NUREG/CR-7240 

ORNL/TM- 2017/46

Impact of Operating 

Parameters on Extended 

BWR Burnup Credit 

Office of Nuclear Regulatory Research
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NUREG/CR-7240 

ORNL/TM-2017/46

Impact of Operating 

Parameters on Extended 

BWR Burnup Credit 

Manuscript Completed: June 2017

Date Published: January 2018

Prepared by: 

Brian J. Ade 

William (B. J.) Marshall 

Germina Ilas 

Benjamin R. Betzler 

Stephen M. Bowman 

Oak Ridge National Laboratory 

Managed by UT-Battelle, LLC 

Oak Ridge, TN 37831-6170 

Mourad Aissa, NRC Project Manager

NRC Job Code V6452 

Office of Nuclear Regulatory Research 

iii

ABSTRACT

The technical basis for extended boiling water reactor (BWR) burnup credit beyond peak reactivity for 

spent nuclear fuel (SNF) transportation and dry storage cask systems is under evaluation in a research 

program being conducted by Oak Ridge National Laboratory (ORNL) under contract with the NRC Office 

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

for BWR Fuel, identified and ranked parameters of importance. The highest ranking parameters (axial 

coolant density distributions, control blade usage, and axial burnup profiles) were studied in NUREG/

CR-7224, Axial Moderator Density Distributions, Control Blade Usage, and Axial Burnup Distributions for 

Extended BWR Burnup Credit. This report studies several parameters of medium importance, including 

fuel temperature, operating history, specific power, and bypass water density. A summary of the effect of 

each of these parameters is provided in this report. 

In addition, the correlation of various operating parameters is studied here. Because BWRs use control 

blades during operation, there can be significant changes to the local axial power shape, coolant density 

profile, and other parameters when the blades are inserted. Simultaneously using limiting conditions for 

all parameters may be unrealistic. When the control blades are inserted deeply into the reactor (a 

limiting condition), the power is reduced, and the void fraction decreases (a less limiting condition). This 

study identifies the impacts of using assembly-specific conditions for the control blade history, coolant 

density profile, burnup profile, and fuel temperature profile. Cask reactivity is reduced by using 

assembly-specific operating conditions versus combining limiting conditions for the individual 

parameters of interest, but the magnitude of the reactivity reduction varies based on each assembly and 

its operating conditions. Finally, a summary of the present studies is presented within the context of 

previous studies. The conclusions summarize the technical basis for extended BWR burnup credit as a 

result of the past and present studies.

v 

TABLE OF CONTENTS 

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

TABLE OF CONTENTS........................................................................................................................v

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

LIST OF TABLES................................................................................................................................. ix

EXECUTIVE SUMMARY..................................................................................................................... .xi

ABBREVIATIONS AND ACRONYMS.............................................................................................. .xiii

1 INTRODUCTION.............................................................................................................................1-1

2 CODES, METHODS, AND MODELS .............................................................................................2-1

2.1 Codes and Methods..................................................................................................................2-1

2.1.1 TRITON...........................................................................................................................2-2

2.1.2 ORIGEN..........................................................................................................................2-3

2.1.3 KENO..............................................................................................................................2-3

2.2 Models.......................................................................................................................................2-4

2.2.1 GBC-68 Cask..................................................................................................................2-4

2.2.2 GE14...............................................................................................................................2-7

3 IMPACT OF OPERATING PARAMETERS ON CASK REACTIVITY ..........................................3-1

3.1 Background...............................................................................................................................3-1

3.2 Description of Studies...............................................................................................................3-2

3.2.1 Fuel Temperature............................................................................................................3-2

3.2.2 Bypass Water Density.....................................................................................................3-4

3.2.3 Specific Power.................................................................................................................3-4

3.2.4 Operating History.............................................................................................................3-5

3.3 Results.....................................................................................................................................3-11

3.3.1 Fuel Temperature...........................................................................................................3-11

3.3.2 Bypass Water Density................................................................................................. ...3-15

3.3.3 Specific Power................................................................................................................3-17

3.3.4 Operating History ...........................................................................................................3-18

3.4 Summary and Recommendations...........................................................................................3-21

4 IMPACT OF ASSEMBLY-SPECIFIC CONDITIONS ON CASK REACTIVITY...............................4-1

4.1 Background................................................................................................................................4-1

4.2 Methodology ..............................................................................................................................4-1

4.2.1 Base Conditions ...............................................................................................................4-1

4.2.2 Assembly-Specific Conditions..........................................................................................4-2

4.3 Results.......................................................................................................................................4-5

4.4 Summary and Recommendations...........................................................................................4-19

5 CONCLUSIONS.............................................................................................................................. .5-1

5.1 Summary of Previous Studies...................................................................................................5-1 

3.4.1 Fuel Temperature..............................................................................................................3-21

3.4.2 Bypass Water Density.......................................................................................................3-21

3.4.3 Specific Power...................................................................................................................3-22

3.4.4 Operating History...............................................................................................................3-22

5.1.1 Axial Coolant Density Distributions......................................................................................5-1

5.1.2 Control Blade Usage............................................................................................................5-1

5.1.3 Axial Burnup Profiles............................................................................................................5-1
6 REFERENCES..................................................................................................................................................6-1

5.3 Assembly-Specific Conditions....................................................................................................................5-3

5.2 Operating Paramaters................................................................................................................................5-2

5.2.1 Fuel Temperature.............................................................................................................................5-2

5.2.2 Bypass Water Density......................................................................................................................5-3

