Axial Moderator Density 

Distributions, Control Blade 

Usage, and Axial Burnup 

Distributions for Extended 

BWR Burnup Credit

Office of Nuclear Regulatory Research

NUREG/CR-7224

ORNL/TM-2015/544

Axial Moderator Density 

Distributions, Control Blade 

Usage, and Axial Burnup 

Distributions for Extended 

BWR Burnup Credit

Manuscript Completed: April 2016 

Date Published: August 2016

Prepared by: William (B.J.) Marshall, Brian J. Ade,

Stephen Bowman, Jesus S. Martinez-Gonzalez*

Oak Ridge national Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6170

*Universidad Politecnica de Madrid

c/ José Gutiérrez Abascal, 2-28006 Madrid Spain

Mourad Aissa, NRC Project Manager

NRC Job Code Number V6452

Office of Nuclear Regulatory Research

NUREG/CR-7224

ORNL/TM-2015/544

iii

ABSTRACT

Applications for certificates of compliance for spent nuclear fuel (SNF) dry storage and 

transportation systems must include criticality safety analyses demonstrating that these systems 

are subcritical. This requirement also applies to applications for (specific) licenses for 10 Code 

of Federal Regulations (CFR) Part 72 SNF storage facilities. As part of the licensing process, 

the US Nuclear Regulatory Commission (NRC) staff reviews analyses of pressurized water 

reactor (PWR) SNF that credit the reduction in assembly reactivity caused by depletion of fissile 

nuclides and buildup of neutron-absorbing nuclides during power operation. These reviews are 

conducted according to the guidance in the Division of Spent Fuel Storage and Transportation 

Interim Staff Guidance (ISG) 8, Revision 3. This credit for reactivity reduction during depletion is 

commonly referred to as burnup credit (BUC). However, BUC for boiling water reactor (BWR) 

SNF is not addressed in ISG-8.

NUREG/CR-7194, Technical Basis for Peak Reactivity Burnup Credit for BWR Spent Nuclear 

Fuel in Storage and Transportation Systems (April 2015), provides a technical basis for peak 

reactivity BWR BUC methods in SNF dry storage and transportation systems. Members of the 

nuclear industry have expressed interest in extending BWR BUC beyond these peak reactivity 

methods. This report documents the studies performed to assess the impacts of (1) axial 

moderator density distributions, (2) control blade usage, and (3) axial burnup profiles on 

extended BWR BUC. Each of these parameters was identified as high importance in 

NUREG/CR-7158, Review and Prioritization of Technical Issues Related to Burnup Credit for 

BWR Fuel. This report evaluates the impact of each of these phenomena, with the objective of 

identifying limiting conditions and assumptions in BWR BUC analyses. 

The data used in this report are BWR core follow data from a recent cycle that contained four 

different modern BWR fuel assembly design types: GE14, GNF2, SVEA-96 Optima 2, and 

ATRIUM-10. The data from the nodal simulator has 25 axial nodes and includes more than 240 

time steps for the 690-day cycle. Variables such as the moderator density, power level, burnup, 

and control blade positions can be extracted from the simulated data. The studies documented 

herein draw on this data set because it contains sufficient detail to model axial moderator 

density profiles (and other variables that need to be analyzed, such as control blade usage and 

axial burnup profiles) and because the data also use modern fuel assemblies in a modern BWR 

cycle.

Axial moderator densities in BWRs can vary by 80% or more within a fuel assembly at a single 

location at any time during core operations. The axial moderator density distributions shift during 

an operating cycle and from one cycle to the next as assembly power varies with depletion, 

control blade use, and other core operating parameters. Two studies were performed related to 

axial moderator density distributions: (1) a study investigating the frequency with which the 

moderator density must be updated during the reactor cycle depletion calculations to obtain 

accurate results (termed temporal fidelity study throughout this document) and (2) a study of the 

effect of the axial moderator density distribution on storage and transportation system reactivity. 

The second study includes an assessment of limiting axial moderator density profiles and an 

investigation of axial profile parameterization that could identify limiting profiles without requiring 

extensive depletion and subsequent keff calculations.

Control blade use is entirely different in BWR plants than in PWR plants. PWRs are typically 

operated with all rods out of the core during power operations, and reactivity control is 

maintained with adjustments to soluble boron concentration. BWRs rely on control blade 
iv

insertion to maintain power distribution and reactivity control throughout the cycle. The control 

blades are inserted to different distances into the core for different durations at different times 

during the cycle. Use of a control blade in a BWR hardens the neutron spectrum, resulting in 

increased 239Pu production. Based on increased plutonium with control blade usage, increased 

control blade usage is expected to result in increased cask reactivity. Due to the top-peaked 

axial fission distribution in typical SNF storage and transportation casks, the operating 

conditions experienced in the top portion of the fuel assembly have a disproportionately large

effect on cask reactivity. A combination of hypothetical and realistic profiles are used in this 

study to establish sensitivity to the blade insertion distance, duration, and time in assembly life 

and to assess the potential magnitude of these effects.

The effect of axial burnup profiles on BWR SNF is expected to be similar to that seen for PWR 

SNF: that is, low burnup near the top end of the fuel assembly is expected to cause an increase 

in discharged fuel reactivity when compared to a uniform profile assumption. Conversely, the 

axial burnup profiles that result from BWR operation are expected to be different from those 

resulting from PWR operations because of the differences in axial moderator density and control 

blade effects between PWR and BWR operations. A set of 624 BWR axial burnup profiles was 

used to generate a range of cask keff values at burnups of 30, 40, and 50 GWd/MTU, including 

both the actinide-only and the actinide-plus-fission-product isotope sets. This report presents 

the analysis of the calculation results, including the range of keff values which result from the 

profiles considered, the magnitude of the end effect associated with the profiles, potential 

indicators for relative reactivity of axial burnup profiles, and a brief examination of the effect of 

the discharge burnup of the assembly from which each profile is taken on cask keff. This analysis 

is performed for models that neglect the presence of natural enrichment blankets and for 

models that include these blanket regions.

The studies in this report lead to many important conclusions. This report provides specific 

recommendations based on the analyses described to help identify limiting cases or conditions 

for modeling the impact of axial moderator density distributions, control blade usage, and axial 

burnup profiles on BWR BUC in storage and transportation casks. Because the detailed data 

used in these studies were only readily available from one source and only covered a single 

cycle of operations from a single plant, these recommendations should be regarded as 

instructive but preliminary in nature. Future work can be performed to demonstrate wider 

applicability of the conclusions drawn here. Future work will also include the impact of correlated 

operating parameters such as the impact of control blade insertion on moderator density 

distribution and fuel temperature.
v

CONTENTS

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

LIST OF FIGURES........................................................................................................ vii

LIST OF TABLES .......................................................................................................... xi

1 INTRODUCTION ....................................................................................................... 1

2 CODES, METHODS, AND MODELS ........................................................................ 3

2.1 Codes and Methods..................................................................................................... 3

2.1.1 TRITON ........................................................................................................... 3

2.1.2 KENO............................................................................................................... 4

2.1.3 STARBUCS ..................................................................................................... 5

2.2 Models......................................................................................................................... 6

2.2.1 GBC-68............................................................................................................ 6

2.2.2 GE14................................................................................................................ 9

3 POTENTIAL BWR DATA SOURCES ..................................................................... 13

3.1 Core Follow Data........................................................................................................13

3.2 EPRI Reports on Peach Bottom and Hatch ................................................................13

3.3 Grand Gulf Data .........................................................................................................13

3.4 Swedish Interim Storage Facility Data ........................................................................14

3.5 Commercial Reactor Critical Data...............................................................................14

3.6 Radiochemical Assay Data.........................................................................................14

4 AXIAL MODERATOR DENSITY DISTRIBUTIONS ................................................ 15

4.1 Void Fraction Variability within the Core......................................................................15

4.2 Void Fraction Variability for a Single Assembly ...........................................................16

4.3 Selection of Limiting Profiles.......................................................................................17

4.4 Profiles Used ..............................................................................................................20

4.4.1 Profiles Used in the Temporal Fidelity Study ...................................................20

4.4.2 Profiles Used in Axial Moderator Density Profile Study....................................22

4.5 Results .......................................................................................................................22

4.5.1 Temporal Fidelity Study...................................................................................23

4.5.2 Axial Moderator Density Study ........................................................................29

4.6 Summary and Recommendations...............................................................................40

5 CONTROL BLADE USAGE .................................................................................... 43

5.1 Control Blade Histories ...............................................................................................43

5.2 Results .......................................................................................................................49

5.2.1 Effect of Control Blade Insertion on 239Pu........................................................49
vi

5.2.2 Control Blade Study with Hypothetical Histories..............................................51

5.2.3 Control Blade Study with Realistic Histories ....................................................57

5.3 Summary and Recommendations...............................................................................59

6 AXIAL BURNUP PROFILES................................................................................... 61

6.1 Characteristics of Profiles Used..................................................................................62

6.2 Results for Models Without Blankets ..........................................................................64

6.2.1 Cask keff Results..............................................................................................64

6.2.2 End Effect .......................................................................................................68

6.2.3 Burnup Profile Selection..................................................................................70

6.2.4 Effect of Assembly Burnup ..............................................................................75

6.3 Results for Models with Blankets ................................................................................76

6.3.1 Cask keff Values...............................................................................................77

6.3.2 End Effect .......................................................................................................80

6.3.3 Burnup Profile Selection..................................................................................81

6.3.4 Effect of Assembly Burnup ..............................................................................86

6.4 Summary and Recommendations...............................................................................87

7 CONCLUSIONS ...................................................................................................... 91

7.1 Axial Moderator Density Distributions .........................................................................91

7.2 Control Blade Usage...................................................................................................91

7.3 Axial Burnup Profiles ..................................................................................................92

8 REFERENCES ........................................................................................................ 95

9 GLOSSARY............................................................................................................. 97

APPENDIX A: REALISTIC CONTROL BLADE HISTORIES.................................... A-1
vii

LIST OF FIGURES

Figure 2.1 SCALE sequences, modules, and codes used for KENO calculations 

based on explicit TRITON depletion calculations in this report ............................. 4

Figure 2.2 STARBUCS process to generate KENO models .................................................. 6

Figure 2.3 Radial view of the GBC-68 cask model in KENO in the VAN lattice...................... 7

Figure 2.4 Axial view of GBC-68 cask KENO model.............................................................. 8

Figure 2.5 TRITON model of the (a) DOM and (b) VAN lattice .............................................. 9

Figure 2.6 (a) DOM lattice and (b) VAN lattice, both in storage cell in GBC-68.....................10

Figure 2.7 (a) Axial moderator density profile and (b) axial burnup profile ............................11

Figure 4.1 Cycle-average axial void fraction profiles for each fuel assembly 

in the reactor .......................................................................................................16

Figure 4.2 Axial void profiles for selected first- (left), second- (middle), and higher 

cycle (right) fuel assemblies ................................................................................17

Figure 4.3 Cycle average axial void profiles for SVEA-96 Optima 2 (upper left), 

GNF2 (upper right), GE14 (lower left), and ATRIUM 

(lower right) assemblies.......................................................................................19

Figure 4.4 Cycle average void profiles for (a) first-, (b) second-, and (c) third- or 

higher cycle fuel assemblies................................................................................20

Figure 4.5 Axial fission distribution for BWR SNF in GBC-68 ...............................................21

Figure 4.6 Selected axial void profiles used for the temporal fidelity study with the 

maximum exit void fraction variance case (MV) on the left and the high 

variance and high integral void fraction case (HA) on the right ............................22

Figure 4.7 TRITON model used for the temporal fidelity study .............................................23

Figure 4.8 Cycle average (one step), two step, and every step (23 steps) moderator 

density temporal fidelity schemes for MV (top) and HA (bottom) .........................24

Figure 4.9 239 Pu atom density as a function of burnup for the MV case ...............................25

Figure 4.10 GBC-68 results for the MV moderator profile, AO isotope set..............................27

Figure 4.11 GBC-68 results for the MV moderator profile, AFP isotope set............................27

Figure 4.12 GBC-68 results for the HA moderator profile, AO isotope set ..............................28

Figure 4.13 GBC-68 results for the HA moderator profile, AFP isotope set ............................28

Figure 4.14 Moderator density profiles used in moderator density study ................................33

Figure 4.15 Detail of top five nodes of moderator density profiles ..........................................33

Figure 4.16 GBC-68 cask keff values (AFP isotope set) as a function of moderator 

density in top node ..............................................................................................35

Figure 4.17 GBC-68 cask keff values (AFP isotope set) as a function of moderator 

density in top two nodes......................................................................................35

Figure 4.18 GBC-68 cask keff values (AFP isotope set) as a function of moderator 

density in top three nodes ...................................................................................36

Figure 4.19 GBC-68 cask keff values (AO isotope set) as a function of moderator 

density in top node ..............................................................................................36

Figure 4.20 GBC-68 cask keff values (AO isotope set) as a function of moderator 

density in top three nodes ...................................................................................37

Figure 4.21 GBC-68 cask keff values (AFP isotope set) as a function of moderator 

density in VAN lattice ..........................................................................................37

Figure 4.22 GBC-68 cask keff values (AFP isotope set) as a function of moderator 

density in entire assembly ...................................................................................38
viii

Figure 4.23 GBC-68 cask keff values (AO isotope set) as a function of moderator 

density in entire assembly ...................................................................................38

Figure 5.1 Selected control blade histories from the available operating data ......................44

Figure 5.2 Core map showing control blade numbering scheme ..........................................45

Figure 5.3 Burnup-integrated control blade fraction..............................................................45

Figure 5.4 239Pu concentration as a function of burnup for HH1, HH2, HH12, and 

HH13 control blade histories ...............................................................................49

Figure 5.5 239Pu concentration as a function of burnup for HH1, HH2, HH14, HH15, 

and HH16 control blade histories.........................................................................50

Figure 5.6 AO and AFP criticality results as a function of blade insertion depth ...................54

Figure 5.7 Axial fission distribution for several hypothetical histories....................................55

Figure 5.8 Axial distribution of 239Pu .....................................................................................56

Figure 5.9 Axial distribution of 155Gd.....................................................................................56

Figure 5.10 Axial fission distribution for the limiting realistic history and the unrodded 

hypothetical history..............................................................................................59

Figure 6.1 Selected normalized burnup profiles from assemblies with EOC burnups 

less than 25 GWd/MTU .......................................................................................63

Figure 6.2 Selected normalized burnup profiles from assemblies with EOC burnups 

between 25 and 40 GWd/MTU ............................................................................63

Figure 6.3 Selected normalized burnup profiles from assemblies with EOC burnups 

greater than 40 GWd/MTU ..................................................................................64

Figure 6.4 Eight limiting axial burnup profiles. ......................................................................68

Figure 6.5 Cask keff values for distributed and uniform burnup profiles,

AO isotope set.....................................................................................................69

Figure 6.6 Cask keff values for distributed and uniform burnup profiles, 

AFP isotope set...................................................................................................70

Figure 6.7 Cask keff versus top node relative burnup, AO isotope set ...................................71

Figure 6.8 Cask keff versus sum of top three nodes’ relative burnup, AO isotope set............71

Figure 6.9 Cask keff versus sum of top six nodes’ relative burnup, AO isotope set................72

Figure 6.10 Cask keff versus sum of top 11 nodes’ relative burnup, AO isotope set ................72

Figure 6.11 Cask keff versus top node relative burnup, AFP isotope set .................................73

Figure 6.12 Cask keff versus sum of top three nodes’ relative burnup, AFP isotope set ..........73

Figure 6.13 Cask keff versus sum of top six nodes’ relative burnup, AFP isotope set..............74

Figure 6.14 Cask keff versus sum of top 11 nodes’ relative burnup, AFP isotope set ..............74

Figure 6.15 Cask keff value versus burnup of assembly generating profile, AO isotope 

set, no blankets modeled.....................................................................................76

Figure 6.16 Cask keff value versus burnup of assembly generating profile, AFP isotope 

set, no blankets modeled.....................................................................................76

Figure 6.17 Cask keff values for distributed and uniform burnup profiles, AO isotope set, 

blanketed fuel......................................................................................................80

Figure 6.18 Cask keff values for distributed and uniform burnup profiles, AFP isotope 

set, blanketed fuel ...............................................................................................81

Figure 6.19 Cask keff versus top node relative burnup, AO isotope set, 

blankets modeled ................................................................................................82

Figure 6.20 Cask keff versus sum of top three nodes’ relative burnup, AO isotope set, 

blankets modeled ................................................................................................82

Figure 6.21 Cask keff versus sum of top six nodes’ relative burnup, AO isotope set, 

blankets modeled ................................................................................................83

Figure 6.22 Cask keff versus sum of top 11 nodes’ relative burnup, AO isotope set, 

blankets modeled ................................................................................................83
ix

Figure 6.23 Cask keff versus top node relative burnup, AFP isotope set, 

blankets modeled ................................................................................................84

Figure 6.24 Cask keff versus sum of top three nodes’ relative burnup, AFP isotope set, 

blankets modeled ................................................................................................84

Figure 6.25 Cask keff versus sum of top six nodes’ relative burnup, AFP isotope set, 

blankets modeled ................................................................................................85

Figure 6.26 Cask keff versus sum of top 11 nodes’ relative burnup, AFP isotope set, 

blankets modeled ................................................................................................85

Figure 6.27 Cask keff value versus burnup of assembly-generating profile, AO isotope 

set, blankets modeled .........................................................................................87

Figure 6.28 Cask keff value versus burnup of assembly-generating profile, AFP isotope 

set, blankets modeled .........................................................................................87

Figure A.1 Control blade history RH1 (blade location 3,4) ..................................................A-1

Figure A.2 Control blade history RH2 (blade location 4,4) ..................................................A-1

Figure A.3 Control blade history RH3 (blade location 7,4) ..................................................A-2

Figure A.4 Control blade history RH4 (blade location 2,5) ..................................................A-2

Figure A.5 Control blade history RH5 (blade location 3,5) ..................................................A-2

Figure A.6 Control blade history RH6 (blade location 4,5) ..................................................A-3

Figure A.7 Control blade history RH7 (blade location 2,6) ..................................................A-3

Figure A.8 Control blade history RH8 (blade location 3,6) ..................................................A-3

Figure A.9 Control blade history RH9 (blade location 4,6) ..................................................A-4

Figure A.10 Control blade history RH10 (blade location 6,6) ................................................A-4

xi

LIST OF TABLES

Table 2.1 Isotopes included in the AO and AFP isotope sets ............................................... 5

Table 4.1 Results of lifetime average moderator density study............................................29

Table 4.2 Axial moderator profiles from selected assemblies ..............................................31

Table 4.3 Constructed axial moderator profiles ...................................................................32

Table 4.4 GBC-68 cask keff values for 10 actual assembly moderator density profiles, 

AO isotope set.....................................................................................................34

Table 4.5 GBC-68 cask keff values for 10 actual assembly moderator density profiles, 

AFP isotope set...................................................................................................34

Table 4.6 GBC-68 cask keff values for constructed profiles, AO isotope set.........................39

Table 4.7 GBC-68 cask keff values for constructed profiles, AFP isotope set.......................39

Table 4.8 GBC-68 cask keff values for uniform moderator densities, AO isotope set............40

Table 4.9 GBC-68 cask keff values for uniform moderator densities, AFP isotope set..........40

Table 5.1 Criticality results for HH1–HH32..........................................................................53

Table 5.2 Criticality results for RH1-RH10...........................................................................58

Table 6.1 Cask keff distribution data for the unblanketed fuel models ..................................65

Table 6.2 Top ten most reactive axial burnup profiles, AO isotope set ................................66

Table 6.3 Top ten most reactive axial burnup profiles, AFP isotope set ..............................66

Table 6.4 Eight highly reactive normalized axial burnup profiles .........................................67

Table 6.5 Cask keff distribution data for the blanketed fuel models ......................................77

Table 6.6 Top ten most reactive axial burnup profiles, AO isotope set, 6-in. 

blankets modeled ................................................................................................78

Table 6.7 Top ten most reactive axial burnup profiles, AFP isotope set ..............................78

Table 6.8 Reactivity reduction introduced by modeling blankets .........................................79

Table 6.9 Cask keff results for 10 selected 12-in. blanket profiles, AO isotope set ...............79

Table 6.10 Cask keff results for 10 selected 12-in. blanket profiles, AFP isotope set..............79

1

1 INTRODUCTION

Applicants for certificates of compliance for spent nuclear fuel (SNF) transportation and dry 

storage systems perform analyses to demonstrate that these systems are adequately subcritical 

according to the requirements of Title 10 of the Code of Federal Regulations (CFR) Parts 71 

and 72 [1]. For pressurized water reactor (PWR) SNF, these analyses may credit the reduction 

in assembly reactivity caused by depletion of fissile nuclides and buildup of neutron-absorbing 

nuclides during power operation. This credit for reactivity reduction during depletion is 

commonly referred to as burnup credit (BUC). US Nuclear Regulatory Commission (NRC) staff 

review BUC analyses according to the guidance in the Division of Spent Fuel Storage and 

Transportation Interim Staff Guidance (ISG) 8, Revision 3 [2], “Burnup Credit in the Criticality 

Safety Analyses of PWR Spent Fuel in Transportation and Storage Casks.”

ISG-8 does not address BUC for boiling water reactor (BWR) SNF. However, NUREG/CR-7194, 

Technical Basis for Peak Reactivity Burnup Credit for BWR Spent Nuclear Fuel in Storage and 

Transportation Systems (April 2015) [3], does provide a technical basis for peak reactivity BWR 

BUC methods. Peak reactivity occurs when the effective multiplication factor (keff) for an 

assembly or 2-dimensional (2D) slice reaches its highest value at some burnup beyond 

beginning of life (BOL). This common feature of BWR assemblies is caused by the burnable 

absorber depleting at a more rapid rate than the fuel. Members of the nuclear industry have 

expressed interest in extending BWR BUC beyond these peak reactivity methods to higher 

burnups. This report documents the studies performed to assess the impacts of axial moderator 

density distributions, control blade usage, and axial burnup profiles on extended BWR BUC. In 

this document, extended BWR BUC is defined as credit for the reduction in reactivity at burnups 

greater than the peak reactivity burnup. The impact of each of these phenomena is evaluated to 

identify limiting conditions and assumptions for use in extended BWR BUC analyses. Unless 

otherwise noted in the text, a limiting parameter is defined as that which leads to higher 

reactivity when the SNF is loaded into a storage and transportation system, commonly referred 

to as a cask.

Axial moderator densities in BWRs can vary by 80% or more within a fuel assembly at a single 

location at any time during core operations. This is in stark contrast to axial moderator densities 

in PWRs, which experience water density variations of approximately 10% from core inlet to 

outlet. Therefore, there is no directly applicable PWR BUC methodology for treating moderator 

density variations of the magnitude experienced in BWR operations. The axial distributions 

generated in a BWR also shift within a cycle and from one cycle to the next as assembly power 

varies with depletion, control blade use, and other core operating parameters. The studies 

presented in Section 4 of this report are designed to address the key aspects of modeling these 

axial moderator density distributions.

