at high burnup. This section will discuss how 

these models have been changed to provide a best-estimate prediction for these alloys. 

3.1.1 Hydrogen pickup in Zircaloy-2 

The recent data comparison shown in Section 2.3.2 found that a constant hydrogen pickup 

fraction is not appropriate for hydrogen pickup in Zircaloy-2. In addition, it was found that the 

hydrogen pickup in new Zircaloy-2 where the vendors have better control over the alloy 

composition and second-phase precipitate (SPP) size is different from older Zircaloy. 

Correlations were developed for the hydrogen pickup in older and new Zircaloy-2 as a function of 

burnup. These correlations are given below. 

For older Zircaloy-2: 

BU

Bu

HTot ⎟ + ⋅ ⎠

⎞ ⎜

⎝

⎛

+

− 0.316

1

1.3 47.8exp

Where: 

HTot = total hydrogen, ppm (wt) 

BU = local axial burnup, MWd/kgU (only valid to 50 MWd/kgU) 

For new Zircaloy-2: 

H = 22.8 + exp( ) 0.117(BU − 20) Tot

Where: 

HTot = total hydrogen, ppm (wt) 

BU = local axial burnup, MWd/kgU (valid up to 70 MWd/kgU) 

It is noted that the correlation for older Zircaloy-2 is only valid to 50 MWd/kgU. This is because 

there is no data available above 50 MWd/kgU. For older Zircaloy, when the burnup exceeds 50 

MWd/kgU, it is recommended that the correlation for newer Zircaloy plus 6.1 (the difference 

between these correlations at 50 MWd/kgU) be used. FRAPCON-3.4 will be modified to include 

these equations for hydrogen pickup in Zircaloy-2 cladding under BWR conditions. In addition, a 

new variable will be added to select between new Zircaloy-2 and older Zircaloy-2. 
3.2 

Figure 3.1 shows the data and the correlations that have been developed for hydrogen pickup in 

old and new Zircaloy-2 as well as the previous model used in FRAPCON-3.3. The data for the 

older fuel types is primarily from Japanese reactors. The standard deviation, σ, of this correlation 

is 9.69 ppm that appears to remain relatively constant up to 45 MWd/kgU. The standard 

deviation for the correlation for newer Zircaloy-2 can be seen to be burnup dependent with the 

scatter in the data significantly increasing above a local burnup of 49 MWd/kgU. Therefore, the 

calculation of standard deviation has been broken into two separate burnup ranges of 0 to 49 

MWd/kgU where σ = 10.76 ppm and for burnups between 49 to 65 MWd/kgU where σ = 60.62 

ppm. The distribution of the predicted-minus-measured is close to a normal distribution within a 

given burnup range such that use of normal statistics is assumed to be valid. 

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80

Local Axial Burnup [MWd/kgU]

Hydrogen Content [ppm] 

Old Zircaloy-2 New Zircaloy-2

FRAPCON-3.3 FRAPCON-3.4 Old Zircaloy-2

FRAPCON-3.4 New Zircaloy

Figure 3.1 Comparison of recent Zircaloy-2 hydrogen pickup data to new correlations 

for old and new Zircaloy-2 cladding 

3.1.2 Corrosion in ZIRLOTM 

The data comparison in Section 2.3.1 where the ZIRLOTM model in FRAPCON-3.3 was 

compared to two high exposure rods (A06 & A12) (CSN, ENUSA, 2002) found that the model 

underpredicts oxide thickness at high burnup (>70 GWd/MTU). The model in FRAPCON-3.3 

for ZIRLOTM had been the same as the model for Zircaloy-4, but the final oxide thickness was 

reduced by a factor of 2.0 (Lanning et al, 2005a). In order to provide a better fit to the data, the 

following changes were made to the Zircaloy-4 model for the modeling of ZIRLOTM. 

• The value used for weight gain from the previous time step was increased by a factor of 

2.0. 

• The calculated thickness for the current time step was decreased by a factor of 2.0. 

• The activation energy for post transition oxidation, Q2, was decreased by a factor of 0.99. 
3.3 

Figure 3.2 shows the FRAPCON predictions of oxide thickness as a function of fuel duty index 

(FDI) using the old model (FRAPCON-3.3) and the new model (FRAPCON-3.4). The 

FRAPCON-3 predictions are performed for one of the high exposure rods, A06, and for several 

other typical PWR rods where power history and design information is known that allowed 

cladding temperatures and fuel duty index (FDI) to be calculated for a given PWR design 

assuming ZIRLOTM cladding. Also shown in this figure is a large quantity of ZIRLOTM oxide 

thickness data (Knott et al., 2003). 

0

20

40

60

80

100

120

0 200 400 600 800 1000

Fuel Duty Index

Oxide Thickness, 

μ

m

ZIRLO Data A06 REP Na 8 Base TSQ002 BFM034

 (a) 

0

20

40

60

80

100

120

0 200 400 600 800 1000

Fuel Duty Index

Oxide Thickness, 

μ

m

ZIRLO Data A06 Rep Na8 Base TSQ002 BFM034

 (b) 

Figure 3.2 ZIRLOTM data vs. burnup and (a) FRAPCON-3.3 and (b) FRAPCON-3.4 

model predictions for several sample PWR rods 

It can be seen from this figure that the model in FRAPCON-3.3 begins to underpredict the oxide 

thickness by a FDI of 700. However, the new model shows good predictions out to a FDI of 900. 

It is difficult to calculate the uncertainty of this model as the actual temperature and time for each 
3.4 

data point in Figure 3.2 is not known. However, a standard deviation of 20% is estimated based 

on the data comparisons seen here and in Figures 3.3 and 3.4. 

The new end of life predictions for the high burnup rods, A06 and A12 are shown in Figures 3.3 

and 3.4 with the measured oxide thickness at end of life. It can be seen from these figure that the 

new correlation provide significantly better prediction of the oxide layer thickness for these rods. 

FRAPCON-3.4 was modified to include these adjustments to the equations for corrosion in 

ZIRLOTM cladding under PWR conditions. With the new ZIRLOTM, corrosion model, the 

hydrogen pickup predictions still predicted the data very well. Therefore, the ZIRLOTM was kept 

the same in FRAPCON-3.4 as it was in FRAPCON-3.3. 

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, 

μ

m

Data Lower Bound Data Median Data Upper Bound

Old ZIRLO Correlation New ZIRLO Correlation

Figure 3.3. Old and New ZIRLOTM model predictions for end of life oxide thickness for 

rod A06 
3.5 

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, 

μ

m

Data Lower Bound Data Median Data Upper Bound

Old ZIRLO Correlation New ZIRLO Correlation

Figure 3.4 Old and New ZIRLOTM model predictions for end of life oxide thickness for 

rod A12 

3.1.3 Corrosion and Hydrogen Pickup in M5TM 

The data comparison in Section 2.3.1 where the M5TM model in FRAPCON-3.3 was compared to 

a high exposure rod (N05) (Segura, 2002) found that the model overpredicts oxide thickness at 

high burnup (>70 GWd/MTU). The model in FRAPCON-3.3 for M5TM had been the same as the 

model for Zircaloy-4, but the final oxide thickness was reduced by a factor of 2.3. In order to 

provide a better fit to the data, the following changes were made to the Zircaloy-4 model for the 

modeling of M5TM. 

• The activation energy for pre transition oxidation, Q1, was reduced by a factor of 0.85. 

• The onset of post transition oxidation was increase from 2 μm to 7 μm. 

• The activation energy for post transition oxidation, Q2, was increased by a factor of 1.09. 

Figure 3.5 shows the FRAPCON predictions of oxide thickness as a function of burnup using the 

old model (FRAPCON-3.3) and the new model (FRAPCON-3.4). The FRAPCON-3 predictions 

are performed for the high exposure rod, N05, and for several other typical PWR rods assuming 

M5TM cladding. Also shown in this figure is a large quantity of M5TM oxide thickness data 

(Mardon and Waeckel, 2003). 

It can be seen from Figure 3.5 that the model in FRAPCON-3.3 began to overpredict the oxide 

thickness by 30-40 GWd/MTU. However, the new model shows good predictions out to 70 

GWd/MTU. It is difficult to calculate the uncertainty of this model as the actual temperature and 

time for each data point in Figure 3.5 is not known. However, a standard deviation of 20% is 

estimated based on the data comparisons seen here and in Figure 3.6. 
3.6 

0

10

20

30

40

50

60

0 20 40 60 80

Burnup, GWd/MTU

Oxide Thickness, 

μ

m

N05 M5 Data REP Na 8 Base TSQ002 BFM034

 (a) 

0

10

20

30

40

50

60

0 20 40 60 80

Burnup, GWd/MTU

Oxide Thickness, 

μ

m

N05 M5 Data Rep Na8 Base TSQ002 BFM034

 (b) 

Figure 3.5 M5TM data vs. burnup and (a) FRAPCON-3.3 and (b) FRAPCON-3.4 model 

predictions for several sample PWR rods 
3.7 

The new end of life predictions for the high burnup rod, N05 are shown in Figure 3.6 with the 

measured oxide thickness at end of life. It can be seen from this figure that the new correlation 

provide an excellent prediction of the oxide layer thickness for this rod. FRAPCON-3.4 was 

modified to include these adjustments to the equations for corrosion in M5TM cladding under 

PWR conditions. 

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000 3500 4000

Axial Elevation, mm

Oxide Thickness, 

μ

m

Data Lower Bound Data Median Data Upper Bound

Old M5 Correlation New M5 Correlation

Figure 3.6 Old and New M5TM model predictions for end of life oxide thickness for rod 

N05 

In FRAPCON-3.3, the hydrogen pickup fraction for M5 was 7.5%. However, this pickup fraction 

was based on comparisons to hydrogen concentration data plotted as a function of burnup. 

Hydrogen concentration is not directly a function of burnup, but rather of oxide thickness and 

hydrogen pickup fraction. Since the FRAPCON-3.3 model overpredicted oxide thickness, it was 

reduced as described above. Therefore, in order to get the same hydrogen concentrations at a 

given burnup, the pickup fraction had to be increased for the new model. A pickup fraction of 

10% was found to provide the best fit to these data. Figure 3.7 shows a plot of the hydrogen 

concentration data with FRAPCON-3.4 hydrogen concentration predictions at end of life at 

various axial elevations for three typical PWR cases. FRAPCON-3.4 was modified to use a 

pickup fraction of 10% for hydrogen pickup in M5TM cladding under PWR conditions. It is 

difficult to calculate the uncertainty of this model as the oxide thickness for each data point in 

Figure 3.7 is not known. However, a standard deviation of 20 ppm is estimated based on the data 

comparisons seen in Figure 3.7. 
3.8 

0

20

40

60

80

100

120

140

160

0 20 40 60 80

Local Burnup, GWd/MTU

Hydrogen Concentration, 

ppm

M5 Data REP Na8 Base TSQ002 BFM034

Figure 3.7 Hydrogen concentration data for M5TM and FRAPCON-3.4 predictions of 

hydrogen for typical PWR cases 

3.2 Radial Power Profile in HWR 

The TUBRNP (Lassman et al. 1994) model in FRAPCON-3.3 predicts the radial power profiles 

within the fuel pellet as a function of uranium and plutonium isotopic concentration and burnup. 

The version of this subroutine contains one parameter that is modified to account for HWR 

conditions. The constant p1 is changed from 3.45 to 2.45 for HWR conditions. Comparison to 

data and other neutronic code predictions have demonstrated that this adjustment does not 

correctly account for the differences in heavy water and light water reactor conditions. 

Since the original release of FRAPCON-3, a second paper has been published on the 

modifications to TUBRNP to correctly model HWR conditions (Lassman et al. 1998). This paper 

stated that the original TUBRNP model could be modified to be applicable to HWR conditions if 

the fission and capture cross sections for each uranium and plutonium isotopes were updated 

based on a HWR neutron spectrum and if the constant p1 was changed from 3.45 to 2.21. The 

neutron spectrum in a HWR has relatively more neutrons in the thermal region and relatively 

fewer neutrons in the fast region. Therefore the spectrum-averaged fission and capture cross 

sections will be different for LWR and HWR conditions. 

Lassman et al. (1998) did not provide the spectrum-averaged cross sections that they used to 

update this model. The current TRANSURANUS code developers were contacted and the cross 

section values that are used in TUBRNP for HWR conditions were provided. 

The internal version of FRAPCON-3.4 was modified to use the recommended value of p1 and 

fission and capture cross sections for HWR conditions. The predictions of this modified version 

of FRAPCON-3.4 were compared to rods that had electron probe microanalysis (EPMA) data of 

the fission product, Nd (Lassmann et al., 1998). This fission product is immobile in UO2 and the 

concentration of Nd is related to the fission density and thus can be converted to burnup. Figures 

3.8 and 3.9 show the original TUBRNP and the modified TUBRNP predictions of radial burnup 

distribution for two different rod sections irradiated at Halden and DR3. 
3.9 

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1

Normalized Fuel Radius

Burnup, GWd/MTU

Nd Data Original TUBRNP Modified TUBRNP

Figure 3.8 Burnup distribution in rod section F9-3-44 with U-235 enrichment of 5%, 

irradiated to 39 GWd/MTU in the Halden reactor

0

50

100

150

200

250

0 0.2 0.4 0.6 0.8 1

Normalized Fuel Radius

Burnup, GWd/MTU

Nd Data Original TUBRNP Modified TUBRNP

Figure 3.9 Burnup distribution in rod section AF21-2-8 with U-235 enrichment of 1.5%, 

irradiated to 72.2 GWd/MTU in the DR3 reactor
3.10 

Figure 3.10 shows a comparison of the predictions of the TUBRNP model for a rod with 7% U235 irradiated in the Halden reactor compared to the Halden predictions made using FTEMP. 

0.8

0.9

1

1.1

1.2

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6

Radius, cm

Relative Power

FTEMP-0 GWd/MTU TUBRNP-0 GWd/MTU

FTEMP-20 GWd/MTU TUBRNP-20 GWd/MTU

Figure 3.10 Radial power profile in IFA-558 as predicted by FTEMP and TUBRNP with 

U-235 enrichment of 7%, irradiated in the Halden reactor

It can be seen from these figures that the modified version of TUBRNP provides slightly better 

predictions of the edge peaking, particularly for the lower burnup section seen in Figure 3.8. For 

the comparison in Figure 3.9, the modified version of TUBRNP only provides slightly less edge 

peaking. It can also be seen that the TUBRNP predictions are almost identical to the FTEMP 

predictions at beginning of life and similar thereafter. The modified version of TUBRNP was 

added to FRAPCON-3.4. Based on data comparisons and comparisons to other codes, it can be 

estimated that the radial power profile model in FRAPCON-3.4 has a standard deviation of about 

2.5%. The modified version of TUBRNP will be compared to a more detailed neutronics code 

(such as WIMS) calculation of radial power in HWR prior to the release of FRAPCON-3.4. 

3.3 Radial Power Profile in UO2-Gd2O3

Based on the success of using TUBRNP to model the radial power profile for UO2 and MOX 

under LWR and HWR conditions, it was thought that if the model was modified to track the 

neutron absorption and quantity of the neutron absorbing isotopes of gadolinium, Gd-155 and Gd157 then this model could be used to predict the radial power profile of UO2-Gd2O3 fuel. 

This approach was attempted, but the results predicted by TUBRNP were not reasonable in that 

they did not match neutronic code predictions done at Halden ( Klecha 2005, Volkov et al. 2002) 

and the centerline temperature predictions in FRAPCON-3 did not match centerline temperature 

measurements from Halden test rods with centerline thermocouples. 

The centerline temperature comparisons for Halden UO2-Gd2O3 rods shown in Section 2.1.7.2 

were performed using the radial power profiles provided by Halden for various burnups and 

radial positions. A lookup and interpolation routine was used to calculate the radial power for 

each time step and location in FRAPCON-3. This approach provided good predictions of 
3.11 

centerline temperature for these rods, however, the radial power profiles used here were specific 

for these rods and the Halden reactor and could not be independently verified. 

In order to model the radial power profile for UO2-Gd2O3, a typical rod was modeled in WIMS 

for 0, 2, 4, 6, 8, and 10 wt% Gd2O3 at various burnup levels for LWR and HWR conditions. The 

results of these calculations were put into FRAPCON-3.4 as a data table and a lookup and 

interpolation routine was used to calculate the radial power profile. This lookup table is used for 

burnup values less than 7 GWd/MTU in FRAPCON-3.4. The WIMS calculations for the case 

with 10 wt% Gd2O3 showed that all the Gd-155 was gone (<0.1%) by about 7 GWd/MTU and all 

the Gd-157 was gone by about 5 GWd/MTU. Beyond this burnup level, the neutron absorbing 

isotopes, Gd-155 and Gd-157, have converted to non-neutron absorbing isotopes and the radial 

power profile is very similar to the radial power profile for UO2. For burnup levels greater than 7 

GWd/MTU, the TUBRNP model is used to calculate the radial power profile for UO2-Gd2O3. 