5.2.3 Specific Power...................................................................................................................................5-3

5.2.4 Operating History...............................................................................................................................5-3

 vi
vii

LIST OF FIGURES 

Figure 1 SCALE sequences and modules used for depletion and criticality calculations 

in this report................................................................................................................ 2-2

Figure 2 Radial view of the GBC-68 cask model in KENO in the VAN lattice .......................... 2-5

Figure 3 Axial view of GBC-68 cask KENO model ................................................................... 2-6

Figure 4 TRITON model of the (a) DOM and (b) VAN lattice ................................................... 2-7

Figure 5 (a) DOM lattice and (b) VAN lattice, both in storage cell in GBC-68 .......................... 2-8

Figure 6 (a) Axial coolant void profile and (b) axial burnup profile............................................ 3-2

Figure 7 Fuel temperature distributions for all assemblies at BOC (left) and EOC (right). 

The bold black line represents the core-average fuel temperature profile.................. 3-3

Figure 8 Burnup distribution at EOC for first-, second-, and third-cycle fuel assemblies.......... 3-8

Figure 9 Power history for Forsmark 3 assembly ..................................................................... 3-9

Figure 10 Number of irradiation cycles for BWR assemblies in the GC-859 database [17] ..... 3-10

Figure 11 Effect of fuel temperature on cask keff (AO isotope set).......................................... 3-11

Figure 12 Effect of fuel temperature on cask keff (AFP isotope set) ........................................ 3-12

Figure 13 Effect of fuel temperature on 235U and 239Pu in the non-Gd bearing fuel pins ...........3-13

Figure 14 Cycle-average fuel temperature profiles selected to analyze the effect of axial 

fuel temperature shape on cask reactivity ................................................................ 3-14

Figure 15 Effect of bypass water density on cask keff (AO isotope set) .................................... 3-15

Figure 16 Effect of bypass water density on cask keff (AFP isotope set) .................................. 3-15

Figure 17 Effect of bypass water density on 235U and 239Pu node-averaged atomic density .... 3-17

Figure 18 Effect of specific power on cask reactivity ................................................................ 3-18

Figure 19 Effect of operating history on cask reactivity ............................................................ 3-20

Figure 20 Base conditions used for the coolant void fraction, burnup, and fuel temperature 

axial profiles................................................................................................................ 4-2

Figure 21 Base and assembly-specific cycle-average conditions for the coolant void fraction, 

burnup, and fuel temperature axial profiles ................................................................ 4-3

Figure 22 Control blade insertion depth as a function of time for assembly A1.......................... 4-5

Figure 23 Control blade insertion depth as a function of time for assembly A1.......................... 4-5

Figure 24 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A1 during time interval 1................................ 4-7

Figure 25 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A1 during time interval 2................................ 4-7

Figure 26 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A1 during time interval 3................................ 4-7

Figure 27 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A1 during time interval 4................................ 4-8

Figure 28 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A1 during time interval 5................................ 4-8

Figure 29 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 1................................ 4-8

Figure 30 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 2................................ 4-9

Figure 31 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 3................................ 4-9

Figure 32 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 4................................ 4-9

Figure 33 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 5.............................. 4-10
viii

Figure 34 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 6.............................. 4-10

Figure 35 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 7.............................. 4-10

Figure 36 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 8.............................. 4-11

Figure 37 Cask ∆keff values for the AO (left) and AFP (right) isotope sets at an assembly 

average discharge burnup of 25 GWd/MTHM.......................................................... 4-13

Figure 38 Cask ∆keff values for the AO (left) and AFP (right) isotope sets at an assembly 

average discharge burnup of 50 GWd/MTHM.......................................................... 4-14

Figure 39 Axial fission distribution for assembly A1 CVBT case at assembly average 

discharge burnup values of 25 and 50 GWd/MTHM for the AO and AFP 

isotope sets .............................................................................................................. 4-16

Figure 40 Comparison of the base burnup profile and assembly-specific burnup profile 

for A1........................................................................................................................4-17

Figure 41 235U (left), 239Pu (middle), and 155Gd (right) concentration for A1 CVBT case at 

25 and 50 GWd/MTHM ............................................................................................ 4-17

Figure 42 235U (left), 239Pu (right), assembly A1 using the base and assembly-specific 

burnup profiles at 50 GWd/MTHM............................................................................ 4-18
ix

LIST OF TABLES 

Table 1 Isotopes included in the AO and AFP isotope sets .............................................. 2-4

Table 2 Operating history scenarios.................................................................................. 3-6

Table 3 Burnup characteristics derived from core-follow data........................................... 3-7

Table 4 Cask reactivity as a function of fuel temperature................................................ 3-12

Table 5 Cask reactivity as function of bypass water density reduction............................ 3-16

Table 6 Cask keff as function of change in specific power ............................................... 3-18

Table 7 Cask reactivity as function of operating history .................................................. 3-19

Table 8 Summary of conditions used for correlated parameter calculations..................... 4-4

Table 9 Cask reactivity data for the AO isotope set at 25 GWd/MTHM .......................... 4-12

Table 10 Cask reactivity data for the AFP isotope set at 25 GWd/MTHM......................... 4-12

Table 11 Cask reactivity data for the AO isotope set at 50 GWd/MTHM .......................... 4-13

Table 12 Cask reactivity data for the AFP isotope set at 50 GWd/MTHM......................... 4-14

Table 13 Summary of the impact of studied parameters on cask reactivity ........................ 5-5

xi

EXECUTIVE SUMMARY 

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 

per the requirements of Title 10 of the Code of Federal Regulations (10 CFR) Parts 71 and 72. 