As with axial moderator density distributions, control blade use is entirely different in BWR 

plants from control rod use in PWRs. PWRs are typically operated with all rods out of the core 

during power operations, and reactivity control is maintained with adjustments to soluble boron 

concentration. BWRs cannot use soluble poisons because boiling would cause the poison to be 

deposited on fuel rod surfaces within the core. Instead, BWRs rely on control blade insertion to 

maintain power distribution and reactivity control throughout the cycle. Control blades are 

inserted at different distances into the core for varying durations and at various times during the 

cycle. Section 5 presents studies of the sensitivity of BWR SNF reactivity to control blade use. A 

combination of hypothetical and realistic profiles is used to establish the sensitivity of cask keff to

the blade insertion distance, duration, and time in assembly life.
2

The effect of axial burnup profiles on BWR SNF is expected to be similar to that seen for PWR 

SNF: that is, low burnup near the top end of the fuel assembly is expected to cause an increase 

in discharged fuel reactivity compared with a uniform profile assumption. Conversely, the axial 

burnup profiles resulting from BWR operation are expected to be different from those resulting 

from PWR operations because of the differences in axial moderator density and control blade 

effects between PWR and BWR operations. The studies presented in Section 6 use a similar 

approach to established methodologies in PWR BUC to assess the impact of BWR axial burnup 

profiles on discharged SNF reactivity.

Before the three studies discussed above, Section 2 describes the codes, methods, and models 

employed in the depletion and criticality safety analyses performed in the studies. Section 3 

provides a discussion of the available data sets that were considered for use in these studies 

and the data set that was selected. Details of the studies are presented in Sections 4–6: axial 

moderator density distributions are covered in Section 4, control blade use is described in 

Section 5, and axial burnup profiles are presented in Section 6. Final conclusions are in 

Section 7.
3

2 CODES, METHODS, AND MODELS

2.1 Codes and Methods

BUC analyses require the use of a series of codes and models to simulate fuel depletion in the 

core and SNF reactivity in the storage and transportation system. The SCALE code system [4] 

was used for all calculations in this work. 

2.1.1 TRITON

TRITON is a multipurpose SCALE control module for transport, depletion, and sensitivity and 

uncertainty analysis [5]. TRITON can be used to provide automated, problem-dependent, cross

section processing followed by multigroup transport calculations for one-, two-, or threedimensional (1D, 2D, or 3D) configurations. This functionality can be used in tandem with the 

ORIGEN depletion and decay module to predict time-dependent isotopic concentrations, source 

terms, and decay heat; and it can be used to generate few-group homogenized cross sections 

for nodal core calculations. In this work, TRITON automated resonance self-shielding (BONAMI 

/CENTRM/PMC), 2D neutron transport (NEWT), and fuel depletion calculations (ORIGEN) in a 

series of coupled transport-depletion calculations (depletion steps) to simulate the full depletion 

history. Following the depletion calculations, ORIGEN was used again to decay the SNF 

isotopic compositions to simulate the cooling time experienced in a spent fuel pool before

loading into the storage and transportation system.

TRITON performed 2D lattice depletion calculations over a range of varying operating 

conditions. The transport model included a set of 94 nuclides corresponding to the “addnux=2” 

option (default in TRITON), while more than 2,000 nuclides were tracked during the ORIGEN

depletion and decay calculations. The gadolinium-bearing fuel pins were modeled with seven 

equal-area radial rings to accurately capture the radial dependence of the gadolinium depletion. 

This modeling approach provides adequate solution accuracy in a reasonable computational 

time [6]. The 238-group ENDF/B-VII.0 neutron cross section library was used for all calculations. 

After the TRITON depletion calculations were complete, the output files generated during these 

calculations were post-processed to generate depleted and decayed fuel composition files for 

use in subsequent criticality calculations for the storage system. Figure 2.1 is a flow chart

showing the steps used in a typical TRITON depletion calculation followed by KENO 

calculations. In this figure, the library management code COUPLE facilitates the update of the 

cross section and flux data that ORIGEN requires for depletion calculations. The update is 

based on the NEWT transport solution.

The TRITON calculations documented in this report were performed with SCALE 6.2 Beta4, 

which was configured under the SCALE quality assurance plan in March 2015. This version of 

SCALE was used because deficiencies in the SCALE 6.1 implementation of the timetable option 

in TRITON precluded the simulations needed for the current work. In addition, the NEWT 

transport module runs significantly faster in SCALE 6.2, reducing the computational burden of 

the calculations performed.

The timetable block is used extensively in TRITON calculations. It was provided to modify 

properties of regions in the model during depletion, and it is commonly used to vary the soluble 

boron concentration in PWR cores. In this work, the timetable block adjusted the moderator 

densities in each node during depletion. The input includes changes in the number densities to 

be made and the times at which the changes are to be made.
4

Figure 2.1 SCALE sequences, modules, and codes used for KENO calculations based on 

explicit TRITON depletion calculations in this report

2.1.2 KENO

The Criticality Safety Analysis Sequence (CSAS)/KENO performed reactivity calculations for the 

GBC-68 computational benchmark model described later in this section. The sequence provides 

automated problem-dependent cross section processing followed by 3D multigroup Monte Carlo 

neutron transport calculations to solve the keff eigenvalue problem. All calculations were 

performed using the 238-group neutron cross section library based on ENDF/B-VII.0 data. All 

KENO calculations performed in this report used SCALE 6.1.3 [4].

Two different sets of nuclides can be used for fuel modeling in the CSAS models: (1) major 

actinides only (AO) and (2) major and minor actinides and major fission products (AFP). The 

nuclides used in the AO and AFP nuclide sets are taken from NUREG/CR-7109 [7] and are the 

same as those typically used when calculating PWR BUC. The same isotope sets are 

appropriate for use in BWR BUC because the same nuclides result from fission in both types of 

light water reactors. Table 2.1 provides the BUC nuclides considered in the AO and AFP sets. 

155Gd is included in the AFP set, but 157Gd is not.
5

Table 2.1 Isotopes included in the AO and AFP isotope sets

10 AO isotopes 

234U 235U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 16O

29 major and minor actinides and major fission products (AFPs)

234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu

241Am 243Am 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm

150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd 16O

2.1.3 STARBUCS

The STARBUCS sequence provides an automated link between ORIGEN-ARP depletion 

calculations and CSAS criticality safety calculations. STARBUCS creates depleted fuel 

compositions based on pregenerated ORIGEN libraries, a fresh fuel description, and an input 

irradiation history. The sequence performs a depletion and decay calculation for each axial node 

in the cask model using the ORIGEN-ARP methodology and generates a material composition 

that can be directly entered into KENO. All STARBUCS calculations performed in this report use 

SCALE 6.1.3 [4].

The ORIGEN-ARP methodology performs ORIGEN depletion calculations using cross section 

libraries pregenerated for specific configurations as a function of burnup, and for discrete values 

of parameters characterizing these configurations (e.g., enrichment, moderator density). The 

pregenerated cross sections are interpolated using the ARP code over a range of varying fuel 

assembly properties, including burnup and moderator density. The interpolation scheme retains 

the accuracy of the explicit TRITON calculations used to pregenerate the cross section libraries. 

Figure 2.2 provides a flow chart showing the process of generating KENO models using 

STARBUCS.

A limitation of STARBUCS is that it can only use a single ORIGEN library in a calculation. Since 

the GE14 assembly design type examined in this work is modeled with two lattices—full and 

vanished—two STARBUCS calculations are needed to determine depleted compositions for the 

entire assembly. The compositions from the individual depletion calculations are combined to 

make a single set of compositions representing the depleted and decayed fuel compositions in 

each KENO calculation.
6

Figure 2.2 STARBUCS process to generate KENO models

2.2 Models

2.2.1 GBC-68

The GBC-68 computational benchmark model was developed in Reference [8] as a generic 

BUC cask for modeling BWR SNF. The KENO model of the fuel loaded in the cask explicitly

represents each fuel rod, including its gap and cladding. Part-length rods are truncated at the 

appropriate elevation so that both the full lattice (referred to as full or dominant) and the 

vanished lattice are included explicitly in the KENO model. Section 2.2.2 includes further 

discussion of lattice modeling. The fuel assembly channel model is simplified in KENO, 

represented with constant thickness and squared corners. All fuel assemblies are assumed to 

contain fuel with identical compositions and irradiation histories. KENO calculations performed 

with depleted fuel compositions generated by TRITON assume a single average composition for 

nongadolinium fuel and seven unique compositions for the rings modeling the gadolinium pins in 

each axial node. KENO calculations performed with depleted fuel compositions calculated in 

STARBUCS assume a single average composition for all fuel in all pins within an axial node. 

The cross sections generated for the ORIGEN-ARP depletion represent the entire node, 

effectively smearing residual gadolinium burnable absorber into all fuel pins. The impact of this 

approximation is small since there is an insignificant amount of such residual burnable absorber 

at the burnups examined in these studies. All KENO models contain 25 axial nodes, each 6 

inches in length (15.24 cm). This report references the nodes by numbering them from 1 to 25 

from top to bottom within the assembly. Figure 2.3 shows a radial view of the GBC-68 half-cask 

model depicting the cask body, basket, and fuel assemblies. Figure 2.4 shows an axial view of 

the model with each unique axial fuel composition shown in a different color.
7

Figure 2.3 Radial view of the GBC-68 cask model in KENO in the VAN lattice

Stainless steel

Water
8

Figure 2.4 Axial view of GBC-68 cask KENO model

VAN lattice

66” (167.64cm)

DOM lattice

84” (213.36cm)
9

2.2.2 GE14

GE14 is the only fuel assembly design type used in these studies. This assembly has a 10 × 10 

array of fuel pins and contains two large central water rods, each of which displaces four fuel 

rods. The GE14 fuel assembly can contain many axial levels with varying fuel enrichment and 

gadolinium loading. Owing to the presence of part-length fuel rods, which terminate at 

approximately half the total height of the fuel assembly, the GE14 fuel assembly contains two 

primary axial zones (or levels). These two axial regions are the dominant (DOM or full) and 

vanished (VAN) lattices. A 2D slice through one of these axial zones is referred to as a lattice. 

The full lattice has a fuel rod occupying every position in the fuel pin array. The vanished lattice 

is located axially above the part-length rods, so these rods are in effect vanished from the 

lattice. TRITON representations of the DOM and VAN lattices are shown in Figure 2.5. All 

gadolinium-bearing rods contain the same absorber loading in both the DOM and VAN lattices. 

Two-dimensional representations of the two lattices in the KENO model of GBC-68 for use with 

STARBUCS-generated depleted compositions are shown in Figure 2.6. No axial enrichment 

zoning is modeled for any calculations in this report aside from the investigation of natural 

enrichment axial blankets in Section 6.3.

(a) (b)

Figure 2.5 TRITON model of the (a) DOM and (b) VAN lattice
10

(a) (b)

Figure 2.6 (a) DOM lattice and (b) VAN lattice, both in storage cell in GBC-68

The GE14 fuel assembly was chosen for the studies herein, as it is the most common fuel 

assembly type used in US BWRs, contains advanced geometry features commonly seen in 

modern BWR fuel assemblies (e.g., water rods, part-length rods), is commonly loaded with pins 

enriched to near 5.0 wt % 235U, and typically contains many gadolinium-bearing fuel pins. 

Results from studying various characteristics in a modern, highly heterogeneous fuel lattice 

such as the GE14 can be extended to other highly heterogeneous fuel configurations. A 

previous study [9] has shown that the GE14 assembly design is more reactive than smaller GE 

lattices (7 × 7, 8 × 8, and 9 × 9) for most burnups. Other lattice sizes may be more reactive at 

high burnup [9], but moderator density distribution, control blade history, and axial burnup profile

effects are expected to be largely independent of assembly lattice size. Off-nominal 

temperature/density conditions for the moderator inside the cask model have not been 

considered. Differing fuel-to-water ratios among the different lattices may cause different 

responses to these off-nominal conditions and should also be examined.

The fuel assembly design used in these studies is based on an actual assembly from the 

detailed core follow data described in Section 3. All TRITON depletion calculations used 

4.5 wt % 235U in all pins and 15 gadolinium-bearing rods with 7 wt % Gd2O3. This single 

assembly design is used throughout the calculations to assess the effect of the different axial 

moderator density distributions, control blade histories, and axial burnup profiles independent of 

any effects potentially caused by differing fuel or absorber loadings. Additional enrichments, 

gadolinium loadings, or gadolinium-bearing pin patterns are not considered in this report. The 

sensitivities examined in this report are not expected to have a significant impact on any of 

these parameters. Each of the parameters being studied is varied singly to isolate its effect on 

discharged fuel reactivity. All other parameters, including specific power, fuel temperature, and 

moderator temperatures, are unchanged throughout these studies. The axial moderator density 

profile used in the control blade studies is shown in Figure 2.7a. The axial burnup profile used in 

studies of the axial moderator density profile and control blade use can be found in Figure 2.7b. 

The characteristics of higher reactivity fuel assemblies with regard to the axial moderator 

density distribution and burnup profile are presented in Sections 4 and 6, respectively.
11

 

(a) (b)

Figure 2.7 (a) Axial moderator density profile and (b) axial burnup profile

13

3 POTENTIAL BWR DATA SOURCES

This section includes brief descriptions of the data sources available for axial moderator density 

distributions, control blade usage, and axial burnup profiles, along with an assessment of the

data for their application to the planned studies. The area of study requiring the greatest amount 

of detailed data is the axial moderator density distribution study because of the need to examine 

modeling assumptions related to the frequency with which the node-wise moderator density 

must be changed in the simulation. Most of the data are judged to be insufficient for the planned 

studies, and information regarding these data sets is provided in Sections 3.2–3.6. The most 

common shortcomings are the lack of detailed operating data as a function of time (i.e., multiple 

state points per cycle), lack of recent or current data (most available data are from older fuel 

assembly design types), and the limited number of locations within the core having data. The 

description of the core follow data used for the studies documented in this report is provided in 

Section 3.1; the data sets described in the subsequent subsections are not used in this work. 

3.1 Core Follow Data

Through another joint NRC and Oak Ridge National Laboratory (ORNL) project, the ORNL BWR 

BUC project gained access to proprietary operating data for a BWR core’s single cycle. The 

data include inlet and outlet conditions and traveling in-core probe (TIP) data. These data 

include CASMO-SIMULATE [10] core follow data for every fuel assembly in the reactor. The 

data were obtained from a recent cycle that contained four different modern BWR fuel assembly 

design types: GE14, GNF2, SVEA-96 Optima 2, and ATRIUM-10. Each fuel assembly has been 

modeled with 25 different axial nodes, and the 690-day cycle was simulated using more than 

240 time steps. The size of the time steps varies slightly, but all steps are less than 5 effective 

full power days in length. State variables such as the moderator density, power level, exposure, 

and control state can be extracted from the simulated data [10]. This data set was ideal for the 

studies documented herein because the simulated data contain sufficient detail to model axial 

moderator density profiles, control blade usage, and axial burnup profiles. The data are from a 

cycle that features modern fuel assemblies in a modern BWR cycle.

3.2 EPRI Reports on Peach Bottom and Hatch

The Electric Power Research Institute (EPRI) report for Peach Bottom [11] contains operating 

data (average inlet and outlet conditions) and TIP measurements for cycles 1 and 2 for Peach 

Bottom Unit 2. Very similar data exist for cycles 1–3 of Hatch Unit 1 [12, 13]. When these cycles 

operated, the reactors used 7 × 7 and 8 × 8 fuel assembles with very little gadolinium and few 

liquid water features (i.e., water rods). Thermal-hydraulic (T-H) data are limited to inlet and 

outlet conditions. The older design of these assemblies and the availability of only inlet and 

outlet T-H conditions make these sources inadequate for analyzing axial void profiles.

3.3 Grand Gulf Data

ORNL supported the NRC in 2006 for MELCOR analysis of the Grand Gulf Nuclear Station [14]. 

The data available for that analysis included reactor cycles 3, 4, 5, 11, 12, and 13 and 

configurations with 8 × 8, 9 × 9, and 10 × 10 fuel arrays. The fuel data provided by GE and 

Areva covered a diversity of assembly designs and axial moderator density profiles by assembly 

type. However, only average axial data were available, and the data are proprietary.
14

3.4 Swedish Interim Storage Facility Data

Data are available for a series of calorimetric measurements performed at the central interim 

storage facility for SNF (Clab) operated by the Swedish Nuclear Fuel and Waste Management 

Company (SKB) [15]. A variety of assembly types, including 8 × 8, 9 × 9, and 10 × 10 arrays, 

were among the 25 assemblies from eight Swedish reactors measured. Both GE and SVEA 

assembly designs were included, so this is another data set that can be compared across 

different design types. The axial moderator density profiles provided are lifetime average values 

by node and therefore cannot be used to support a temporal fidelity study. The data are not 

adequate for an axial distribution study because they have fairly low precision and generally 

represent older operating histories. The fuel assemblies included in this data set were irradiated 

between 1974 and 1996.

3.5 Commercial Reactor Critical Data

The commercial reactor critical data support validation efforts conducted as part of the Yucca 

Mountain Project. Several of these reports provide detailed information on early cycles of 

operation for Grand Gulf Unit 1 [16], LaSalle Unit 1 [17], and Quad Cities Unit 2 [18]. These 

reports contain detailed information about axial burnup profiles and moderator density profiles 

for each assembly in a specific operating cycle and for all prior cycles that those assemblies 

experienced. The data are generally only reported for 2–3 state points per cycle and are 

therefore not useful for a temporal fidelity study. All the cycles considered contain older fuel 

types and operational strategies. More recent operations are likely to be characterized by higher 

specific power for assemblies, extensive use of gadolinium burnable absorbers, and high void 

fractions.

3.6 Radiochemical Assay Data

Data are available for a large number of radiochemical assay (RCA) samples from a variety of 

programs conducted over the years. Two examples include data from Forsmark Unit 3 [19] and 

Limerick [20]. Very detailed information is contained in these reports for the conditions near the 

location or locations at which RCA samples have been taken. Unfortunately, this data coverage 

does not extend to the entire core, so it does not provide insight into the full range of operating 

conditions, burnup profiles, or axial moderator density profiles present in a core.
15

4 AXIAL MODERATOR DENSITY DISTRIBUTIONS

Because of the boiling of the coolant in a BWR, the moderator density (or void fraction) changes 

significantly as a function of axial position in the reactor. For each fuel assembly in the reactor, 

the power generated by the assembly has a significant impact on the moderator density change 

from the bottom to the top of the fuel assembly. Many different factors contribute to the power 

produced by a fuel assembly, including assembly design, burnup, control blade position, 

neighboring fuel assemblies, and assembly position within the core. The effects of these factors 

can be clearly observed in the moderator density profile data.

This section documents studies of two different aspects of axial moderator density distributions. 

The first is a study investigating the frequency with which the moderator density must be 

updated during depletion calculations to obtain accurate results. This study is termed temporal 

fidelity study throughout this document. The second study directly examines the effect of the 

axial moderator density distribution on storage and transportation system reactivity. This second 

study includes both an assessment of limiting axial moderator density profiles and an 

investigation of axial profile parameterization. In this context, parameterization is the 

determination of a single quantitative value to describe an axial moderator profile. The 

parameterization would potentially serve in identifying limiting profiles without performing 

depletion and subsequent keff calculations. The second study is referred to as the axial 

moderator density study throughout this document.

The primary goal of the studies presented in this section is to analyze the effects of the 

moderator density (alternatively, void fraction) axial profile on cask reactivity. To understand 

these effects, a number of different axial profiles must be generated for testing. BWR design 

and operation data typically consider void fraction instead of moderator density. Therefore, 

discussions in this section focus on void fractions for consistency with industry practice. The 

void fractions are converted to moderator density for use in SCALE input files.

4.1 Void Fraction Variability within the Core

The variability of the void fraction is very large over the entire reactor. Figure 4.1 shows plots of 

the cycle-average axial void profiles for all 624 fuel assemblies in the detailed core follow data 

set. Nodes are numbered 1–25 progressing from the top to the bottom of the core. The color of 

each line indicates the radial distance of the fuel assembly from the centerline of the core, 

ranging from dark blue for assemblies near the center of the core to dark red for the assemblies 

farther from it. In general, high void fraction assemblies exist near the center of the core, while 

low void fraction assemblies are typically near the radial periphery of the core. In Figure 4.1, a 

bold black line plots the core-average void profile. For a single axial node, the void fraction can 

change by as much as 65% across the core, illustrating the highly variable nature of the void 

fraction in modern BWRs. Figure 4.1 indicates depressions in the void fraction for certain axial 

levels due to the effect of the spacer grids in the fuel assemblies.
16

Figure 4.1 Cycle-average axial void fraction profiles for each fuel assembly in the reactor

4.2 Void Fraction Variability for a Single Assembly

The axial void profile data have been divided into first-, second-, and later-cycle fuel assemblies. 

This classification has been derived because the available operating data did not include 

information on the number of cycles for which a fuel assembly has been present in the core. 

First-cycle fuel assemblies are readily identified because the beginning of cycle (BOC) exposure 

is 0.0 GWd/MTU, but it is not clear which fuel assemblies are second-, third-, or higher cycle 

fuel assemblies. The BOC exposure of the axial center node (node 13) was used to make a 

determination for the remaining fuel assemblies. If the BOC node 13 exposure is greater than 

zero but less than 30 GWd/MTU, then the fuel assembly is a second-cycle fuel assembly. If the 

BOC node 13 exposure is greater than or equal to 30 GWd/MTU, then the fuel assembly is 

assumed to be a later cycle fuel assembly.

The void fraction profile varies significantly over time for a single assembly within a single cycle,

as well as over the life of the fuel assembly. Figure 4.2 plots the axial void profile for a first-, 

second-, and later cycle fuel assembly in the core. The color scheme shows the cycle depletion 

step number of the core follow data. Therefore, blue colors are early in the cycle, and red colors 

are late in the cycle. Because only a single cycle of data exists, each of the three axial profiles 

in Figure 4.2 is from a different assembly. However, the axial shapes of the void profiles are 

largely similar among first-, second-, and later-cycle fuel assemblies. The effect of the 

gadolinium absorber is apparent in the first-cycle fuel assembly (left plot in Figure 4.2). The blue 

lines, which represent time (depletion) steps near the beginning of the cycle, are nearly hidden 

by the later steps. The change in the axial void profile directly correlates with the reactivity of the 

fuel assembly due to depletion of the gadolinium absorber. As gadolinium is consumed, the void 

fraction increases due to higher relative power in that fuel assembly. Late in the cycle, the fuel 
17

depletion leads to lower power in the assembly, and the void fraction then begins to decrease. 

In the second-cycle fuel assembly (middle plot in Figure 4.2), the exit void fraction begins at a 

relatively high value, above 80%, and then decreases fairly consistently throughout the cycle. 

For the later-cycle fuel assembly (right plot in Figure 4.2), relatively little fissile material is left in 

the assembly, so the axial void profile decreases from the beginning to the end of the cycle as 

the assembly produces progressively less power as the cycle proceeds. Note that the void 

fraction values are larger in the first two cycles (greater than 80% at the top of the assembly), 

while the values are much smaller for the later cycle (only 60% at the top of the assembly).