The burnup values output by WIMS do not directly correspond with those in FRAPCON-3. In 

WIMS, a constant power of 40 MW/MTU (5.73 kW/ft) was used for these calculations. However, 

in reality, while the gadolinium is burning out in a fuel rod, the power level is much less than this 

due to neutron absorption by gadolinium. The power level and burnup in WIMS best corresponds 

to the power level and burnup in the neighboring UO2 fuel rods. The power profiles provided by 

WIMS are best described as a function of time. In order to account for this, an effective burnup is 

calculated in FRAPCON-3.4 to use in the interpolation routine where the burnup increment for 

each time step is the burnup calculated by FRAPCON-3 times the ratio of 5.73 kW/ft to the actual 

fuel rod power. 

The FRAPCON-3.4 predictions were compared to those made using the radial power profiles 

calculated by Halden and to the measured temperature data from IFA-636 (Tverberg et al 2005, 

Volkov et al 2002, Tolonen & Tverberg, 2005) and from IFA-681 (Tolonen & Tverberg, 2005, 

Tolonen & Andres 2005, Klecha 2005). Plots of these comparisons are shown in Figures 3.11-

3.16. It is noted that the measured temperature for IFA-636 Rod 4 (solid pellets) was estimated 

by Halden from IFA-636 Rod 2 thermocouple measurements. It can be seen from these figures 

that using the new data table to calculate radial power profile, FRAPCON-3.4 predicts centerline 

temperature values as well as those using the Halden data tables. It is concluded that the new 

data table is well within the accuracy of measured rod power and temperatures. 
3.12 

0

200

400

600

800

1000

1200

0 100 200 300 400 500 600 700 800

Time, Days

Temperature, °C

636 Rod 2 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.11 Centerline temperature measurements and predictions for IFA-636 Rod 2 

with hollow pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses 

the Halden table of radial power profiles. The FRAPCON-3.4 prediction 

uses the new table of radial power profiles 

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

Rod Average Burnup, GWd/MTU

Temperature, °C

636 Rod 4 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.12 Centerline temperature measurements and predictions for IFA-636 Rod 4 

with solid pellets and 8 wt% Gd2O3 (Solid pellet temperatures are estimated 

from measurements made on hollow pellets in IFA-636 Rod 2.) The 

FRAPCON-3.3 prediction uses the Halden table of radial power profiles. 

The FRAPCON-3.4 prediction uses the new table of radial power profiles 
3.13 

0

200

400

600

800

1000

1200

1400

0 50 100 150

Time Days

Temperature, °C

Rod 2 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.13 Centerline temperature measurements and predictions for IFA-681 Rod 2 

with solid pellets and 2 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses 

the new table of radial power profiles 

0

200

400

600

800

1000

1200

0 50 100 150

Time Days

Temperature, °C

Rod 3 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.14 Centerline temperature measurements and predictions for IFA-681 Rod 3 

with solid pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses the 

Halden table of radial power profiles. The FRAPCON-3.4 prediction uses 

the new table of radial power profiles 
3.14 

0

200

400

600

800

1000

1200

1400

0 50 100 150

Time Days

Temperature, °C

Rod 4 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.15 Centerline temperature measurements and predictions for IFA-681 Rod 4 

with hollow pellets and 2 wt% Gd2O3. The FRAPCON-3.3 prediction uses 

the Halden table of radial power profiles. The FRAPCON-3.4 prediction 

uses the new table of radial power profiles 

0

200

400

600

800

1000

1200

1400

0 50 100 150

Time Days

Temperature, °C

Rod 6 Data FRAPCON-3.3 FRAPCON-3.4

Figure 3.16 Centerline temperature measurements and predictions for IFA-681 Rod 6 

with hollow pellets and 8 wt% Gd2O3. The FRAPCON-3.3 prediction uses 

the Halden table of radial power profiles. The FRAPCON-3.4 prediction 

uses the new table of radial power profiles 
3.15 

3.4 Fuel Thermal Expansion at High Temperature 

The original model in FRAPCON-3.3 and FRAPTRAN 1.3 for UO2 thermal expansion is given 

below. 

⎟

⎠

⎞ ⎜

⎝

⎛ − = − +

Δ

kT

E K T K K

L

L D

1 2 3 exp

0

Where: 

L0

ΔL =linear strain caused by thermal expansion with a reference of 300K 

K1=1.0x10-5 

K2=3.0x10-3

K3=4.0x10-2

ED=6.9x10-20

k = 1.38x10-23

This model was found to underpredict data above 2200K in Section 2.1.4. The coefficients in this 

model were updated to provide a better fit of all the data. The updated coefficients are given 

below. 

K1=9.80x10-6 

K2=2.61x10-3

K3=3.16x10-1

ED=1.32x10-19

Figure 3.17 shows a plot of the original and the new model with all the available data as a 

function of temperature. It can be seen that the modified model provides a better fit to the data 

above 2300K. This new models has been added to FRAPCON-3.4 and FRAPTRAN 1.4. The 

standard deviation of this model relative to the data in Figure 3.16 is 0.0015 ΔL/L. 
3.16 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Expansion, 

ΔL/L

FRAPCON-3.3 Gronvold

Baldock Burdick

Other MATPRO References Martin References

Updated Model

Figure 3.17 Original and modified UO2 thermal expansion model with available data as a 

function of temperature. 

3.5 Gas Thermal Conductivity at High Temperature 

The original model for gas thermal conductivity used in FRAPCON-3.3 and FRAPTRAN 1.3 is 

given below. 

B k = AT

Where: 

k = thermal conductivity, W/m-K 

T = temperature, K 

The coefficients A and B that are used for each gas species is given in Table 3.1. 

Table 3.1 Original A and B coefficients used in FRAPCON-3.3 and FRAPTRAN 1.3 

Gas A B 

He 2.639x10-3 0.7085 

Ar 2.986x10-4 0.7224 

Kr 8.247x10-5 0.8363 

Xe 4.351x10-5 0.8616 

H2 1.097x10-3 0.8785 

N2 5.314x10-4 0.6898 
3.17 

This model was found to underpredict gas conductivity at high temperature. Because of this the 

model parameters, A and B were updated to provide a better fit to the data. The updated 

coefficients for each gas are shown in Table 3.2. 

Table 3.2 Modified A and B coefficients 

Gas A B 

He 2.531x10-3 0.7146 

Ar 4.090x10-4 0.6748 

Kr 1.966x10-4 0.7006 

Xe 9.825x10-5 0.7334 

H2 1.349x10-3 0.8408 

N2 2.984x10-4 0.7799 

Figures 3.18-3.23 show plots of the original and the new models with all the available data as a 

function of temperature. It can be seen that the modified models provides a better fit to the high 

temperature Ar, Kr, Xe, H2 and N2 data. These updated models have been added to FRAPCON3.4 and FRAPTRAN 1.4. The standard deviation for each of these models relative to the data is 

stated in the caption for each figure. 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.18 Original and modified model for He thermal conductivity (σ=0.00899) 
3.18 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.19 Original and modified model for Ar thermal conductivity (σ=0.000966) 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.20 Original and modified model for Kr thermal conductivity (σ=0.000886) 
3.19 

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0.04

0.05

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.21 Original and modified model for Xe thermal conductivity (σ=0.000534) 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.22 Original and modified model for H2 thermal conductivity (σ=0.0167) 
3.20 

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Updated Model

Figure 3.23 Original and modified model for N2 thermal conductivity (σ=0.000197) 

3.6 Steam Conductivity 

The steam conductivity model in FRAPCON-3.3 is 

ksteam =1.76x10−4 + 5.87x10−5

( ) T − 273.15 +1.04x10−7( ) T − 273.15 2

− 4.51x10−11( ) T − 273.15 3

Where: 

ksteam = the steam conductivity, W/m-K 

T = the gas temperature, K. 

The steam conductivity model employed in FRAPTRAN-1.3 for temperatures less than or equal 

to 973.15K is 

ksteam = −2.8516x10−8 + 9.424x10−10T − 6.005x10−14T2

( )p

T

+

1.009p

2

T2

( ) T − 273.15 4.2

− 8.4083x10−3 −1.19998x10−5T − 6.706x10−8T2 − 4.51x10−11T3

Where: 

p = gas pressure, Pa. 

For temperatures above 973.15K, the model employed in FRAPTRAN-1.3 is 
3.21 

ksteam = 4.44x10−6T1.45 + 9.45x10−5 2.1668x10−9 p

T

⎛

⎝

⎜ ⎞

⎠

⎟

1.3

The steam conductivity model in MATPRO is 

( ) ( )

() () () 4 5 7 2 11 3

2 4.2

2

8 10 14 2

17.6 10 5.87x10 273 1.08x10 273 4.51x10 273

273

1.009 2.8516x10 9.424x10 6.005x10

+ × + − + − − −

− = − + − +

− − − −

− − −

T T T

T T

p

T

p ksteam T T

for temperatures less than or equal to 973.15K, and 

ksteam = 4.44x10−6T1.45 + 9.5x10−5 2.1668x10−9 p

T

⎛

⎝

⎜

⎞

⎠

⎟

1.3

for temperatures above 973.15 

The models in FRAPCON-3.3, FRAPTRAN-1.3 and MATPRO were compared to the ASME 

adopted value of steam conductivity at 107

 Pa. These comparisons are shown in Figure 3.24. It 

can be seen from this figure that the MATPRO model predicts the conductivity well, while the 

models in FRAPCON-3.3 and FRAPTRAN 1.3 do not. Because of this, the model described 

above was used for steam conductivity in both FRAPCON and FRAPTRAN. 

-0.1200

-0.1000

-0.0800

-0.0600

-0.0400

-0.0200

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.1200

0.06 0.07 0.08 0.09 0.1 0.11 0.12

Experimental Values (W/m-K)

ASME (1968)

Hagrman et al. (1993)

FRAPTRAN-1.3

FRAPCON-3.3

Figure 3.24 Comparison of low temperature steam conductivity models from MATPRO, 

FRAPTRAN-1.3, and FRAPCON-3.3 with adopted values of experimental 

data from ASME. 
3.22 

This updated model has been added to FRAPCON-3.4 and FRAPTRAN 1.4. 

3.7 Cladding Irradiation Creep 

The data comparisons in Section 2.5.2.1 identified that the cladding creep model in FRAPCON3.3 over-predicts the irradiation creep rate in PWR SRA cladding. In addition, this model is used 

for both SRA and RXA cladding, despite the observations of different creep behavior between the 

two types of cladding. A literature search was performed to select a model that provides a bestestimate prediction of cladding irradiation creep for both SRA and RXA cladding tubes. 

The model given by Limback and Andersson (Limback et al., 1996) was selected for cladding 

irradiation creep in FRAPCON-3.4. This model uses a thermal creep model described by Matsuo 

(1987) and an empirical irradiation creep rate with tuned model parameters that were fit to data 

set by Franklin et al.(1983). This model was modified by PNNL to use effective stress rather 

than hoop stress as an input so that the difference in creep behavior during tensile and 

compressive creep would be modeled correctly. Several of the fitting coefficients were 

consequently changed to accommodate this modification. In addition, a temperature dependent 

term was added to the formula for irradiation creep strain rate. This model has different 

parameters for SRA and RXA cladding types, and provides much more reasonable creep strains 

in the LWR range of temperature and cladding hoop stresses than the current model in 

FRAPCON-3.3. This model is described below. 

The steady state thermal and irradiation creep rates are given by: 

⎟

⎠

⎞ ⎜

⎝

⎛ −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = RT

Q

E

a

T

E A

n

i eff

th sinh exp

σ

ε&

( ) 1 2 C0 f T C

eff

C

irr ε& = ⋅φ ⋅σ ⋅

Where 

th irr ε& ,ε& - thermal and irradiation strain rate, respectively (in/in/hr) 

These rates are added together so: 

th irr th irr ε& = ε& + ε& +

The saturated primary hoop strain is given by: 

( ) 0.109 2.05 0.0216 2 tanh(35500 ) −

+ + = ⋅ − ⋅ th irr th irr

s

p ε ε& ε&

The total thermal strain is given by: 

( ( t)) t th irr th irr

s

H p = − − ⋅ ⋅ + ⋅ + + ε ε 1 exp 52 ε& ε&

In FRAPCON-3.4, strain rate is used. Taking the derivative with respect to time of the 

expression above gives: 

( ) th irr th irr

th irr

s

p

H t

t + +

+ − ⋅ ⋅ +

⋅

⋅ ⋅ = ε ε

ε ε

ε & & & & exp 52

2

52

2

1

2

1

Where: 

T – temperature (K) 

t – time (hours) 

σeff – effective stress, MPa 

φ – fast neutron flux, n/m2-s 
3.23 

Table 3.3 lists the parameters used in these equations for SRA and RXA cladding types 

Table 3.3 Parameters for FRAPCON-3.4 creep equation for SRA and RXA cladding 

Parameter Units Values for SRA Cladding Values for RXA 

Cladding 

A* K/MPa/hr 1.08E9* 5.47E8* 

E MPA 1.149E5-59.9*T 

ai MPa-1 650{1-0.56[1-exp(-1.4E-27*Φ1.3)]} 

Φ = fast neutron fluence (n/cm2) 

n unitless 2.0 3.5 

Q kJ/mole 201 

R kJ/mol-K 0.008314 

C0 (n/m2-s)-C1

MPa-C2 

4.0985E-24 1.87473E-24 

C1 unitless 0.85 

C2 unitless 1.0 

f(T)* unitless T<570K 0.7283 

570<T<625K -7.0237+0.0136T 

T>625K 1.4763 

0.7994 

-3.18562+0.00699132T 

1.1840 

*Parameters changed from original Limback equation 

The effective stress in the cladding is found using the principal stresses at the midwall radius 

using the thick wall formula as follows: 

( )

2 2

0

2

2 2

2 2

i

i o o i

i i o o

r r r

r

r r P P

P r P r

−

− − +

σ =

( )

2 2

0

2

2 2

2 2

i

i o o i

i i o o

t r r

r

r r P P

P r P r

−

− − −

σ =

2 2

0

2 2

i

i i o o

l

r r

Pr P r

−

− σ =

Where: 

Pi – inner pressure 

Po – outer pressure 

ri – inner radius 

ro – outer radius 

r – radius within tube 

σr – radial stress 

σt – tangential stress 

σl – longitudinal stress 

The effective stress, σeff, is then given by: 

( ) ( )( )( ) 2 2 2

σ eff = 0.5 σ l − σ t + σ t − σ r + σ r − σ l
3.24 

This equation has been added to FRAPCON-3.4 for the calculation of creep strain rate. The 

model predictions were compared to creep data from two PWR rods that were used in the original 

FRAPCON-3 model assessment (Lanning et al., 1997). The creep predictions using the original 

creep model in FRAPCON-3.3 and using the modified Limback creep model in FRAPCON-3.4 

are shown in Figures 3.25 and 3.26. These data are taken from actual fuel rods at the end of each 

cycle. However, for these rods, no data was taken at the end of the first cycle. The linear 

decrease in hoop strain ends when the fuel and cladding come in contact and no further 

creepdown is possible. It can be seen from these figures that the new cladding creep model 

provides better prediction of creep than the original creep model in FRAPCON-3.3. Over the 

range of fluences in which data are available, the new model appears to predict these data well. 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2E+25 4E+25 6E+25 8E+25 1E+26 1.2E+26

Rod Average Fluence, n/m2

Average Hoop Strain, %

FRAPCON-3.3 Data Updated Creep Model

Figure 3.25 Predicted and measured cladding creepdown using the original and new 

creep models from the 2nd and 3rd cycle rods in the AN0-2 PWR assembly, 

TSQ002 
3.25 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2E+25 4E+25 6E+25 8E+25 1E+26

Rod Average Fluence, n/m2

Average Hoop Strain, %

FRAPCON-3.3 Data Updated Creep Model

Figure 3.26 Predicted and measured cladding creepdown using the original and new 

creep models from the 3rd, 4th, and 5th cycle rods in the Oconee PWR 

assembly, 15309 

Creep data was obtained from irradiated tubes in order to further validate the selected creep 

model. Data was found on irradiated SRA cladding tubes (Franklin, 1983, Soniak et al., 2002 and 

Gilbon et al., 2000) and on irradiated RXA cladding tubes (Franklin, 1983, Soniak et al., 2002, 

Gilbon et al., 2000, and Sontheimer et al., 1994). These data span a temperature range of 570K to 

625K, an effective stress range of 40-130 MPa, and a fast neutron flux range of 1x1017 – 2x1018

n/m2-s that comes the range of LWR fuel rod operation. Figures 3.27 and 3.28 show the results of 

these predictions. It appears that the uncertainty in Figure 3.28 is increasing with increasing 

strain. It should be noted however, that the strain values in Figure 3.28 are significantly less than 

those in Figure 3.27. A relative standard error for the predictions is 14.5% for SRA cladding and 

21.6% for RXA cladding. FRAPCON-3.4 will be modified to use the creep model described in 

this section. 
3.26 

0

0.005

0.01

0.015

0.02

0.025

0 0.005 0.01 0.015 0.02 0.025

Measured hoop strain, in/in

Predicted hoop strain, in/in

Franklin Soniak 350°C Soniak 320°C Gilbon Predicted=Measured

Figure 3.27 Predicted vs. measured cladding creepdown using the new creep model from 

creepdown data from irradiated SRA tubes 

-0.002

0

0.002

0.004

0.006

0.008

-0.002 0 0.002 0.004 0.006 0.008

Measured hoop strain, in/in

Predicted hoop strain, in/in

Franklin Soniak 350°C Soniak 320°C

Gilbon BWR ROPE-1 IFA 585 BWR

Predicted=Measured

Figure 3.28 Predicted vs. measured cladding creepdown using the new creep model from 

creepdown data from irradiated RXA tubes 
4.1 

4.0 Sensitivity Analysis 

Material properties modeled in FRAPCON-3.3 include fuel thermal conductivity, fuel thermal 

expansion, cladding oxide thermal conductivity, cladding thermal conductivity, gas thermal 

conductivity, fission gas release, cladding corrosion, fuel swelling, thermal and irradiation creep 

of irradiated cladding, cladding yield strength, Young’s modulus of cladding, cladding axial 

growth, and cladding thermal expansion. By modeling material properties, important fuel rod 

performance parameters, such as rod internal gas pressure, peak fuel centerline temperature, and 

cladding permanent (i.e. plastic) hoop strain, can be predicted up to high burnup levels (65 

GWd/MTU). These parameters are used for licensing analyses. 