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, Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel 

in Transportation and Storage Casks. 

The technical basis for extended BWR BUC (beyond peak reactivity) is under evaluation in a 

research program being conducted by Oak Ridge National Laboratory (ORNL) under contract with 

the NRC Office of Research. NUREG/CR-7158, Review and Prioritization of Technical Issues 

Related to Burnup Credit for BWR Fuel, identifies and ranks parameters of importance to BWR 

BUC. NUREG/CR-7224, Axial Moderator Density Distributions, Control Blade Usage, and Axial 

Burnup Distributions for Extended BWR Burnup Credit, summarizes impacts of the three 

parameters of highest importance: (1) axial coolant density distributions, (2) control blade usage, 

and (3) axial burnup profiles on extended BWR BUC. 

NUREG/CR-7158 identifies several other reactor operating parameters of moderate importance 

that warranted in-depth analysis, such as fuel temperature, specific power, operating history, 

bypass water density, and the correlation of operating conditions. Impacts of these operating 

conditions are documented herein. Assessments were performed using a 10 × 10 GE14 fuel 

assembly model in the GBC-68 cask model. This model has served as the reference configuration 

in previous studies. Assembly depletion, decay, and cask criticality simulations were performed 

using the SCALE code system. 

Fuel temperature, specific power, power history, and bypass water density were independently 

varied for the assembly depletion calculations, while all other parameters were held constant so 

the individual impact of each of the varied parameters on cask reactivity could be ascertained. 

Results indicated that impacts of these four factors are small compared to previously studied 

parameters: coolant density, control blade exposure, and burnup profile. 

To study the importance of the correlation of operating parameters, base conditions were selected 

that result in limiting cask reactivity estimates for the assembly-specific conditions of interest

(control blade usage, coolant density, axial burnup profile, and fuel temperature). Assemblyspecific conditions were substituted for the base conditions to determine the impact of using 

assembly-specific (correlated) data for the control blade, coolant density, burnup profile, and fuel 

temperature. Results indicate that cask reactivity is reduced by using assembly-specific conditions 

versus conditions that are individually limiting. However, the magnitude of this reduction is highly 

dependent on the chosen assembly and its specific conditions. 

Results of these studies provide specific insight on the significance of changes in the operating 

parameters considered and their effects on cask reactivity. Detailed data used in these studies 

were available from a single source and covered a single cycle of operation from a single plant, 

so specific recommendations on how to handle operating parameters within extended BUC 

analyses have not been made. Future work can be performed to demonstrate wider applicability 

of these conclusions if or when additional data become available.

xiii

ABBREVIATIONS, ACRONYMS, AND TERMINOLOGY 

1D 

2D

3D

One-Dimensional 

Two-Dimensional 

Three-Dimensional 

actinide-only (AO) isotope set

a limited set of isotopes that include only actinide elements and oxygen (see Table 1)

actinide-plus-fission-product (AFP) isotope set 

a set of isotopes that is less limited than an actinide-only isotope set, including more 

actinide isotopes than the actinide-only set, some major fission product isotopes, and 

oxygen (see Table 1, taken from NUREG/CR-7108)

AFP Actinides and major Fission Products 

AO actinide only

assembly-specific conditions

a set of operating conditions experienced by a specific fuel assembly

assembly-specific conditions study

a series of calculations used to determine the effect of simulating assembly-specific 

operating conditions for the control blade history, coolant density profile, and axial burnup 

profile; used lieu of limiting but uncorrelated data for these parameters. 

axial coolant density study

a series of calculations used to determine the effect of various axial coolant density 

distributions during depletion on the keff value of the SNF uniformly loaded in a storage 

and/or transportation system.

BA Burnable Absorber 

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 a storage and/or transportation system for fuel assemblies 

CFR Code of Federal Regulations

correlated parameters

assembly conditions that are connected; the term is used interchangeably with assemblyspecific conditions. 

CSAS Criticality Safety Analysis Sequence in SCALE

CV case ID (control blade + void fraction = CV) that uses assembly-specific conditions for the 

control blade history and coolant density (void fraction), while base conditions are used for 

the burnup profile and fuel temperature. 

CVB case ID (control blade + void fraction + burnup profile = CVB) that uses assembly-specific 

conditions for control blade history, coolant density, and burnup profile, while the base fuel 

temperature is used. 
xiv

CVBT case ID (control blade + void fraction + burnup profile + fuel temperature = CVBT) that

uses assembly-specific conditions for all parameters being tested. 

distributed burnup profile 

any nonuniform axial representation of accumulated burnup in a fuel assembly 

DOM Dominant or full fuel assembly lattice 

end effect 

the difference in the calculated keff for an SNF 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.

ENDF Evaluated Nuclear Data File 

EOC End Of Cycle 

EOL End Of Life 

extended BWR BUC

crediting reactivity reduction due to fuel depletion, and potentially credtiting buildup of

neutron-absorbing nuclides at burnups beyond peak reactivity burnup

GE General Electric Company 

GWd Gigawatt day 

ISG Interim Staff Guidance 

KENO SCALE’s 3D Monte Carlo criticality transport module 

limiting conditions/assumptions

assumptions which lead to higher keff values for the fuel contained in a storage or 

transportation system

LEU Low Enriched Uranium 

MTHM Metric Tons of Heavy Metal 

MTU Metric Tons of Uranium; in LEU systems, MTU and MTHM are equivalent 

MW Megawatt 

MWd Megawatt Day 

NEWT SCALE’s 2D neutron transport solver used in the TRITON sequence

NRC US Nuclear Regulatory Commission

OH Operating History 

ORIGEN

Oak Ridge Isotope Generation, a SCALE module used to simulate irradiation and decay of 

materials

ORNL Oak Ridge National Laboratory

pcm percent mille, equivalent to 10-5

peak reactivity

a condition in which the effective multiplication factor (keff) for an assembly or a 2D slice of 

the assembly is higher at some burnup than it is at BOL. This is a common feature of BWR 

assemblies caused by depletion of the BA 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 

(see NUREG/CR-7194). 