Figure 4.2 Axial void profiles for selected first- (left), second- (middle), and higher cycle 

(right) fuel assemblies

4.3 Selection of Limiting Profiles

In this report, the profiles expected to be the most limiting were applied to a single assembly 

design to perform a study that isolates the effect of the axial void profile. However, some axial 

void profiles may be unique to certain fuel assemblies. To determine whether this is the case, all 

axial void profiles in the core were averaged over the cycle and then plotted to visually inspect 

the uniqueness of certain profiles to certain fuel assembly types. Each figure in this section 

represents the cycle-average void profile for that particular assembly type. Within each 

assembly type, different designs contain enrichment and gadolinium rods that vary in position 

and poison content. The impact on axial void distribution of variations in fuel assembly design 

for the same fuel assembly type have not been studied in this work. 

Figure 4.3 plots the cycle-average void profile for each assembly by assembly type. In these 

figures, the color of the line denotes how many cycles of irradiation a certain fuel assembly has 

accrued (first cycle is red, second cycle is blue, and later cycle is green). The SVEA-96 Optima 

2 (SVEA-96) fuel is the only fuel assembly type that contains fuel for all categories; therefore, 

the variability of the average void profile is significant. For the GE14 fuel assemblies, there is 

significant separation between second- and later cycle fuel assemblies, but there is a more 

continuous distribution of void profiles for the SVEA-96 fuel assemblies. The reason for this 

behavior is that there are significantly more SVEA-96 fuel assemblies used in this cycle than
18

any other type. Data from additional plants and cycles could further elucidate potential axial void 

profile variation and its causes.

Figure 4.4 plots the cycle-average axial void profiles for each assembly, but each plot now 

corresponds to first- (Figure 4.4a), second- (Figure 4.4b), and later cycle (Figure 4.4c) fuel 

assemblies. In this figure, the color of the line denotes fuel assembly type: SVEA-96 is plotted 

using purple, GNF2 is plotted using blue, GE14 is plotted using green, and ATRIUM is plotted 

using red. SVEA-96 and GNF2 are the only fuel assembly types containing fresh fuel 

(Figure 4.4a). The axial void profiles in Figure 4.4a for the SVEA-96 and GNF2 fuel types result 

in nearly identical void profiles for the fresh fuel; the axial void profiles for the GNF2 fuel span 

the axial void profiles for the SVEA-96 fuel. In Figure 4.4b (second-cycle fuel), only SVEA-96 

and GE14 fuel exist, and the GE14 fuel results in axial void profiles with higher average void 

fraction values (further right) than the SVEA-96 fuel. However, there is still significant overlap 

between the two fuel assembly types. Because there are significantly more SVEA-96 fuel 

assemblies than GE14 fuel assemblies in the core, more data are available for SVEA-96 fuel 

assemblies than for GE14 fuel assemblies. In Figure 4.4c (later-cycle fuel), the axial void 

profiles for the GE14, ATRIUM, and SVEA-96 fuel assemblies overlap each other. Several

SVEA-96 fuel assemblies have higher average void fractions than the others, but this may be 

due to the choice of exposure boundaries used to define first-, second-, and later cycle fuel 

assemblies, or it may be related to the location of these fuel assemblies in the core.

These results indicate that the void profile is more sensitive to exposure and core position than 

to fuel assembly type. The studies herein apply the most limiting profiles to the GE14 fuel 

assembly design to isolate the impact of the void profile on cask reactivity.
19

Figure 4.3 Cycle average axial void profiles for SVEA-96 Optima 2 (upper left), GNF2

(upper right), GE14 (lower left), and ATRIUM (lower right) assemblies

 First-cycle assembly

 Second-cycle assembly

 Higher cycle assembly
20

(a) (b) (c)

Figure 4.4 Cycle average void profiles for (a) first-, (b) second-, and (c) third- or higher

cycle fuel assemblies

4.4 Profiles Used

The requirements of the temporal fidelity study and the axial moderator density study are 

different, and they drive the selection of different types of axial moderator profiles. The goal of 

the temporal fidelity study is to determine how frequently the moderator density distribution must 

be updated during depletion calculations. The best data for this study contain highly variable 

moderator density distributions. The axial moderator density study is expected to be dominated 

by profiles with high void fractions in the top portions of the assembly for an extended period of 

operation. These profiles have inherently low variability and are therefore likely to be excluded 

from the temporal fidelity study despite being of significant interest in conservative cask 

reactivity determinations. The following subsections discuss the selection process for the 

profiles used in each of the studies.

4.4.1 Profiles Used in the Temporal Fidelity Study

To perform depletion calculations that result in conservative reactivity determinations for SNF in 

casks, one must determine how fine a time scale must be used to capture the time-varying 

effects of key variables. Sections 4.1 and 4.2 presented the significant variability of the coolant 

void fraction both throughout the core (variability in space) and within each fuel assembly 

(variability as a function of time or burnup). With such significant variability in void fraction, the 

question of how large an impact this variability ultimately has on SNF cask criticality must be 

answered. A temporal fidelity study has been performed to answer this question.

To begin this study, the fission distribution in a fuel cask filled with depleted BWR fuel

assemblies was estimated as seen in Figure 4.5. The figure clearly shows that the majority of 

fissions in a flooded BWR fuel storage cask occur near the top of the cask; this effect is known 

as the end effect, which is well documented for PWR fuel [21]. These results were generated as 

part of earlier work for the NRC [22] that examined the effect of fuel reconfiguration on storage 

and transportation systems. This plot was generated as part of this study to identify the most 

important axial regions of a spent BWR assembly for cask reactivity. The fuel represented in 
21

Figure 4.5 is based on the GE14 design, also being used in the present studies, and has been 

depleted to 35 GWd/MTU. Figure 4.5 indicates that the fuel assembly reactivity in the cask is 

dominated by the upper portion of the fuel assembly. As discussed in Section 5.2.2, deviations 

from this axial profile could be caused by significant periods of depletion with control blades 

inserted between 50% and 75% of the core height. There are no realistic control blade 

exposures that exhibit that type of behavior and, as discussed in Section 5.2.3, all the realistic

control blade histories included in this report result in top peak distributions similar to the one 

shown in Figure 4.5.

Figure 4.5 Axial fission distribution for BWR SNF in GBC-68

Because the upper portion of the fuel assembly has such a significant impact on cask criticality, 

axial profiles that have a significant change in the exit void fraction over the cycle were chosen 

for the temporal fidelity study. A search algorithm was used on the operating data to determine 

which fuel assemblies underwent the maximum change over the cycle. In general, the latercycle fuel assemblies have more significant axial void fraction variability over a single cycle than 

the first- or second-cycle fuel assemblies, but they also tend to exhibit lower cycle-average void 

fractions than the first- or second-cycle fuel assemblies. Because of these complexities, axial 

void profiles from two different assemblies were chosen for the temporal fidelity study. The axial 

void profile from the fuel assembly with the most variability (MV) but with a relatively low 

average void fraction was selected. The variance of the void fraction over core height is 

calculated for each assembly at each time step. The variance of the set of variance values is 

then calculated for each assembly over the cycle, and the largest value identifies the MV 

assembly. In other words, the MV profile represents the assembly with the greatest change in 

axial void profile over the cycle. Another axial void profile from a fuel assembly with relatively 

high variability and high average (HA) void fraction was also chosen for the temporal fidelity 

study because the high integral void fraction case is likely to result in more conservative 

discharged fuel keff values. The two selected axial void fraction profiles are presented in 

Figure 4.6, with the high exit variability case (MV) on the left plot and the high integral void 

fraction case (HA) on the right plot. As before, the figures show the void fraction over the 
22

assembly height, with early cycle steps in blue shifting to late cycle steps in red. Testing the 

profiles that are highly variable over a cycle ensures that the resulting temporal fidelity required 

for modeling will be sufficient for all other fuel assemblies with lower void fraction variability. The 

results of the study will demonstrate what temporal fidelity is required for void fraction modeling.

Figure 4.6 Selected axial void profiles used for the temporal fidelity study with the 

maximum exit void fraction variance case (MV) on the left and the high 

variance and high integral void fraction case (HA) on the right

4.4.2 Profiles Used in Axial Moderator Density Profile Study

The cycle average moderator density profiles for all 624 assemblies in the detailed core follow 

data are available for use in the axial moderator density distribution effect study. These data are

presented in Figure 4.1. Figure 4.5 shows that the upper portion of a fuel assembly determines 

its reactivity in the storage and transportation cask, so the upper portion will drive determination

of the limiting void profiles. The main goals of this study are (1) to confirm these logical 

inferences and (2) to clarify, if possible, the length of the upper portion of the assembly that is 

relevant to reactivity determinations. It is unlikely that a completely defensible formulation can 

be developed to proscriptively provide the limiting profile in all cases; however, a process 

through which limiting candidates can be identified and screened to determine limiting 

conditions will be proposed.

4.5 Results

This section provides the results of the temporal fidelity study and the axial moderator density 

profile study. The temporal fidelity study results include both TRITON and KENO results, while 

the axial moderator density profile study is focused on KENO results derived from STARBUCS 

depletion calculations.
23

4.5.1 Temporal Fidelity Study

To determine the temporal fidelity required for updating moderator density during depletion, 2D 

TRITON depletion models were generated for each axial level of the fuel assembly (25 in total). 

Each model used 23 depletion steps per cycle and was depleted for three cycles (69 total 

depletion steps) and a zero-power (decay) period of 30 days between consecutive cycles. Each 

depletion step was 30 days in length, so a full cycle lasted 690 days and reached a burnup of 

approximately 15.5 GWd/MTU. The power in each TRITON model was adjusted to result in a 

discharge burnup profile that corresponds to the fuel assembly whose void profile is shown in 

the left of Figure 4.6 (MV). A 2D representation of the TRITON model used in the temporal 

fidelity study is presented in Figure 4.7 and the axial burnup profile used is shown in Figure 

2.7(b). The fuel lattice shown in Figure 4.7 is the full lattice; however, the vanished lattice was 

also modeled to represent regions above the part-length rods. As discussed in Section 2.2, no 

axial enrichment zoning is modeled in this study. Because only a single cycle of operating data 

exists, the axial profile was not varied between the three cycles; the same axial moderator 

density profile was modeled for all three consecutive cycles. Although this is not an accurate 

physical description, it is conservative, as any moderator profile that is limiting would be further 

limiting if the assembly were to experience that axial moderator density profile for three 

consecutive cycles. Furthermore, the axial burnup and temperature profiles are held constant to 

isolate the effect of axial moderator profile modeling in this study.

Figure 4.7 TRITON model used for the temporal fidelity study

The operating data were used to generate a TRITON timetable for each node in which the 

moderator density is modified as a function of time. Because the operating data exist on a much 

finer timescale than is reasonable for TRITON depletion calculation run times, the moderator 

density must be time-averaged over each depletion step. This averaging process was 

performed for a variety of different intervals (1, 2, 4, 7, 13, or 23) per cycle. For example, in the 

23-step case, the moderator density was modified for every depletion step; and in the 1-step 

case, the moderator density was held constant at the cycle-average value. For this study, the 

depletion steps (23 steps per cycle, 69 total steps) were held constant for all moderator density 

averaging schemes. The 1-, 2-, and 23-step schemes for the MV and HA cases are presented 

Bypass flow in interassembly gap or water 

rods (grey)

Fuel rod (red)

Fuel rod containing gadolinium (green 

w/rings)

Heated coolant flow in assembly (yellow)

Channel box and fuel rod cladding (magenta)
24

in Figure 4.8 for node 3; all other temporal fidelity step schemes have been omitted to enhance 

clarity of the figure.

Figure 4.8 Cycle average (one step), two step, and every step (23 steps) moderator

density temporal fidelity schemes for MV (top) and HA (bottom)

The key comparison of these temporal fidelity studies is the full-detail (23 steps per cycle) and 

the cycle-average cases. An adequate number of depletion steps should be performed in order 

to accurately predict isotopic compositions regardless of the temporal fidelity of the moderator 

density. The depletion step size used in this study was less than 0.7 GWd/MTU. The most 

accurate treatment possible is to modify the moderator density with every depletion step. 

However, if a cycle-average void fraction approach results in a relatively small bias, then a more 

simplified approach—such as the approach used in STARBUCS/ORIGEN-ARP—is possible. 

The moderator density cannot be modified as a function of time in STARBUCS, so this type of 

approach can only be used if a cycle-average moderator density profile provides sufficient 

accuracy. A cycle-average approach would also be advantageous because a licensee would not 

need extensive operating history data, which would probably be difficult to obtain.

0.3	

0.35	

0.4	

0.45	

0.5	

0.55	

0	 100	 200	 300	 400	 500	 600	 700	

Coolant	Density	(g/cc)	

Cycle	Time	(days)	

Every	Step	

Two	Steps	

Cycle-Average	

0.05	

0.07	

0.09	

0.11	

0.13	

0.15	

0.17	

0.19	

0.21	

0.23	

0.25	

0	 100	 200	 300	 400	 500	 600	 700	

Coolant	Density	(g/cc)	

Cycle	Time	(days)	

Every	Step	

Two	Steps	

Cycle-Average	
25

In Figure 4.9, the 239Pu atom density is plotted as a function of node-average burnup for the 23-

step and the cycle-average moderator density schemes for the third axial node from the top of 

the core in the MV case. This node extends from approximately 320 cm to 335 cm above the 

bottom of the fuel, and it is selected because it is the node that exhibits the maximum fission 

density in Figure 4.5. Figure 4.9 shows that 239Pu number densities generated with the cycleaverage void fraction compare quite well when compared to the 23-step reference case, with 

differences in isotopic content of +/- 1% above 10 GWd/MTU burnup. The difference at the 

discharge burnup of ~40 GWd/MTU is approximately 0.4%. The line plotting the difference in 

239Pu between the two cases (cycle average minus 23-step divided by 23-step) shows a distinct 

trend. At the start and end of each cycle, the 239Pu atom densities are very close because the 

integral void history is the same for both cases through these points. In other words, the area 

under each of the curves plotted in Figure 4.8 is equal when integrated to these points. At 

burnup points that lie between the beginning and end of each cycle, the void history is not 

equal, leading to a bias. The small differences in the 239Pu number density at the end of cycle

(EOC) points are the result of the differences between detailed and average moderator density 

treatment. These results suggest that if the average void fraction is modeled for each node in 

the assembly, then the prediction of the end of life (EOL) 239Pu number densities will be 

sufficiently accurate. The true measure of whether the cycle-average void fraction approach 

provides sufficient accuracy will be determined by the spent fuel cask criticality calculations, 

which take into account all isotopes along with 239Pu. The assessment of 239Pu is included only 

to provide some background regarding the physics of the different temporal void fraction 

modeling approaches.

Figure 4.9

239 Pu atom density as a function of burnup for the MV case

The percent difference between the 23-step and cycle-average cases is plotted on 

the secondary axis

The depleted isotopic compositions which result from the TRITON depletion calculations are 

used in KENO calculations to determine the keff value for the GBC-68 cask model loaded with 

fuel depleted with the different profiles and modeling approaches. The KENO calculations are 
26

performed for both the HA and MV profiles for both the detailed 23-step and the average 1-step 

moderator density averaging scheme depletion calculations for both the AO and AFP isotope 

sets.

Figure 4.10 shows the MV profile results for the AO isotope set, and Figure 4.11 shows them for 

the AFP isotope set. The results are shown as a function of assembly average burnup. The keff

values that correspond to the use of the average moderator density in the depletion calculations 

are shown with a solid blue line. The keff values that correspond to the use of detailed moderator 

density data in the depletion calculations are shown with a dashed red line. These lines are read 

on the primary vertical axis and show close agreement throughout the full burnup range 

considered. The difference between the two keff values (keff for the cycle average void fraction 

minus keff for the detailed void history) is shown with the dotted green line, which is read on the 

secondary vertical axis. The uncertainty in each KENO-calculated keff is approximately 

0.00010 Δkeff, so the uncertainty in the difference between the two values is about 0.00014 Δkeff. 

Any difference less than 0.00028 Δkeff represents less than two standard deviations and 

therefore cannot be considered statistically significant at a 95% confidence level. The difference 

between the keff values is small, and the detailed moderator density treatment is usually slightly 

more reactive than the average moderator density treatment. The shape of the difference as a 

function of burnup for the AO isotope set shown in Figure 4.10 closely follows the difference in 

239Pu number densities shown in Figure 4.9. The differences for the AFP isotope set shown in 

Figure 4.11 are generally smaller than the differences seen for the AO isotope set. The largest 

difference between the two sets of results is approximately 0.0013 Δkeff for the AFP isotope set 

at 25.3 GWd/MTU burnup, where the detailed moderator density treatment is more reactive. 

The average moderator density treatment is never more than 0.0005 Δkeff more reactive than 

the detailed treatment. The average moderator density treatment tends to be slightly less 

reactive than the detailed treatment, but there are some exceptions to this tendency.

The results for the HA profile are shown for the AO isotope set in Figure 4.12 and for the AFP 

isotope set in Figure 4.13. These results are shown as a function of assembly average burnup. 

The results for the HA assembly are similar to those for the MV assembly, though the 

differences between the average and detailed depletion calculations may be slightly smaller in 

the HA profile. As shown in Figure 4.6, the HA profile has less variability than the MV profile, so 

smaller differences would be expected. It is difficult to definitively assert that the difference 

between the average and detailed treatments is smaller for the HA profile given the small size of 

the differences resulting from both treatments for both profiles. The largest differences between 

the two sets of results again occurs at a burnup of 25 GWd/MTU in the AFP isotope set, though 

for the HA profile the difference is only 0.0007 Δkeff, where the detailed moderator profile result 

is more reactive. The average moderator density results are generally slightly less reactive for 

the HA profile, just as they were for the MV profile.
27

Figure 4.10 GBC-68 results for the MV moderator profile, AO isotope set

Figure 4.11 GBC-68 results for the MV moderator profile, AFP isotope set
28

Figure 4.12 GBC-68 results for the HA moderator profile, AO isotope set

Figure 4.13 GBC-68 results for the HA moderator profile, AFP isotope set

The temporal fidelity study focuses primarily on cycle average behaviors because only a single 

cycle of detailed data is available in the core follow data set. The effect of multiple cycles of 

operation can be approximated by considering a series of three different assemblies in different 

cycles of operation within the single cycle data set used. Three assemblies—a first cycle, 

second cycle, and later cycle—were selected to create a composite profile to test the use of 

lifetime average behavior instead of cycle average behavior. Depletion calculations were 

performed using TRITON for the detailed void history model, cycle average void values, and a 
29

lifetime average value. In the detailed model, the moderator density was updated in each node 

with each depletion step. The cycle average model updated the moderator density in each node

once per cycle. The lifetime average model did not vary the moderator density during depletion. 

The results of these calculations are provided in Table 4.1 for the AO and AFP isotope sets. 

These results indicate that, as expected, a set of cycle average values reproduces the detailed 

depletion history with little deviation. The lifetime average results deviate from the detailed 

history by almost 0.2% Δk for the AO isotope set and about half of that for the AFP set. In the

both cases, the calculated keff result is a higher (conservative) value, but with only a single test,

this cannot be considered a generic result. Instead, the results indicate that use of a cycle 

average moderator density value causes no loss in fidelity, but a lifetime average value may 

introduce a relatively small discrepancy. Without further investigation using real lifetime average 

data for an assembly, it is impossible to assert that the lifetime average value will always be 

conservative, and it is thus not recommended.

Table 4.1 Results of lifetime average moderator density study

Density model AO AFP

keff σ keff σ

Detailed 0.80609 0.00010 0.72266 0.00010

Cycle average 0.80615 0.00010 0.72256 0.00010

Lifetime average 0.80794 0.00010 0.72368 0.00010

The results of this study demonstrate that despite the large variability of axial moderator profiles 

over a single cycle of operation and between cycles, cycle average moderator densities appear 

adequate to use in each axial node. This approach greatly simplifies depletion calculations. It 

should be emphasized that the averaging considered in this study is for each node over a single 

cycle of operation for the assembly, and that the axial moderator density profile is retained. A 

fuel assembly typically experiences several cycles of operation, with moderator density profiles 

varying within each cycle as shown in Figure 4.2. The first one or two cycles are high power 

cycles with a relatively high average void fraction but correspondingly lower variability, similar to 

the HA profile. The last cycle will see a larger change in moderator densities as the assembly 

average power decreases near EOL for the assembly, as seen in the MV profile. The depletion 

calculations performed to examine these profiles effectively assumed that each profile was 

experienced for three cycles of operation, which is not physically possible. Even so, the results 

show that even for the unrealistic case in which the maximum variability is experienced multiple 

times, only a small potential nonconservatism exists due to average void profile modeling. The 

largest difference resulting from the calculations performed in this study for cycle average 

values is just over 0.1% Δkeff, so a penalty of 0.25% Δkeff is judged to be sufficient to cover any 

potential nonconservatism resulting from using cycle average moderator density profiles for 

assemblies that have experienced typical use in a BWR core. This penalty should be applied to 

all assemblies, even those that are discharged after a single cycle of operation. The penalty 

need not be increased for assemblies reaching typical discharge burnups as long as the lowest 

density cycle average value is used. Although the data studied here are drawn from a single 

cycle, two different types of profiles are studied that cover the range of profile variations 

expected in BWR core operations.

4.5.2 Axial Moderator Density Study

The results of the temporal fidelity study indicate that cycle average moderator density profiles 

are adequate for making reactivity predictions for SNF casks containing discharged BWR 

assemblies. Based on this conclusion, STARBUCS can be used to study the effects of a range 
30

of moderator profiles, since variable moderator densities as a function of burnup are not 

needed. The STARBUCS calculations are all performed with the same axial burnup profile and 

specific power to isolate the effect of the axial moderator profile. The specific power and burnup 

profile were taken from the assembly that generated the MV moderator profile used in the 

temporal fidelity study. They are therefore representative, but no attempt was made to identify a 

bounding set of parameters. Separate calculations are performed for the DOM and VAN lattices, 

and the depleted fuel compositions from the appropriate lattice are used in the KENO model.

Figure 4.5 demonstrates that the upper portion of a discharged BWR assembly dominates 

reactivity in a storage cask or transportation package. It has also been shown that low 

moderator densities lead to higher discharged assembly reactivity [9] owing to a combination of 

lower moderation leading to lower burnup and a harder neutron spectrum generating more 239Pu 

per unit burnup in these regions. A set of cycle-averaged axial moderator profiles was selected 

to include those with low moderator density in the upper portions of the assembly, as well as all 

the profiles with at least one node with the minimum density for all profiles. Using engineering 

judgement, other profiles were added based on whether they were potentially limiting. The 

moderator density values and fuel design types for the 10 actual assembly profiles are shown in 

Table 4.2. Moderator density profiles from all 4 design types used in the core follow data set 

were considered, but only GNF2 and SVEA assemblies contained the high void profiles of 

interest for this study. Some increases in moderator density are noted as elevation increases in 

these data. These apparently anomalous values are due to changes in flow area or mixing 

causing slowing of the liquid phase and hence increased moderator density.