Models incorporated in FRAPCON-3.3 are based on both physical and empirical relationships 

that are continuously compared and adapted to experimental data as it becomes available. 

Experimental data can exhibit scatter and may be scarce under certain conditions like high burnup 

or high temperature. Consequently, there is uncertainty in the derived models. In addition to 

model uncertainty, manufacturing and power history parameters are also sources for uncertainty 

that may influence the code output. Since fuel performance predictions generated by FRAPCON3.3 are based on interdependent material response models, manufacturer metrics, and power 

histories, uncertainty does not propagate linearly to the code output. Nevertheless, the influence 

of each type of uncertainty can be evaluated by iteratively biasing individual parameters both 

positively and negatively and comparing the subsequent output with a baseline case. This has 

been the approach taken by fuel vendors in their fuel performance methodologies that have been 

approved by NRC. Individual parameters are readily categorized by the three types of 

uncertainty considered here. Another approach of sampling multiple uncertainties in a Monte 

Carlo approach could also be used and has been proposed by one fuel vendor (Arimescu, 2008). 

Prior to applying an approach such as this, it is necessary to know what uncertainties will have an 

impact on the outputs of interest so those uncertainties can be included in the sampling. In order 

to determine this a study similar to the study performed below would have to first be performed. 

Other researchers have done work to examine the sensitivity of various models and predictions in 

FRAPCON-3 and FRAPTRAN (Vallejo et al. 2004, del Barrio et al. 2006, del Barrio et al. 2007). 

These studies provided valuable insight into the sensitivity of these codes to changes in various 

parameters. This report will show the sensitivity of selected model uncertainties, manufacturing 

uncertainties, and power uncertainties on the code prediction of rod internal gas pressure, fuel 

centerline temperature, and cladding strain for sample BWR and PWR cases. It should be noted 

that the sensitivity to these parameters could change based on differences in power history or fuel 

rod design. 

The manufacturing uncertainties used in this report represent an average value of the tolerances 

given by fuel rod fabricators. Individual parameters influenced by manufacturing uncertainty 

include cladding inner diameter, cladding thickness, cladding roughness, pellet outer diameter, 

theoretical pellet density, pellet re-sinter density, pellet roughness, pellet dish diameter and depth, 

rod fill gas pressure, and rod plenum length. The model uncertainties used in this report are 

based on uncertainty in parameters used to fit the aforementioned material property models to 

experimental data as demonstrated in Section 2.0, which may significantly influence output 

values generated by FRAPCON-3.3. Finally, power uncertainty includes uncertainties associated 

with the measurement of steady state power and anticipated operational occurrences (AOOs), 

which typically result in brief power pulses above the steady state power output that last for 

varying lengths of time. Although these power transients are anticipated, the uncertainty 
4.2 

associated with their intensity and duration may influence the fuel performance predicted by 

FRAPCON-3.3 

The purpose of this study is to evaluate the influence of manufacturing, model, and power 

uncertainties on fuel performance parameter outputs of interest generated by FRAPCON-3. 

Establishing the effects of these sources of uncertainty will facilitate more accurate comparisons 

between modeled and experimentally observed fuel performance. In addition, they will establish 

which uncertainties are important for inclusion in licensing analyses. This study was performed 

using the released version of FRAPCON-3.3 as discussed in Section 2. 

4.1 Outputs of Interest 

Material response models incorporated in FRAPCON-3 enable three important fuel rod 

performance parameters of regulatory interest to be predicted. These output parameters include 

the rod internal gas pressure, peak fuel centerline temperature, and cladding permanent hoop 

strain. Each parameter is significant as the predicted value may indicate whether or not the fuel 

rod will exceed the specific acceptable fuel design limits under designated conditions for 

licensing analyses. The significance of each parameter is discussed in the following subsections. 

4.1.1 Rod Internal Gas Pressure 

Rod internal gas pressure is predicted by FRAPCON-3 through models that account for the 

thermal expansion of the cladding and the fuel. Fission gas release from the fuel pellets is also 

considered in the rod internal pressure calculation. Rod internal pressure is a critical parameter in 

fuel rod performance because it contributes to the development of hoop strains endured by the 

cladding, which may lead to excessive pressure in the rod that could cause cladding lift off 

(pellet/cladding gap re-opening at high burnup), hydride reorientation (circumferential hydrides 

reorienting to radial hydrides that embrittle the cladding), and/or cladding failure. 

4.1.2 Peak Fuel Centerline Temperature 

Peak fuel centerline temperature is a critical parameter predicted by FRAPCON-3. By modeling 

the conductivity of the fuel, gap, cladding, and corrosion layer, the fuel centerline temperature 

can be predicted. Low gap conductivity resulting from cladding lift off or excessive fission gas 

release results in significant increase in fuel centerline temperature. When the peak fuel 

centerline temperature predicted by FRAPCON-3 exceeds the melting temperature of the fuel, 

FRAPCON-3 will indicate that fuel failure has occurred based on NRC design criteria. 

4.1.3 Cladding Permanent Hoop Strain 

Fuel rod cladding, which is typically composed of a zirconium-based alloy, surrounds the fuel 

and prevents fuel from entering the reactor coolant system. Should the cladding fail, fuel may be 

transported from the fuel rod to the reactor vessel contaminating the entire primary coolant loop 

with fissile material. Fuel rod cladding typically fails by cracking due to pellet-clad mechanical 

loads, or bursting due to gas pressure (preceded by ballooning) during a power transient or LOCA, 

respectively. In order for a cladding to balloon and eventually burst, a significant amount of 

plastic circumferential, or hoop, strain (i.e., εhoop) must manifest within the cladding. By 

predicting the hoop strain in the cladding, FRAPCON-3 can identify conditions that would be 

conducive for cladding failure. The standard review plan (Standard Review Plan Section 4.2, 
4.3 

2007) states that transient induced uniform deformation (elastic + plastic) should not exceed 1% 

strain. 

4.1.4 Other Outputs of Interest 

Although the outputs listed above are significant fuel rod performance parameters, there are 

several other outputs of regulatory interest. Among these are the volume-average fuel 

temperature (i.e. stored energy), gap conductance, and the cladding hydrogen concentration. 

Hydrogen concentration is important for determining the cladding strain capability and propensity 

for failure. The significance of choosing rod internal pressure, peak fuel centerline temperature, 

and cladding permanent hoop strain as outputs of interest is that these are directly measured and 

generally representative of fuel rod performance. 

4.2 Selection of Base Cases 

In order to evaluate the influence of the different types of uncertainty on the output of 

FRAPCON-3, a base case must be established for both PWR and BWR fuel performance 

calculations. The purpose of this section is to describe the fuel design parameters, power 

histories, and axial power profiles that are used as code input to define these base cases. 

The base cases employed in this study utilized a 17x17 PWR and a 10x10 BWR with typical 

design parameters required for FRAPCON-3 code input published in NUREG-1754 (O’Donnell 

et al, 2001) and are presented in Table 4.1. 

Table 4.1 Typical fuel design parameters used for base case code input (NUREG-1754) 

PWR BWR

Description of Design Parameter 17x17 10x10

Pitch (mm, in ) 12.6, 0.498 13.0, 0.510

Cladding OD (mm, in ) 9.4, 0.370 10.0, 0.395

Cladding Thickness (mm, in) 0.610, 0.024 0.660, 0.026

Cladding ID (mm, in ) 8.18, 0.322 8.68, 0.343

Gap Thickness (mm, in ) 0.084, 0.0033 0.089, 0.0035

Fuel Pellet Diameter (mm, in ) 8.0, 0.315 8.5, 0.336

Plenum Spring Diameter (mm, in ) 8.0, 0.315 8.5, 0.336

Pellet Length (mm, in ) 11.4, 0.45 11.4, 0.45

Dish Diameter (mm, in ) 4.01, 0.158 0, 0

Dish Depth (mm, in ) 0.287, 0.0113 0, 0

Plenum Length (mm, in ) 254, 10 254, 10

Turns in Plenum Spring 28 31

Plenum Spring Wire Diameter (mm, in ) 1.27, 0.05 1.27, 0.05

Helium Fill Gas Pressure (MPa, psi) 2.41, 350 0.69, 100

Active Fuel Length (m, in ) 3.66, 144 3.66, 144

System Coolant Pressure (MPa, psi) 15.5, 2250 7.14, 1035

Coolant Inlet Temperature (°C, °F ) 288, 550 277, 530

Coolant Flow Rate (x106

 kg/m2, x106 lb/ft2) 12.47, 2.55 5.13, 1.05

Enrichment (atom %) 4.5 4

Pellet Density (% TD) 95 95

Limit on Pellet Density Increase (% TD) 0.9 0.9

Fuel Surface Roughness (μm, in ) 2.0, 3x10-5 2.0, 3x10-5

Cladding Surface Roughness (μm, in ) 0.5, 2x10-5 0.5, 2x10-5

Cladding Material Zircaloy-4 Zircaloy-2

Cold Work (%) 50 0
4.4 

It is acknowledged that the fill gas pressure of 350 psi that was used for the PWR case is higher 

than the fill gas pressure for many modern rods (175 psi). A brief study was performed to 

confirm that relative differences caused by biasing other parameters were the same for both initial 

fill gas pressures. 

In addition to selecting prototypical fuel design parameters for the desired base cases, the power 

histories and axial power profiles were also designated specific input values. Both the PWR and 

BWR cases were evaluated up to a rod average burnup of 65 GWd/MTU. Although different 

factors, such as core management, may introduce uncertainty, the power histories and axial power 

profiles presented here are assumed to be representative and employed for comparison. In order 

to evaluate the influence of power uncertainties at various levels of burnup, individual conditions 

were examined in which AOOs were implemented at 30, 40, and 50 GWd/MTU. At the time of 

the AOO, the output power was increased 50% for a period of 4hrs. This AOO was selected as 

the more limiting AOO for temperature, pressure and strain than an overpower of 25% that is 

held for 12 hrs. Power histories for the PWR and BWR base cases are presented in Figure 4.1 

without an AOO. A symmetrical power profile was selected for both the PWR and BWR base 

cases and is presented in Table 4.2. A modern BWR power profile is more peaked than this 

profile, but a brief study confirmed that the relative effects of the uncertainties would be the same 

by running several of the cases discussed in the following section using a more peaked axial 

power profile. 

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70

Rod Average Burnup (GWd/MTU)

Rod Average Power (kW/ft)

PWR

BWR

Figure 4.1 Power histories for PWR and BWR base cases without AOO 
4.5 

Table 4.2 Axial power profile used for PWR and BWR base case input 

4.3 Effects of Manufacturing Uncertainties 

Manufacturing uncertainties stem from the range of tolerances used in fuel rod fabrication. 

Variation in cladding and pellet metrics, such as cladding thickness and pellet diameter, can 

influence geometric relationships between the cladding and the fuel like the pellet-cladding gap. 

Consequently, the end of life rod internal pressure, peak fuel centerline temperature, and cladding 

permanent hoop strain (εhoop) predictions generated by FRAPCON-3 may be influenced by 

manufacturing uncertainties. The purpose of this section is to present and discuss comparisons 

between base cases and cases biased by manufacturing uncertainty. Tolerances presented in this 

section were not chosen arbitrarily, and are considered typical of industry. Comparisons for PWR 

and BWR cases are presented in Tables 4.3 and 4.4, respectively, and discussed in the following 

subsections. 

If tolerances are greater than those assumed in these tables, this may change the conclusions from 

this sample calculation on sensitivity. Also, this sample calculation only examined individual 

changes in manufacturing tolerances rather than the combined effects from all sources. 

Combined effects of manufacturing uncertainties will have a more significant impact on fuel 

performance. 

Axial Axial

Elevation Power

(mm) Profile

0 0.63

305 0.83

610 1.03

914 1.08

1219 1.08

2438 1.08

2743 1.08

3048 1.03

3353 0.83

3660 0.63
4.6 

Table 4.3 Comparison between unbiased output and output biased by manufacturing uncertainty for a 17x17 PWR 

 Cladding Inner Diameter Cladding Thickness Cladding Roughness

Condition Responses Unbiased + 0.04 mm - 0.04 mm + 0.04 mm - 0.04 mm + 0.3 mm - 0.3 mm

No AOO Rod Internal Pressure (MPa) 12.16 12.81 11.57 12.17 12.07 12.24 12.02

Peak Fuel Centerline T (°C) 1590 1586 1594 1591 1588 1594 1586

30 Rod Internal Pressure (MPa) 13.25 13.83 12.69 13.34 13.24 13.29 13.16

GWd/MTU Peak Fuel Centerline T (°C) 2319 2314 2325 2321 2317 2325 2314

Cladding Permanent εhoop (%) 0.4354 0.4343 0.4365 0.4323 0.4384 0.4378 0.4325

40 Rod Internal Pressure (MPa) 14.13 14.75 13.44 14.15 14.13 14.19 14.00

GWd/MTU Peak Fuel Centerline T (°C) 2079 2074 2084 2080 2077 2085 2073

Cladding Permanent εhoop (%) 0.3575 0.3570 0.3579 0.3550 0.3604 0.3598 0.3552

50 Rod Internal Pressure (MPa) 14.20 14.71 13.61 14.32 14.17 14.33 14.19

GWd/MTU Peak Fuel Centerline T (°C) 1788 1783 1793 1789 1787 1793 1782

Cladding Permanent εhoop (%) 0.2672 0.2661 0.2680 0.2656 0.2692 0.2693 0.2655

 Pellet Outer Diameter Pellet Density Pellet Re-Sinter Density

Condition Responses Unbiased + 0.013 mm - 0.013 mm + 0.91% TD - 0.91% TD + 0.4% TD - 0.4% TD

No AOO Rod Internal Pressure (MPa) 12.16 12.02 12.35 11.93 12.28 11.82 12.42

Peak Fuel Centerline T (°C) 1590 1590 1589 1571 1609 1581 1599

30 Rod Internal Pressure (MPa) 13.25 13.03 13.48 13.02 13.48 12.98 13.49

GWd/MTU Peak Fuel Centerline T (°C) 2319 2320 2318 2295 2344 2308 2331

Cladding Permanent εhoop (%) 0.4354 0.4365 0.4336 0.4285 0.4425 0.4318 0.4384

40 Rod Internal Pressure (MPa) 14.13 13.92 14.29 13.93 14.14 13.79 14.36

GWd/MTU Peak Fuel Centerline T (°C) 2079 2080 2077 2056 2101 2068 2090

Cladding Permanent εhoop (%) 0.3575 0.3587 0.3562 0.3517 0.3634 0.3546 0.3605

50 Rod Internal Pressure (MPa) 14.20 14.01 14.45 14.05 14.25 13.96 14.52

GWd/MTU Peak Fuel Centerline T (°C) 1788 1789 1787 1768 1807 1778 1798

Cladding Permanent εhoop (%) 0.2672 0.2682 0.2658 0.2617 0.2726 0.2646 0.2700
4.7 

Table 4.3 (continued). Comparison between unbiased output and output biased by manufacturing uncertainty for a 17x17 PWR 

 Pellet Roughness Pellet Dish Diameter & Depth Rod Fill Pressure

Condition Responses Unbiased + 0.5 mm - 0.5 mm + 0.5 &0.05 mm - 0.5 &0.05 mm + 69 kPa - 69 kPa