PWR Pressurized Water Reactor 
xv

reactivity

in this document, a term used interchangeably with keff, not meant in the strict technical 

sense of relative distance from the critical condition

relative burnup

burnup of an assembly or region of an assembly compared to another assembly or region

relative reactivity

reactivity of an assembly, region of an assembly, or model compared to another assembly,

region, or model 

SNF Spent Nuclear Fuel 

TIP Traveling In-core Probe 

TRITON

SCALE’s arbitrary-geometry depletion sequence that automates cross section processing, 

neutron transport, and depletion calculations for 1D, 2D, or 3D geometries. 

uniform profile

an axial profile that is a single, constant value over the entire axial length 

VAN Vanished fuel assembly lattice 

XSPROC

SCALE’s cross section processing module

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 

per the requirements of Title 10 of the Code of Federal Regulations (10 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. 

BUC for boiling water reactor (BWR) SNF is not addressed in ISG-8, but a technical basis for 

peak reactivity BWR BUC methods is provided in NUREG/CR-7194 [[3] ]. Peak reactivity occurs

when the effective multiplication factor (keff) for a lattice—a two-dimensional (2D) axial slice of the 

assembly—reaches its highest value at some burnup beyond beginning of life (BOL). This is a

common feature of BWR assemblies caused by depletion of the burnable absorber (BA) at a more 

rapid rate than depletion of the fuel. There is potential interest within the nuclear industry to extend 

BWR BUC to higher burnups beyond peak reactivity burnup. In this document, extended BWR

BUC is defined as credit for the reduction in reactivity at burnups greater than the peak reactivity

burnup. Studies assessing the impacts of axial coolant density distributions, control blade usage,

and axial burnup profiles on extended BWR BUC are documented in NUREG/CR-7224 [4]. The 

impact of each of these phenomena was evaluated to identify limiting conditions and assumptions

for use in extended BWR BUC analyses.

Analysis of the time-dependent nature of the axial coolant density in NUREG/CR-7224 indicated 

that use of cycle-averaged coolant density values (averaged in time, not in space) results in a 

relatively small bias less than 0.25% Δkeff. The axial coolant density study highlights the need to 

use a true axial coolant density profile, as the importance of the axial top portion of a spent BWR

fuel assembly greatly outweighs the bottom and middle portions. Use of a uniform core-averaged 

coolant density profile (e.g., 40% void), or use of a graded profile constructed by averaging the 

coolant density in each axial node over multiple assemblies results in nonconservative SNF cask

reactivity values. Limiting profiles with low coolant densities at the axial top of the fuel assembly

can be constructed by selecting a limiting axial coolant density profile from available data, or they

can be constructed by selecting the minimum density in each axial node from a collection of

applicable actual profiles.

BWRs are operated using the control blades during operation as a means of reactivity control, so 

the usage of the control blades impacts SNF reactivity. Investigations to study the impact of

control blade usage are documented in NUREG/CR-7224, indicated that control blade insertion of

less than 50% into the core has almost no impact on cask reactivity. The control blade study also 

indicated that the limiting conditions are those that result in the control blade being inserted deeply

into the core for long periods of time, especially near the end of life (EOL). Although it is unrealistic

to fully insert the control blades, full- or near-full-depth control blade insertion for the entire 

irradiation results in increases in cask reactivity of 4.0–4.5% Δkeff compared to no control blade 

insertion. Based on the study of realistic control blade histories, a reactivity penalty of 0.6–1.2%

Δkeff (as compared to no control blade insertion) may be sufficient to cover possible operating

histories.
1-2

As NUREG/CR-7224 indicates, the effect of axial burnup profiles on BWR SNF is significant. The 

cask keff values resulting from the profiles used in that study ranged up to 7.6% Δkeff. Low burnup 

near the top end of the fuel assembly results in a significant end effect, leading to high cask keff

sensitivity to the selected burnup profile. Distributed rather than uniform burnup profiles should be 

used for analysis, as end effects of up to 12.7% Δkeff were observed.

NUREG/CR-7158 [5], Review and Prioritization of Technical Issues Related to Burnup Credit for

BWR Fuel, indicates that the topics studied in NUREG/CR-7224—axial coolant density profile,

control blade history, and burnup profile—are of high importance. NUREG/CR-7158 indicates that

there are several other parameters of importance to BWR BUC, including fuel temperature,

operating history, specific power, and bypass water density. The effect of each of these 

parameters is summarized in Section 3.