Two additional profiles were created to explore various aspects or approaches to axial 

moderator distribution modeling. First, a minimum density profile was created by using the 

minimum moderator density in each node from all profiles. This approach was considered 

because it represents a simple analysis technique which might be useful, especially for fixed 

assembly inventories, if the resulting profile conservatively bounds all actual profiles without 

introducing a large penalty. An average profile was created by averaging the moderator density 

in each node across all 624 profiles. This approach was expected to be nonlimiting, but the 

reactivity effect of this approach is quantified to assess its impact. The minimum density and 

average density profiles are provided in Table 4.3. In summary, a minimum density profile is 

constructed because it might prove simple and conservative; two additional approaches are 

included to determine the magnitude of the nonconservatism associated with them.

The use of a constant moderator density in all nodes was also investigated. The use of a single 

density will result in overpredictions of keff if nonphysical but conservative moderator densities 

are used in lower nodes within the fuel assembly. This condition would be met if the assembly 

outlet density were used for the entire assembly. However, if the associated penalty is small,

then such a simplifying approach may prove useful in analysis. The minimum moderator density 

in any node in the data set (Table 4.2) is 0.1077 g/cm3, so this value is used. A series of 

additional lower densities was also considered to examine the sensitivity of cask reactivity to 

this single moderator density. The other values considered were 0.107 g/cm3, 0.105 g/cm3, and 

0.1 g/cm3. A uniform profile equal to 0.4531 g/cm3(40% void) was also considered. This profile 

was also expected to be nonlimiting, but it is investigated because 40% void is frequently used 

as a core average value. It should be noted that the maximum moderator density profile 

(minimum void fraction) crosses the 40% void uniform profile three nodes from the top of the 

assembly in Figure 4.14.
31

Table 4.2 Axial moderator profiles from selected assemblies

Prof. 1 Prof. 2 Prof. 3 Prof. 4 Prof. 5 Prof. 6 Prof. 7 Prof. 8 Prof. 9 Prof. 10

GNF2 SVEA GNF2 GNF2 GNF2 GNF2 SVEA GNF2 SVEA SVEA

0.1251 0.1208 0.1272 0.1270 0.1279 0.1282 0.1247 0.1312 0.1258 0.1259

0.1197 0.1077 0.1218 0.1216 0.1226 0.1229 0.1119 0.1258 0.1132 0.1133

0.1186 0.1312 0.1207 0.1207 0.1216 0.1219 0.1346 0.1245 0.1357 0.1358

0.1343 0.1298 0.1359 0.1363 0.1370 0.1373 0.1328 0.1392 0.1339 0.1340

0.1238 0.1258 0.1257 0.1262 0.1268 0.1272 0.1285 0.1287 0.1297 0.1299

0.1471 0.1483 0.1486 0.1496 0.1500 0.1503 0.1503 0.1509 0.1515 0.1517

0.1427 0.1461 0.1440 0.1456 0.1457 0.1460 0.1477 0.1460 0.1488 0.1490

0.1527 0.1497 0.1536 0.1559 0.1558 0.1562 0.1509 0.1554 0.1521 0.1523

0.1698 0.1740 0.1704 0.1734 0.1730 0.1733 0.1748 0.1716 0.1758 0.1761

0.1668 0.1750 0.1669 0.1710 0.1705 0.1707 0.1751 0.1679 0.1762 0.1765

0.1957 0.1876 0.1956 0.1999 0.1996 0.1998 0.1871 0.1960 0.1883 0.1887

0.2090 0.2115 0.2084 0.2129 0.2134 0.2134 0.2105 0.2083 0.2116 0.2121

0.2141 0.2189 0.2128 0.2179 0.2195 0.2193 0.2170 0.2120 0.2182 0.2187

0.2466 0.2415 0.2447 0.2496 0.2526 0.2522 0.2389 0.2433 0.2400 0.2405

0.2690 0.2693 0.2661 0.2715 0.2752 0.2746 0.2660 0.2640 0.2669 0.2675

0.2853 0.2883 0.2809 0.2870 0.2910 0.2905 0.2837 0.2778 0.2843 0.2848

0.3298 0.3264 0.3248 0.3309 0.3344 0.3339 0.3209 0.3209 0.3213 0.3218

0.3691 0.3684 0.3645 0.3707 0.3739 0.3736 0.3620 0.3591 0.3623 0.3627

0.4122 0.4139 0.4073 0.4148 0.4174 0.4173 0.4056 0.4007 0.4061 0.4065

0.4787 0.4766 0.4735 0.4819 0.4834 0.4835 0.4672 0.4657 0.4682 0.4685

0.5545 0.5507 0.5466 0.5563 0.5570 0.5587 0.5391 0.5398 0.5422 0.5430

0.6419 0.6394 0.6336 0.6405 0.6424 0.6446 0.6275 0.6318 0.6314 0.6329

0.7109 0.7107 0.7083 0.7107 0.7118 0.7121 0.7065 0.7077 0.7074 0.7079

0.7461 0.7456 0.7453 0.7461 0.7460 0.7463 0.7445 0.7451 0.7449 0.7450

0.7549 0.7549 0.7549 0.7549 0.7549 0.7549 0.7548 0.7549 0.7548 0.7548

(All densities in g/cm3; Top of assembly at top of table)
32

Table 4.3 Constructed axial moderator profiles

Minimum moderator density Average moderator density

0.1208 0.2020

0.1077 0.1961

0.1186 0.2095

0.1298 0.2164

0.1238 0.2159

0.1471 0.2380

0.1427 0.2398

0.1497 0.2506

0.1698 0.2717

0.1668 0.2764

0.1871 0.3002

0.2083 0.3225

0.2120 0.3357

0.2389 0.3670

0.2640 0.3958

0.2778 0.4194

0.3209 0.4598

0.3591 0.4993

0.4007 0.5395

0.4657 0.5903

0.5391 0.6433

0.6275 0.6956

0.7065 0.7309

0.7445 0.7500

0.7548 0.7552

(All densities in g/cm3; Top of assembly at top of table)

All profiles considered in this analysis are shown in Figure 4.14. This figure is similar to 

Figure 4.1, except that it shows moderator density instead of void fraction, and it includes a 

limited number of profiles. Figure 4.15 is a detailed view of the profiles near the top end of the 

assembly, excluding the 40% void case. It is clear from the figure that more than one actual 

assembly profile contributes to the minimum moderator density profile.
33

Figure 4.14 Moderator density profiles used in moderator density study

Figure 4.15 Detail of top five nodes of moderator density profiles

Results were generated at 30, 40, and 50 GWd/MTU with both the AO and AFP isotope sets

using ORIGEN libraries generated for this study. The results for the 10 assembly moderator 

density profiles are provided in Table 4.4 for the AO isotope set and in Table 4.5 for the AFP 

isotope set. The reactivity rankings of the profiles are very similar, though not identical, across 

all burnups and with both sets of isotopes, indicating that the effect of the moderator profile is 
34

consistent with respect to burnup and isotopes modeled. The keff differences are small, as are 

the differences in the moderator profiles used to generate them.

Table 4.4 GBC-68 cask keff values for 10 actual assembly moderator density profiles, AO 

isotope set

Profile 30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ keff σ keff σ

1 0.92150 0.00010 0.90669 0.00010 0.89406 0.00010

2 0.92095 0.00010 0.90594 0.00010 0.89348 0.00010

3 0.92083 0.00010 0.90560 0.00010 0.89301 0.00010

4 0.92072 0.00010 0.90540 0.00010 0.89277 0.00010

5 0.92037 0.00010 0.90514 0.00010 0.89249 0.00010

6 0.92018 0.00010 0.90500 0.00010 0.89200 0.00010

7 0.91970 0.00010 0.90435 0.00010 0.89142 0.00010

8 0.91924 0.00010 0.90380 0.00010 0.89091 0.00010

9 0.91929 0.00010 0.90384 0.00010 0.89078 0.00010

10 0.91916 0.00010 0.90386 0.00010 0.89079 0.00010

Table 4.5 GBC-68 cask keff values for 10 actual assembly moderator density profiles, AFP 

isotope set

Profile 30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ keff σ keff σ

1 0.86367 0.00010 0.84389 0.00010 0.82709 0.00010

2 0.86335 0.00010 0.84344 0.00010 0.82645 0.00010

3 0.86336 0.00010 0.84304 0.00010 0.82614 0.00010

4 0.86329 0.00010 0.84299 0.00010 0.82639 0.00010

5 0.86304 0.00010 0.84285 0.00010 0.82614 0.00010

6 0.86293 0.00010 0.84260 0.00010 0.82583 0.00010

7 0.86230 0.00010 0.84211 0.00010 0.82528 0.00010

8 0.86207 0.00010 0.84178 0.00010 0.82485 0.00010

9 0.86196 0.00010 0.84157 0.00010 0.82476 0.00010

10 0.86206 0.00010 0.84158 0.00010 0.82473 0.00010

The keff results are used to identify trends with the moderator density profiles. Figure 4.16 shows 

the keff values at 50 GWd/MTU for the AFP isotope set versus the top node moderator density. It 

is clear that there is a trend of increasing reactivity with lower moderator density within a given 

fuel assembly type. It is further evident that the correlations depend on fuel design type or core 

position. The separation of these effects is not attempted in this study, but it is likely that the 

differences in the moderator profiles are caused by the unique axial characteristics of the 

different fuel assembly design types. BWR BUC applications will need to consider the potential 

for multiple correlations such as those manifested in this work. However, the general trend of 

increasing reactivity with decreasing moderator density is clear within both fuel assembly design 

types. Similar plots are created by summing the moderator density of the top two nodes 

(Figure 4.17) and the top three nodes (Figure 4.18). The trend of increasing reactivity with 

decreasing moderator density is still evident, as it is with AO isotope set results for the top node 

(Figure 4.19) and the top three nodes (Figure 4.20). This trend starts to break down if all the 

nodes in the VAN lattice are considered, as shown in Figure 4.21. The moderator profile 

summed over the entire axial extent of the assembly is a poor indicator of relative reactivity, as 

shown in Figure 4.22 for the AFP isotope set and Figure 4.23 for the AO isotope set. These 

results confirm indications from earlier work, as shown in Figure 4.5, that (1) the upper portion of 
35

the assembly determines reactivity and (2) that low moderator densities lead to higher 

discharged reactivities.

Figure 4.16 GBC-68 cask keff values (AFP isotope set) as a function of moderator density 

in top node

Figure 4.17 GBC-68 cask keff values (AFP isotope set) as a function of moderator density 

in top two nodes
36

Figure 4.18 GBC-68 cask keff values (AFP isotope set) as a function of moderator density 

in top three nodes

Figure 4.19 GBC-68 cask keff values (AO isotope set) as a function of moderator density 

in top node
37

Figure 4.20 GBC-68 cask keff values (AO isotope set) as a function of moderator density 

in top three nodes

Figure 4.21 GBC-68 cask keff values (AFP isotope set) as a function of moderator density 

in VAN lattice
38

Figure 4.22 GBC-68 cask keff values (AFP isotope set) as a function of moderator density 

in entire assembly

Figure 4.23 GBC-68 cask keff values (AO isotope set) as a function of moderator density 

in entire assembly

The results for the two constructed profiles are provided in Table 4.6 for the AO isotope set and 

Table 4.7 for the AFP isotope set. The difference between the keff calculated for each 

constructed profile is compared with the limiting actual assembly profile, and the results are also 

included in the appropriate table.
39

The results indicate that the minimum density profile can be used to conservatively bound the 

reactivity of the actual assemblies at all burnups and with both isotope sets. The margin 

provided by the minimum density profile is small for this set of assemblies. For the AO isotope 

set it ranges from 0.12% Δkeff at 30 GWd/MTU to 0.19% Δkeff at 50 GWd/MTU. The difference 

from the actual profiles is smaller for the AFP isotope set: 0.07% Δkeff at 30 GWd/MTU, 

increasing to 0.14% Δkeff at 50 GWd/MTU. The minimum density profile yielding a more reactive 

assembly is expected and is a potential approach to simplifying the treatment of axial moderator 

profiles in BWR BUC, especially considering the small penalty associated with the approach. 

However, the small margin provided would not provide a significant margin against more limiting 

profiles or a large margin to offset potential uncertainties in predicted moderator density 

distributions. Nevertheless, the minimum density profile approach is viable. The primary 

challenge for its application by a cask vendor is likely to be the collection of a significant and 

appropriate database of moderator density profiles.

The average void profile is clearly nonconservative, as expected. The average moderator 

density profile is from 3.0% to 4.2% Δkeff less reactive than the limiting profile for the AO isotope 

set and from 2.0% to 2.9% Δkeff less reactive for the AFP isotope set. This is evidence that the 

discharged assembly reactivity is highly sensitive to moderator density profile and that lower 

densities lead to higher reactivities. In the top node, the average profile has approximately 67% 

higher moderator density than the minimum case and nearly 62% higher moderator density than 

the limiting profile. The absolute differences are on the order of 0.08 g/cm3, but at the high exit 

void fractions, this represents a significant relative change. Averaging of moderator densities 

from different profiles is clearly not an acceptable approach to treating the axial moderator 

density in BWR BUC.

Table 4.6 GBC-68 cask keff values for constructed profiles, AO isotope set

Profile 30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ Δ* keff σ Δ* keff σ Δ*

Minimum 0.92268 0.00010 0.00118 0.90821 0.00010 0.00152 0.89599 0.00010 0.00193

Average 0.89143 0.00010 -0.03007 0.87037 0.00010 -0.03632 0.85179 0.00010 -0.04227

*Difference from limiting profile; positive value indicates constructed profile is more reactive

Table 4.7 GBC-68 cask keff values for constructed profiles, AFP isotope set

Profile 30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ Δ* keff σ Δ* keff σ Δ*

Minimum 0.86438 0.00010 0.00072 0.84478 0.00010 0.00090 0.82848 0.00010 0.00139

Average 0.84364 0.00010 -0.02003 0.81910 0.00010 -0.02479 0.79799 0.00010 -0.02910

*Difference from limiting profile; positive value indicates constructed profile is more reactive

The results for the constant moderator density cases are provided in Table 4.8 for the AO 

isotope set and Table 4.9 for the AFP isotope set. The difference between the keff calculated for 

each moderator density is compared to the limiting actual assembly profile, and the results are 

also included in the appropriate table.

A constant density representing a 40% void fraction leads to large underpredictions of cask 

reactivity. For the AO isotope set, the difference from the limiting actual profile is approximately 

6.9% Δkeff at 30 GWd/MTU, and increases to almost 10% Δkeff at 50 GWd/MTU. The differences 

are smaller in the AFP case, ranging from 4.8% to 7.4% Δkeff. As noted previously, this core 
40

average of 40% void fraction yields a higher moderator density in the top three nodes of the 

core than any actual assembly profile. This case provides additional proof that any averaging 

approach that increases moderator density in the upper portion of the assembly is likely to yield 

nonconservative keff calculations for discharged fuel assemblies.

As expected, the results show that a uniform low moderator density can be used conservatively 

to bound actual assembly profiles. The penalty associated with this approach varies significantly 

between the AO and AFP isotope sets, and it also increases with burnup. Using the minimum 

actual moderator density (0.1077 g/cm3from Profile 2 in Table 4.2) leads to keff values that are 

1.6% to 2.0% Δkeff more reactive than the limiting profile for the AO isotopes set and 0.6% to 

0.7% more reactive for the AFP set. The increase in this penalty is linear, with decreasing 

moderator density over the range considered. Currently operating BWR plants may have exit 

void fractions of 90% or more, which would lead to moderator densities on the order of 0.07 

g/cm3. The reactivity effect of these lower moderator densities can be extrapolated from the 

results shown in Tables 4.8 and 4.9, but the limiting actual profile would also become more 

reactive at these higher void fractions because of the lower outlet moderator densities. 

The results generated clearly show that a uniform moderator density value could be used 

conservatively. As with other aspects of analysis, however, any applicant that chooses this 

approach would have to provide justification for the specific moderator density used.

Table 4.8 GBC-68 cask keff values for uniform moderator densities, AO isotope set

Density

(g/cm3)

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ Δ* keff σ Δ* keff σ Δ*

40% void 0.85278 0.00009 -0.06872 0.82235 0.00010 -0.08434 0.79467 0.00010 -0.09940

0.1 0.94073 0.00010 0.01922 0.92878 0.00010 0.02197 0.91891 0.00010 0.02485

0.105 0.93843 0.00010 0.01692 0.92581 0.00010 0.01900 0.91568 0.00010 0.02161

0.107 0.93742 0.00010 0.01591 0.92462 0.00010 0.01780 0.91452 0.00010 0.02046

0.1077 0.93711 0.00010 0.01560 0.92432 0.00010 0.01751 0.91403 0.00010 0.01997

*Difference from limiting profile; positive value indicates constructed profile is more reactive

Table 4.9 GBC-68 cask keff values for uniform moderator densities, AFP isotope set

Density

(g/cm3)

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

keff σ Δ* keff σ Δ* keff σ Δ*

40% void 0.81541 0.00010 -0.04826 0.78298 0.00010 -0.06091 0.75351 0.00010 -0.07358

0.1 0.87235 0.00010 0.00845 0.85341 0.00010 0.00966 0.83766 0.00010 0.01076

0.105 0.87066 0.00010 0.00676 0.85155 0.00010 0.00780 0.83549 0.00010 0.00859

0.107 0.86998 0.00010 0.00608 0.85067 0.00010 0.00692 0.83451 0.00010 0.00762

0.1077 0.86993 0.00009 0.00603 0.85040 0.00010 0.00666 0.83412 0.00010 0.00723

*Difference from limiting profile; positive value indicates constructed profile is more reactive

4.6 Summary and Recommendations

The purpose of this section was to document studies examining the effects of axial moderator 

density profiles on extended BWR BUC. Further studies examining other phenomena related to 

extended BWR BUC are provided in Sections 5 and 6 as part of a technical basis for extended 

BUC. These studies are intended apply to fuel beyond peak reactivity; studies examining peak 

reactivity methods were documented in Marshall, Ade, et al. [3]. Two separate studies were 
41

performed in this section: a temporal fidelity study and an axial moderator density study. The 

temporal fidelity study was required to examine the modeling approaches necessary for 

capturing the reactivity impacts of temporal variations in the axial moderator density profile, and 

the axial moderator density study was performed to determine the effect of these axial profiles 

once they were established. The results of the temporal fidelity study, presented in Section

4.5.1, indicate that cycle average moderator density profiles can be used in depletion 

calculations with the addition of a modest reactivity penalty. The axial moderator density profile 

study results, presented in Section 4.5.2, show that low moderator densities in the top few 

nodes of the profile lead to conservative reactivity determinations. Averaging the moderator 

densities across assemblies or nodes is not appropriate and will lead to nonconservative 

reactivity determinations.

The following are recommendations of these studies.

 A cycle-averaged moderator density can be used in each node of an axial moderator 

density profile for depletion calculations for simplicity, with an appropriate penalty for 

conservatism.

 A reactivity penalty of 0.25% Δkeff is recommended to cover potential differences 

between detailed and cycle average moderator density treatments in depletion 

calculations. This penalty is nearly twice the magnitude of the largest discrepancy 

between detailed and average moderator density modeling observed in this study.

 A limiting axial moderator density profile will have low moderator densities in the top 

nodes of the assembly. Each applicant should present and defend the method used to 

identify limiting profiles.

 A limiting axial moderator density profile can be constructed by selecting the minimum 

density in each axial node from a collection of applicable actual profiles.

 Use of average moderator densities determined from consideration of multiple 

assemblies or multiple axial nodes will result in reactivity underprediction.

 A single moderator density value can be used conservatively in all nodes if it bounds the 

moderator densities in all nodes of the assembly.

43

5 CONTROL BLADE USAGE

5.1 Control Blade Histories

This section summarizes the analyses performed for the effects of control blade history on cask 

reactivity. To understand these effects, a number of different control blade histories need to be 

generated for testing. In the context of this study, control blade history refers to the position 

(height of insertion) of a control blade as a function of an adjacent fuel assembly’s time in the 

reactor core. 

In general, use of a control blade in a BWR hardens the neutron spectrum, resulting in 

increased 239Pu production and decreased gadolinium consumption. Cask reactivity is expected 

to increase with control blade usage in extended BWR BUC because the increased 239Pu 

production will add more positive reactivity than the small negative reactivity resulting from 

increased residual gadolinium. In addition, owing to the top-peaked axial fission distribution in 

typical fuel storage and transportation casks, the operating conditions experienced in the top 

portion of the fuel assembly have a disproportionate effect on cask reactivity. As a result, it is 

expected that especially deeper control blade insertion will be more limiting than shallower

control blade insertion. From previous and ongoing work [23], it is also expected that control 

blade insertion near the end of assembly life will result in higher keff values than control blade 

insertion near BOL. For early control blade insertion, 239Pu builds up and then has time to 

deplete after the control blade is removed. For late control blade insertion, there is less time for 

the 239Pu to deplete before the fuel is discharged, leading to higher cask reactivity.

Gross reactivity control in BWRs is achieved primarily through the use of control blades inserted 

in the core during operation. This is a significant deviation from PWR operation that uses a 

soluble boron shim as a primary means of reactivity control during operation. The highly variable 

use of control blades to maintain power level and operational margins during operation makes 

BWR modeling significantly more complex.

This analysis used many control blade histories from the single cycle of core follow data 

described in Section 3.1. Because the data contain sufficient detail to model control blade 

histories and use modern fuel assemblies in a modern BWR cycle, this data set was used for 

the studies documented in this section. For illustration, actual control blade insertion histories for 

three selected locations are plotted in Figure 5.1. These three locations are selected to show 

the variety of control blade use in BWR operations. Each of these histories is extracted from the 

core follow data discussed in Section 3.1 and will be explicitly considered in this study along 

with seven other histories. A core map for the cycle of data used is shown in Figure 5.2, with the 

control blade layout and numbering scheme indicated. Each box in Figure 5.2 represents four 

fuel assemblies, and each “+” represents a cruciform control blade that can be inserted in the 

center channels between the four assemblies. The position indices provided in Figure 5.1 are 

(x,y) coordinates. For example, Position (4,6) is four positions to the right and six positions down 

in Figure 5.2. Symmetric locations showed a high degree of similarity in control blade use in the 

core follow data set.
44

Figure 5.1 Selected control blade histories from the available operating data
45

Figure 5.2 Core map showing control blade numbering scheme

Results from Section 4 indicate that the end effect (top-peaked axial fission distribution) has a 

significant impact on cask reactivity results. Axial peaking at the top of the fuel assembly is 

primarily due to relatively low burnup and increased plutonium production caused by reduced 

moderation in the top portion of the fuel assembly. The axial fission distribution in a fuel cask 

filled with depleted BWR fuel is shown in Figure 4.5. Most BWR fuel cask axial fission 

distributions will follow the same basic shape shown in Figure 4.5. The shape of the fission data 

indicates that the upper portion of the fuel assembly will have a significant impact on the 

reactivity of the fuel cask. With the axial fission distribution shape in mind, the burnup-integrated 

nodal control blade history (insertion fraction) was extracted and plotted (see Figure 5.3) for 

each of the 624 fuel assemblies in the core. 