No AOO Rod Internal Pressure (MPa) 12.16 12.26 12.03 12.00 12.35 12.30 12.03

Peak Fuel Centerline T (°C) 1590 1597 1583 1589 1590 1589 1590

30 Rod Internal Pressure (MPa) 13.25 13.32 13.08 13.31 13.47 13.44 13.06

GWd/MTU Peak Fuel Centerline T (°C) 2319 2329 2309 2318 2320 2318 2320

Cladding Permanent εhoop (%) 0.4354 0.4397 0.4302 0.4322 0.4356 0.4345 0.4356

40 Rod Internal Pressure (MPa) 14.13 14.20 13.90 14.07 14.36 14.31 13.95

GWd/MTU Peak Fuel Centerline T (°C) 2079 2089 2068 2078 2079 2078 2080

Cladding Permanent εhoop (%) 0.3575 0.3613 0.3535 0.3512 0.3578 0.3573 0.3579

50 Rod Internal Pressure (MPa) 14.20 14.33 14.03 14.08 14.39 14.39 14.04

GWd/MTU Peak Fuel Centerline T (°C) 1788 1797 1778 1787 1788 1787 1789

Cladding Permanent εhoop (%) 0.2672 0.2711 0.2634 0.2589 0.2673 0.2669 0.2676

 Rod Plenum Length

Condition Responses Unbiased +1 Pellet Length -1 Pellet Length

No AOO Rod Internal Pressure (MPa) 12.16 11.96 12.38

Peak Fuel Centerline T (°C) 1590 1589 1590

30 Rod Internal Pressure (MPa) 13.25 12.92 13.59

GWd/MTU Peak Fuel Centerline T (°C) 2319 2319 2320

Cladding Permanent εhoop (%) 0.4354 0.4349 0.4353

40 Rod Internal Pressure (MPa) 14.13 13.79 14.41

GWd/MTU Peak Fuel Centerline T (°C) 2079 2078 2079

Cladding Permanent εhoop (%) 0.3575 0.3573 0.3577

50 Rod Internal Pressure (MPa) 14.20 13.96 14.58

GWd/MTU Peak Fuel Centerline T (°C) 1788 1788 1788

Cladding Permanent εhoop (%) 0.2672 0.2671 0.2676
4.8 

Table 4.4 Comparison between unbiased output and output biased by manufacturing uncertainty for a 10x10 BWR 

 Cladding Inner Diameter Cladding Thickness Cladding Roughness

Condition Responses Unbiased + 0.04 mm - 0.04 mm + 0.04 mm - 0.04 mm + 0.3 mm - 0.3 mm

No AOO Rod Internal Pressure (MPa) 5.37 5.56 4.99 5.37 5.37 5.36 5.41

Peak Fuel Centerline T (°C) 1234 1266 1237 1235 1232 1237 1230

30 Rod Internal Pressure (MPa) 5.30 5.63 4.94 5.31 5.29 5.30 5.13

GWd/MTU Peak Fuel Centerline T (°C) 1868 1864 1874 1870 1866 1876 1860

Cladding Permanent εhoop (%) 0.3180 0.1902 0.3253 0.3158 0.3202 0.3231 0.3134

40 Rod Internal Pressure (MPa) 6.56 6.84 6.28 6.57 6.56 6.69 6.56

GWd/MTU Peak Fuel Centerline T (°C) 1729 1723 1735 1730 1727 1738 1721

Cladding Permanent εhoop (%) 0.2683 0.2599 0.2733 0.2660 0.2714 0.2736 0.2643

50 Rod Internal Pressure (MPa) 6.73 7.00 6.46 6.74 6.73 6.89 6.66

GWd/MTU Peak Fuel Centerline T (°C) 1530 1525 1535 1532 1528 1538 1522

Cladding Permanent εhoop (%) 0.2067 0.1997 0.2121 0.2051 0.2083 0.2109 0.2020

 Pellet Outer Diameter Pellet Density Pellet Re-Sinter Density

Condition Responses Unbiased + 0.013 mm - 0.013 mm + 0.91% TD - 0.91% TD + 0.4% TD - 0.4% TD

No AOO Rod Internal Pressure (MPa) 5.37 5.24 5.46 5.18 4.83 5.28 5.40

Peak Fuel Centerline T (°C) 1234 1234 1233 1218 1248 1231 1240

30 Rod Internal Pressure (MPa) 5.30 5.18 5.41 5.13 5.45 5.23 5.35

GWd/MTU Peak Fuel Centerline T (°C) 1868 1869 1867 1843 1893 1857 1879

Cladding Permanent εhoop (%) 0.3180 0.3213 0.3102 0.3097 0.3263 0.3068 0.3234

40 Rod Internal Pressure (MPa) 6.56 6.43 6.67 6.59 6.63 6.47 6.62

GWd/MTU Peak Fuel Centerline T (°C) 1729 1730 1728 1705 1750 1719 1738

Cladding Permanent εhoop (%) 0.2683 0.2708 0.2653 0.2614 0.2743 0.2634 0.2726

50 Rod Internal Pressure (MPa) 6.73 6.59 6.84 6.59 6.78 6.64 6.94

GWd/MTU Peak Fuel Centerline T (°C) 1530 1532 1528 1511 1548 1521 1539

Cladding Permanent εhoop (%) 0.2067 0.2094 0.2031 0.2009 0.2113 0.2016 0.2113
4.9 

Table 4.4 (continued). Comparison between unbiased output and output biased by manufacturing uncertainty for a 10x10 BWR 

 Pellet Roughness Pellet Dish Diameter & Depth Rod Fill Pressure

Condition Responses Unbiased + 0.5 mm - 0.5 mm + 0.5 & 0.05 mm - 0.5 & 0.05 mm + 69 kPa - 69 kPa

No AOO Rod Internal Pressure (MPa) 5.37 5.11 5.45 NA NA 5.67 5.25

Peak Fuel Centerline T (°C) 1234 1240 1227 NA NA 1230 1235

30 Rod Internal Pressure (MPa) 5.30 5.30 5.12 NA NA 5.36 5.08

GWd/MTU Peak Fuel Centerline T (°C) 1868 1884 1852 NA NA 1862 1872

Cladding Permanent εhoop (%) 0.3180 0.3270 0.3077 NA NA 0.3134 0.3197

40 Rod Internal Pressure (MPa) 6.56 6.69 6.56 NA NA 6.80 6.46

GWd/MTU Peak Fuel Centerline T (°C) 1729 1744 1711 NA NA 1725 1734

Cladding Permanent εhoop (%) 0.2683 0.2759 0.2585 NA NA 0.2664 0.2704

50 Rod Internal Pressure (MPa) 6.73 6.86 6.51 NA NA 6.82 6.63

GWd/MTU Peak Fuel Centerline T (°C) 1530 1543 1515 NA NA 1525 1534

Cladding Permanent εhoop (%) 0.2067 0.2136 0.1979 NA NA 0.2024 0.2089

 Rod Plenum Length

Condition Responses Unbiased +1 Pellet Length -1 Pellet Length

No AOO Rod Internal Pressure (MPa) 5.37 5.18 5.62

Peak Fuel Centerline T (°C) 1234 1233 1234

30 Rod Internal Pressure (MPa) 5.30 5.11 5.51

GWd/MTU Peak Fuel Centerline T (°C) 1868 1867 1869

Cladding Permanent εhoop (%) 0.3180 0.3174 0.3194

40 Rod Internal Pressure (MPa) 6.56 6.31 6.84

GWd/MTU Peak Fuel Centerline T (°C) 1729 1728 1730

Cladding Permanent εhoop (%) 0.2683 0.2676 0.2693

50 Rod Internal Pressure (MPa) 6.73 6.62 6.95

GWd/MTU Peak Fuel Centerline T (°C) 1530 1530 1530

Cladding Permanent εhoop (%) 0.2067 0.2069 0.2059
4.10 

4.3.1 Cladding Inner Diameter 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting cladding inner 

diameter by the manufacturing tolerance of ±0.04mm are presented in Table 4.3 for comparison. 

The average variance in rod internal pressure is 4.5% and ranges from 3.60% at the positively 

biased 50 GWd/MTU condition to 5.40% at the positively biased no AOO condition. Peak fuel 

centerline temperature and cladding permanent hoop strain values varied from the base case by 

less than 0.3% and 0.4%, respectively. Based on these observations, it appears that 

manufacturing uncertainty in cladding inner diameter has the potential to influence the rod 

internal pressure generated by FRAPCON-3. A tendency for rod internal pressure to increase and 

decrease with cladding inner diameter was observed. However, peak fuel centerline temperatures 

and cladding permanent hoop strains varied inversely with cladding inner diameter. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting 

cladding inner diameter by the manufacturing tolerance of ±0.04mm are presented in Table 4.4 

for comparison. The average variance in rod internal pressure is 5.0% and ranges from 3.64% to 

7.00% under the positively and negatively biased no AOO conditions, respectively. Although the 

other peak fuel centerline temperatures varied by less than 0.4%, the positively biased peak fuel 

centerline temperature with no AOO exceeded the base case by 2.6%. In addition, an outlying 

variation in cladding permanent hoop strain of 40.2% was observed at the positively biased 30 

GWd/MTU condition. This is likely due to the gap not being closed in this case at the time of the 

AOO. With exception of this case, the average variance of the permanent cladding hoop strain is 

2.7% and ranges from 1.86% under the negatively biased 40 GWd/MTU condition to 3.39% 

under the positively biased 50 GWd/MTU condition. It appears that manufacturing uncertainty in 

cladding inner diameter has no significant influence on rod internal pressure and no effect on 

peak fuel centerline temperature or an increase in cladding permanent hoop strain predictions. A 

tendency for rod internal pressure to increase and decrease with cladding inner diameter was 

observed. However, peak fuel centerline temperatures and cladding permanent hoop strains 

typically varied inversely with cladding inner diameter. 

4.3.2 Cladding Thickness 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting cladding thickness 

by the manufacturing tolerance of ±0.04mm are presented in Table 4.3 for comparison. The 

maximum variance for each of the three outputs of interest is less than 1.0% from the base case, 

which indicates that manufacturing uncertainty in cladding thickness does not significantly affect 

outputs of interest generated FRAPCON-3. Although the variance is negligible, a tendency for 

rod internal pressure and peak fuel centerline temperature to increase and decrease with cladding 

thickness was observed. However, cladding permanent hoop strain values tended to vary 

inversely with cladding thickness. 
4.11 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting 

cladding thickness by the manufacturing tolerance of ±0.04mm are presented in Table 4.4 for 

comparison. The average variance each of these outputs of interest is less than 1% from the base 

BWR case. It appears that manufacturing uncertainty in cladding thickness has no influence on 

outputs of interest from FRAPCON-3. Although the differences were negligible, a tendency for 

rod internal pressure and peak fuel centerline temperature to increase and decrease with cladding 

thickness was observed. However, cladding permanent hoop strain values tended to vary 

inversely with cladding thickness. 

4.3.3 Cladding Roughness 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting cladding roughness 

by the manufacturing tolerance of ±0.3μm are presented in Table 4.3 for comparison. The 

maximum variance for each of the three outputs of interest is less than 1.2% from the base PWR 

case, which indicates that manufacturing uncertainty in cladding roughness does not have an 

effect on outputs of interest from FRAPCON-3. Although the variance was negligible, a 

tendency for rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop 

strain to increase and decrease with cladding roughness was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting 

cladding roughness by the manufacturing tolerance of ±0.3μm are presented in Table 4.4 for 

comparison. Rod internal pressure values vary from the base case by 1.2% on average and range 

from 0.02% to 3.24% at the positively and negatively biased 30 GWd/MTU conditions, 

respectively. Peak fuel centerline temperatures vary from the base case by less than 1%. 

Cladding permanent hoop strain exhibits an average variance of 1.8%, ranging from 1.45% at the 

negatively biased 30 GWd/MTU condition to 2.27% at the negatively biased 50 GWd/MTU 

conditions. Based on these observations, it appears that manufacturing uncertainty in cladding 

roughness has no influence on the outputs of interest generated by FRAPCON-3. Although the 

variance was negligible, a tendency for rod internal pressure, peak fuel centerline temperature, 

and cladding permanent hoop strain to increase and decrease with cladding roughness was 

observed. 

4.3.4 Pellet Outer Diameter 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting pellet outer diameter 

by the manufacturing tolerance of ±0.013mm are presented in Table 4.3 for comparison. The 

average variance for rod internal pressure is 1.5% and ranges from 1.11% at the negatively biased 

40 GWd/MTU condition to 1.80% at the negatively biased 50 GWd/MTU condition. Peak fuel 

centerline temperature and permanent cladding hoop strain values typically differ from the base 

case by less than 0.5%. Based on these observations, it appears that manufacturing uncertainty in 

pellet outer diameter has no effect on the outputs of interest from FRAPCON-3. Although the 

variance was small, a tendency for rod internal pressure to vary inversely with pellet outer 
4.12 

diameter was observed. However, a tendency for peak fuel centerline temperature and cladding 

permanent hoop strain to increase and decrease with pellet outer diameter was also observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting pellet 

outer diameter by the manufacturing tolerance of ±0.013mm are presented in Table 4.4 for 

comparison. Rod internal pressure values vary from the base case by 2.0% on average. This 

variance ranges from 1.66% at the negatively biased 50 GWd/MTU condition to 2.29% at the 

positively biased no AOO and 30 GWd/MTU conditions. Fuel centerline temperatures differ 

from the base case by less than 0.1% on average. The average variance between cladding 

permanent hoop strains predicted from the base case and cases biased by uncertainty in pellet 

outer diameter is 1.4%. This variance ranges from 0.93% under the positively biased 40 

GWd/MTU conditions to 2.45% under the negatively influenced 30 GWd/MTU condition. Based 

on these observations, it appears that manufacturing uncertainty in the pellet outer diameter has 

no effect on the outputs of interest generated by FRAPCON-3. Although the variance was small, 

a tendency for rod internal pressures to vary inversely with increasing and decreasing pellet outer 

diameter was observed. However, a tendency for peak fuel centerline temperature and cladding 

permanent hoop strain to increase and decrease with pellet outer diameter was also observed. 

4.3.5 Theoretical Pellet Density 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting theoretical pellet 

density (TD) by the manufacturing tolerance of ±0.91%TD are presented in Table 4.3 for 

comparison. The average variance for rod internal pressure is 1.2% and ranges from 0.05% at the 

negatively biased 40 GWd/MTU condition to 1.91% at the positively biased no AOO condition. 

Peak fuel centerline temperature varies from the base case by 1.1% on average and ranges from 

1.04% at the positively biased 30 GWd/MTU condition to 1.23% at the negatively biased no 

AOO condition. Cladding permanent hoop strain values vary by 1.8% on average and ranges 

from 1.58% at the positively biased 30 GWd/MTU condition to 2.06% at the positively biased 50 

GWd/MTU condition. Based on these observations, it appears that manufacturing uncertainty in 

theoretical pellet density has no influence on the outputs of interest generated by FRAPCON-3. 

Although the variation was insignificant, a tendency for rod internal pressure, peak fuel centerline 

temperature, and cladding permanent hoop strain to vary inversely with pellet theoretical density 

was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting 

theoretical pellet density (TD) by the manufacturing tolerance of ±0.91% are presented in Table 

4.4 for comparison. Rod internal pressure values vary from the base case by 2.0% on average 

excluding an outlier at the negatively biased no AOO condition, which varied by 10%. This 

variance is most likely due to less gas release in this case, which resulted in less pressure. 

Variance in rod internal pressure ranged from 0.47% in the positively biased 40 GWd/MTU 

condition to 3.43% in the positively biased no AOO condition. Peak fuel centerline temperature 

varied by 1.3% on average and ranged from 1.17% at the negatively biased no AOO condition to 

1.39% at the positively biased 40 GWd/MTU condition. Cladding permanent hoop strain varied 

by 2.5% on average and ranged from 2.23% to 2.81% at the negatively and positively biased 50 
4.13 

GWd/MTU conditions, respectively. Overall, it appears that manufacturing uncertainty in 

theoretical pellet density has low to moderate influence on outputs of interest generated by 

FRAPCON-3. A tendency for rod internal pressure, peak fuel centerline temperature, and 

cladding permanent hoop strain to vary inversely with pellet theoretical density was observed. 

4.3.6 Pellet Re-Sinter Density 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting pellet re-sinter 

density by the manufacturing tolerance of ±0.4% TD are presented in Table 4.3 for comparison. 

In-reactor densification can have significant consequences for fuel performance and is described 

in greater detail in U.S. NRC Regulatory Guide 1.126 (U.S. NRC, 1978). The average variance 

for rod internal pressure is 2.1% and ranges from 1.62% at the negatively biased 40 GWd/MTU 

condition to 2.78% at the positively biased no AOO condition. Peak fuel centerline temperature 

and cladding hoop strain values differ from the base case by less than 1%. Based on this, it 

appears that manufacturing uncertainty in pellet re-sinter density has a small influence on outputs 

of interest generated by FRAPCON-3. Although the variation was small, a tendency for rod 

internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain to vary 

inversely with pellet re-sinter density was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting pellet 

re-sinter density by the manufacturing tolerance of ±0.4% TD are presented in Table 4.4 for 

comparison. In-reactor densification can have significant consequences for fuel performance and 

is described in greater detail in U.S. NRC Regulatory Guide 1.126. Rod internal pressure values 

vary from the base case by 1.4% on average and range from 0.68% in the negatively biased no 

AOO condition to 3.23% in the negatively biased 50 GWd/MTU condition. Peak fuel centerline 

temperatures differ from the base case by 0.6% or less. Cladding permanent hoop strain 

exhibited an average variance of 2.2% ranging from 1.60% in the negatively biased 40 

GWd/MTU condition to 3.52% in the positively biased 30 GWd/MTU condition. Based on this, 

it appears that manufacturing uncertainty in pellet re-sinter density has a small influence on 

outputs of interest generated by FRAPON-3. Although the variation was small, a tendency for 

rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain to 

vary inversely with pellet re-sinter density was observed. 