NUREG/CR-7158 also indicates that the correlation of various operating parameters, or conditions

experienced by an individual assembly, warrant further study. Because BWRs use control blades

during operation, significant changes to the local axial power shape, coolant density profile, and

other parameters can result when the blades are inserted. Previous studies [4] separately

examined the reactor’s operating parameters that impact fuel cask reactivity. These studies

identified limiting conditions for fuel cask reactivity or the direction of trends with cask reactivity

(e.g., lower coolant densities result in higher cask reactivity). However, it may be unrealistic to use 

limiting conditions simultaneously for all parameters. When the control blades are inserted deep 

into the reactor (a limiting condition), then the power is reduced, and the void fraction decreases

(a less limiting condition). The study documented in Section 4 identifies the impacts of using 

assembly-specific conditions for the control blade history, coolant density profile, burnup profile,

and fuel temperature profile. Cask reactivity is reduced by using assembly-specific operating

conditions rather than combining limiting conditions for the individual parameters of interest, but

the magnitude of the reactivity reduction varies based on each assembly and its operating

conditions.

Finally, Section 5 summarizes the present studies within the context of the previous studies cited 

above. The conclusions summarize the technical basis for extended BWR BUC as a result of the 

past and present studies.
2-1

CODES, METHODS, AND MODELS 

Codes and Methods 

The analyses documented in this report were performed using a series of codes and models to 

simulate fuel assembly irradiation and SNF reactivity in an SNF storage or transportation cask. 

The codes, associated data, and models used are summarized in this section. The assembly and 

cask configurations used in these studies are consistent with those used in NUREG/CR-7224 [4].

The computational procedure included the following main steps:

1. Conduct depletion simulation to determine the isotopic composition of the irradiated fuel 

assembly at its discharge from the reactor.

2. Conduct decay simulation of the discharged assembly’s isotopic composition to determine 

the nuclides present at five years of cooling time after discharge from the reactor.

3. Perform a criticality calculation for the GBC-68 cask to determine the effective 

multiplication constant (keff) using the isotopic composition of the SNF obtained in step 2. 

These computational steps and the SCALE modules and codes involved are illustrated in Figure 1 

and are further described in this section. Version 6.2.1 of the SCALE code system [6] was used 

for all calculations in this work. 
2-2

Figure 1 SCALE sequences and modules used for depletion and criticality calculations in 

this report 

TRITON 

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

and uncertainty analysis [8,9]. In this work, the TRITON t-depl sequence was used to simulate the 

assembly depletion history via a series of coupled neutron transport and depletion calculations. As 

illustrated in Figure 1, the TRITON flow chart includes automated problem-dependent cross 

section processing (XSPROC), multigroup deterministic neutron transport (NEWT), and depletion 

(ORIGEN) calculations over a series of time steps to cover the assembly irradiation history from 

the onset of its irradiation to the time of its discharge from reactor. 

Through collaboration between NRC and Oak Ridge National Laboratory (ORNL) , the ORNL 

BWR BUC project obtained proprietary operating data for a single cycle of a BWR core. The data 

include inlet and outlet conditions, traveling in-core probe (TIP) data, and simulated core-follow

data for every fuel assembly in the reactor. The data were obtained from a recent cycle that 

included four different modern BWR fuel assembly design types. Each fuel assembly was

modeled with 25 different axial nodes, and the 690-day cycle was simulated using more than 240 

time steps. The lengths of the time steps vary slightly, but all steps are less than 5 effective full 

power days long. State variables needed for the studies documented here were extracted from 

the simulated data.
2-3

TRITON two-dimensional (2D) simulations were performed for each axial slice (node) defined in 

the core-follow simulations [4] from which the assembly design and operating data were taken (25 

nodes in total). For consistency, the same basic modeling assumptions and options used in 

previous calculations [4] were also used in the TRITON calculations for this work, as summarized 

below:

• The transport model includes a set of 94 nuclides corresponding to the “addnux=2” option 

(default in TRITON), while more than 2,000 nuclides are tracked by the ORIGEN depletion 

and decay calculations.

• The gadolinium-bearing fuel rods in the assembly are modeled with seven equal-area radial 

rings to accurately capture the radial dependence of the gadolinium depletion [8].

• The 252-group ENDF/B-VII.1 neutron cross section library is used for neutron transport with 

the NEWT code.

• The detailed power history is modeled in the TRITON calculations by directly specifying the 

power in the TRITON depletion specification. The timetable block, which is used extensively in 

the TRITON calculations, modifies properties of selected materials in the model during 

depletion. In this study, the timetable block is used to adjust coolant densities, fuel 

temperatures, and the presence or absence of the control blade during depletion calculations. 

ORIGEN 

ORIGEN is the SCALE depletion and decay simulation code used to determine time-dependent 

nuclide concentrations, activities, and radiation source terms for more than 2,000 isotopes 

involved in transmutation, fission, and radioactive decay processes [9]. In addition to its use in this 

work as part of the TRITON depletion sequence, ORIGEN is also used to perform standalone 

radioactive decay simulations to determine the change in isotopic composition of the assembly’s 

fuel after its discharge from the reactor. The decay library used with ORIGEN is based on

ENDF/B-VII.1 data [10].

 KENO 

The Criticality Safety Analysis Sequence (CSAS)/KENO is used to perform reactivity calculations 

for the GBC-68 cask model. 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 are performed using the transport code KENO V.a and the 

252-group neutron cross section library based on ENDF/B-VII.1 data.