Figure 5.3 Burnup-integrated control blade fraction
46

The burnup-integrated control blade fraction for each node is defined as the fraction of the node 

total burnup for which a control blade was inserted adjacent to the fuel assembly in that 

particular axial node. Note that the burnup-integrated control blade history for an assembly 

would be summed over the entire assembly life. Therefore, the integrated control blade history 

inherently would include the operating history of all cycles for an assembly; however, only one 

cycle of data is available for this study. The data in Figure 5.3 indicate that certain fuel 

assemblies experience much higher control blade insertion fractions than others. These 

assemblies are likely to be more limiting with respect to cask criticality than fuel assemblies with 

lower control blade insertion fractions. 

Because of the varied control blade usage in BWRs, as illustrated in Figures 5.1 and 5.3, similar 

fuel assemblies can experience significantly varied control blade histories. To study the effect of 

control blade usage on BWR fuel cask reactivity, a number of hypothetical control blade 

histories have been used, along with some histories from actual operating data. The total 

irradiation time for each of these histories is 2070 days, which is intended to represent three 

2-year cycles with a capacity factor of approximately 95%. The hypothetical control blade 

histories are used to investigate the important effects of varied control blade usage, whereas the 

realistic control blade histories are used to determine the magnitude of reactivity penalties 

compared with hypothetical control blade histories. All control blade histories considered in this 

study have been evaluated using the same axial power distribution, the same axial moderator 

density distribution, and the same burnup, thus isolating the effect of the control blade history. 

This isolation of the control blade effect is nonphysical because control blade insertion will 

impact the axial moderator density distribution, assembly power, and fuel temperatures; but this 

isolation approach is used to examine each effect separately. The combined effect of these 

correlated parameter changes will be studied in future work. 

A description of the hypothetical control blade histories is as follows:

1. Control blades are removed for the entire irradiation.

2. Control blades are inserted 100% for the entire irradiation.

3. Control blades are inserted 24% (6 nodes) for the entire irradiation.

4. Control blades are inserted 52% (13 nodes) for the entire irradiation.

5. Control blades are inserted 76% (19 nodes) for the entire irradiation.

6. Control blades are inserted 24% for the first half and then are removed for the remaining 

irradiation.

7. Control blades are removed for the first half then are inserted 24% for the remaining

irradiation.

8. Control blades are inserted 52% for the first half then are removed for remaining 

irradiation.

9. Control blades are removed for the first half and then are inserted 52% for the remaining 

irradiation.

10. Control blades are inserted 76% first half and then are removed for remaining irradiation.
47

11. Control blades are removed for the first half and then are inserted 76% for remaining 

irradiation.

12. Control blades are inserted 100% the first half and then are removed for remaining 

irradiation.

13. Control blades are removed for the first half and then are inserted 100% for remaining 

irradiation.

14. Control blades are inserted 100% for the first third and then are removed for remaining

irradiation.

15. Control blades are inserted 100% for the second third and then are removed for 

remaining irradiation.

16. Control blades are inserted 100% for the last third of the irradiation.

17. Control blades are fully removed for 360 days and then are inserted 100% for 360 days, 

alternating through the end of the irradiation.

18. Control blades are fully removed for 240 days and then are inserted 100% for 240 days, 

alternating through the end of the irradiation.

19. Control blades are fully removed for 120 days and then are inserted 100% for 120 days, 

alternating through the end of the irradiation.

20. Control blades are fully removed for 360 days and then are inserted 48% for 360 days, 

alternating through the end of the irradiation.

21. Control blades are fully removed for 240 days and then are inserted 48% for 240 days, 

alternating through the end of the irradiation.

22. Control blades are fully removed for 120 days and then are inserted 48% for 120 days, 

alternating through the end of the irradiation.

23. Control blade is inserted 56% (14 nodes) for the entire irradiation.

24. Control blade is inserted 60% (15 nodes) for the entire irradiation.

25. Control blade is inserted 64% (16 nodes) for the entire irradiation.

26. Control blade is inserted 68% (17 nodes) for the entire irradiation.

27. Control blade is inserted 72% (18 nodes) for the entire irradiation.

28. Control blade is inserted 80% (20 nodes) for the entire irradiation.

29. Control blade is inserted 84% (21 nodes) for the entire irradiation.

30. Control blade is inserted 88% (22 nodes) for the entire irradiation.
48

31. Control blade is inserted 92% (23 nodes) for the entire irradiation.

32. Control blade is inserted 96% (24 nodes) for the entire irradiation.

The hypothetical histories (HHs) are designated according to the history numbers in the list 

above. For example, HH2 is hypothetical history 2, which represents the control blades inserted 

100% in depth for the entire irradiation. Because the fuel assembly and cask models are 

constructed using 25 axial nodes, exact insertion percentages of 25%, 50%, and 75% are 

impossible to model directly. Therefore, 24%, 52%, and 76% are used. 

HH1–HH16 were designed to test the sensitivity of three major aspects of control blade usage 

for BWR fuel cask criticality: (1) the length of time (burnup) for which a control blade is inserted, 

(2) the depth (or elevation) to which the control blade is inserted, and (3) the time at which the 

control blade is inserted (early in irradiation vs. late in irradiation). As discussed earlier in this 

section, control blades that are inserted deeper in the core for longer irradiation times and later 

in life are expected to result in higher cask reactivity than the converse. HH17–HH22 were 

designed to test the sensitivity of frequent, short control blade insertions vs. longer, lessfrequent control blade insertions. HH23–HH32 were designed to allow determination of the 

sensitivity to control blade insertion depth in a more detailed manner. 

In addition to the HHs, ten realistic control blade histories have been extracted from the 

operating data discussed in Section 3.1. Because only one cycle of operating data exists, the 

realistic control blade histories have been constructed so that the history for a single 690-day 

cycle is repeated for three consecutive cycles. Many control blades in BWRs, such as those 

near the core periphery, are used sparingly. Therefore, these control blade histories have been 

excluded from analysis. There are situations in which peripheral control blades would be used 

extensively, such as to suppress power in an assembly with a leaking fuel rod or in a fresh 

assembly located near the periphery in an uprated plant. These exceptions should be noted in 

reviewing control blade use assumptions. Control blades are typically inserted in a similar 

fashion in four symmetric locations in the core, so only one symmetric location is simulated 

rather than four nearly identical histories for different control blade locations. The ten chosen 

realistic histories (RHs) are chosen because these control blades are used frequently and/or are

inserted deeply into the core. Plots depicting the control blade insertion depth as a function of 

time for these ten realistic histories are provided in Appendix A.

The ten realistic histories and their core locations are summarized as follows:

1. Location [3,4]: two short insertions during the cycle, one above 60% inserted.

2. Location [4,4]: four long insertions in the cycle, two of which are above 60% inserted;

highest integral control blade history of the realistic histories.

3. Location [7,4]: two relatively long insertions, both greater than 70% inserted.

4. Location [2,5]: one insertion up to 40% inserted.

5. Location [3,5]: one relatively short insertion, up to 90% inserted.

6. Location [4,5]: one long insertion, up to 100% inserted.

7. Location [2,6]: three short insertions, one late in the cycle, up to 80% inserted.
49 

8. Location [3,6]: one short insertion up to 35% inserted and one long insertion up to 100% 

inserted. 

9. Location [4,6]: two long insertions, both to a maximum of 100% inserted. 

10. Location [6,6]: one long insertion up to 85% inserted, and one short insertion near the 

end of the cycle, up to 100% inserted. 

RHs are designated according to the history numbers in the list above.

 Results 

This section provides isotopic and criticality results for the hypothetical and realistic control 

blade histories. 

5.2.1 Effect of Control Blade Insertion on 239Pu 

As discussed in Section 5.1, insertion of control blades in BWRs increases plutonium production 

relative to identical conditions without control blades inserted. This increase is due to the 

hardening of the neutron spectrum, which increases the parasitic absorption of neutrons in 238U. 

To illustrate this effect, the 239Pu atom density has been extracted from the TRITON simulation 

results and compared for various hypothetical control blade histories. Figure 5.4 plots the 239Pu 

atom density as a function of burnup for the top axial node in the simulations using four 

hypothetical histories: HH1, HH2, HH12, and HH13. The top axial node has a low moderator 

density and a low burnup due to the axial moderator density profile and the axial power profile 

applied for the simulations. HH1 has the control blade withdrawn for the entire irradiation, HH2 

has the control blade inserted for the entire irradiation, HH12 has the control blade inserted for 

the first half of irradiation, and HH13 has the control blade inserted for the last half of irradiation. 

Figure 5.4 239Pu concentration as a function of burnup for HH1, HH2, HH12, and HH13 

control blade histories 
50

Figure 5.4 shows that the control-blade-out and control-blade-in cases bracket the cases in 

which control blades were inserted for either the first or last half of irradiation. Figure 5.4 also 

shows that the end-of-life (EOL) plutonium concentration for HH13 (inserted second half) is 

higher than that of HH12 (inserted first half), indicating that later control blade insertion is likely 

to result in higher cask reactivity than early control blade insertion. This is primarily due to the 

rates at which plutonium is produced and consumed in reactors. For the HH12 case, plutonium 

concentration increases quickly through the first half of irradiation because of the presence of 

the control blade; when the control blade is removed, 239Pu is preferentially depleted because 

the fission cross section of 239Pu is larger than that of 235U. In the HH13 case, plutonium 

increases more slowly; and when the blade is inserted, 239Pu is produced more rapidly, and then 

the fuel is immediately discharged. This leaves no opportunity for the 239Pu to deplete toward 

the lower concentration resulting from unrodded operation before being discharged. 

The same effect can be found in Figure 5.5, which plots the plutonium concentration as a 

function of burnup for HH14 (control blade fully inserted for the first third of operation), HH15

(control blade fully inserted for the second third of operation), and HH16 (control blade fully 

inserted for the last third of operation), as well as for HH1 and HH2. Again, the 239Pu 

concentrations for HH14, HH15, and HH16 are bracketed by the 100% inserted (HH2) and 

100% withdrawn (HH1) cases. As expected when comparing HH14, HH15, and HH16, the case 

with the latest control blade insertion produces the highest discharge 239Pu concentration, 

whereas the case with the earliest control blade insertion produces the lowest discharge 239Pu 

concentration, indicating that later control blade insertion has a greater impact on discharge 

239Pu than earlier control blade insertion. 

Figure 5.5

239Pu concentration as a function of burnup for HH1, HH2, HH14, HH15, and 

HH16 control blade histories
51

5.2.2 Control Blade Study with Hypothetical Histories

The study of moderator density profiles specified in Section 4.5.2 used STARBUCS extensively 

for generating depleted fuel compositions that corresponded to a variety of specified moderator 

density profiles. In this study, however, TRITON was used to generate all depleted fuel 

compositions, as the use of varying control blade histories is not possible in STARBUCS. The 

need to use TRITON for all depletion calculations significantly increased the computational 

requirements, as lattice depletion calculations are needed for every axial node of every control 

blade history used. All TRITON calculations were performed using the same axial moderator 

density profile and the same axial burnup profile. The moderator density profile corresponds to 

the average moderator density profile developed in Section 4, indicated by the thick black line in 

Figure 4.1. The average profile was used in this study because the key output is not the 

absolute reactivity of the cask but the relative difference among the different control blade 

histories. The axial burnup profile and associated power density correspond to the assembly in 

the core associated with the MV moderator density profile used in the temporal fidelity study in 

Section 4. The axial burnup profile is shown in Figure 2.7b. Additional studies involving other 

assembly design types and fuel lattice designs may be needed to demonstrate the applicability 

of the conclusions of this work more broadly.

The ft71f001 file (ORIGEN concentration file) generated during the TRITON calculations was 

post-processed using ORIGEN to extract the isotopics for all depletion materials, and then a 5-

year decay was performed to simulate cooling in a spent fuel pool. The isotopic number 

densities from the ORIGEN decay calculations were extracted and then converted into a 

composition file for use with CSAS/KENO. This process was performed for each axial node of 

each control blade history simulated. 

In the axial moderator profile studies presented in Section 4, a number of cumulative burnups 

were simulated (i.e., 30, 40, 50 GWd/MTU); however, in this study, a single burnup value 

(assembly-averaged burnup of 45.2 GWd/MTU) with node burnups that correspond to the 

selected axial burnup profile is used. Other burnup values are not simulated in this study, as the 

burnup of the top end of the assembly changes significantly less than the assembly average.

The top end of the assembly generally controls reactivity, so this is the most relevant 

consideration. The effects of control blade exposure are expected to scale with burnup, so lower 

burnups should see smaller differences than higher burnups.

The KENO GBC-68 criticality results for HH1–HH32, for AO and AFP isotope sets can be found 

in Table 5.1. The data in Table 5.1 have been sorted from highest to lowest keff values. The top 

three histories (in different orders) for both the AO and AFP isotope sets are HH2 (control 

blades inserted 100% for the entire fuel assembly life), HH32 (96% inserted for entire assembly 

life), and HH31 (92% inserted for entire assembly life). The maximum difference between these 

cases is 0.93% Δkeff for the AO isotope set and 0.14% Δkeff for the AFP isotope set. These 

results confirm that the most limiting conditions are virtually fully inserted control blades, which 

harden the spectrum and produce more plutonium. The next most limiting cases are (in different 

orders): HH13 (control blade inserted fully for second half of assembly life), HH16–HH19, and 

HH30 (88% inserted for entire assembly life). In HH16, the control blade is inserted fully for the 

last third of irradiation. HH17–HH19 alternate the control blades fully in and fully out at regular 

time intervals, resulting in a similar integral control blade history for each case.

Based on the results in Table 5.1, it is clear that increased control blade insertion produces 

higher cask reactivity, as many of the highest reactivity cases have integral control blade 

histories of 50% or more (100% for HH2). Comparison of HH12 and HH13 shows the sensitivity 
52

of keff to the time period in the assembly irradiation history when the control blade is inserted. In 

both HH12 and HH13, the control blade was inserted fully for 50% of the irradiation time; 

however, there is a significant difference in keff between the two cases. HH13 differs from HH12 

by 1.30% and 1.54% Δkeff for the AO and AFP isotope sets, respectively. As expected from 

239Pu results in Figure 5.4, late control blade insertion is much more limiting than early control 

blade insertion. This is further confirmed by comparing HH14, HH15, and HH16, which simulate 

a fully inserted control blade in either the first, second, or third cycle of operation, and withdrawn 

for the rest of the irradiation time. HH16, which has blades inserted in the last third of assembly 

life, produces higher reactivity than HH14 and HH15. These results are expected based on the 

239Pu results shown in Figure 5.5. The results in Table 5.1 clearly indicate that control blade 

insertion later in assembly life produces higher cask reactivity than similar control blade 

insertion earlier in life. 
53 

Table 5.1 Criticality results for HH1–HH32 

AO isotope set AFP isotope set 

History keff* History keff*

HH2 0.87394 HH31 0.77464 

HH32 0.87124 HH2 0.77336 

HH31 0.86468 HH32 0.77323 

HH13 0.85978 HH30 0.76146 

HH17 0.85407 HH13 0.75865 

HH16 0.85282 HH16 0.75158 

HH18 0.85206 HH17 0.75111 

HH19 0.85197 HH18 0.75041 

HH30 0.85018 HH29 0.75039 

HH12 0.84678 HH19 0.74981 

HH15 0.84421 HH28 0.74524 

HH14 0.84175 HH12 0.74326 

HH29 0.84056 HH5 0.74284 

HH28 0.83503 HH15 0.74217 

HH5 0.83304 HH27 0.74178 

HH11 0.83276 HH26 0.74037 

HH1 0.83268 HH25 0.73878 

HH4 0.83265 HH14 0.73843 

HH26 0.83265 HH24 0.73587 

HH21 0.83263 HH11 0.73246 

HH3 0.83263 HH20 0.73222 

HH9 0.83261 HH10 0.73221 

HH25 0.83261 HH23 0.73219 

HH22 0.83261 HH4 0.73214 

HH10 0.83259 HH21 0.73205 

HH6 0.83256 HH7 0.73205 

HH20 0.83256 HH8 0.73204 

HH7 0.83253 HH22 0.73201 

HH8 0.83251 HH9 0.73200 

HH23 0.83249 HH3 0.73197 

HH24 0.83229 HH6 0.73193 

HH27 0.83228 HH1 0.73192 

*

All keff calculations have estimated standard deviations  0.0001. 

Note that many of the lower cases in Table 5.1 for both the AO and AFP isotope sets differ by 

very little. For the AO isotope set, the lower 17 cases vary by a total of 0.05%; and for the AFP 

isotope set, the lower 13 cases vary by the same amount. This indicates very little sensitivity to 

the variations in the control blade history represented by these cases. A closer look at the 

control blade history for these particular cases indicates that none includes full-depth control 
54

blade insertion, although a number of them have control blade insertion depths of 76%, whereas

all of the highest reactivity cases have virtually full-depth control blade insertion. This result 

suggests once again that there is a significant sensitivity associated with control blade insertion 

depth.

HH23–HH32 were used to ascertain a detailed understanding of the cask reactivity as a function 

of control blade insertion depth. HH23–HH32 are combined with HH1–HH5 to simulate the 

control blade remaining in one axial location for the entire irradiation over all axial levels. The 

AO and AFP criticality results from HH1–HH5 and HH23–HH32 are plotted in Figure 5.6 as a 

function of control blade insertion depth.

The keff results for the AO and AFP isotope sets show marked differences once the blade is 

inserted more than halfway into the assembly. The AO curve is flat in the lower three quarters of 

the assembly, indicating that control blade insertion in the bottom portion of the fuel assembly 

has little impact on cask reactivity. For the upper seven nodes in the fuel assembly, cask 

reactivity increases significantly, indicating that cask reactivity is extremely sensitive to control 

blade insertion in the uppermost portions of the fuel assembly. The high sensitivity in the upper 

portion of the fuel assembly is due to the highly top-peaked axial fission distribution (Figure 4.5) 

in SNF within transportation and storage casks. The profile for the AFP isotope set is generally 

similar, but it has some differences. Control blade insertion in the bottom half of the assembly 

does not impact cask reactivity, consistent with the results seen for the AO set. Cask reactivity 

starts to increase slowly once the blade is inserted more than halfway into the assembly and 

then increases quickly from about node 6 to node 3. Cask reactivity drops slightly when the 

blade is inserted in the either of the top two nodes. The discharge burnups in both of these 

nodes are below 20 GWd/MTU, so residual gadolinium burnable absorber remains at these 

elevations. The poisoning effect of this residual absorber overwhelms the reactivity increases 

associated with additional 239Pu production in these nodes and causes significant perturbation of 

the axial fission distribution in the cask.

Figure 5.6 AO and AFP criticality results as a function of blade insertion depth
55

The AFP axial fission distributions for a range of hypothetical histories (insertions of 100%, 84%, 

76% and 0%) are shown in Figure 5.7. Hypothetical histories with the control blade inserted 

more than halfway into the assembly show at least some shift in the fission distribution to the 

middle elevations of the cask.

The axial distribution of 239Pu is shown for HH05 in Figure 5.8, and that of 155Gd is shown in 

Figure 5.9. HH05 inserts the control blade into the bottom 19 nodes (76%), while HH29 inserts 

the control blade into the bottom 21 nodes (84%). In this range, as shown in Figure 5.8, the 

239Pu generation in the upper regions of the full lattice results in a higher 239Pu concentration 

than at the top of the assembly. The 239Pu concentration increases moving up the assembly as 

the moderator density decreases and the neutron spectrum shifts to higher energies. Node 11 is 

the first node of the vanished lattice, and the spectrum softens significantly at this elevation 

because of the additional water coolant in the lattice occupying the vanished rod locations. The 

239Pu concentration increases again until node 6, which is the first unrodded node. Figure 5.8 

clearly illustrates the impact of the control blade on the neutron spectrum and thus 239Pu 

generation. The 239Pu concentration decreases in the top few nodes as the burnup decreases.

The lower burnups result in a significant amount of residual gadolinium. The axial profile of the

155Gd concentration is considerably simpler and is driven nearly entirely by burnup. The large 

concentration in the top two nodes is a direct result of the low burnup of these nodes. The 

overall cask keff drops for rod insertions into the uppermost two nodes (as illustrated in 

Figure 5.6) because the axial fission distribution shifts more strongly into these nodes, which 

contain significant residual gadolinium. Shifting the fission distribution more strongly into these 

nodes results in greater parasitic neutron absorption in the residual gadolinium, thus reducing 

reactivity. The additional 239Pu produced when these nodes are rodded has a small effect on 

reactivity due to a shift in the fission distribution into these nodes with high concentrations of 

residual gadolinium.

Figure 5.7 Axial fission distribution for several hypothetical histories
56

Figure 5.8 Axial distribution of 239Pu

Figure 5.9 Axial distribution of 155Gd

The axial fission profiles shown in Figure 5.7 demonstrate that significant departures from the 

expected top-peaked fission profile shown in Figure 4.5 are possible with these hypothetical 

histories. The interaction among assemblies within the cask can be strongly influenced by the 

alignment of the fission distributions; so cask reactivity can be affected not only by differences in 

discharged isotopic number densities caused by rodded operations, but also by shifts in the 

fission distributions. Although not shown in this report, fission profiles resulting from histories 

with the control blades inserted approximately halfway into the assembly for the entire 
57

irradiation can generate double peaked (top and middle) fission distributions. These profiles are 

potentially susceptible to source convergence difficulties in Monte Carlo simulations, and results 

must be examined for indications of source convergence problems.

5.2.3 Control Blade Study with Realistic Histories

To compare the hypothetical histories with realistic histories, control blade insertion data were 

extracted from the available operating data. The control blade insertion depths were then 

plotted, and certain histories were selected for analysis. Because only one cycle of data exists

for the operating data, the full-length control blade histories were constructed by simulating a 

selected single-cycle control blade history repeatedly for three consecutive cycles. Fuel 

assemblies are unlikely to experience significant operational periods with control blades inserted 

for three consecutive cycles because of fuel assembly shuffling and decreased fuel reactivity 

with burnup. In general, fresh fuel assemblies are placed relatively close to the center of the 

core and then moved to the radial periphery of the core. The control blades relatively close to 

the center of the core are typically used frequently, as they have the greatest effect on core 

reactivity, while the control blades near the periphery are not frequently used during operation. 

In addition, control blades are not typically used significantly at EOC owing to the reduction of 

total core reactivity as a result of fuel depletion. This cycle-by-cycle movement of fuel 

assemblies, preferential use of certain control blade locations, and limited use of control blades 

at EOC are likely to lead to fuel assemblies that experience more control blade insertion near 

BOL and less control blade insertion near EOL. Therefore the simulation of three cycles with 

large integral control blade histories should produce conservative criticality results when 

compared with typical operation. 