4.3.7 Pellet Roughness 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting pellet roughness by 

the manufacturing tolerance of ±0.5μm are presented in Table 4.3 for comparison. The average 

variances in rod internal pressure, peak fuel centerline temperature, and permanent cladding 

values are 1.0, 0.47, and 1.2%, respectively. The maximum variance detected for any value was 

1.69% for rod internal pressure at the negatively biased 40 GWd/MTU condition. Based on this, 

it appears that manufacturing uncertainty in pellet roughness has no influence on FRAPCON-3 

output. Although the variation was insignificant, a tendency for rod internal pressure, peak fuel 

centerline temperature, and cladding permanent hoop strain to increase and decrease with pellet 

roughness was observed. 
4.14 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting pellet 

roughness by the manufacturing tolerance of ±0.5μm are presented in Table 4.4 for comparison. 

Rod internal pressure values vary from the base case by 2.1% on average and range from 0.08% 

at the negatively biased 40 GWd/MTU conditions to 4.78% at the positively biased no AOO 

condition. Peak fuel centerline temperatures differ by less than 1.00% from the base. Cladding 

permanent hoop strain exhibited an average variance of 3.4% ranging from 2.83% at the 

positively biased 30 GWd/MTU and 40 GWd/MTU conditions to 4.26% at the negatively biased 

50 GWd/MTU condition. Based on this, it appears that manufacturing uncertainty in pellet 

roughness has a low to moderated influence on FRAPCON-3 output. A tendency for rod internal 

pressure, peak fuel centerline temperature, and cladding permanent hoop strain to increase and 

decrease with pellet roughness was observed. 

4.3.8 Pellet Dish Diameter and Depth 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting pellet dish diameter 

and depth by the manufacturing tolerances of ±0.5 and 0.05mm, respectively, are presented in 

Table 4.3 for comparison. Rod internal pressure varied by 1.2% on average and ranged from 

0.41% at the positively biased 30 GWd/MTU condition to 1.62% at the negatively biased no 

AOO condition. Peak fuel centerline temperature values vary at most by 0.05% at the positively 

biased 50 GWd/MTU condition. Cladding permanent hoop strain values vary, on average, by 

1.0% and range from 0.04% to 3.11% at the negative and positive 50 GWd/MTU conditions, 

respectively. These results indicate that manufacturing uncertainty in pellet dish diameter and 

depth has no influence on the outputs of interested generated by FRAPCON-3. Although the 

variation was insignificant, a tendency for rod internal pressure, peak fuel centerline temperature, 

and cladding permanent hoop strain to vary inversely with pellet dish diameter and depth was 

observed. 

BWR

The fuel design used in this study were not dished on-end. Therefore, the influence of 

manufacturing uncertainty in pellet dish diameter and depth were not evaluated for the BWR base 

case. For dished BWR pellets, the effect of variation in the dish dimnsions are expected to be 

similar to the PWR case. 

4.3.9 Rod Fill Pressure 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting rod fill pressure by 

the manufacturing tolerances of ± 10psi (≈ 0.07MPa) are presented in Table 4.3 for comparison. 

Rod internal pressure varies by 1.3% on average and ranges from 1.06% in the negatively biased 

no AAO condition to 1.44% in the negatively biased 30 GWd/MTU condition. Peak fuel 

centerline temperatures and cladding hoop strain values vary by less than 0.5%. Overall, it 

appears that manufacturing uncertainty in rod fill pressure has no influence on rod the outputs of 

interest generated by FRAPCON-3. Although the variation was insignificant, a tendency for rod 
4.15 

internal pressure to increase and decrease with rod fill pressure was observed. However a 

tendency for peak fuel centerline temperatures and cladding permanent hoop strains to vary 

inversely with rod fill pressure was also observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting rod fill 

pressure by the manufacturing tolerance of ± 10psi (≈ 0.07MPa) are presented in Table 4.4 for 

comparison. Rod internal pressure values vary from the base case by 2.7% on average and range 

from 1.13% at the positively biased 30 GWd/MTU condition to 5.71% in the positively biased no 

AOO condition. Fuel centerline temperatures, on the other hand, varied by 0.33% or less. 

Cladding permanent strain variances averaged 1.1% and range from 0.53% at the negatively 

biased 30 GWd/MTU condition to 2.08% at the positively biased 50 GWd/MTU condition. 

Based on these observations, it appears that manufacturing uncertainty in rod fill pressure has low 

to moderate influence on the outputs of interest generated by FRAPCON-3. A tendency for rod 

internal pressure to increase and decrease with rod fill pressure was observed. However a 

tendency for peak fuel centerline temperatures and cladding permanent hoop strains to vary 

inversely with rod fill pressure was also observed. 

4.3.10 Rod Plenum Length 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting rod plenum length by 

the manufacturing tolerances of ± 1 pellet length are presented in Table 4.3 for comparison. Rod 

internal pressure varies by 2.2% on average and ranges from 1.59% in the positively biased no 

AOO condition to 2.69% in the negatively biased 50 GWd/MTU condition. Peak fuel centerline 

temperatures and cladding hoop strain values vary by less than 0.5%. Overall, it appears that 

manufacturing uncertainty in rod plenum length has no influence on outputs of interest generated 

by FRAPCON-3. Although variances were insignificant, a tendency for rod internal pressure, 

peak fuel centerline temperature, and cladding permanent hoop strain to vary inversely with rod 

plenum length was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting rod 

plenum length by the manufacturing tolerance of ± 1 pellet length are presented in Table 4.4 for 

comparison. Rod internal pressure values vary from the base case by 3.6% on average and range 

from 1.55% in the positively biased 50GWd/MTU condition to 4.64% in the negatively biased no 

AOO condition. Peak fuel centerline temperatures and cladding permanent hoop strains, on the 

other hand, varied by 0.44% or less. Based on these observations, it appears that uncertainty in 

rod plenum length has low to moderate influence on the outputs of interest generated by 

FRAPCON-3. A tendency for rod internal pressure, peak fuel centerline temperature, and 

cladding permanent hoop strain to vary inversely with rod plenum length was observed. 

4.4 Effects of Model Uncertainties 

Model uncertainties stem from uncertainties in the models used to simulate the material response 

of the fuel rod in service. Uncertainty in model fitting parameters resulting from scatter in 

experimental data may significantly influence fuel rod performance predictions generated by 

FRAPCON-3. The purpose of this section is to present and discuss comparisons between base 
4.16 

cases and cases biased by model uncertainty. Comparisons for PWR and BWR cases are 

presented in Tables 4.5 and 4.6, respectively, and discussed in the following subsections. 
4.17 

Table 4.5 Comparison between unbiased output and output biased by model uncertainties for a 17x17 PWR 

 Fuel Thermal Conductivity Fuel Thermal Expansion Oxide Conductivity

Condition Responses Unbiased + 0.5 W/m-K - 0.5 W/m-K * 1.15 / 1.15 + 0.5 W/m-K - 0.5 W/m-K

No AOO Rod Internal Pressure (MPa) 12.16 9.77 18.46 12.19 12.09 12.03 12.76

Peak Fuel Centerline T (°C) 1590 1345 2012 1590 1590 1584 1601

30 Rod Internal Pressure (MPa) 13.25 9.77 18.34 13.26 13.21 13.14 13.65

GWd/MTU Peak Fuel Centerline T (°C) 2319 1952 2772 2318 2320 2313 2333

Cladding Permanent εhoop (%) 0.4354 0.3169 0.5531 0.5163 0.3645 0.4343 0.4381

40 Rod Internal Pressure (MPa) 14.13 10.56 18.66 14.01 14.05 13.96 14.65

GWd/MTU Peak Fuel Centerline T (°C) 2079 1731 2549 2078 2079 2068 2106

Cladding Permanent εhoop (%) 0.3575 0.2463 0.4938 0.4277 0.2966 0.3551 0.3633

50 Rod Internal Pressure (MPa) 14.20 10.40 18.96 14.08 14.21 14.06 14.80

GWd/MTU Peak Fuel Centerline T (°C) 1788 1484 2260 1787 1788 1771 1852

Cladding Permanent εhoop (%) 0.2672 0.1693 0.4145 0.3239 0.2165 0.2643 0.2885

 Cladding Conductivity Gas Conductance Fission Gas Release

Condition Responses Unbiased + 5 W/m-K - 3 W/m-K + 0.02 W/m-K - 0.02 W/m-K * 2 / 2

No AOO Rod Internal Pressure (MPa) 12.16 11.81 12.19 12.02 12.26 14.17 10.60

Peak Fuel Centerline T (°C) 1590 1573 1604 1588 1591 1599 1583

30 Rod Internal Pressure (MPa) 13.25 12.96 13.56 13.24 13.29 14.93 11.86

GWd/MTU Peak Fuel Centerline T (°C) 2319 2301 2336 2317 2321 2324 2315

Cladding Permanent εhoop (%) 0.4354 0.4283 0.4400 0.4345 0.4362 0.4321 0.4366

40 Rod Internal Pressure (MPa) 14.13 13.84 14.28 14.11 14.13 15.83 12.76

GWd/MTU Peak Fuel Centerline T (°C) 2079 2063 2093 2077 2081 2085 2073

Cladding Permanent εhoop (%) 0.3575 0.3504 0.3606 0.3571 0.3582 0.3556 0.3583

50 Rod Internal Pressure (MPa) 14.20 13.82 14.38 14.22 14.28 16.14 12.72

GWd/MTU Peak Fuel Centerline T (°C) 1788 1774 1800 1786 1790 1795 1781

Cladding Permanent εhoop (%) 0.2672 0.2605 0.2702 0.2668 0.2678 0.2671 0.2659
4.18 

Table 4.5 (continued) Comparison between unbiased output and output biased by model uncertainties for a 17x17 PWR 

 Cladding Corrosion Fuel Swelling Irradiation Creep

Condition Responses Unbiased * 1.4 / 1.4 + 0.3 - 0.3 * 1.1 / 1.4

No AOO Rod Internal Pressure (MPa) 12.16 12.73 12.03 12.19 12.16 12.16 12.31

Peak Fuel Centerline T (°C) 1590 1601 1583 1589 1590 1590 1590

30 Rod Internal Pressure (MPa) 13.25 13.36 13.11 13.35 12.89 13.22 13.39

GWd/MTU Peak Fuel Centerline T (°C) 2319 2333 2312 2319 2319 2319 2319

Cladding Permanent εhoop (%) 0.4354 0.4390 0.4336 0.4379 0.4331 0.4355 0.4352

40 Rod Internal Pressure (MPa) 14.13 14.64 13.92 14.16 13.46 14.07 14.27

GWd/MTU Peak Fuel Centerline T (°C) 2079 2108 2066 2079 2079 2079 2079

Cladding Permanent εhoop (%) 0.3575 0.3651 0.3542 0.3626 0.3506 0.3575 0.3575

50 Rod Internal Pressure (MPa) 14.20 14.80 13.76 14.27 13.73 14.19 14.30

GWd/MTU Peak Fuel Centerline T (°C) 1788 1848 1768 1787 1788 1788 1788

Cladding Permanent εhoop (%) 0.2672 0.2920 0.2629 0.2760 0.2541 0.2672 0.2668

 Yield Strength Young's Modulus Axial Growth

Condition Responses Unbiased * 1.3 / 1.1 + 5 MPa - 10 MPa * 1.5 / 1.5

No AOO Rod Internal Pressure (MPa) 12.16 12.16 12.16 12.16 12.16 11.53 12.61

Peak Fuel Centerline T (°C) 1590 1590 1590 1590 1590 1590 1590

30 Rod Internal Pressure (MPa) 13.25 13.21 13.25 13.25 13.25 12.43 13.75

GWd/MTU Peak Fuel Centerline T (°C) 2319 2317 2320 2319 2319 2319 2319

Cladding Permanent εhoop (%) 0.4354 0.4322 0.4364 0.4354 0.4354 0.4352 0.4350

40 Rod Internal Pressure (MPa) 14.13 14.14 14.13 14.13 14.13 13.32 14.58

GWd/MTU Peak Fuel Centerline T (°C) 2079 2077 2079 2079 2079 2079 2078

Cladding Permanent εhoop (%) 0.3575 0.3542 0.3587 0.3575 0.3575 0.3574 0.3574

50 Rod Internal Pressure (MPa) 14.20 14.20 14.20 14.20 14.20 13.54 14.76

GWd/MTU Peak Fuel Centerline T (°C) 1788 1786 1788 1788 1788 1788 1787

Cladding Permanent εhoop (%) 0.2672 0.2642 0.2683 0.2672 0.2672 0.2676 0.2669
4.19 

Table 4.5 (continued) Comparison between unbiased output and output biased by model uncertainties for a 17x17 PWR 

 Cladding Thermal Expansion

Condition Responses Unbiased * 1.3 / 1.3

No AOO Rod Internal Pressure (MPa) 12.16 12.11 12.18

Peak Fuel Centerline T (°C) 1590 1590 1590

30 Rod Internal Pressure (MPa) 13.25 13.21 13.27

GWd/MTU Peak Fuel Centerline T (°C) 2319 2319 2319

Cladding Permanent εhoop (%) 0.4354 0.4315 0.4383

40 Rod Internal Pressure (MPa) 14.13 14.06 14.15

GWd/MTU Peak Fuel Centerline T (°C) 2079 2079 2079

Cladding Permanent εhoop (%) 0.3575 0.3532 0.3607

50 Rod Internal Pressure (MPa) 14.20 14.13 14.22

GWd/MTU Peak Fuel Centerline T (°C) 1788 1788 1788

Cladding Permanent εhoop (%) 0.2672 0.2620 0.2711
4.20 

Table 4.6 Comparison between unbiased output and output biased by model uncertainties for a 10x10 BWR 

 Fuel Thermal Conductivity Fuel Thermal Expansion Oxide Conductivity

Condition Responses Unbiased + 0.5 W/m-K - 0.5 W/m-K * 1.15 / 1.15 + 0.5 W/m-K - 0.5 W/m-K

No AOO Rod Internal Pressure (MPa) 5.37 3.93 9.59 5.42 5.22 5.38 5.37

Peak Fuel Centerline T (°C) 1234 1104 1572 1232 1234 1232 1236

30 Rod Internal Pressure (MPa) 5.30 4.35 11.49 5.22 5.30 5.29 5.30

GWd/MTU Peak Fuel Centerline T (°C) 1868 1524 2359 1866 1869 1866 1872

Cladding Permanent εhoop (%) 0.3180 0.1811 0.4883 0.3868 0.2546 0.3174 0.3190

40 Rod Internal Pressure (MPa) 6.56 4.65 12.52 6.59 6.55 6.56 6.57

GWd/MTU Peak Fuel Centerline T (°C) 1729 1410 2215 1728 1729 1726 1733

Cladding Permanent εhoop (%) 0.2683 0.1555 0.4243 0.3274 0.2154 0.2688 0.2686

50 Rod Internal Pressure (MPa) 6.73 4.68 12.80 6.92 6.85 6.74 6.90

GWd/MTU Peak Fuel Centerline T (°C) 1530 1251 1994 1527 1531 1527 1535

Cladding Permanent εhoop (%) 0.2067 0.1093 0.3531 0.2525 0.1649 0.2063 0.2073

 Cladding Conductivity Gas Conductance Fission Gas Release

Condition Responses Unbiased + 5 W/m-K - 3 W/m-K + 0.02 W/m-K - 0.02 W/m-K * 2 / 2

No AOO Rod Internal Pressure (MPa) 5.37 5.16 4.86 5.38 5.37 6.87 3.91

Peak Fuel Centerline T (°C) 1234 1219 1247 1232 1235 1258 1218

30 Rod Internal Pressure (MPa) 5.30 5.11 5.51 5.29 5.30 7.41 5.41

GWd/MTU Peak Fuel Centerline T (°C) 1868 1845 1889 1865 1871 1885 1851

Cladding Permanent εhoop (%) 0.3180 0.3086 0.3249 0.3164 0.3199 0.3135 0.3119

40 Rod Internal Pressure (MPa) 6.56 6.24 6.73 6.56 6.57 8.14 5.16

GWd/MTU Peak Fuel Centerline T (°C) 1729 1709 1746 1726 1732 1741 1712

Cladding Permanent εhoop (%) 0.2683 0.2621 0.2725 0.2675 0.2698 0.2602 0.2700

50 Rod Internal Pressure (MPa) 6.73 6.62 6.84 6.73 6.89 8.45 5.35

GWd/MTU Peak Fuel Centerline T (°C) 1530 1512 1545 1527 1533 1543 1516

Cladding Permanent εhoop (%) 0.2067 0.2003 0.2107 0.2050 0.2088 0.2012 0.2067
4.21 

Table 4.6 (continued) Comparison between unbiased output and output biased by model uncertainties for a 10x10 BWR 