Two sets of nuclides are 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 [11] and are the same as those 

typically used when performing PWR BUC calculations. The same isotope sets are used for BWR 

BUC studies because the same nuclides result from fission in both PWR and BWR types of light 

water reactors. Table 1 provides the BUC nuclides considered in the AO and AFP sets. 
2-4

Table 1 Isotopes included in the AO and AFP isotope sets 

10 AO isotopes 

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

29 AFP Isotopes

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

 

Models 

GBC-68 Cask 

The GBC-68 computational benchmark model was developed in NUREG/CR-7157 [12] 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 in the General Electric Company 

(GE)14 fuel assemblies. Partial length rods are truncated at the appropriate elevation so that both 

the full lattice (referred to as full or dominant and abbreviated as DOM) and the vanished lattice

(VAN) are included explicitly in the KENO model. Section 2.2.2 includes further discussion of the 

GE14 assembly modeling. The fuel assembly channel model is simplified in KENO and is

represented with constant thickness and squared corners. All fuel assemblies in the GBC-68 cask 

model are assumed to contain fuel with identical compositions and irradiation histories. KENO 

calculations performed with depleted fuel compositions generated by TRITON and ORIGEN 

assume a single average composition for fuel without gadolinium, as well as seven unique 

compositions for the rings modeling the gadolinium fuel pins in each axial node. 

All KENO models contain 25 axial nodes, each of which is 6 inches in length (15.24 cm). Figure 2 

shows a radial view of the GBC-68 half-cask model depicting the cask body, basket, and fuel 

assemblies. Figure 3 shows an axial view of the model with each unique axial fuel composition 

presented in a different color. 
2-5

Figure 2 Radial view of the GBC-68 cask model in KENO in the VAN lattice 

Stainless steel

Water
2-6

Figure 3 Axial view of GBC-68 cask KENO model 

VAN lattice

66 in (167.64cm)

DOM lattice

84 in (213.36cm)
2-7

GE14 

GE14 is the only fuel assembly design used in these studies. It 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 enrichments and gadolinium loading. 

Due to the presence of partial length fuel rods which terminate at approximately half the total 

height of the fuel assembly, the GE14 fuel assembly contains two primary axial levels which are 

known as zones. These two axial zones are the DOM (dominant) and the VAN (vanished) lattices. 

A 2D slice through one of these axial zones is referred to as a lattice. The DOM lattice has fuel 

rods 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 removed or vanished from the lattice. TRITON 

representations of the DOM and VAN lattices are shown in Figure 4. 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 are shown in Figure 5. Axial 

enrichment zoning is not modeled for any calculations presented in this report; rather, a single 

enrichment of 4.5 wt% 235U is used throughout the entire axial length of the fuel assembly.

 

(a) (b)

Figure 4 TRITON model of the (a) DOM and (b) VAN lattice 
2-8

(a) (b)

Figure 5 (a) DOM lattice and (b) VAN lattice, both in storage cell in GBC-68 

The GE14 fuel assembly was chosen for these studies because it is the most common fuel 

assembly type used in current US BWRs. It contains advanced geometry features commonly 

seen in modern BWR fuel assemblies (e.g., water rods, part-length rods). It is commonly loaded 

with pins enriched to near 5.0 wt % 235U, and it 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 [5] showed 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 [5], 

but coolant density distribution, control blade history, axial burnup profile, and other effects 

examined in this study are expected to be largely independent of assembly lattice size. 

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

core-follow data described in Section 3 of NUREG/CR-7224 [4]. All TRITON depletion calculations 

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

single assembly design is used throughout the calculations to assess the important effects of 

operating parameters and assembly-specific conditions independent of any effects that may have 

been caused by differing fuel or absorber loadings. Additional enrichments, gadolinium loadings, 

or gadolinium-bearing pin patterns are not considered in this report, but they have been previously 

analyzed [3]. The items examined in this report are not expected to have a significant sensitivity to 

differing fuel loadings or loading patterns. 
3-1

IMPACT OF OPERATING PARAMETERS ON CASK REACTIVITY 

Background 

Previous review and prioritization of technical issues related to BUC for BWR SNF [5] resulted in 

identifying phenomena and parameters important to BWR BUC methodology and providing 

recommendations for further BWR BUC research. Three of the research objectives categorized as 

high priorities were (1) identification and use of axial burnup profiles, (2) treatment of axial coolant

density profile, and (3) treatment of control blade usage during depletion. These three topics have 

been investigated and documented [4]. Another priority recommendation [5] for BWR BUC, 

categorized as medium impact, consisted of investigation of reactor operating parameters in fuel 

depletion calculations. Fuel temperature, specific power, and bypass water density were listed as 

candidates for future studies. These three latter parameters are included, along with operating 

history, in the studies discussed in this section of the report. 

To study these parameters, some basic assumptions are required. As previously stated, the GE14 

fuel assembly and the GBC-68 SNF cask model have been used for all calculations. The axial 

void fraction and axial burnup profiles were assumed to be the same as those used in 

NUREG/CR-7224 [4] and are shown in Figure 6. Actual nodal average burnup values are given in 

Figure 6, which are used directly in the studies in this section as no burnup variation is considered 

(assembly average burnup = 45.2 GWd/MTHM). Previous studies [4] and the assembly-specific 

conditions study documented in Section 4 conserve the shape of the burnup profile, but they scale 

the values to facilitate comparison to other burnup profiles. 
3-2

 (a) Void fraction profile (b) Burnup profile

Figure 6 (a) Axial coolant void profile and (b) axial burnup profile 

Description of Studies 

Fuel Temperature 

The main fuel temperature study is meant to determine the sensitivity of fuel cask reactivity to 

changes in fuel temperature. A limited analysis of the effect of the axial fuel temperature profile 

was conducted to determine if axially uniform or axially profiled fuel temperatures should be used 

in this primary study. The results of this study indicate that the sensitivity of the cask’s reactivity to 

the fuel temperature profile (i.e., axial shape) is very small (less than 0.1% ∆keff). As a result, the 

fuel temperature study documented in this section uses a single fuel temperature in all fuel rods, 

with no axial or radial variation.