The cask criticality results for RH1–RH10 can be found in Table 5.2, and plots depicting the 

control blade insertion depth as a function of time can be found in Appendix A. The data in 

Table 5.2 have been sorted from highest to lowest reactivity. The total spread (highest minus 

lowest) of realistic profile cask criticality data for the AO and AFP isotope is 0.49% and 0.59% 

Δkeff, respectively. Initially, one might expect that RH2, which includes the highest integral 

control blade history, would also produce the highest cask reactivity. However, RH2 has the 

seventh-highest cask reactivity for both the AO and AFP isotope sets. This is the case because, 

although RH2 has the most frequent control blade usage, it contains only one instance per cycle 

when the control blade is inserted to a depth greater than 80% into the core. By contrast, RH9, 

which produces the highest cask reactivity for both the AO and AFP isotope sets, has two 

relatively lengthy control blade insertions, both at depths of greater than 90% into the core. Two 

clear conclusions can be drawn from these results, along with those shown in Figure 5.6. 

Because of the high sensitivity to very deep control blade insertion, realistic histories that have 

control blade insertions of greater than ~80% of the length of the fuel result in a noticeable 

impact on cask reactivity. By contrast, cases with control blade insertions of less than ~50% of 

the fuel length are virtually indiscernible (within the statistical deviation) from the base case with 

control blades withdrawn (HH1). 
58

Table 5.2 Criticality results for RH1-RH10 

AO isotope set AFP isotope set

History keff* History keff*

RH9 0.83733 RH9 0.73781

RH8 0.83627 RH6 0.73583

RH3 0.83610 RH8 0.73533

RH6 0.83569 RH3 0.73532

RH10 0.83440 RH10 0.73397

RH5 0.83304 RH5 0.73300

RH2 0.83278 RH2 0.73281

RH1 0.83258 RH7 0.73248

RH4 0.83253 RH4 0.73210

RH7 0.83247 RH1 0.73188

*All keff calculations have estimated standard deviations 

 0.0001.

The most limiting realistic history (RH9) differs from the most limiting hypothetical history (HH2

for the AO isotope set and HH31 for the AFP isotope set) by 3.66% and 3.68% Δkeff for the 

AO and AFP isotope sets, respectively. The differences between RH9 and HH2 indicate that the 

assumption of fully inserted rods for the entire irradiation is an overly conservative assumption. 

Comparing RH9 with HH1 (control blades withdrawn) shows differences of 0.49% and 0.59% 

Δkeff for the AO and AFP isotope sets, respectively. This difference indicates that neglecting 

control blade insertion during depletion could result in nonconservative cask criticality values of 

~0.6% Δkeff. The axial fission distribution for RH09, shown in Figure 5.10, agrees closely with 

that for the unrodded depletion (HH01). However, this difference should not be viewed as a 

bounding estimate of the effect, because the result is based on only a single cycle of control 

blade histories. Additional data from other plants and for an entire assembly life would be 

needed to generate a more generically applicable estimate of the cask reactivity impact of 

realistic control blade usage.

In addition to Figure 5.10, the axial fission distributions from the rest of the realistic histories 

were plotted and analyzed. However, plots of these fission distributions have been omitted from 

the document, as they do not deviate significantly from the fission profiles shown in Figure 5.10.

None of the simulated realistic histories result in middle- or double-peaked fission distributions, 

so it is very unlikely that a fission distribution other than top-peaked would be observed in an 

actual fuel assembly or cask. This analysis shows that the significant shifts in the fission shape 

are only an effect of modeling inserted blades at specific depths for very prolonged periods of 

irradiation. These extreme conditions are unlikely to occur in actual reactor operation. 
59

Figure 5.10 Axial fission distribution for the limiting realistic history and the unrodded

hypothetical history

5.3 Summary and Recommendations

This section documents studies examining the effects of control blade insertion on extended 

BWR BUC. Two sets of control blade histories were analyzed as part of this study: (1) 

hypothetical histories to examine key effects of control blade insertion depth, length, and time in 

cycle and (2) realistic histories constructed from available operating data. The important effects 

ascertained using the HHs are compared with the results based on RHs to determine 

approximate differences associated with simulations of fuel assemblies over the entire 

irradiation. The results of the hypothetical control blade histories indicate three effects that result 

in increased cask reactivity: (1) control blades inserted deeply into the core, (2) control blades 

inserted near EOL, and (3) control blades inserted for longer periods of time (or burnup). In 

particular, cask reactivity is especially sensitive to control blade insertion deeply into the core 

due to the axially top-peaked fission distribution (end effect) typical in BWR storage and 

transportation casks. It has also been demonstrated that, under some hypothetical analysis 

conditions, it is possible to change this axial fission distribution in ways that probably are not 

representative of actual discharged fuel assemblies and have minimal effect on cask reactivity.

The results of this study indicate that neglecting control blade insertion during depletion could 

result in nonconservative cask criticality values of approximately 0.6% Δkeff. Additional operating 

data from other plants would be needed to generate a more generically applicable estimate of 

the cask reactivity impact of realistic control blade usage.

Key observations of this study are summarized as follows.

 Control blade insertions of 50% or less for the entire depletion have virtually no impact 

on cask reactivity.
60

 Although unrealistic, the most limiting case for the AFP isotope set is 92% blade 

insertion for the entire irradiation, which increases cask reactivity by 4.3% Δkeff

(compared with unrodded irradiation). The limiting case for the AO isotope set, full 

control blade insertion for the entire irradiation, is also unrealistic and results in a cask 

reactivity increase of 4.1% Δkeff (compared with unrodded irradiation).

 Deeper control blade insertions (80% of the active fuel length or higher) have a 

considerably greater impact than frequent shallower insertions. 

 Deep control blade insertions in the last third of life have greater impact (~1%) on 

reactivity than similar insertions earlier in life.

 Control blades inserted more than half way into the core for significant periods can 

cause significant shifts in axial fission distribution. Insertions in the range of 75% to 85% 

for the entire depletion appear to maximize the observed shift in the cask. Analysis 

assumptions or simplifications regarding control blade use which introduce these shifts, 

such as partial control blade insertion for an extended period, are unnecessary and 

should be avoided because such shifts do not result from the realistic histories.

 Fuel assemblies are unlikely to experience significant operational periods with control 

blade insertion late in life because of lower reactivity and placement near the core 

periphery; therefore the limiting cases examined here are considered conservative.

 Some fuel assemblies may experience exceptional control blade use. This would be the 

result of suppressing assembly power because of leaking fuel rods or high assembly 

reactivity early in life.

 Based on the limiting realistic histories examined, a penalty of ~0.6% to 1.2% Δkeff may 

be sufficient to account for control blade insertion effects. Applicants should provide a 

justification that any reactivity penalty taken is sufficient to account for rodded operations 

and should identify a process for handling assemblies that violate the underlying 

assumptions used in generating the penalty.
61

6 AXIAL BURNUP PROFILES

This section focuses on the effects of axial burnup profiles on cask reactivity and makes 

recommendations for identifying and using potentially limiting burnup profiles. Initially, a set of 

profiles had to be generated, as no BWR database analogous to the PWR database used in 

Wagner, DeHart, and Parks [21] currently exists. The set of profiles generated for this work are 

the normalized EOC axial burnup profiles for all 624 assemblies in the core follow data set. The 

BWR profile set generated is more limited than the PWR database but was sufficient for use in 

this study. The axial burnup profiles were used to generate a range of cask keff values at 

multiple burnups for each of the profiles considered, including both the AO and AFP isotope 

sets. Analysis of the calculation results is presented, including the range of keff values that result 

from the profiles considered, the magnitude of the end effect associated with the profiles, 

potential indicators of relative reactivity of axial burnup profiles, and a brief examination of the 

effect of the discharge burnup of the assembly from which each profile is taken on cask keff. This 

analysis is performed both for models that neglect the presence of natural enrichment blankets 

and for models that include these blanket regions. Finally, a summary of the findings on axial 

burnup profiles is presented.

Most of the BWR SNF in the domestic inventory has reduced-enrichment (typically natural) 

blankets. A routine modeling simplification made in PWR BUC is that no blankets are present, 

and this assumption is conservative because it significantly increases the quantity of fissile 

material in the relatively high-reactivity ends of the assembly. The assembly ends have high 

reactivity because they have low burnup; this effect was studied extensively for PWR SNF in 

Wagner, DeHart, and Parks [21]. The examination of the effects of BWR axial burnup profiles 

thus starts with the same modeling simplification: that the axial blankets are not present in the 

discharged fuel assemblies. This also provides a basis for comparison of the results of this 

study with those generally established for PWR axial burnup profile effects in [21]. The profiles 

used in this study were generated by a 3D core simulator model that appropriately represented 

the fuel as manufactured, (i.e., with blankets), but the GBC-68 cask model introduces a 

modeling simplification of full-enrichment fuel over the entire length of the assembly. The 

examination of axial burnup profile effects is extended in Section 6.3 to include explicit modeling 

of the blankets with the as-built natural enrichment. This further study allows for a quantification 

of the margin introduced by neglecting blankets and a comparison of limiting profiles in both 

blanketed and unblanketed models.

All depletion calculations used for analyses documented in this section were performed using 

the STARBUCS sequence within SCALE 6.1.3 [4]. Separate calculations were required for the 

full and vanished lattices, as only one ORIGEN library can be used in a STARBUCS calculation. 

Scenarios modeling axial blankets required four STARBUCS calculations, because the initial 

enrichment for natural enrichment blankets is different from that for the enriched nonblanket 

sections of the assembly. The difference in initial enrichments requires different ORIGEN 

libraries and thus separate STARBUCS calculations. The relevant SCALE composition inputs 

generated by STARBUCS were collected and inserted into a KENO model of the GBC-68 cask 

[8] loaded with GE14 fuel. All depletion parameters aside from the axial burnup profile—

including specific power, axial moderator density, and operating history—were kept constant so 

that the only parameter that changed was the axial burnup profile. This single-variable approach 

is consistent with the treatments for axial moderator density (Section 4) and control blade usage 

(Section 5) in isolating each effect for study.
62

The ORIGEN libraries used in the STARBUCS depletions were all generated without control 

blade insertion. The effects of rodded operation are discussed in Section 5; and any impact of 

exposure to control rods on the burnup profile itself will be included in the axial burnup profiles 

considered in this study, because they were extracted from actual plant data. The impact of 

correlated parameters will be studied in future work.

6.1 Characteristics of Profiles Used

The EOC burnup profiles were generated for all 624 assemblies in the core follow data set used 

in Sections 4 and 5 and described in Section 3.1. These profiles were normalized to enable 

comparisons among profiles independent of burnup of the assembly from which the profile was 

taken. Representative profiles from low-burnup assemblies are shown in Figure 6.1, 

intermediate-burnup in Figure 6.2, and relatively high-burnup in Figure 6.3. The top of the 

assembly corresponds to low node numbers, i.e., node 1 is at the top of the assembly and node 

25 is at the bottom.

Figure 6.1 shows normalized burnup profiles from assemblies that have experienced one cycle 

of irradiation. All of these assemblies have EOC burnups of less than 25 GWd/MTU. It is clear 

that there are two general profile shapes. The flatter profiles show evidence of control blade 

insertion, as the burnup in the lower portions of these assemblies is suppressed relative to the 

unrodded profiles, which manifest a much more bottom-skewed profile. The profiles resulting 

from rodded assemblies are shown with a dashed line, and the others with a solid line. The 

variation among profiles is significant; the difference between the maximum and minimum 

relative burnup at node 5 (relative to the top of the assembly) in the profiles shown is on the 

order of 30%. This variation is expected to lead to a large range of calculated cask keff values for 

these profiles.

Figure 6.2 shows normalized burnup profiles for assemblies that have experienced multiple 

cycles of irradiation and have EOC burnups between 25 and 40 GWd/MTU. In general, the 

burnup profiles are more similar in this burnup range than the first-cycle profiles shown in 

Figure 6.1. There is one profile that shows a more bottom-skewed burnup profile than the 

others, shown with a dashed line. Another profile has a unique profile at the top end of the 

assembly (low node number). This feature, hereafter referred to as the hockey stick, is present 

for many more profiles in the high-burnup profiles shown in Figure 6.3 and is related to a longer 

top axial blanket. Most fuel assemblies, 568 of the 624, have 6 in. top and bottom natural 

enrichment blankets. The remaining 56 profiles have a 12 in. long natural blanket, which results 

in the lower relative burnup in node 2 compared with the other profiles. Even considering the 

hockey stick feature, the variability among profiles is less for the intermediate-burnup profiles 

than for the low-burnup profiles. The range of relative burnups at node 5 is approximately 0.18; 

this is about 60% of the variation seen in the low-burnup profiles.

Figure 6.3 shows normalized burnup profiles for assemblies that have experienced multiple 

cycles of irradiation and have EOC burnups of greater than 40 GWd/MTU. Several profiles with 

the hockey stick feature are evident, shown with dotted lines, as are two profiles with a 

noticeably bottom-skewed profile. There is slightly less variability in the high-burnup profiles 

than in the intermediate-burnup profiles. The range of relative burnups at node 5 for profiles 

shown in Figure 6.3 is approximately 0.15, representing 83% of the variation seen in the 

intermediate-range profiles and a 50% reduction relative to the low-burnup profiles at the same 

elevation.
63

Each of the profiles shown in Figures 6.1–6.3 has a minimum relative burnup for the selected 

burnup range in at least one node. Each profile in each figure is shown in a unique color, but 

colors are reused from one figure to another.

Figure 6.1 Selected normalized burnup profiles from assemblies with EOC burnups less 

than 25 GWd/MTU

Figure 6.2 Selected normalized burnup profiles from assemblies with EOC burnups 

between 25 and 40 GWd/MTU
64

Figure 6.3 Selected normalized burnup profiles from assemblies with EOC burnups 

greater than 40 GWd/MTU

6.2 Results for Models Without Blankets

Results are presented in this section for all 624 normalized axial burnup profiles from the core 

follow data at assembly average burnup values of 30, 40, and 50 GWd/MTU. Cask keff values 

are determined for all three assembly average burnup values for each of the 624 profiles, 

regardless of the EOC burnup of the assembly from which the profile was taken. These models 

include the modeling simplification of full-length enriched fuel and are performed for both the AO 

and AFP isotope sets. A uniform axial burnup profile that is depleted with the same depletion 

conditions and axial moderator distribution as the nonuniform profiles is included for 

comparison.

The depletion calculations for the blanket nodes are performed in STARBUCS; the ORIGEN 

libraries are generated with the appropriate moderator density and number of rods for each axial 

location in the core, but with higher fuel enrichment. The GE14 assembly model includes the full 

and vanished lattices, but not a reduced enrichment section for the axial blankets.

6.2.1 Cask keff Results

The analysis of the reactivity effects of axial burnup profiles starts with a presentation of the 

cask keff values. These data are presented here and analyzed further in Sections 6.2.2, 6.2.3, 

and 6.2.4. Table 6.1 shows the minimum, average, and maximum keff values for each burnup for 

the AO and AFP isotope sets, as well as the standard deviation of the keff values for each 

distribution. The values presented in the table show that a wide range of cask keff values result 

from the 624 normalized axial burnup profiles analyzed at each of the three considered burnups 

and that the range increases with burnup. For the AO isotope set, the range is about 3.3% Δk at 

30 GWD/MTU and increases to almost 5% Δk at 50 GWd/MTU. For the AFP isotope set, the 

range is 4% Δk at 30 GWd/MTU and increases to 6.1% Δk at 50 GWd/MTU. The range of cask 
65

keff values is relatively constant in terms of standard deviations, with all six distributions (two

isotope sets at each of three burnups) having a width between 3.35 and 3.77 standard 

deviations.

Table 6.1 Cask keff distribution data for the unblanketed fuel models

AO isotope set AFP isotope set

Burnup (GWd/MTU) 30 40 50 30 40 50

Minimum 0.85722 0.82286 0.79255 0.81010 0.77259 0.73988

Maximum 0.89052 0.86527 0.84241 0.85027 0.82220 0.80089

Average 0.87505 0.84535 0.81854 0.83154 0.79842 0.76911

Standard deviation (Δk) 0.00883 0.01201 0.01477 0.01132 0.01481 0.01763

The ten most reactive profiles are identified and their associated cask keff values are provided 

for the AO isotope set in Table 6.2 for each of the three burnup values considered. For the 50 

GWd/MTU burnup values, the ten most reactive profiles that result from assemblies with 6-in. 

blankets are also identified. None of the profiles with 12-in. axial blankets (profile numbers over 

400 listed in Table 6.2) is in the ten most reactive profiles at 30 or 40 GWd/MTU. Aside from the 

12-in. blanket (hockey stick) profiles appearing in the list, the top few profiles are generally 

consistent among the three burnups considered. Several of the profiles result in cask keff values 

that are statistically equivalent, but the range from the most reactive to the tenth most reactive 

profiles is large enough that there is high confidence that the most reactive profile is captured in 

the list presented.

The ten most reactive profiles are identified and their associated cask keff values are provided 

for the AFP isotope set in Table 6.3 for each of the three burnup values considered. For the 40 

and 50 GWd/MTU burnup values, the ten most reactive profiles that result from assemblies with 

6-in. blankets are also identified. None of the profiles from assemblies with 12-in. blankets 

(profile numbers over 400 listed in Table 6.3) is in the ten most reactive profiles at 

30 GWd/MTU. The 50 GWd/MTU burnup point is dominated by 12-in. blanket profiles; the 29 

most reactive profiles result from these hockey stick profiles. These profiles become limiting at 

high burnup as the relative reactivity difference between the low-burnup top end of the assembly 

and the high-burnup middle portion of the assembly becomes greater. The low relative burnup 

in the top nodes causes the reactivity of that portion of the assembly to drop more slowly with 

burnup, and this difference increases with burnup. The limiting 6-in. blanket profiles are fairly 

consistent at each burnup, as with the AO isotope set. Several profiles yield statistically 

equivalent cask keff values, which is also consistent with the AO isotope set results. The limiting 

profiles are largely the same, although in a slightly different order, for the AFP and AO isotope 

sets.
66

Table 6.2 Top ten most reactive axial burnup profiles, AO isotope set

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

50 GWd/MTU,

only 6-in. blanket 

profiles

Profile Cask keff Profile Cask 

keff

Profile Cask 

keff

Profile Cask keff

31 0.89052 40 0.86527 443 0.84241 40 0.84190

52 0.89028 31 0.86505 442 0.84210 52 0.84167

22 0.89028 22 0.86488 452 0.84206 31 0.84166

77 0.89018 52 0.86487 447 0.84192 22 0.84166

11 0.89016 37 0.86483 444 0.84192 37 0.84138

40 0.89016 36 0.86468 40 0.84190 36 0.84137

81 0.89014 54 0.86466 52 0.84167 39 0.84135

36 0.89011 35 0.86463 31 0.84166 35 0.84133

67 0.89003 39 0.86456 22 0.84166 16 0.84124

39 0.89000 81 0.86450 441 0.84151 54 0.84123

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

Table 6.3 Top ten most reactive axial burnup profiles, AFP isotope set

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

Profile Cask keff Profile Cask keff Profile Cask keff

40 0.85027 443 0.82220 443 0.80089

52 0.85022 452 0.82196 452 0.80078

31 0.85018 31 0.82193 447 0.80036

35 0.85005 40 0.82190 442 0.80020

22 0.85000 444 0.82168 444 0.80007

54 0.84999 52 0.82166 441 0.79975

36 0.84999 442 0.82153 445 0.79962

77 0.84997 441 0.82148 446 0.79949

39 0.84991 447 0.82144 422 0.79876

81 0.84991 22 0.82143 424 0.79873

Only 6-in. blanket profiles

No profiles with 12-in.

blankets in the 10 most 

reactive

31 0.82193 40 0.79591

40 0.82190 52 0.79567

52 0.82166 22 0.79559

22 0.82143 31 0.79553

35 0.82124 36 0.79553

36 0.82122 37 0.79541

54 0.82121 11 0.79529

39 0.82121 35 0.79519

11 0.82120 39 0.79517

16 0.82111 54 0.79516

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

Table 6.4 lists eight axial burnup profiles that occur in the top ten most reactive profiles, from 

assemblies with 6-in. blankets for multiple burnups with both the AO and AFP isotope sets. The 

profiles are plotted in Figure 6.4, showing clearly similar traits in the limiting profiles. The top 

end of the fuel assembly drives reactivity because of its low burnup but relatively high plutonium

content relative to the low burnup in the last node of the assembly. Nodes adjacent to the lowest 
67

node also have higher burnup, and thus lower reactivity, than the nodes adjacent to the top 

node. The profiles also come from assemblies that have experienced a single cycle of operation 

that has been at least primarily unrodded.

Table 6.4 Eight highly reactive normalized axial burnup profiles

Prof. 31 Prof. 52 Prof. 22 Prof. 40 Prof. 36 Prof. 39 Prof. 54 Prof. 35

0.169 0.172 0.168 0.168 0.169 0.170 0.172 0.170

0.455 0.455 0.456 0.454 0.456 0.457 0.456 0.457

0.596 0.594 0.598 0.596 0.598 0.599 0.596 0.598

0.743 0.744 0.744 0.743 0.744 0.745 0.747 0.745

0.837 0.838 0.837 0.837 0.838 0.840 0.841 0.838

0.933 0.937 0.933 0.934 0.934 0.936 0.940 0.934

0.979 0.983 0.977 0.978 0.979 0.981 0.985 0.979

1.013 1.019 1.013 1.013 1.013 1.015 1.020 1.014

1.018 1.024 1.018 1.018 1.017 1.019 1.023 1.018

1.041 1.044 1.045 1.042 1.041 1.042 1.042 1.041

1.101 1.104 1.108 1.104 1.101 1.102 1.102 1.102

1.146 1.141 1.154 1.150 1.146 1.147 1.138 1.148

1.171 1.158 1.180 1.175 1.171 1.171 1.155 1.173

1.218 1.204 1.228 1.223 1.219 1.219 1.201 1.220

1.247 1.229 1.257 1.253 1.248 1.248 1.226 1.249

1.234 1.215 1.244 1.239 1.235 1.235 1.212 1.236

1.219 1.209 1.230 1.226 1.222 1.222 1.206 1.223

1.249 1.245 1.259 1.256 1.252 1.252 1.243 1.253

1.278 1.275 1.287 1.283 1.281 1.280 1.274 1.281

1.324 1.325 1.330 1.327 1.326 1.325 1.324 1.326

1.361 1.367 1.359 1.359 1.361 1.359 1.367 1.360

1.345 1.359 1.325 1.333 1.340 1.338 1.361 1.338

1.206 1.224 1.175 1.190 1.199 1.196 1.229 1.196

0.896 0.912 0.865 0.881 0.889 0.886 0.917 0.886

0.222 0.223 0.213 0.218 0.220 0.219 0.225 0.219

(Top of assembly is at top of table)
68 

Figure 6.4 Eight limiting axial burnup profiles 

6.2.2 End Effect 

The difference between cask keff calculated using a distributed burnup profile and using a 

uniform profile is called the end effect. When the end effect is positive, modeling of the 

distributed burnup profile is more conservative. Figure 6.5 shows the distributed-burnup profile 

cask keff values and the uniform-burnup profile cask keff value for all three burnups for the AO 

isotope set. Figure 6.6 shows the same results for the AFP isotope set. The distributed profiles 

in both figures are sorted from least reactive to most reactive, so the horizontal axis represents 

the reactivity ranking of all 624 profiles. The end effect is calculated for each profile. 