 Cladding Corrosion Fuel Swelling Irradiation Creep

Condition Responses Unbiased *1.4 /1.4 + 0.3 - 0.3 * 1.1 / 1.4

No AOO Rod Internal Pressure (MPa) 5.37 5.37 5.38 5.45 4.91 5.35 5.40

Peak Fuel Centerline T (°C) 1234 1237 1231 1233 1235 1234 1234

30 Rod Internal Pressure (MPa) 5.30 5.30 5.29 5.28 5.12 5.29 5.35

GWd/MTU Peak Fuel Centerline T (°C) 1868 1873 1865 1867 1869 1868 1868

Cladding Permanent εhoop (%) 0.3180 0.3193 0.3172 0.3264 0.2643 0.3187 0.3124

40 Rod Internal Pressure (MPa) 6.56 6.57 6.56 6.60 6.32 6.54 6.62

GWd/MTU Peak Fuel Centerline T (°C) 1729 1734 1725 1728 1729 1729 1729

Cladding Permanent εhoop (%) 0.2683 0.2690 0.2685 0.2819 0.2545 0.2688 0.2658

50 Rod Internal Pressure (MPa) 6.73 6.90 6.73 6.93 6.60 6.71 6.78

GWd/MTU Peak Fuel Centerline T (°C) 1530 1536 1526 1527 1531 1530 1531

Cladding Permanent εhoop (%) 0.2067 0.2076 0.2061 0.2238 0.1880 0.2072 0.2042

 Yield Strength Young's Modulus Axial Growth

Condition Responses Unbiased * 1.3 / 1.1 + 5 MPa - 10 MPa * 1.5 / 1.5

No AOO Rod Internal Pressure (MPa) 5.37 5.37 5.37 5.37 5.37 5.17 5.52

Peak Fuel Centerline T (°C) 1234 1234 1234 1234 1234 1234 1234

30 Rod Internal Pressure (MPa) 5.30 5.21 5.30 5.30 5.30 5.11 5.43

GWd/MTU Peak Fuel Centerline T (°C) 1868 1865 1869 1868 1868 1868 1868

Cladding Permanent εhoop (%) 0.3180 0.3126 0.3199 0.3180 0.3180 0.3181 0.3181

40 Rod Internal Pressure (MPa) 6.56 6.56 6.56 6.56 6.56 6.32 6.73

GWd/MTU Peak Fuel Centerline T (°C) 1729 1725 1730 1729 1729 1729 1729

Cladding Permanent εhoop (%) 0.2683 0.2679 0.2703 0.2683 0.2683 0.2682 0.2691

50 Rod Internal Pressure (MPa) 6.73 6.65 6.73 6.73 6.73 6.64 6.91

GWd/MTU Peak Fuel Centerline T (°C) 1530 1520 1532 1530 1530 1531 1529

Cladding Permanent εhoop (%) 0.2067 0.1942 0.2091 0.2067 0.2067 0.2073 0.2063
4.22 

Table 4.6 (continued) Comparison between unbiased output and output biased by model uncertainties for a 10x10 BWR 

 Cladding Thermal Expansion

Condition Responses Unbiased *1.3 /1.3

No AOO Rod Internal Pressure (MPa) 5.37 5.34 5.39

Peak Fuel Centerline T (°C) 1234 1234 1234

30 Rod Internal Pressure (MPa) 5.30 5.30 5.29

GWd/MTU Peak Fuel Centerline T (°C) 1868 1868 1868

Cladding Permanent εhoop (%) 0.3180 0.3123 0.3212

40 Rod Internal Pressure (MPa) 6.56 6.56 6.55

GWd/MTU Peak Fuel Centerline T (°C) 1729 1729 1729

Cladding Permanent εhoop (%) 0.2683 0.2653 0.2706

50 Rod Internal Pressure (MPa) 6.73 6.71 6.65

GWd/MTU Peak Fuel Centerline T (°C) 1530 1531 1530

Cladding Permanent εhoop (%) 0.2067 0.2039 0.2079
4.23 

4.4.1 Fuel Thermal Conductivity 

The fuel thermal conductivity model was biased by ±0.5 W/m-K, which bounds most of the 

experimental data below 4.7 W/m-K that is in the temperature range if interest (T>400°C) 

presented in Figure 4.2. 

0

1

2

3

4

5

6

7

8

9

0369

Measured Thermal Conductivity, W/m-K

Predicted Thermal Conductivity, 

W/m-K

Unirradiated Data Irradiated Data Lower Bound Upper Bound

Figure 4.2 Predicted and measured thermal conductivity data with ±0.5 W/m-K as upper 

and lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the fuel thermal 

conductivity model by ± 0.5 W/m-K are presented in Table 4.5 for comparison. Rod internal 

pressure varies by 31.7% on average and ranges from 19.66% to 51.83% at the positively and 

negatively biased no AOO conditions, respectively. Peak fuel centerline temperatures vary by 

20.0% on average and range from 15.37% at the positively biased no AOO condition to 26.59% 

at the negatively biased no AOO condition. Cladding permanent hoop strain values averaged 

35.9% and ranged from 27.03% at the negatively biased 30 GWd/MTU condition to 55.13% at 

the negatively biased 50 GWd/MTU condition. Based on these observations, it is clear that 

model uncertainty in the fuel thermal conductivity model significantly influences the outputs of 

interest generated by FRAPCON-3. A trend for rod internal pressure, peak fuel centerline 

temperature, and cladding permanent hoop strain values to vary inversely with thermal 

conductivity was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting fuel 

thermal conductivity model by ± 0.5 W/m-K are presented in Table 4.6 for comparison. Rod 

internal pressure values vary from the base case by 60.1% on average and range from 17.91% to 
4.24 

116.79% at the positively and negatively biased 30 GWd/MTU conditions, respectively. Peak 

fuel centerline temperatures vary from the unbiased case by 22.2% on average and range from 

10.51% at the positively biased no AOO condition to 30.35% at the negatively biased 50 

GWd/MTU condition. Cladding permanent hoop strains vary by 52.5% on average and range 

from 42.04% at the positively biased 40 GWd/MTU condition to 70.83% at the negatively biased 

50 GWd/MTU condition. Based on these observations, it is clear that model uncertainty in the 

fuel thermal conductivity model significantly influences the outputs of interest generated by 

FRAPCON-3. A trend for rod internal pressure, peak fuel centerline temperature, and cladding 

permanent hoop strain values to vary inversely with thermal conductivity model bias was 

observed. 

4.4.2 Fuel Thermal Expansion 

The fuel thermal expansion model was biased by ±15%, which bounds nearly all the data 

presented in Figure 4.3. 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Expansion, 

ΔL/L

MATPRO Gronvold Baldock

Burdick Other MATPRO References Martin References

Lower Bound Upper Bound

Figure 4.3 UO2 thermal conductivity model and available data with ±15% as upper and 

lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the fuel thermal 

expansion model by either multiplying or dividing by a factor of 1.15 are presented in Table 4.5 

for comparison. Rod internal pressure and peak fuel centerline temperature values vary from the 

unbiased condition by less than 1% and 0.1%, respectively. The small variation is because the 

gap is closed at high power and/or high burnup for the cases considered. Thermal expansion 

effects on fuel temperature will be important near BOL and at lower rod powers when the gap is 

open. Cladding permanent hoop strain values vary by 18.6% on average and range form 16.28% 

at the negatively biased 30 GWd/MTU condition to 21.22% at the positively biased 50 

GWd/MTU condition. Although model uncertainty in the fuel thermal expansion model does not 
4.25 

appear to influence rod internal pressure or peak fuel centerline temperature at the burnups and 

rod powers considered, it does appear to affect the cladding permanent hoop stress values 

predicted by FRAPCON-3. Since the gap was closed, it is difficult to determine the quantitative 

influence of fuel thermal expansion model uncertainty on rod internal pressure and peak fuel 

centerline temperature when the gap is open near BOL. However, a trend for cladding permanent 

hoop strain to increase and decrease with the fuel thermal expansion model was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting fuel 

thermal expansion model by either multiplying or dividing by a factor of 1.15 are presented in 

Table 4.6 for comparison. Rod internal pressure and peak fuel centerline temperature values vary 

by less than 2.81 and 0.2% from the base case, respectively. The small variation is because the 

gap is closed at high power and/or high burnup for the cases considered. Cladding permanent 

hoop strain values vary from the base case by 21.0% on average and range from 19.72% at the 

negatively biased 40 GWd/MTU case to 22.16% at the positively biased 50 GWd/MTU condition. 

Although uncertainty in fuel thermal expansion model does not appear to influence rod internal 

pressure or peak fuel centerline temperature, it does appear to significantly influence the cladding 

permanent hoop stress values predicted by FRAPCON-3. Since the gap was closed, it is difficult 

to determine the quantitative influence of fuel thermal expansion model uncertainty on rod 

internal pressure and peak fuel centerline temperature when the gap is open near BOL. However, 

a trend for cladding permanent hoop strain to increase and decrease with the fuel thermal 

expansion model was observed. 

4.4.3 Cladding Oxide Conductivity 

The cladding oxide conductivity model was biased by ±0.5 W/m-K, which bound the 

experimental data presented in Figure 4.4. 
4.26 

0

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500 2000

Temperature (K)

Thermal Conductivity (W/m-K)

MATPRO Model Kingery w/porosity Kingery 100% dense

bulk data Lower Bound Upper Bound

Figure 4.4 ZrO2 thermal conductivity model and available data with ±0.5 W/m-K as 

upper and lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the cladding oxide 

conductivity model by ±0.5 W/m-K are presented in Table 4.5 for comparison. Rod internal 

pressure values varied from the base case by 2.5% on average and ranged from 0.82% at the 

positively biased 30 GWd/MTU condition to 4.26% in the negatively biased 50 GWd/MTU 

condition (68 μm oxide). Peak fuel centerline temperatures varied from the base case by 1.0% 

and ranged from 0.28% in the positively biased 30 GWd/MTU condition to 3.59% in the 

negatively based 50 GWd/MTU condition. Cladding permanent hoop strain values varied by 

2.0% on average and ranged from 0.25% at the positively biased 30 GWd/MTU condition to 

7.97% in the negatively biased 50 GWd/MTU condition. Overall it appears that uncertainty in 

oxide thermal conductivity has a small influence on the outputs of interest generated by 

FRAPCON-3. Although the variance was small, a tendency for rod internal pressure, peak fuel 

centerline temperature, and cladding permanent hoop strain to vary inversely with cladding oxide 

conductivity was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

cladding oxide conductivity model by ±0.5 W/m-K are presented in Table 4.6 for comparison. 

Average variance in rod internal pressure between the unbiased and biased model conditions is 

0.4%, which includes a larger variance of 2.51% at the negatively biased 50 GWd/MTU 

condition (21 μm oxide). Excluding that larger variance, the rod internal pressure varies from the 
4.27 

unbiased base case by 0.01% at the positively biased 40 GWd/MTU condition to 0.24% at the 

positively biased no AOO condition. Peak fuel centerline temperature and cladding permanent 

hoop strain values vary from the base case by less than 0.5%. Overall, it appears that uncertainty 

in the oxide conductivity does not influence the rod internal pressure, fuel centerline temperature, 

or cladding permanent hoop strain values predicted by FRAPCON-3. Since the variance is very 

small, it is difficult to discern trends between rod internal pressure, peak fuel centerline 

temperature, and cladding permanent hoop strain with cladding oxide conductivity. However, a 

tendency for rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop 

strain to vary inversely with cladding oxide conductivity was observed. 

4.4.4 Cladding Conductivity 

The cladding conductivity model was biased by +5/-3 W/m-K, which bounds nearly all the 

experimental data presented in Figure 4.5. 

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO Recent Data

Recent Data (Bunnell) Lower Bound Upper Bound

Figure 4.5 Zircaloy thermal conductivity model and available data with +5/-3 W/m-K as 

upper and lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the cladding 

conductivity model by +5 W/m-K and -3 W/m-K are presented in Table 4.5 for comparison. Rod 

internal pressure values varied from the base case by 1.8% on average and range from 0.28% to 

2.84% at the negatively and positively biased no AOO conditions, respectively. Peak fuel 

centerline temperatures varied from the base case by less than 1%. Cladding permanent hoop 

strain values varied by 1.5% on average and range from 0.87% at the negatively biased 40 

GWd/MTU case to 2.51% at the positively biased 50GWd/MTU case. Overall, it appears that 

model uncertainty in the cladding conductivity model has no significant influence on the outputs 

of interest generated by FRAPCON-3. Despite the lack of a significant influence, a tendency for 
4.28 

rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain to 

vary inversely with cladding conductivity was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

cladding conductivity model by +5 W/m-K and -3W/m-K are presented in Table 4.6 for 

comparison. Rod internal pressure values vary from the unbiased case by 4.0% on average and 

range from 1.57% in the positively biased 50 GWd/MTU condition to 9.51% in the negatively 

biased no AOO condition. Peak fuel centerline temperatures vary from the based case by 1.1% 

on average and range form 1.00% in the negatively biased 50 GWd/MTU condition to 1.22% in 

the positively biased 30 GWd/MTU condition. The cladding permanent hoop strain values varied 

from the base case by 2.4% on average and ranged from 1.57% at the negatively biased 40 

GWd/MTUcondition to 3.10% at the positively biased 50 GWd/MTU condition. Based on this, it 

appears that model uncertainty in the cladding conductivity model has no significant influence on 

the outputs of interest generated by FRAPCON-3. Although the variance was small, a tendency 

for rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values to vary inversely with cladding conductivity was observed. 

4.4.5 Gas Conductance 

The gas conductance model was biased by ±5%, which bounds nearly all the experimental data 

presented in Figure 4.6. 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 500 1000 1500 2000 2500 3000

Temperature, K

Thermal Conductivity, W/m-K

MATPRO Data used by MATPRO

Recent Data Lower Bound

Upper Bound

Figure 4.6 Helium thermal conductivity model and available data with ±5% as upper 

and lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the gas conductance 

model by ±5% are presented in Table 4.5 for comparison. Rod internal pressure, peak fuel 
4.29 

centerline temperature, and cladding permanent hoop strain values varied by less than 1.15%. 

Based on this, it appears that model uncertainty in the gas conductance model has no significant 

influence over the outputs of interest generated by FRAPCON-3. Despite the lack of a significant 

effect, a tendency for rod internal pressure, peak fuel centerline temperature, and cladding 

permanent hoop strain to decrease with enhanced gas conductivity was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the gas 

conductance model by ±5% are presented in Table 4.6 for comparison. Rod internal pressure, 

peak fuel centerline temperature, and cladding permanent hoop strain values varied from the base 

case by less than 1%. Based on this, it appears that model uncertainty in the gas conductance 

model has no significant influence over the outputs of interest generated by FRAPCON-3. 

Despite the lack of a significant effect, a tendency for rod internal pressure, peak fuel centerline 

temperature, and cladding permanent hoop strain to decrease with enhanced gas conductivity was 

observed. 

4.4.6 Fission Gas Release 

The fission gas release model was biased by multiplying or dividing gas diffusivity, D, by 2. The 

nominal model is shown in Figure 4.7. The biased models shown in Figures 4.8 and 4.9 bound 

most of the experimental data. 

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Measured FGR

Predicted FGR

Steady State Power Ramped

Figure 4.7 Nominal predicted vs. measured fission gas release 
4.30 

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Measured FGR

Predicted FGR

Steady State Power Ramped

Figure 4.8 Predicted vs. measured fission gas release for upper bound model with D*2 

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Measured FGR

Predicted FGR

Steady State Power Ramped

Figure 4.9 Predicted vs. measured fission gas release for lower bound model with D/2 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the fission gas 

release model by *2 or /2 are presented in Table 4.5 for comparison. Rod internal pressures 

varied by 12.3% from the base case on average and ranged from 9.69% at the negatively biased 

40 GWd/MTU condition to 16.57% at the positively biased no AOO condition. Peak fuel 

centerline and cladding permanent hoop strain values varied from the base case by less than 0.6% 

and 0.8%, respectively. Based on this, it appears that model uncertainty in the fission gas release 

model has significant influence over rod internal pressure values and little influence on peak fuel 
4.31 

centerline temperature or cladding permanent hoop strain values generated by FRAPCON-3. The 

impact on fuel temperature would be more significant if the gap were open, e.g., at lower burnup. 

As expected, rod internal pressure significantly increased with increased fission gas release. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

fission gas model by *2 or /2 are presented in Table 4.6 for comparison. Rod internal pressures 

varied by 23.6% from the base case on average and ranged from 2.04% to 39.93% between the 

negatively and positively biased 30 GWd/MTU conditions, respectively. Peak fuel centerline and 

cladding permanent hoop strain values varied from the base case by less than 2.0% and 3.0%, 

respectively. Based on this, it appears that model uncertainty in the fission gas release model has 

significant influence over rod internal pressure values and little influence on peak fuel centerline 

temperature or cladding permanent hoop strain values generated by FRAPCON-3. The impact on 

fuel temperature would be more significant if the gap were open, e.g., at lower burnup. As 

expected, rod internal pressure significantly increased with increased fission gas release. 

4.4.7 Cladding Corrosion 

The cladding corrosion model was biased by ±40%. The nominal model is shown in Figure 4.10. 

The models biased to bound nearly all experimental data are shown in Figures 4.11 and 4.12. 