Nine values are used for the fuel temperature sensitivity studies, covering a range from 596.1 to 

1,296.1 K in 100 K increments. A nodal fuel temperature of 796.1 K was reported as the core- and 

cycle-averaged temperature over all fuel assemblies in the available core-follow data for a BWR 

core’s single cycle [4]. This temperature was used as the nominal value for previous studies 

conducted in this project [3,4], and it was also used as a basis for selecting the fuel temperatures 

in this study. 

The range used for the fuel temperature in this work includes the range of temperatures available 

for all assemblies in the core-follow data at all time steps in the cycle [4]. The overall maximum 
3-3

nodal fuel temperature in the core-follow data is less than 1,100 K at any time point during the 

cycle. However, to cover higher temperatures that may occur during operation [13] and to ensure

consistency with data used previously in similar BWR studies [5,14], the range was extended to 

~1,300 K. 

Increased fuel temperature during BWR depletion calculations leads to increased production of 

actinides important to BUC (239Pu in particular) [5,14]. Consequently, it leads to an increase in 

cask reactivity. This effect is primarily due to the change in the neutronic environment by 

resonance Doppler broadening of 238U cross sections with increasing temperature that leads to 

increased 239Pu production. 

The distributions of fuel temperatures for core-follow data in all 624 assemblies at beginning of 

cycle (BOC) and end of cycle (EOC) are illustrated in Figure 7. In this context, BOC and EOC 

correspond to the first and last full-power steps in the cycle. The cycle- and core-average fuel 

temperature profile is plotted as a bold black line. The atypical shapes in the BOC fuel 

temperature distributions are due to the presence of control blades inserted directly adjacent to 

those fuel assemblies. 

Figure 7 Fuel temperature distributions for all assemblies at BOC (left) and EOC (right). 

The bold black line represents the core-average fuel temperature profile 
3-4

Bypass Water Density 

Consistent with NUREG/CR-7224, the nominal value of the bypass water density for the cycle of 

operation studied is 0.73549 g/cm3

, which corresponds to the subcooled water circulated outside 

the assembly channel and within the two large water rods in the assembly. This bypass water is 

shown in pink in Figure 4. No relevant published data were found regarding the axial shape or the 

range of bypass water density variations that may occur under normal BWR operation. For that 

reason, no axial variation is considered for this study. To quantify the impact due to changes in 

the bypass density during operation, the sensitivity study discussed here considered a range of 

values between the nominal density and 10% less than the nominal density. 

For sensitivity studies in this work, 11 values were used for the bypass water density to cover a 

range from nominal to a 10% density reduction in 1% increments. A decrease in bypass water 

density will cause hardening of the neutron spectrum and consequently an increase in plutonium 

production, and it will also affect the production of other actinides and fission products sensitive to 

changes in the neutron spectrum. The magnitude of this effect will depend on the magnitude of

the change in water density. As previously stated, published data quantifying the actual range of 

bypass density values was not found. However, a 10% reduction in bypass density is expected to 

bound the variation in bypass density for normal operation. 

Specific Power 

The assembly depletion simulations in this report account for the axial variation of the assembly 

burnup, which is illustrated in Figure 6. Given the linear relationship between specific power 

(MW/MTHM) and burnup (MWd/MTHM) for the assembly, the specific power axial profile 

averaged over life and the burnup axial profile at discharge are the same shape (i.e., the 

normalized axial distribution is the same). This study was undertaken to determine the cask 

reactivity sensitivity to changes in the specific power independent of the shape of the burnup 

profile and independent of the power history—to determine the cask reactivity sensitivity to the 

rate at which the assembly reaches a certain burnup value. 

To achieve this, the specific power sensitivity study considered 90% and 110% specific power 

variations relative to then nominal power. The same relative power distribution is used in all three 

cases: (1) nominal, (2) 90% of nominal, and (3) 110% of nominal. However, the specific power in 

a given node is adjusted to correspond to 100%, 90%, or 110% relative to its value for the nominal 

case. The same number of depletion steps is used in all three cases. Because the assembly 

burnup at discharge is the same in these three cases, the change in specific power requires the 

change in the total irradiation time to conserve the burnup. For the nominal case [4], the total 

irradiation time is 2,070 days (690 days per cycle × 3 cycles). For cases with specific power at 

90% relative to nominal, the total irradiation time is 2,300 days, and for cases with specific power 

at 110% relative to nominal, the total irradiation time is 1,882 days. Derivation of the irradiation 

times for each of the three cases is described by the equation shown below:

pp0tt0 = kk 0tt1 ⇒ tt1 = tt0

kk ,

where pp0 and tt0 are the specific power and irradiation time for the nominal case, kk is the specific 

power multiplier (0.9 or 1.1) for the perturbed case, and tt1 is the irradiation time for the perturbed 

case.
3-5

Operating History 

In the context of BUC applications, the term operating history usually refers to cycle length, 

downtime between cycles, and power level for each cycle. The operating history scenarios 

investigated in this study (Table 2) are used to assess the effect of the power level and downtime 

for a given assembly burnup at discharge. Detailed analysis of the effect of the burnup profile is 

provided in NUREG/CR-7224 [4]. This study is focused on determining the cask reactivity 

sensitivity to variation of power and downtime throughout the irradiation history. 