The end effect values for the AO isotope set increase with burnup as expected, although note 

that all 624 profiles have a positive end effect by 30 GWd/MTU. This result is influenced by the 

modeling simplification made by using fully enriched fuel in place of natural blankets. At 

30 GWd/MTU, the end effect varies from 0.3% ∆k to 3.6% ∆k; at 50 GWd/MTU, the minimum 

end effect has increased to 3.7% ∆k, and the maximum value is 8.6% ∆k. 

The end effect values for the AFP isotope set also increase with burnup, as expected. As with 

the AO isotope set, all profiles result in positive end effects by 30 GWd/MTU. The magnitude of 

the end effects is significantly greater for the AFP set than for the AO set. The end effect ranges 

from 1.6% ∆k to 5.7% ∆k at 30 GWd/MTU and from 6.6% ∆k to 12.7% ∆k at 50 GWd/MTU. 

These numbers are larger than the results presented in Wagner, DeHart, and Parks [21], but the 

burnup profiles considered in that work were exclusively unblanketed fuel. 

These end effect values are quite large, and extrapolation to lower burnups would indicate that 

positive end effects could exist below 20 GWd/MTU. Positive end effects in this burnup range 

would potentially impact peak reactivity methods, such as those described in Marshall, Ade, et 

al. [3], since those methods typically assume a 2D planar representation of the fuel assembly. A 

positive end effect would indicate that this approach is potentially nonconservative without 
69 

considering distributed burnup profile effects. The burnup profiles that exist in the peak reactivity 

burnup range of 7–20 GWd/MTU might be significantly different from EOC profiles. The residual 

gadolinium burnable absorber would also potentially impact the results at these lower burnups. 

Residual burnable absorber concentrations are much lower by EOC and are therefore not a 

significant contribution to cask reactivity. Additional work is needed to examine this potential 

residual burnable absorber effect at lower burnups, because the burnup profiles used in this 

study are all EOC profiles. 

Figure 6.5 Cask keff values for distributed and uniform burnup profiles, AO isotope set 
70 

Figure 6.6 Cask keff values for distributed and uniform burnup profiles, AFP isotope set 

6.2.3 Burnup Profile Selection 

The work presented in this section includes 624 axial burnup profiles and calculates the GBC-68 

cask keff resulting from all fuel assemblies loaded in the cask experiencing the same axial 

burnup profile. Many of these profiles are not close to limiting, as shown in Section 6.2.1, so a 

more efficient approach is desired. This section presents a method that may be used to assess 

the relative reactivity of different axial burnup profiles based on an examination of the relative 

burnup of the top end of the profile (assembly). This technique is suggested by the results of the 

studies performed for PWR BUC in Wagner, DeHart, and Parks [21]. 

An examination of the relative burnup at the top end of the profile generally indicates the relative 

reactivity for profiles taken from similar assemblies. The primary questions to be answered in 

detail are (1) how many nodes need to be considered and (2) how similar must the assemblies 

be. The cask keff values resulting from all 624 profiles are plotted versus the relative burnup 

summed over a given number of nodes at the top of the profile for all 3 burnup values. Separate 

data sets are plotted for the 568 profiles with 6-in. blankets and the 56 profiles with 12-in. 

blankets. Figure 6.7 shows the cask keff results for the AO isotope set and just the top node 

relative burnup. A general trend is clearly evident: lower relative burnups lead to higher cask keff

values. However, several different bands are visible in the data. Figure 6.8 presents the cask keff

values versus the sum of the top three node relative burnups. The data are much more closely 

clustered along a single trend for each blanket length, especially at 40 and 50 GWd/MTU. 

Considering too many nodes can also decrease the quality of the fit. This phenomenon is shown 

in Figures 6.9 and 6.10, which consider the top 6 node and top 11 node relative burnups, 

respectively. Note that the top 11 nodes constitute the entire vanished lattice, and significant 

spread in the data is evident in Figure 6.10, as it is in Figure 6.7. Similar results are observed for 

the AFP isotope set, as shown in Figures 6.11 through 6.14. 
71

Figure 6.7 Cask keff versus top node relative burnup, AO isotope set

Figure 6.8 Cask keff versus sum of top three nodes’ relative burnup, AO isotope set
72

Figure 6.9 Cask keff versus sum of top six nodes’ relative burnup, AO isotope set

Figure 6.10 Cask keff versus sum of top 11 nodes’ relative burnup, AO isotope set
73

Figure 6.11 Cask keff versus top node relative burnup, AFP isotope set

Figure 6.12 Cask keff versus sum of top three nodes’ relative burnup, AFP isotope set
74

Figure 6.13 Cask keff versus sum of top six nodes’ relative burnup, AFP isotope set

Figure 6.14 Cask keff versus sum of top 11 nodes’ relative burnup, AFP isotope set

The profiles with 6-in. blankets come from four different assembly design types that have 

different numbers of part-length rods of differing lengths. Clearly, not all axial features must be 

identical for the relative burnup to be a strong indicator of relative reactivity for the profiles. The 

part-length rods end, in all cases, several feet from the top of the assembly and thus are not in 

the region that dominates discharged assembly reactivity. However, the differing blanket lengths 

cause differences in the relevant region of the assembly and therefore do cause different trends. 

It appears that models without axial blankets require consideration of approximately the top 
75

1.5 ft—in this case, three 6-in. nodes—to generate reliable predictions of relative reactivity for 

the associated cask keff values. An applicant would need to justify the exact number of nodes or 

axial lengths used in any such profile selection scheme.

The relative positions of the trends for the profiles resulting from assemblies with 6-in. and 12-in.

blankets also shift for different burnups and different numbers of nodes considered as the 

relative reactivity indicator. This clearly demonstrates that each population of profiles resulting 

from assemblies with significantly different features must be considered separately. In this case, 

a limited number of candidate 6-in. and 12-in. blanket profiles could be selected and depleted. 

The consideration of multiple burnup profiles is not eliminated, but the ability to identify a much 

more limited set of profiles is a significant improvement over including all 624 profiles.

6.2.4 Effect of Assembly Burnup

In this study, the normalized axial burnup profiles for all 624 assemblies from a single cycle of 

operation were generated and analyzed, assuming depletion to three fixed burnups of 30, 40, 

and 50 GWd/MTU. As documented in Wagner, DeHart, and Parks [21], burnup profiles in 

different burnup ranges may have different characteristics. The applicability of the profiles used 

in this study to low burnups was discussed in Section 6.2.2. It has been demonstrated for PWR 

fuel that burnup profiles tend to flatten as burnup increases, allowing the use of profiles taken 

from lower discharged burnups at higher burnups [21]. To examine the application of this 

conclusion to BWR fuel, a cursory examination of the reactivity resulting from profiles taken from 

assemblies in different burnup ranges is warranted.

The database of PWR axial burnup profiles used in Wagner, DeHart, and Parks [21], available 

in Cacciapouti and Volkinburg [24], contains more than 3000 profiles from a range of different 

plants and fuel designs. The set of profiles analyzed in this study contains 624 profiles from a 

single plant, although 4 different fuel design types are represented. The more limited nature of 

the data set used here precludes the type of detailed examination of narrow burnup bins, with a 

large number of profiles in each bin, presented in Wagner, DeHart, and Parks [21]. Instead, a 

more general examination is performed with the goal of determining the reactivity resulting from 

profiles taken from assemblies with high discharged burnups compared with profiles taken from 

assemblies with lower burnups.

Figure 6.15 shows the cask keff values resulting from the 568 profiles with 6-in. blankets at 

50 GWd/MTU for the AO isotope set. Figure 6.16 shows these data for the AFP isotope set. All 

the keff values presented are calculated at a discharge burnup of 50 GWd/MTU. The horizontal 

axis shows the EOC burnup of the assembly from which the profile was taken. Three burnup 

bins are chosen, somewhat arbitrarily, as EOC assembly average burnup of (1) <25 GWd/MTU, 

(2) between 25 and 40 GWd/MTU, and (3) >40 GWd/MTU. These ranges are consistent with 

those considered in Section 6.1 (see Figures 6.1–6.3). A line added to each figure showing the 

highest keff value within each bin demonstrates that cask keff values decrease by 0.5% – 1% Δk

from one axial profile burnup bin to the next higher bin. This is another aspect of burnup profile 

selection typical of PWR BUC that may also be advantageous in extended BWR BUC; excess 

margin may be removed from the analysis at high burnup by considering only normalized 

profiles from similarly high-burnup assemblies.
76

Figure 6.15 Cask keff value versus burnup of assembly generating profile, AO isotope set, 

no blankets modeled

Figure 6.16 Cask keff value versus burnup of assembly generating profile, AFP isotope 

set, no blankets modeled

6.3 Results for Models with Blankets

This subsection presents results similar to those provided in Section 6.2. In this subsection, 6-in.

natural blankets are modeled for all 624 profiles. A set of 10 of the 56 profiles with 12-in.
77

blankets is also modeled realistically, that is with the 12-in. blanket length modeled with natural 

enrichment fuel initially. The effect of modeling the blankets is examined with respect to the 

cask keff values, the end effect values, the prediction of the relative reactivity of the profiles, and 

the impact of the EOC assembly burnup that generated the profile on cask keff.

6.3.1 Cask keff Values

Table 6.5 shows the minimum, average, and maximum keff values for each burnup for the AO 

and AFP isotope sets, as well as the standard deviation of the keff values for each distribution. 

The values presented in the table show that a wide range of cask keff values result from the 624 

axial burnup profiles analyzed and that the range increases with burnup. For the AO isotope set, 

the range is 3.8% Δk at 30 GWD/MTU and increases to 6.4% Δk at 50 GWd/MTU. For the AFP 

isotope set, the range is 4.9% Δk at 30 GWd/MTU and 7.6% Δk at 50 GWd/MTU. The range of 

cask keff values is relatively consistent in terms of standard deviations, with all six distributions 

(two isotope sets at each of three burnups) having widths between 3.6 and 4.1 standard 

deviations. These ranges are slightly larger than for the unblanketed fuel models and tend to be 

wider (in terms of standard deviations) at lower burnup values.

Table 6.5 Cask keff distribution data for the blanketed fuel models

 AO isotope set AFP isotope set

30 40 50 30 40 50

Minimum 0.83747 0.78955 0.74592 0.77978 0.72556 0.67667

Maximum 0.87507 0.84162 0.80970 0.82842 0.78949 0.75287

Average 0.85778 0.81773 0.78011 0.80618 0.75993 0.71728

Standard deviation 0.00908 0.01306 0.01677 0.01216 0.01682 0.02104

The ten most reactive profiles and their associated cask keff values are provided for the AO 

isotope set in Table 6.6 for each of the three burnup values considered. None of the 12-in.

blanket (hockey stick) profiles is in the ten most reactive profiles at any burnup. The top few 

profiles are generally consistent among the three burnups considered. Several of the profiles 

result in statistically equivalent cask keff values, but the range from the most reactive to the tenth 

most reactive profiles is large enough that there is high confidence that the most reactive profile 

is captured in the list presented.

The ten most reactive profiles and their associated cask keff values are provided for the AFP 

isotope set in Table 6.7 for each of the three burnup values considered. As was observed for 

the AO isotope set, none of the hockey stick profiles is in the ten most reactive profiles at any 

burnup. As with the AO isotope set, the limiting 6-in. blanket profiles are fairly consistent at each 

burnup. Also consistent with the AO isotope set results, several profiles yield statistically 

equivalent cask keff values. The same profiles are limiting, though in a slightly different order, for 

the AFP and AO isotopes sets. Generally, the limiting profiles are also the ones identified for 

unblanketed fuel, as discussed in Section 6.2.1. A selection of limiting profiles for models with 

no axial blankets is shown in Table 6.4 and Figure 6.6 in Section 6.2.1. Unlike the unblanketed 

results presented in Section 6.2.1, however, no hockey stick profiles are limiting for either 

isotope set for any burnup. This demonstrates that modeling these longer blankets with their 

actual enrichment makes them nonlimiting compared with the other profiles considered in 

this study.
78

Table 6.6 Top ten most reactive axial burnup profiles, AO isotope set, 6-in.

blankets modeled

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

Profile Cask keff Profile Cask keff Profile Cask keff

63 0.87507 40 0.84162 63 0.80970

40 0.87500 81 0.84148 52 0.80961

69 0.87487 31 0.84147 31 0.80960

81 0.87483 52 0.84146 40 0.80954

52 0.87481 63 0.84143 77 0.80947

31 0.87479 77 0.84141 69 0.80938

36 0.87477 69 0.84140 81 0.80935

77 0.87476 22 0.84133 36 0.80928

22 0.87471 36 0.84124 35 0.80923

39 0.87463 37 0.84107 22 0.80907

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

Table 6.7 Top ten most reactive axial burnup profiles, AFP isotope set

30 GWd/MTU 40 GWd/MTU 50 GWd/MTU

Profile Cask keff Profile Cask keff Profile Cask keff

31 0.82842 40 0.78949 40 0.75287

77 0.82837 52 0.78942 52 0.75277

63 0.82833 63 0.78938 63 0.75253

40 0.82833 31 0.78936 31 0.75252

35 0.82831 77 0.78935 22 0.75250

36 0.82823 81 0.78925 77 0.75250

22 0.82823 36 0.78918 81 0.75245

69 0.82821 69 0.78916 69 0.75239

52 0.82820 35 0.78906 54 0.75223

81 0.82812 22 0.78900 36 0.75219

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

The reduction in cask keff caused by modeling the 6-in. blanket regions was calculated for each 

of the 624 profiles. The minimum, maximum, average, and standard deviations of the values for 

the keff reduction are presented in Table 6.8 for all three burnups for the AO and AFP isotope 

sets. The values in the table are all shown as positive values but should be understood to 

indicate a lowering of reactivity by including the blankets in the assembly model. Cask keff

values are, on average, 3% Δk lower at 30 GWd/MTU because of the blankets for the AO 

isotope set. The average reactivity reduction increases in magnitude with burnup to 4.4% Δk at 

40 GWd/MTU and 5.8% Δk at 50 GWd/MTU. The reactivity reduction caused by modeling the 

blankets is larger for the AFP isotope set. Credit for blankets is likely to be a fixture of extended 

BWR BUC, given the large reactivity margin associated with modeling them and the large 

number of assemblies in the inventory with blankets.
79

Table 6.8 Reactivity reduction introduced by modeling blankets

AO Isotope Set AFP Isotope Set

Burnup (GWd/MTU) 30 40 50 30 40 50

Minimum 0.01295 0.02039 0.02856 0.01903 0.02888 0.03917

Maximum 0.05055 0.07246 0.09235 0.06767 0.09280 0.11537

Average 0.03024 0.04427 0.05815 0.04126 0.05843 0.07476

Standard deviation (Δk) 0.00908 0.01306 0.01677 0.01216 0.01682 0.02104

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

Including the natural blankets in the assembly models significantly reduces the reactivity of the 

hockey stick profiles. Results presented so far have modeled only 6-in. natural blankets, even 

for the hockey stick profile assemblies, which in reality contain 12-in. top blankets. Tables 6.9

and 6.10 provide the cask keff values for ten hockey stick profiles at 30 and 50 GWd/MTU 

considering the AO and AFP isotope sets, respectively. The results presented contain three 

different modeling assumptions: no blankets, 6-in. blankets, and the actual 12-in. top blanket

with a 6-in. bottom blanket. At 30 GWd/MTU, the top node blanket causes the majority of the 

reactivity change from the unblanketed assumption. This reverses at 50 GWd/MTU so that the 

second blanket node is responsible for the majority of the reactivity change.

Table 6.9 Cask keff results for 10 selected 12-in. blanket profiles, AO isotope set

30 GWd/MTU 50 GWd/MTU

Profile 

number

No 

blanket

6-in.

blanket

12-in. 

blanket

No

blanket

6-in.

blanket

12-in. 

blanket

349 0.88157 0.85846 0.84003 0.83791 0.79099 0.74476

352 0.88197 0.85849 0.84008 0.83849 0.79139 0.74497

424 0.88369 0.86077 0.84243 0.84048 0.79484 0.74938

426 0.88302 0.86020 0.84197 0.83974 0.79391 0.74867

427 0.88311 0.86016 0.84199 0.83966 0.79402 0.74845

437 0.88041 0.85636 0.83843 0.83621 0.78878 0.74176

439 0.88074 0.85696 0.83854 0.83707 0.78916 0.74227

441 0.88425 0.86142 0.84318 0.84151 0.79611 0.75071

583 0.88004 0.85682 0.83952 0.83388 0.78774 0.74281

584 0.87972 0.85688 0.83955 0.83399 0.78773 0.74314

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)

Table 6.10 Cask keff results for 10 selected 12-in. blanket profiles, AFP isotope set

30 GWd/MTU 50 GWd/MTU

Profile 

number

No 

blanket

6-in. 

blanket

12-in. 

blanket

No 

blanket

6-in. 

blanket

12-in. 

blanket

349 0.84305 0.80999 0.78168 0.79588 0.73722 0.67229

352 0.84358 0.81002 0.78177 0.79635 0.73759 0.67275

424 0.84534 0.81289 0.78512 0.79873 0.74129 0.67791

426 0.84469 0.81235 0.78436 0.79747 0.74029 0.67671

427 0.84470 0.81222 0.78450 0.79759 0.74004 0.67652

437 0.84177 0.80806 0.77941 0.79382 0.73421 0.66865

439 0.84195 0.80801 0.77969 0.79467 0.73493 0.66894

441 0.84607 0.81395 0.78593 0.79975 0.74274 0.67916

583 0.84031 0.80759 0.78069 0.79015 0.73229 0.66956

584 0.84030 0.80788 0.78052 0.79059 0.73274 0.67022

(Monte Carlo uncertainty in all calculated keff values is approximately 0.00010 Δkeff.)
80

6.3.2 End Effect

The uniform burnup profile used as the reference in this section also models 6-in. natural 

enrichment blankets to be consistent with the distributed burnup profile assembly model. 

Figure 6.17 shows the distributed burnup profile cask keff values and the uniform burnup profile 

cask keff value for all three burnups for the AO isotope set. Figure 6.18 shows the same results 

for the AFP isotope set. The distributed profiles in both figures are sorted from least reactive to 

most reactive, so the horizontal axis represents a reactivity ranking of the 624 burnup profiles.

The end effect values for the AO isotope set increase with burnup, as expected. Not all profiles 

generate positive end effects when the blankets are modeled, as opposed to the results 

presented in Section 6.2.2 when the blankets are neglected. As the end effect increases with 

burnup, fewer profiles generate a negative end effect. At 30 GWd/MTU, the end effect varies 

from 1.6% Δk to 2.2% Δk; at 50 GWd/MTU, the minimum end effect has increased to 

1.0% Δk and the maximum value is 5.4% Δk.

The end effect values for the AFP isotopes set also increase with burnup, as expected. Some 

profiles result in negative end effects at 30 and 40 GWd/MTU, as with the AO isotope set. At 

50 GWd/MTU, all profiles result in positive end effects. The magnitude of the end effects is 

significantly greater for the AFP set than for the AO set. The end effect ranges from 1.3% Δk to 

3.6% Δk at 30 GWd/MTU and from 0.4% Δk to 8.0% Δk at 50 GWd/MTU. These numbers are 

larger than the results presented in Wagner, DeHart, and Parks [21], but the assemblies 

considered in that work were exclusively unblanketed fuel. These results, as well as those 

presented in Section 6.2.2, indicate that positive end effects are possible below 20 GWd/MTU. 

Such positive end effects could impact peak reactivity analyses and should be studied further.

Figure 6.17 Cask keff values for distributed and uniform burnup profiles, AO isotope set, 

blanketed fuel
81

Figure 6.18 Cask keff values for distributed and uniform burnup profiles, AFP isotope set, 

blanketed fuel

6.3.3 Burnup Profile Selection

This section examines the method of assessing the relative reactivity of different axial burnup 

profiles based on an examination of the relative burnup of the top end of the profile, discussed 

for unblanketed fuel models in Section 6.2.3.

The following discussion is similar to the text describing the method and results in Section 6.2.3, 

but it is retained to maintain the clarity of the process. It is also important because the 

conclusion differs from that presented previously; the consideration of more nodes appears 

warranted for blanketed fuel assembly models.

The cask keff values resulting from all 624 profiles are plotted versus a given number of nodes 

for all three burnup values. Separate data sets are plotted for the 568 profiles with 6-in. blankets 

and the 56 profiles with 12-in. blankets. Figure 6.19 shows results for the AO isotope set and 

the top node only. A general trend is clearly evident: lower relative burnups lead to higher cask 

keff values. However, there are several different bands evident in the data. Figure 6.20 presents 

the cask keff values versus the sum of the top three node relative burnups. The data are more 

closely clustered along a single trend for each blanket length, especially at 40 and 

50 GWd/MTU. The integrated relative burnup over six nodes is illustrated in Figure 6.21 and 

shows the desired linearity of results. As with the unblanketed fuel models, considering too 

many nodes can also decrease the quality of the fit. This phenomenon is shown in Figure 6.22,

which shows the top 11 nodes, the entire vanished lattice, and significant spread in the data. It

is also evident in Figure 6.19. Similar results are observed for the AFP isotope set, as shown in 

Figures 6.23 through 6.26.
82

Figure 6.19 Cask keff versus top node relative burnup, AO isotope set, blankets modeled

Figure 6.20 Cask keff versus sum of top three nodes’ relative burnup, AO isotope set, 

blankets modeled
83

Figure 6.21 Cask keff versus sum of top six nodes’ relative burnup, AO isotope set, 

blankets modeled

Figure 6.22 Cask keff versus sum of top 11 nodes’ relative burnup, AO isotope set,

blankets modeled
84

Figure 6.23 Cask keff versus top node relative burnup, AFP isotope set, 

blankets modeled

Figure 6.24 Cask keff versus sum of top three nodes’ relative burnup, AFP isotope set, 

blankets modeled
85

Figure 6.25 Cask keff versus sum of top six nodes’ relative burnup, AFP isotope set, 

blankets modeled

Figure 6.26 Cask keff versus sum of top 11 nodes’ relative burnup, AFP isotope set, 

blankets modeled

As discussed in Section 6.2.3, not all axial features must be identical for the relative burnup to 

be a strong indicator of relative reactivity for the profiles. The part-length rods end several feet 

from the top of the assembly, so the changes do not significantly impact discharged assembly 

reactivity among different fuel assembly design types. However, the differing blanket lengths 
86

cause differences in the relevant region of the assembly and therefore do cause different trends. 

It appears that models including axial blankets require consideration of approximately the top 

3 ft—in this case, six 6-in. nodes—to generate reliable predictions of relative reactivity for the 

associated cask keff values. An applicant would need to justify the exact number of nodes or the 

axial length used in any such profile selection scheme. Note that a greater fraction of the fuel 

assembly must be considered in the models that include blankets as compared with the 

unblanketed case, as discussed in Section 6.2.3. 