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Measured Oxide Thickness, microns

Predicted Oxide Thickness

PWR Data Measured=Predicted

Figure 4.10 Nominal predicted vs. measured oxide thickness 
4.32 

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

Measured Oxide Thickness, microns

Predicted Oxide Thickness

PWR Data Measured=Predicted

Figure 4.11 Predicted vs. measured oxide thickness for upper bound model with +40% 

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Measured Oxide Thickness, microns

Predicted Oxide Thickness

PWR Data Measured=Predicted

Figure 4.12 Predicted vs. measured oxide thickness for lower bound model with -40% 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the cladding 

corrosion model by ±40% are presented in Table 4.5 for comparison. Rod internal pressures 
4.33 

varied by 2.5% from the base case on average and ranged from 0.83% at the positively biased 30 

GWd/MTU condition to 4.67% at the positively biased no AOO condition. Peak fuel centerline 

temperatures varied from the base case by 1.0% on average and ranged from 0.33% at the 

negatively biased 30 GWd/MTU condition to 3.36% at the positively biased 50 GWd/MTU 

condition. Cladding permanent hoop strain values varied from the base case by 2.5% on average 

and ranged from 0.41% in the negatively biased 30 GWd/MTU condition to 9.28% in the 

positively biased 50 GWd/MTU condition. Based on this, it appears that model uncertainty in the 

cladding corrosion model has low to moderate influence on the outputs of interest generated by 

FRAPCON-3. It should be noted that cladding corrosion and hydriding can have a significant 

impact on cladding ductility. A tendency for rod internal pressure, peak fuel centerline 

temperature, and cladding permanent hoop strain to increase and decrease with cladding 

corrosion was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

cladding corrosion model by ±40% are presented in Table 4.6 for comparison. Rod internal 

pressures varied by 0.4% from the base case on average and ranged from 0.00% at the negatively 

biased 40 GWd/MTU condition to 2.51% at the positively biased 50 GWd/MTU condition. Peak 

fuel centerline temperatures varied from the base case by 0.3% on average and ranged from 

0.17% at the negatively biased 30 GWd/MTU condition to 0.39% at the positively biased 50 

GWd/MTU condition. Cladding permanent hoop strain values varied from the base case by 0.3% 

on average and ranged from 0.07% in the negatively biased 40 GWd/MTU condition to 0.44% in 

the positively biased 50 GWd/MTU condition. Based on this, it appears that model uncertainty in 

the cladding corrosion model has no significant influence on the outputs of interest generated by 

FRAPCON-3. It should be noted that cladding corrosion and hydriding can have a significant 

impact on cladding ductility. Despite the lack of a significant effect, a tendency for rod internal 

pressure, peak fuel centerline temperature, and cladding permanent hoop strain to increase with 

positively biased cladding corrosion was observed. 

4.4.8 Fuel Swelling 

The fuel swelling model was biased by ±0.3% ΔV/V per 10 GWd/MTU, which bounds nearly all 

the data presented in Figure 4.13 as well as the Halden swelling data shown in Figure 2.69. 
4.34 

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120

Pellet Average Burnup, GWd/MTU

ΔV/V, %

FRAPCON-3.3 Model Data for Model Development

Recent Data Lower Bound

Upper Bound

Figure 4.13 Fuel swelling model and available data with ±0.3% ΔV/V per 10 GWd/MTU 

as upper and lower bounds on the swelling rate 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the fuel swelling 

model by ±0.3 per 10GWd/MTU are presented in Table 4.5 for comparison. Rod internal 

pressure values varied from the base case by 1.6% on average and ranged from 0.00% at the 

negatively biased no AOO condition to 4.75% at the negatively biased 40 GWd/MTU condition. 

Peak fuel centerline temperatures varied from the base case by less than 0.1%. Cladding 

permanent hoop strain values varied form the based case by 2.1% on average and ranged from 

0.03% at the no AOO conditions to 4.90% at the negatively biased 50 GWd/MTU condition. 

There is a significant impact on rod pressure limits based on no-cladding-liftoff criteria where the 

cladding creep rate cannot exceed the fuel swelling rate. Overall, it appears that model 

uncertainty in the fuel swelling model has a small influence over the rod internal pressure and 

cladding permanent hoop strain and little influence on peak fuel centerline temperature values 

generated by FRAPCON-3 at bunrups and LHGRs where the gap is closed. A tendency for rod 

internal pressure and cladding permanent hoop strain to increase and decrease with fuel swelling 

was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the fuel 

swelling model by ±0.3 per 10GWd/MTU are presented in Table 4.6 for comparison. Rod 

internal pressure values varied form the base case by 2.9% on average and ranged from 0.29% at 

the positively biased 30 GWd/MTU condition to 8.47% in the negatively biased no AOO 

condition. Peak fuel centerline temperatures varied from the base case by less than 0.25%. 

Cladding permanent hoop strain values varied from the base case by 7.8% and ranged from 

2.64% to 16.89% at the positively and negatively biased 30 GWd/MTU conditions, respectively. 

There is a significant impact on rod pressure limits based on no-cladding-liftoff criteria where the 
4.35 

cladding creep rate cannot exceed the fuel swelling rate. Overall, it appears that model 

uncertainty in the fuel swelling model has a small to moderate influence on rod internal pressure 

and cladding permanent hoop strain values generated by FRAPCON-3 and little influence on 

peak fuel centerline temperature. Despite the lack of a significant effect, a tendency for rod 

internal pressure and cladding permanent hoop strain to increase and decrease with fuel swelling 

was observed. 

4.4.9 Creep of Irradiated Cladding 

The irradiated cladding creep model was biased by +10%/-40%, which bounds nearly all the data 

presented in Figure 4.14. 

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2E+25 4E+25 6E+25 8E+25 1E+26

Rod Average Fluence, n/m2

Average Hoop Strain, %

FRAPCON-3.3 Data Lower Bound Upper Bound

Figure 4.14 Cladding creep model and available data with +10%/-40% upper and lower 

bound on creep rate. 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the irradiated 

cladding creep model by +10%/-40% are presented in Table 4.5 for comparison. Rod internal 

pressure values varied from the base case by 0.6% on average and ranged from 0.05% to 1.21% at 

the positively and negatively biased no AOO conditions, respectively. Peak fuel centerline 

temperatures and cladding permanent hoop strain values varied form the base case by less that 

0.2%. The impact of cladding creep on fuel temperature will be significant at lower burnups 

when the gap is open. Also, there is a significant impact on rod pressure limits based on nocladding-liftoff criteria where the cladding creep rate cannot exceed the fuel swelling rate. 

Overall, it appears that model uncertainty in the irradiated cladding creep model has no influence 

over the rod internal pressure, peak fuel centerline temperature and cladding permanent hoop 

strain values generated by FRAPCON-3. 
4.36 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

irradiated cladding creep model by +10%/-40% are presented in Table 4.6 for comparison. Rod 

internal pressure and cladding permanent hoop strain values vary form the base case by less than 

1.0 and 1.8%, respectively. Peak fuel centerline temperatures varied form the base case by less 

than 0.1%. The impact of cladding creep on fuel temperature will be significant at lower burnups 

when the gap is open. Also, there is a significant impact on rod pressure limits based on nocladding-liftoff criteria where the cladding creep rate cannot exceed the fuel swelling rate. 

Overall, it appears that model uncertainty in the irradiated cladding creep model has no 

significant influence on rod internal pressure, peak fuel centerline temperature, and cladding 

permanent hoop strain values generated by FRAPCON-3. 

4.4.10 Cladding Yield Strength 

The cladding yield model was biased by adjusting the strength coefficient, K, by ± 30%. The 

nominal model is shown in Figure 4.15. The biased models bound nearly all experimental data as 

shown in Figures 4.16 and 4.17. 

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Measured Yield Stress, MPa

Predicted Yield Stress, MPa

Axial Tests Burst Tests Ring Tests

Figure 4.15 Nominal predicted vs. measured yield stress 
4.37 

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Measured Yield Stress, MPa

Predicted Yield Stress, MPa

Axial Tests Burst Tests Ring Tests

Figure 4.16 Predicted vs. measured yield stress for upper bound model with K*1.3 

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200

Measured Yield Stress, MPa

Predicted Yield Stress, MPa

Axial Tests Burst Tests Ring Tests

Figure 4.17 Predicted vs. measured yield stress for lower bound model with K/1.3 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the strength 

coefficient, K, of the cladding yield strength model by ± 30% are presented in Table 4.5 for 

comparison. Rod internal pressure, peak fuel centerline, and cladding permanent hoop strain 

values varied form the base case by less than 1.1%. Based on this, it appears that model 
4.38 

uncertainty in the cladding yield strength model has little influence over the outputs of interest 

generated by FRAPCON-3. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

strength coefficient, K, of the cladding yield strength model by ± 30% are presented in Table 4.6 

for comparison. Rod internal pressure and peak fuel centerline temperatures varied from the base 

case by less than 1.6% and 0.6% respectively. Cladding permanent hoop strain values varied 

from the base case by 1.7% on average and ranged from 0.15% at the positively biased 40 

GWd/MTU condition to 6.05% at the positively biased 50 GWd/MTU condition. Based on this, 

it appears that model uncertainty in the cladding yield strength model has little influence on rod 

internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain values 

generated by FRAPCON-3. 

4.4.11 Young’s Modulus of Cladding 

The cladding Young’s modulus model was biased by +5/-10GPa, which bounds nearly all the 

data presented in Figure 4.18. 

0

40

80

120

0 40 80 120

Measured Young's Modulus, GPa

Predicted Young's Modulus, GPa

Model Development Data Recent Data Lower Bound Upper Bound

Figure 4.18 Predicted and measured cladding Young’s Modulus data with +5/-10 GPa as 

upper and lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the Young’s modulus 

of cladding model by + 5MPa and -10MPa are presented in Table 4.5 for comparison. Based on 

these results, it appears that model uncertainty in the Young’s modulus of cladding model has no 

influence on rod internal pressure, fuel centerline temperature, or cladding permanent hoop strain 

values predicted by FRAPCON-3. 
4.39 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

Young’s modulus of cladding model by +5 MPa and -10MPa are presented in Table 4.6 for 

comparison. Based on these results, it appears that uncertainty in the Young’s modulus model 

has no effect on rod internal pressure, fuel centerline temperature, or cladding permanent hoop 

strain values predicted by FRAPCON-3. 

4.4.12 Cladding Axial Growth 

The cladding axial growth models for PWR and BWR reactors were biased by ± 50%, which 

bounds most of the data presented in Figures 4.19 and 4.20, respectively. 

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2E+21 4E+21 6E+21 8E+21 1E+22 1.2E+22 1.4E+22

Fast Fluence (n/cm2

, E > 1 MeV)

∆L/Lo (%)

FRAPCON-3.3 Data for FRAPCON Assessment

Recent Data Lower Bound

Upper Bound

Figure 4.19 Cladding axial growth model for PWR cladding with ±50% as upper and 

lower bounds 
4.40 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2E+21 4E+21 6E+21 8E+21 1E+22 1.2E+22 1.4E+22

Fast Fluence (n/cm2

, E > 1 MeV)

∆L/Lo (%)

FRAPCON-3.3 Data for FRAPCON Assessment

Recent Data Lower Bound

Upper Bound

Figure 4.20 Cladding axial growth model for BWR cladding with ±50% as upper and 

lower bounds 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the cladding axial 

growth model by ± 50% are presented in Table 4.5 for comparison. Rod internal pressure values 

varied from the base case by 4.5% on average and ranged from 3.17% at the negatively biased 40 

GWd/MTU condition to 6.23% at the positively biased 30 GWd/MTU condition. Peak fuel 

centerline temperatures varied from the base case by less than 0.1% and cladding permanent hoop 

strain values varied by 0.15% or less. Based on this, it appears that model uncertainty in the 

cladding axial growth model has a small effect on rod internal pressure and no effect on peak fuel 

centerline temperature or cladding permanent hoop strain values predicted by FRAPCON-3. A 

tendency for rod internal to increase or decrease with the cladding axial growth model was 

observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

cladding axial growth model by ± 50% are presented in Table 4.6 for comparison. Rod internal 

pressure values varied form the base case by 2.9% on average and ranged from 1.34% at the 

positively biased 50 GWd/MTU condition to 3.64% at the positively biased 30 GWd/MTU 

condition. Peak fuel centerline temperature and cladding permanent hoop strain values varied by 

less then 0.05% and 0.3%, respectively. Based on this, it appears that model uncertainty in the 

cladding axial growth model has no significant effect on rod internal pressure and no effect on 

peak fuel centerline temperature or cladding permanent hoop strain values predicted by 

FRAPCON-3. Despite the lack of a significant effect, a tendency for rod internal to increase or 

decrease with the cladding axial growth model was observed. 
4.41 

4.4.13 Cladding Thermal Expansion 

The cladding thermal expansion model was biased by ± 30%. Figures 4.21 and 4.22 present 

diametral and axial thermal expansion data, respectively, with most of the experimental bounded 

by the bias. 

0

0.001

0.002

0.003

0.004

0.005

0.006

0 200 400 600 800 1000 1200 1400

Temperature, K

Diametral Thermal Expansion, 

in/in

FRAPCON-3 Data used by MATPRO Recent Data

Lower Bound Upper Bound

Figure 4.21 Cladding diametral thermal expansion model with ±30% as upper and lower 

bounds 

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

0 200 400 600 800 1000 1200 1400

Temperature, K

Axial Thermal Expansion, in/in

FRAPCON-3 Data used by MATPRO Recent Data

Lower Bound Upper Bound

Figure 4.22 Cladding axial thermal expansion model with +30%/-10% as upper and 

lower bounds 
4.42 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the cladding thermal 

expansion model by ± 30% are presented in Table 4.5 for comparison. Rod internal pressure and 

peak fuel centerline temperature values varied from the base case by less than 0.5%. Cladding 

permanent hoop strain values varied from the base case by 1.2% on average and ranged from 

0.67% at the negatively biased 30 GWd/MTU condition to 1.95% at the positively biased 50 

GWd/MTU condition. Based on this, it appears that model uncertainty in the cladding thermal 

expansion model has no significant effect on outputs of interest generated by FRAPCON-3. 

Despite the lack of a significant effect, a tendency for cladding permanent hoop strain to vary 

inversely with cladding thermal expansion was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

cladding thermal expansion model by ± 30% are presented in Table 4.6 for comparison. Rod 

internal pressure values varied form the base case by 0.3% on average and ranged from 0.01% at 

the positively biased 30 GWd/MTU condition to 1.10% at the negatively biased 50 GWd/MTU 

condition. Peak fuel centerline temperatures varied from the base case by less than 0.05%. 

Cladding permanent hoop strain values varied from the based case by 1.1% and ranged from 

0.58% at the negatively biased 50 GWd/MTU condition to 1.79% at the positively biased 30 

GWd/MTU condition. Based on this, it appears that model uncertainty in the cladding thermal 

expansion model has no significant effect on the outputs of interest generated by FRAPCON-3. 

Despite the lack of a significant effect, a tendency for cladding permanent hoop strain to increase 

with decreased cladding thermal expansion was observed. 

4.5 Effects of Power Uncertainties 

Power uncertainties include fluctuations in the steady state power as well as the range of times 

and power levels that may be experienced during an AOO. In this study, the steady state power 

was varied by 10% over the entire power history to account for uncertainties in the calculation of 

steady state power. In addition, an AOO resulting in a 50% increase in power output for a period 

of 4 hrs was also considered. To study the influence of uncertainty in this AOO, two separate 

instances were analyzed. In the first case, the power increase was varied from 40% to 60%. The 

second case consisted of decreasing and increasing the duration of the transient by 1 hour. 