The relative positions of the trends for the 6-in. and 12-in. blankets also shift for different 

burnups and different numbers of nodes considered as the relative reactivity indicator. This 

clearly demonstrates that each population of profiles resulting from assemblies with significantly 

different features must be considered separately. In this case, for example, a limited number of 

candidate 6-in. blanket profiles and 12-in. blanket profiles could be selected and depleted. As 

discussed in Section 6.2.3, a range of burnup profiles will still need to be considered, but this 

case is nonetheless a significant improvement over performing calculations for all 624 profiles.

6.3.4 Effect of Assembly Burnup

A relevant discussion of the differences in analysis approach between this work and Wagner, 

DeHart, and Parks [21] is provided in Section 6.2.4 and should be reviewed before the following 

discussion.

Figure 6.27 shows the cask keff values resulting from the 568 profiles with 6-in. blankets at 

50 GWd/MTU for the AO isotope set; Figure 6.28 provides these same data for the AFP set. All 

the keff values presented are calculated at a discharge burnup of 50 GWd/MTU. The horizontal 

axis shows the EOC burnup of the assembly from which the profile was taken. Three burnup 

bins are chosen somewhat arbitrarily as the EOC assembly average burnup: (1) below

25 GWd/MTU, (2) between 25 and 40 GWd/MTU, and (3) above 40 GWd/MTU. These ranges 

are consistent with those considered in Section 6.1(see Figures 6.1–6.3). A line added to each 

figure, showing the highest keff value within each bin, demonstrates that cask keff values 

decrease by about 1% Δk from one axial profile burnup bin to the next higher bin. This is 

another aspect of burnup profile selection typical of PWR BUC that may also be advantageous 

in extended BWR BUC.
87

Figure 6.27 Cask keff value versus burnup of assembly-generating profile, AO isotope

set, blankets modeled

Figure 6.28 Cask keff value versus burnup of assembly-generating profile, AFP isotope 

set, blankets modeled

6.4 Summary and Recommendations

Section 6 documents studies performed to examine the effect of axial burnup distributions on 

extended BWR BUC. The burnup range examined was 30–50 GWd/MTU. The lower burnup
88

was selected to be higher than the burnups typical of peak reactivity for fuel lattices, whereas 

the upper bound is typical of discharge burnups for BWR assemblies. Detailed calculations were 

performed using 624 axial burnup profiles generated from the core follow data set discussed in 

Section 3.1.

All 624 assemblies considered had natural enrichment blankets at the top and bottom of the 

assembly; 568 had 6-in. blankets at both ends of the assembly. The remaining 56 assemblies 

had 6-in. blankets on the bottom end of the assembly but 12-in. blankets at the top end. The 

profiles resulting from these assemblies are discussed in detail in Section 6.1. Some PWR BUC 

analyses credit blankets while others do not, so both approaches are considered here. Section 

6.2 presents results from models neglecting the blankets and assuming all fuel had the same 

initial enrichment. Section 6.3 presents the results from calculations modeling the 6-in. and in 

some cases the 12-in. blankets. The general trends in the results for both modeling approaches 

are similar.

The profiles used in this study lead to a wide range of cask keff values. The range of calculated 

keff values varies from 3.3% Δk at 30 GWd/MTU for the AO isotope set with no blankets 

modeled, to 7.6% Δk at 50 GWd/MTU for the AFP isotope set with blankets modeled. The range 

is larger with blankets modeled and for the AFP isotope set. The calculated keff values are not 

normally distributed, and the range corresponds to approximately 3–4 standard deviations. The 

most reactive profiles are generally the same with or without blankets for both isotope sets, as 

long as the profiles considered have the same axial features near the top end of the assembly. 

As an example of the effects that differences in axial features, such as blankets, can have, the 

12-in. blanket profiles are significantly more reactive than 6-in. blanket profiles when no blanket 

is modeled.

The end effect was calculated for each profile at each burnup considered. A positive end effect 

indicates that the distributed burnup profile must be considered in the analysis, as it is more 

reactive than the uniform profile at the same burnup. Large positive end effects appear to be 

common for BWR fuel; all 624 profiles had positive end effects for the models neglecting 

blankets at all burnups, and at 50 GWd/MTU when blankets were modeled. The largest end 

effect for the profile with no blankets modeled ranges from 1.6% Δk at 30 GWd/MTU to 12.7% 

Δk at 50 GWd/MTU. The profiles with blankets modeled have end effects of 3.6% Δk to 8.0% 

Δk, also at 30 and 50 GWd/MTU, respectively. These end effects are larger than those typically 

seen in PWR BUC. As discussed in Sections 6.2.2 and 6.3.2, the magnitude of the end effects 

identified in this study also indicates that examination of the 2D approach to peak reactivity 

analyses may be appropriate. The core follow data set used in this study could be used to 

extract burnup profiles from the peak reactivity burnup range of 7–20 GWd/MTU to support such 

an investigation, although no such work has been performed to date.

A method to identify potentially limiting burnup profiles was investigated in Sections 6.2.3 and 

6.3.3. It appears that for models both with and without blankets, such an approach can generate 

a reliable indication of the relative reactivity of profiles taken from assemblies with similar axial 

features near the top end of the assembly. For assemblies with no blankets modeled, it appears 

that around three 6-in. nodes, or a total of 18 in., near the top of the assembly is an optimum 

length for making these determinations. The fuel length that must be considered is longer when 

blankets are modeled, probably on the order of six 6-in. nodes, or a total fuel length of 36 in. 

The number of nodes that should be considered will depend on nodalization and fuel assembly 

characteristics; therefore, the method used by any applicant must be justified. It also appears 

that axial feature differences that are not near the top end—such as differences in the number 

and length of part-length rods or differences in the number and loading of gadolinium pins—do 
89

not need to be tracked to determine limiting axial burnup profiles. The success of these basic 

methods in predicting relative reactivity can greatly simplify the work needed to determine the 

appropriate profile for use in a BWR BUC analysis.

The final aspect considered is the dependence of cask keff on the burnup of the assembly from 

which the profiles were taken. The results are presented in Section 6.2.4 for the models with no 

blankets and in Section 6.3.4 for the models with blankets. Three burnup bins were generated: 

0–25 GWd/MTU, 25–40 GWd/MTU, and >40 GWd/MTU assembly average burnup at EOC. The 

lowest-burnup bin captures all fuel assemblies that were loaded fresh into the cycle for which 

the core follow data set was generated. The separation of high-burnup assemblies into two bins 

at 40 GWd/MTU was largely arbitrary. For the profiles considered in this study, cask keff

decreases as burnup increases. The use of burnup bins to ensure appropriate profiles in each 

burnup range is common in PWR BUC and will likely be useful in BWR BUC, as well.

The following recommendations can be made based on the results of this study:

 The choice of axial burnup profiles can have significant impacts on cask reactivity. The 

range of cask keff values resulting from the profiles used in this study was as large as 

7.6% Δk. Applicants must provide justification for the profiles used in an analysis, 

including the burnups over which uniform and distributed burnup profiles are used.

 The limiting profile resulting from a set of available profiles is largely independent of the 

isotope set used. Axial blanket modeling approaches also have only a small impact on 

identifying the limiting profile for assemblies with 6-in. natural blankets.

 Distributed burnup profiles must be considered for extended BWR BUC. End effects of 

up to 12.7% Δk were identified in this study.

 The relative reactivity of different axial burnup profiles can be predicted reliably by 

considering the relative burnup in the top few nodes. Lower relative burnups lead to 

higher cask keff values. More nodes must be considered if axial blankets are modeled, 

and the relative ranking prediction is reliable only within a population of assemblies with 

blankets of the same length. Other axial feature differences in the top 4 ft of the 

assembly might also require separate consideration. Any scheme used to identify 

potentially limiting axial burnup profiles should be justified.

 Grouping axial burnup profiles into bins based on the EOC burnup of the assembly from 

which the profile was taken is likely to lower calculated cask keff values at higher 

burnups.

91

7 CONCLUSIONS

Many important conclusions relating to BWR BUC beyond peak reactivity can be drawn from the 

studies documented in this report. Similar studies related to peak reactivity analyses are 

documented in Reference 3. These conclusions are drawn from a relatively limited range 

because the core follow data set used represents a single cycle from a single plant. Ideally, 

these studies would have included data from different plants and several cycles of operation to 

provide greater coverage of operating ranges. Unfortunately, the detailed data needed for most 

of the studies were readily available only from one source. Additional work should be performed 

to demonstrate wider applicability of the conclusions drawn here.

7.1 Axial Moderator Density Distributions

Details of the axial burnup profile analyses are presented in Section 4 and summarized in 

Section 4.6. It is clear that the axial moderator density profiles used in modeling fuel depletion 

can have a significant impact on calculated cask keff and must be treated appropriately to ensure 

conservative analysis results. Although the set of profiles analyzed is somewhat limited, being 

based on only one cycle of operation, important conclusions can still be drawn from these 

studies.

 A cycle-averaged moderator density can be used in each node of an axial moderator 

density profile for depletion calculations with an appropriate penalty for conservatism.

 A reactivity penalty of 0.25% Δkeff is recommended to cover potential differences 

between detailed and cycle average moderator density treatments in depletion 

calculations.

 A limiting axial moderator density profile will have low moderator densities in the top 

nodes of the assembly. Each applicant should present and defend the method used to 

identify limiting profiles.

 A limiting axial moderator density profile can be constructed by selecting the minimum 

density in each axial node from a collection of applicable actual profiles.

 Use of average moderator densities determined from consideration of multiple 

assemblies or multiple axial nodes will result in reactivity underprediction.

 A single moderator density value can be used conservatively in all nodes if it is lower 

than the moderator densities in all nodes of the assemblies to be placed in the cask.

7.2 Control Blade Usage

The details of the control blade usage analyses are presented in Section 5 and summarized in 

Section 5.3. Control blade usage can have an impact on cask keff and must be treated 

appropriately to ensure conservative analysis results. The impact is less severe than original 

expectations, given that the control blades need to be inserted more than 50% into the core for 

an extended period before they have a noticeable effect. The set of realistic histories analyzed 

is somewhat limited, being based on only one cycle of operation; but important conclusions can 

be drawn from these studies, especially with consideration of the hypothetical histories used to 

investigate the sensitivity of cask keff to blade position, exposure duration, and time in irradiation.
92 

 Control blade insertions of 50% or less for the entire depletion have virtually no impact 

on cask reactivity. 

 Although unrealistic, the most limiting case for the AFP isotope set is 92% blade 

insertion for the entire depletion; it increases cask reactivity by 4.3% ∆keff. The limiting 

case for the AO isotope set is also unrealistic, full control blade insertion for the entire 

depletion, and results in a cask reactivity increase of 4.1% ∆keff. 

 Deeper and longer-duration control blade insertions have a much greater impact than 

frequent, shallower, shorter-duration insertions. 

 Deep control blade insertions in the last third of life have greater impact (~1%) on 

reactivity than similar insertions earlier in life. 

 Control blades inserted more than halfway into the core for significant periods can cause 

significant shifts in axial fission distribution. These shifts appear not to occur in realistic 

histories. Analysis assumptions or simplifications regarding control blade use which 

introduce these shifts, such as partial control blade insertion for an extended period, are 

unnecessary and should be avoided. 

 Fuel assemblies are unlikely to experience significant operational periods with control 

blade insertion late in life because of lower reactivity and placement near the core 

periphery; therefore the limiting cases considered here may be conservative. 

 Some fuel assemblies may experience exceptional control blade use. This would be the 

result of suppressing assembly power owing to leaking fuel rods or high assembly 

reactivity early in life. 

 Based on the limiting realistic histories examined, a penalty of ~0.6% to 1.2% ∆keff may 

be sufficient to account for control blade insertion effects. Applicants should provide a 

justification that any reactivity penalty taken is sufficient to account for rodded operations 

and should identify a process for handling assemblies that violate the underlying 

assumptions used in generating the penalty. 

 Axial Burnup Profiles 

The details of the axial burnup profile analyses are presented in Section 6 and summarized in 

Section 6.4. It is clear that the axial burnup profiles can have a significant impact on cask keff

and must be treated appropriately to ensure conservative analysis results. Although the set of 

profiles analyzed is not as extensive as that used in Wagner, DeHart, and Parks [21] for PWR 

BUC, important conclusions can still be drawn from these studies. 

 The choice of axial burnup profiles can have significant impacts on cask reactivity. The 

range of cask keff values resulting from the profiles used in this study was as large as 

7.6% ∆k. Applicants must provide justification for the profiles used in an analysis, 

including the burnups over which uniform and distributed burnup profiles are used. 

 The limiting profile resulting from a set of available profiles is largely independent of the 

isotope set used. Axial blanket modeling approaches also have only a small impact on 

identifying the limiting profile for assemblies with 6-in. natural blankets. No axial 

enrichment zoning effects were studied other than the effects of modeling natural 

enrichment blankets at the top and bottom of the fuel assembly. 
93 

 Distributed burnup profiles must be considered for extended BWR BUC. End effects of 

up to 12.7% ∆k were identified in this study. 

 The relative reactivity of different axial burnup profiles can be predicted reliably by 

considering the relative burnup in the top few nodes. Lower relative burnups lead to 

higher cask keff values. More nodes must be considered if axial blankets are modeled, 

and the relative ranking prediction is reliable only within a population of assemblies with 

blankets of the same length. Other axial feature differences in the top 4 ft of the 

assembly might also require separate consideration. Any scheme used to identify 

potentially limiting axial burnup profiles should be justified. 

 Grouping axial burnup profiles into bins based on the EOC burnup of the assembly from 

which the profile was taken is likely to lower calculated cask keff values at higher 

burnups, thereby lowering excess conservatism. 

95

8 REFERENCES

1. US Code of Federal Regulations Title 10, “Energy,” US Nuclear Regulatory Commission, 

Washington, DC (2014).

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and Storage Casks, US Nuclear Regulatory Commission (September 26, 2012).

3. W. J. Marshall, B. J. Ade, S. M. Bowman, I. C. Gauld, G. Ilas, U. Mertyurek, and

G. Radulescu, Technical Basis for Peak Reactivity Burnup Credit for BWR Spent 

Nuclear Fuel in Storage and Transportation Systems, NUREG/CR-7194 (ORNL/TM2014/240), prepared for the US Nuclear Regulatory Commission by Oak Ridge National 

Laboratory, Oak Ridge, Tenn. (April 2015).

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and Design, ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, Oak 

Ridge, Tenn. (June 2011). Available from Radiation Safety Information Computational 

Center at Oak Ridge National Laboratory as CCC-785.

5. M. D. DeHart and S. M. Bowman, “Reactor Physics Methods and Analysis Capabilities in 

SCALE,” Nuclear Technology, 174(2) (May 2011): 196–213.

6. B. J. Ade, SCALE/TRITON Primer: A Primer for Light Water Reactor Lattice Physics 

Calculations, NUREG-7041 (ORNL/TM-2011/21), prepared for the US Nuclear 

Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, Tenn. 

(November 2012).

7. J. M. Scaglione, D. E. Mueller, J. C. Wagner, and W. J. Marshall, An Approach for 

Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses –

Criticality (keff) Predictions, NUREG/CR-7109 (ORNL/TM-2011/514), prepared for the US 

Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, Tenn. 

(April 2012).

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Benchmark for Estimated Reactivity Margin from Fission Products and Minor Actinides in 

BWR Burnup Credit, NUREG/CR-7157 (ORNL/TM-2012/96), prepared for the US 

Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, Tenn. 

(February 2013).

9. D. E. Mueller, S. M. Bowman, W. J. Marshall, and J. M. Scaglione, Review and 

Prioritization of Technical Issues Related to Burnup Credit for BWR Fuel, NUREG/CR7158 (ORNL/TM-2012/261), prepared for the US Nuclear Regulatory Commission by 

Oak Ridge National Laboratory, Oak Ridge, Tenn. (February 2013).

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Proceedings of PHYSOR-2006, Vancouver, BC, Canada (September 10–14, 2006).

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NP-563, Electric Power Research Institute (June 1978).

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NP-562, Electric Power Research Institute (January 1979).
96

13. G. L. Holloway, J. E. Fawks, and B. W. Crawford, Core Design and Operating Data for 

Cycles 2 and 3 of Hatch 1, NP-2106, Electric Power Research Institute (February 1984).

14. R. Chang, et al., State-of-the-Art Reactor Consequence Analysis (SOARCA) Report,

NUREG-1935, US Nuclear Regulatory Commission (2012).

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Fuel at the Swedish Interim Storage Facility, Clab, Svensk Kärnbränslehanterig AB 

(SKB), R-05-62 (December 2006).

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5028092-00, DOC.20040109.0004, Framatome ANP (September 22, 2003).

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LaSalle Unit 1, B00000000-01717-5705-00138, Civilian Radioactive Waste Management 

System Management & Operating Contractor (September 1999).

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Quad Cities Unit 2, B00000000-01717-5705-00096 Revision 01, Civilian Radioactive 

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GN592, Vattenfall Report VNF-1002152744/02 (February 8, 2011).

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Calculations, CAL-DSU-NU-000002 Rev 00A, Office of Civilian Radioactive Waste 

Management (August 2003).

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Burnup in PWR Burnup Credit Analyses, NUREG/CR-6801 (ORNL/TM-2001/273), 

prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, 

Oak Ridge, Tenn. (March 2003).

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Assessment of Hypothetical Spent Fuel Reconfiguration in Spent Fuel Storage Casks 

and Transportation Packages, NUREG/CR-7203 (ORNL/TM-2013/92), prepared for the 

US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, 

Tenn. (September, 2015).

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Function of Burnup in BWR Used Nuclear Fuel, Master’s thesis, Georgia Institute of 

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Water Reactors, YAEC-1937, Yankee Atomic Electric Company (May 1997).
97

9 GLOSSARY

1D one dimensional

2D two dimensional

3D three dimensional

actinide only isotope set a limited set of isotopes with only actinide elements and oxygen

(Table 2.1 lists the isotopes in this set.)

actinide plus major 

fission products 

isotope set

a less limited set of isotopes that includes more actinide isotopes 

than the actinide only set, some major fission product isotopes, 

and oxygen. (Table 2.1 lists the isotopes in this set.)

AFP actinides and major fission products (isotope set)

AO actinide only

axial moderator 

density study

a series of calculations to determine the effect of various axial moderator 

density distributions during depletion on the keff value of the SNF loaded in 

a storage and/or transportation system

axial profile 

parameterization

determination of a single quantitative value to describe an axial moderator 

profile, typically for the purpose of identifying limiting moderator density 

profiles

BOC beginning of cycle

BOL beginning of life

BUC burnup credit

burnup a measure of the energy produced by a fuel assembly or reactor 

per unit mass of initial heavy metal (in this report, initial uranium)

BWR boiling water reactor

Cask generic term for a storage and/or transportation system

CFR Code of Federal Regulations

CSAS Criticality Safety Analysis Sequence (in SCALE)

distributed burnup 

profile

any nonuniform axial representation of accumulated burnup in a 

fuel assembly

DOM dominant or full fuel assembly lattice
98

end effect the difference in calculated keff for a spent fuel system based on 

modeling a distributed burnup profile instead of a uniform burnup 

profile. A positive end effect indicates that the use of a distributed 

burnup profile results in a higher calculated keff value.

EPRI Electric Power Research Institute

EOC end of cycle

EOL end of life

extended BWR BUC crediting reactivity reduction due to fuel depletion at higher 

burnups beyond peak reactivity

GE General Electric

HA high average (specific axial void fraction distribution in this study)

hockey stick profile axial burnup profile unique to a subset of the burnup profiles in the 

set considered in this report, caused by a longer top blanket which 

causes the increase in normalized burnup to start farther from the 

top end of the assembly than for the majority of the profiles 

considered

HH hypothetical history; refers to control blade usage histories

ISG Interim Staff Guidance

limiting conditions/

assumptions

assumptions that lead to higher keff values for fuel contained in a 

storage or transportation system

minimum density profile moderator density profile constructed by selecting the minimum 

moderator density in each node from the entire set of assembly 

profiles

MV most variable (specific axial void fraction distribution in this study)

NRC US Nuclear Regulatory Commission

ORNL Oak Ridge National Laboratory

Peak reactivity phenomenon in which the effective multiplication factor (keff) for an 

assembly or 2D slice is higher after some burnup than it is at BOL; 

a common feature of BWR assemblies caused by depletion of the 

burnable absorber at a more rapid rate than depletion of the fuel

peak reactivity analysis a class of criticality safety methods used to demonstrate safe 

storage of fuel assemblies, discussed in some depth in 

NUREG/CR-7194
99

PWR pressurized water reactor

RCA radiochemical assay

reactivity in this document, used interchangeably with keff; not meant in the 

strict technical sense of relative distance from the critical condition

RH realistic history; refers to control blade usage histories

relative burnup is the burnup of one assembly or region of an assembly in 

comparison to another assembly or assembly region.

relative reactivity reactivity of one assembly, region of an assembly, or model in 

comparison to another.

SKB Svensk Kärnbränslehantering AB (Swedish Nuclear Fuel and 

Waste Management Company)

SNF spent nuclear fuel

T-H thermal-hydraulic

temporal fidelity study a series of calculations to determine the frequency with which the 

axial moderator density fraction must be updated to yield accurate 

keff values for SNF contained in a storage or transportation system

TIP traveling in-core probe

VAN vanished fuel assembly lattice

APPENDIX A: REALISTIC CONTROL BLADE HISTORIES

A-1

APPENDIX A: REALISTIC CONTROL BLADE HISTORIES

This section provides plots of the realistic control blade histories. Ten realistic control blade 

histories have been extracted from the operating data and used throughout the analysis. The 

ten realistic histories (RHs) used in this report and depicted in this section represent control 

blade histories believed to be particularly limiting. That is, control blade histories were selected 

by choosing those that contain especially high integral control blade history (those inserted for a 

long period of time) and those in which control blades are inserted deeply into the core. These 

ten RHs were chosen after the hypothetical history (HH) simulations were completed, so some 

engineering judgment was gained in the process. The realistic control blade histories are plotted 

in Figures A.1–A.10. The plots contain the control blade insertion depth (or elevation) in 

percentage of the active fuel length versus the irradiation time in days. Because only one cycle 

of operating data exists, the control blade history for the single cycle has been repeated three 

times. Each cycle is modeled as 690 days, so the control blade history is repeated on that 

interval to a total time of 2,070 days to correspond to three cycles. 

Figure A.1 Control blade history RH1 (blade location 3,4)

Figure A.2 Control blade history RH2 (blade location 4,4)
A-2

Figure A.3 Control blade history RH3 (blade location 7,4)

Figure A.4 Control blade history RH4 (blade location 2,5)

Figure A.5 Control blade history RH5 (blade location 3,5)
A-3

Figure A.6 Control blade history RH6 (blade location 4,5)

Figure A.7 Control blade history RH7 (blade location 2,6)

Figure A.8 Control blade history RH8 (blade location 3,6)
A-4

Figure A.9 Control blade history RH9 (blade location 4,6)

Figure A.10 Control blade history RH10 (blade location 6,6)




NUREG/CR-7224 Axial Moderator Density Distributions, Control Blade Usage, and Axial Burnup 

Distributions for Extended BWR Burnup Credit