Results of the power uncertainty study are presented in Tables 4.7 and 4.8 and discussed in the 

following subsections. 
4.43 

Table 4.7 Comparison between unbiased output and output biased by power uncertainties for a 17x17 PWR 

 Steady State Height of AOO Pulse Duration of Pulse

Condition Responses Unbiased + 10% - 10% + 60% + 40% + 1hr - 1hr

No AOO Rod Internal Pressure (MPa) 12.16 14.59 9.89 NA NA NA NA

Peak Fuel Centerline T (°C) 1590 1751 1432 NA NA NA NA

30 Rod Internal Pressure (MPa) 13.25 NA NA 13.85 12.60 13.42 12.88

GWd/MTU Peak Fuel Centerline T (°C) 2319 NA NA 2446 2184 2321 2317

Cladding Permanent hoop (%) 0.4354 NA NA 0.5430 0.3249 0.4414 0.4277

40 Rod Internal Pressure (MPa) 14.13 NA NA 14.86 13.01 14.48 13.63

GWd/MTU Peak Fuel Centerline T (°C) 2079 NA NA 2200 1952 2080 2077

Cladding Permanent hoop (%) 0.3575 NA NA 0.4552 0.2584 0.3630 0.3503

50 Rod Internal Pressure (MPa) 14.20 NA NA 15.13 13.30 14.45 13.25

GWd/MTU Peak Fuel Centerline T (°C) 1788 NA NA 1899 1676 1789 1786

Cladding Permanent hoop (%) 0.2672 NA NA 0.3514 0.1846 0.2715 0.2611
4.44 

Table 4.8 Comparison between unbiased output and output biased by power uncertainties for a 10x10 BWR 

 Steady State Height of AOO Pulse Duration of Pulse

Condition Responses Unbiased + 10% - 10% + 60% + 40% +1hr -1hr

No AOO Rod Internal Pressure (MPa) 5.37 5.97 4.21 NA NA NA NA

Peak Fuel Centerline T (°C) 1234 1364 1110 NA NA NA NA

30 Rod Internal Pressure (MPa) 5.30 NA NA 6.22 4.66 5.49 5.04

GWd/MTU Peak Fuel Centerline T (°C) 1868 NA NA 2000 1733 1871 1862

Cladding Permanent εhoop (%) 0.3180 NA NA 0.4210 0.2163 0.3244 0.3081

40 Rod Internal Pressure (MPa) 6.56 NA NA 7.76 5.47 6.72 6.13

GWd/MTU Peak Fuel Centerline T (°C) 1729 NA NA 1849 1606 1732 1725

Cladding Permanent εhoop (%) 0.2683 NA NA 0.3599 0.1775 0.2742 0.2608

50 Rod Internal Pressure (MPa) 6.73 NA NA 8.18 5.72 7.26 6.60

GWd/MTU Peak Fuel Centerline T (°C) 1530 NA NA 1636 1426 1531 1524

Cladding Permanent εhoop (%) 0.2067 NA NA 0.2844 0.1326 0.2111 0.1994
4.45 

4.5.1 Steady State 

PWR

Rod internal pressure and peak fuel centerline temperature values for an unbiased 17X17 PWR 

base case and cases biased by adjusting the steady state power by ±10% are presented in Table 

4.7 for comparison. The average variance in rod internal pressure and peak fuel centerline 

temperature is 20% and 10%, respectively. Based on these results, it is appears that power 

uncertainty in steady state power has a major effect on rod internal pressure and peak fuel 

centerline temperature. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting steady 

state power by ±10% are presented in Table 4.8 for comparison. The average variance in rod 

internal pressure and peak fuel centerline temperature is 15% and 10%, respectively. Based on 

these results it appears that power uncertainty in steady state power has a major effect on rod 

internal pressure and peak fuel centerline temperature. 

4.5.2 Height of AOO Pulse 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the height of AOO 

pulse by ±10% are presented in Table 4.7 for comparison. The average variance in rod internal 

pressure is 5.9% and varies from 4.53% at the positively biased 30 GWd/MTU condition to 

7.98% at the negatively biased 40 GWd/MTU condition. Peak fuel centerline temperatures 

varied from the unbiased case by an average of 6.0% and ranged from 5.47% at the positively 

biased 30 GWd/MTU condition to 6.25% at the positively biased 50 GWd/MTU condition. 

Cladding permanent hoop strain values varied, on average, by 28.0% from the unbiased case. 

Cladding variance ranged from 24.71% at the positively biased 30 GWd/MTU condition to 

31.51% at the positively biased 50 GWd/MTU condition. Based on these results, it appears that 

power uncertainty in AOO pulse height has a moderate effect on rod internal pressure and peak 

fuel centerline temperature, and a major effect on cladding permanent hoop strain values 

generated by FRAPCON-3. A trend for rod internal pressure, peak fuel centerline temperature, 

and cladding permanent hoop strain to increase and decrease with AOO pulse height was 

observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

height of AOO pulse by ±10% are presented in Table 4.8 for comparison. The average variance 

in rod internal pressure is 16.8% and varies from 12.05% at the negatively biased 30 GWd/MTU 

condition to 21.61% at the positively biased 50 GWd/MTU condition. Peak fuel centerline 

temperatures varied, on average, by 7.0% and ranged from 6.80% at the negatively biased 50 

GWd/MTU condition to 7.25% at the negatively biased 30 GWd/MTU condition. Cladding 

permanent hoop strain values varied from the base case by 34.3%, on average and ranged from 

31.98% at the negatively biased 30 GWd/MTU condition to 37.59% at the positively biased 

50GWd/MTU condition. Based on these results it appears that power uncertainty in the AOO 
4.46 

pulse height has a moderate effect on peak fuel centerline temperature, and a major effect on rod 

internal pressure and cladding permanent hoop strain values predicted by FRAPCON-3. A trend 

for rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain to 

increase and decrease with AOO pulse height was observed. 

4.5.3 Duration of AOO Pulse 

PWR

Rod internal pressure, peak fuel centerline temperature, and cladding permanent hoop strain 

values for an unbiased 17X17 PWR base case and cases biased by adjusting the duration of AOO 

pulse by ±1hr are presented in Table 4.7 for comparison. The average variance in rod internal 

pressure is 3.1% and varies from 1.24% at the positively biased 30 GWd/MTU condition to 

6.67% at the negatively biased 50 GWd/MTU condition. Peak fuel centerline temperatures, on 

the other hand, varied by 0.1% or less. Cladding permanent hoop strain values varied by 1.8% on 

average and ranged from 1.38% at the positively biased 30 GWd/MTU condition to 2.28% at the 

negatively biased 50 GWd/MTU condition. Based on this, it appears that power uncertainty in 

the AOO pulse duration has a moderate effect on the outputs of interest generated by FRAPCON3. A trend for rod internal pressure, fuel centerline temperature, and cladding permanent hoop 

strain to increase and decrease with the duration of AOO pulse was observed. 

BWR

Outputs of interest for the unbiased 10X10 BWR base case and cases biased by adjusting the 

duration of AOO pulse by ±1hr are presented in Table 4.8 for comparison. The average variance 

in rod internal pressure is 4.5% and varies from 1.90% at the negatively biased 50 GWd/MTU 

condition to 7.89% at the positively biased 50 GWd/MTU condition. Peak fuel centerline 

temperatures varied by less than 0.5%. Cladding permanent hoop strain values varied from the 

base case by 2.6% on average and ranged from 2.01% at the positively biased 30 GWd/MTU 

condition to 3.53% at the negatively biased 50 GWd/MTU condition. Based on this, it appears 

that power uncertainty in the AOO pulse duration has a moderate effect on the outputs of interest 

generated by FRAPCON-3. A trend for rod internal pressure, fuel centerline temperature, and 

cladding permanent hoop strain to increase and decrease with the duration of AOO pulse was 

observed. 

4.6 Conclusions 

The influence of manufacturing, model, and power uncertainties on outputs of interest generated 

by FRAPCON-3 has been evaluated. Overall, it appears that manufacturing uncertainties have a 

small influence over the outputs of interest. The average variation between unbiased PWR and 

BWR base cases and cases biased by manufacturing uncertainties is typically less than 7%. 

Model uncertainties, on the other hand, significantly influence outputs of interest generated by 

FRAPCON-3 and may result in values that differ from the base cases by as much as 60%. This 

underscores the importance of exercising care in the selection and derivation of models and fitting 

parameters. Finally, evaluation of power uncertainties has revealed variation in steady state 

power has a major impact on centerline temperature and rod internal pressure and that the AOO 

pulse height has a more significant influence than the pulse duration on FRAPCON-3 outputs. In 

particular, cladding permanent hoop strain values can vary from the base case by as much as 34% 

when the AOO pulse height is varied from the base case by ±10%. The following subsections 

summarize the individual sources of uncertainty that have a significant impact on outputs of 

interest generated by FRAPCON-3. 
4.47 

The conclusions of this example sensitivity study could change depending on power histories. 

For example, if the peak power started higher than assumed here and dropped off at lower burnup, 

the gap would be open at lower burnup. This could make cladding creep, fuel swelling and 

fission gas release more important to the peak fuel centerline temperature predictions. 

4.6.1 Rod Internal Pressure 

Individual manufacturing uncertainties only influenced rod internal pressure values by 5% or less, 

however, examination of model uncertainties revealed that rod internal pressure values can be 

significantly influenced by uncertainty in the fuel thermal conductivity and fission gas release 

models. Rod internal pressure values varied, on average, from the PWR and BWR base cases by 

approximately 32% and 60%, respectively, when the fuel thermal conductivity model is biased by 

±0.5W/m-K. Biasing the diffusivity of the fission gas release model by ±2 resulted variations 

from the base case by 12% and 24% for PWR and BWR cases, respectively. Power uncertainty 

also had a significant influence on rod internal pressure. The uncertainty in steady state power 

has a major impact on the prediction of rod internal pressure. In addition, variation in AOO pulse 

height results rod internal pressures varying by 17% from the BWR base case. However, this 

effect was not as significant for the PWR, as the biased AOO pulse height only varied from the 

base case by 6%. 

4.6.2 Peak Fuel Centerline Temperature 

Peak fuel centerline temperature values were insensitive to individual manufacturing uncertainties. 

However, biasing the fuel thermal conductivity model by ±0.5W/m-K resulted in variation from 

the PWR and BWR base cases by 20 and 22%, respectively. Power uncertainties have a major 

impact on peak fuel centerline temperature. 

4.6.3 Cladding Permanent Hoop Strain 

Cladding permanent hoop strain values were insensitive to individual manufacturing uncertainties. 

However, model uncertainty in the fuel thermal conductivity and fuel thermal expansion models 

resulted in significant variation from the PWR and BWR base cases. Biasing the fuel thermal 

conductivity model by ±0.5W/m-K resulted in variations of 36 and 52% from the PWR and BWR 

base cases, respectively. Biasing the fuel thermal expansion model by ±15% resulted in 

variations of 19 and 21% from the PWR and BWR base cases, respectively. Power uncertainties 

also influence cladding permanent hoop strains. In particular, biasing the AOO pulse height by 

±10% resulted in values that varied by 28 and 34% from the PWR and BWR base cases, 

respectively. 

5.1 

5.0 CONCLUSIONS 

The conclusion of this assessment is that both FRAPCON-3.3 and FRAPTRAN-1.3 provide bestestimate predictions of fuel and cladding temperatures and cladding stress and strain. The 

assessments of each model and the assessments of the combined model predictions are shown in 

Section 2. Several areas have been identified as areas that should be re-examined and new 

models developed to improve the model’s predictive capability. These areas are outlined below. 

• Cladding corrosion: The model for hydrogen pickup in Zircaloy-2 under BWR conditions 

was found to over-predict hydrogen data. A new model was developed and is described in 

Section 3.1.1. The model for corrosion of ZIRLOTM was found to under-predict cladding 

corrosion at high burnup (>60 GWd/MTU). New model parameters were developed and are 

described in Section 3.1.2. The model for corrosion of M5TM was found to over-predict 

cladding corrosion at high burnup (>60 GWd/MTU). New model parameters were developed 

and are described in Section 3.1.3. After making this adjustment, it was also necessary to 

change the hydrogen pickup for M5TM as described in Section 3.1.3. 

• Radial power profile: The TUBRNP subroutine that calculates radial power profile was 

updated as recommended by the authors of the subroutine to model the radial power profile in 

the HWR neutron spectrum as well as a LWR neutron spectrum. The details of this update 

are described in Section 3.2. A lookup and interpolation routine was developed and 

implemented in FRAPCON-3.4 to model the radial power profile for UO2-Gd2O3 fuel in both 

HWR and LWR neutron spectrums. The details of this update are described in Section 3.3 

• UO2 thermal expansion: The model for UO2 fuel thermal expansion was found to slightly 

under-predict expansion strain at high temperature between 2500K and 3000K. Although this 

under prediction was within the scatter of the data, new model parameters were developed to 

predict the mean of the expansion strain data at high temperature and are described in Section 

3.4. 

• Gas conductivity: The gas conductivity models do not model the conductivity well for most 

gasses beyond 1100K. This will not affect most of the temperature predictions since the gas 

does not typically exceed 1000K. New data model parameters were developed to better 

predict gas conductivity at high temperature and are described in Section 3.5. 

• Steam conductivity: The steam conductivity models in FRAPCON-3.3 and FRAPTRAN 1.3 

were not the same. In addition, neither model predicted the data well. The models in both 

codes were changed to match the ASME model as described in Section 3.6. This is most 

important in FRAPTRAN-1.3 where the gap may be filled with steam after cladding rupture. 

• Cladding irradiation creep: That the cladding irradiation creep model in FRAPCON-3.3 

predicts creepdown to occur too rapidly. A new model has been selected and compared to 

creepdown data from fuel rods and from in-reactor pressurized cladding tube creep tests. 

This model is described in Section 3.7. 

The influence of manufacturing, model, and power uncertainties on outputs of interest generated 

by FRAPCON-3.3 has been evaluated. Overall, it appears that manufacturing uncertainties on an 

individual basis have a small to moderate or little influence over the outputs of interest. The 

average variation between unbiased PWR and BWR base cases and cases biased by individual 

manufacturing uncertainties is typically less than 5%. Individual model uncertainties, on the 

other hand, significantly influence outputs of interest generated by FRAPCON-3.3 and may result 

in values that differ from the base cases by as much as 60%. This underscores the importance of 

exercising care in the selection and derivation of models and fitting parameters. Finally, 

evaluation of power uncertainties has revealed that the uncertainty on steady state power has a 
5.2 

major impact on the prediction of fuel centerline temperature and rod internal gas pressure. In 

addition, for a 50% overpower even with a 4 hour hold time, the pulse height has a more 

significant influence than the pulse duration on FRAPCON-3.3 outputs. In particular, cladding 

permanent hoop strain values can vary from the base case by as much as 34% when the AOO 

pulse height is varied from the base case by ±10%. The individual sources of uncertainty that 

have a significant impact on outputs of interest generated by FRAPCON-3.3 are summarized 

below. 

• Rod Internal Pressure: Although manufacturing uncertainty only influenced rod internal 

pressure values by 5% or less, examination of model uncertainties revealed that rod internal 

pressure values can be significantly influenced by uncertainty in the fuel thermal conductivity 

and fission gas release models. Rod internal pressure values varied, on average, from the 

PWR and BWR base cases by approximately 32% and 60%, respectively, when the fuel 

thermal conductivity model is biased by ±0.5W/m-K. Biasing the diffusivity of the fission 

gas release model by ±2 resulted variations from the base case by 12% and 24% for PWR and 

BWR cases, respectively. Power uncertainty also had a significant influence on rod internal 

pressure. The uncertainty in steady state power has a major impact on the prediction of rod 

internal pressure. In addition, variation in AOO pulse height results rod internal pressures 

varying by 17% from the BWR base case. However, this effect was not as significant for the 

PWR, as the biased AOO pulse height only varied from the base case by 6%. 

• Peak Fuel Centerline Temperature: Peak fuel centerline temperature values were insensitive 

to manufacturing uncertainty. However, biasing the fuel thermal conductivity model by 

±0.5W/m-K resulted in variation from the PWR and BWR base cases by 20 and 22%, 

respectively. Power uncertainties have a major impact on peak fuel centerline temperature. 

• Cladding Permanent Hoop Strain: Cladding permanent hoop strain values were insensitive to 

manufacturing uncertainty. However, model uncertainty in the fuel thermal conductivity and 

fuel thermal expansion models resulted in significant variation from the PWR and BWR base 

cases. Biasing the fuel thermal conductivity model by ±0.5W/m-K resulted in variations of 

36 and 52% from the PWR and BWR base cases, respectively. Biasing the fuel thermal 

expansion model by ±15% resulted in variations of 19 and 21% from the PWR and BWR 

base cases, respectively. Power uncertainties also influence cladding permanent hoop strains. 

In particular, biasing the AOO pulse height by ±10% resulted in values that varied by 28 and 

34% from the PWR and BWR base cases, respectively. 
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NRC FORM 335

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NUREG/CR-7001

Predictive Bias and Sensitivity in NRC Fuel Performance Codes

October 2009

NRC Job Code N6326

K. J. Geelhood, W.G. Luscher, C.E. Beyer, D. J. Senor, M.E. Cunningham,

D.D. Lanning, and H.E. Adkins

Technical

P.O. Box 999

Pacific Northwest National Laboratory

Richland, WA 99352

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington DC 20555-0001

J.C. Voglewede, NRC Project Manager

The latest versions of the fuel performance codes, FRAPCON-3 and FRAPTRAN, were examined to ensure best estimate

behavior of the codes and to ensure (to the extent possible) that unintentional bias has been eliminated. Each individual

model and type of code prediction was examined and compared to the data that was used to develop the model. In addition,

a brief literature search was performed to determine if more recent data have become available since the original model

development for model comparison. If new data were discovered, these data were compared to the models and code

predictions in FRAPCON-3.3 and FRAPTRAN-1.3 in order to determine if the model is biased. Models or integral effect

prediction found to be biased relative to the data were updated and corrected in the upcoming versions of the codes,

FRAPCON-3.4 and FRAPTRAN 1.4. Areas where modeling may be lacking were noted for further model development.

The details of the updated models are provided in this report.

Subsequently, a sensitivity study was performed on the steady-state code, FRAPCON-3.3 to determine the effects of

uncertainty in model predictions, manufacturing parameters and power history on the code outputs of regulatory interest.

Nuclear fuel performance code

Fission gas release

Rod internal gas pressure

Fuel centerline temperature

Cladding hoop strain

High burnup licensing analyses


UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

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OFFICIAL BUSINESS