Nominal conditions for the axial coolant density and axial burnup profile (Figure 6) are used for all 

assembly modeling parameters for the ten operating histories under consideration. Only assembly 

power history is varied for operating scenarios OH-1 through OH-10—the total discharge burnup 

for each case is the same. The power level per irradiation cycle (and equivalently the cycle 

burnup) and the decay time between irradiation cycles are varied so that the sum of the total 

burnup at EOL is the same for all cases. Table 2 shows that the average of the power of the three 

cycles is 100%, which results in equivalent burnup for all cases. OH-1 through OH-9 were 

constructed based on engineering judgment, while the OH-10 operating scenario was derived 

from available cycle-follow data and is discussed in detail at the end of this section.

Histories OH-1 through OH-3 are used to assess the impact of downtimes between cycles. 

Specific power is the same in each of the three cycles for these histories. History OH-1 represents 

continuous operation at full power with no downtime and is used as a baseline for comparison in 

this section. History OH-1 was used for all other sensitivity studies discussed in Section 3.2. 

History OH-2, which uses typical 30-day downtimes, is intended to assess the effect of using 

typical downtime versus excluding any downtime between cycles. History OH-3 is used to assess 

the impact of long downtime (720 days in this case) preceding the last irradiation cycle of an 

assembly before its discharge. One example of this scenario is an assembly that is moved to a 

storage pool after two irradiation cycles, stored in the pool for approximately two years, and then 

irradiated for a third cycle before being finally discharged. 

Histories OH-4 through OH-7 are used to assess the effect of power variation across the three 

cycles when all the following factors are the same: (1) downtime between cycles, (2) assembly 

burnup at discharge from the reactor, and (3) average power over the assembly’s three cycles of 

irradiation (sum of % power values in Table 2 is 300%). Histories OH-4, OH-5, and OH-6 (highest 

power in first or second cycle, lowest power in third cycle) are considered representative of typical 

operation for most assemblies, whereas OH-7 (highest power in third cycle) is considered

atypical. Scenarios with the highest power in the second cycle are possible for a fuel assembly 

with heavy initial gadolinium poison loadings that are depleted during the first cycle.

Histories OH-8 and OH-9 are used to test the effect of long downtime before the last irradiation 

cycle for a typical and an atypical power history. Except for the 720-day downtime before the third 

irradiation cycle, OH-8 and OH-9 are similar to OH-5 and OH-7, respectively. History OH-10 is 

similar to OH-4 (highest power in first cycle, lowest power in third cycle), but the power in the first 

two cycles is increased, while the third cycle power is significantly decreased. The construction of 

OH-10 is discussed in Sect. 3.2.4.1. All cases summarized in Table 2 are decayed for five years 

after irradiation. 
3-6

Table 2 Operating history scenarios 

History Cycle 1 Cycle 2 Cycle 3

% power downtime (d) % power downtime (d) % power

OH-1 100 0 100 0 100

OH-2 100 30 100 30 100

OH-3 100 30 100 720 100

OH-4 120 30 100 30 80

OH-5 120 30 120 30 60

OH-6 100 30 120 30 80

OH-7 80 30 100 30 120

OH-8 120 30 120 720 60

OH-9 80 30 100 720 120

OH-10 136.15 30 116.53 30 47.33

3.2.4.1 Realistic operating power history based on core-follow data

The available core-follow data [4] used for various operating conditions cover only one cycle of 

operation. Therefore, the available data do not follow the full operating history for any given 

assembly from its first to its last irradiation cycle in the reactor. Based on the available one-cycle 

data, a realistic assembly operating history, identified as OH-10 in Table 2, was derived and 

applied to a three-cycle irradiation simulation. Derivation of this operating history is described in 

this section.

The core-follow data include information about the burnup history as a function of irradiation time 

for each axial node of each of the 624 assemblies in the core. The burnup distributions at EOC for 

the first-, second-, and third-cycle fuel assemblies are illustrated in Figure 8. This figure shows the 

active fuel height on the y-axis and the node burnup on the x-axis for all assemblies; the thick 

black dashed line on these plots represents the average axial EOC burnup distribution for that set 

of fuel assemblies. As in Figure 7, the EOC axial burnup profiles plotted in Figure 8 are colored 

based on their location within the core. Assemblies near the center of the core are colored in red 

and assemblies near the core periphery are colored in blue. 

First-cycle fuel assemblies are easily identified as those with zero burnup at BOC. There are 252 

first-cycle assemblies in the core. On average, the burnup gain over one cycle for the first-cycle 

assemblies is 21.87 GWd/MTHM. Assemblies in the core with an average burnup at BOC of less 

than 25.5 GWd/MTHM (excluding those with zero burnup at BOC) are assumed to have 

undergone one cycle of irradiation and are considered second-cycle assemblies. There are 256 

assemblies that meet this criterion; their burnup characteristics are listed in Table 3. On average, 

the burnup gain over the cycle for the second-cycle assemblies is 18.72 GWd/MTHM. The 116 

assemblies in the core that are not first- or second-cycle assemblies are considered third-cycle 

assemblies. On average, the burnup gain over a cycle for these assemblies is 7.61 GWd/MTHM. 

Some of the assemblies categorized as third-cycle assemblies may have experienced two, three, 

or more irradiation cycles prior to the cycle for which detailed core-follow data are available. These 
3-7

assemblies are categorized as third-cycle assemblies to enable a consistent comparison with the 

other operating history scenarios listed in Table 2, which all consider three cycles of irradiation. 

Based on the assumptions and derivation discussed in this section, a derived typical core threecycle irradiation history has a first-cycle burnup gain of 21.87 GWd/MTHM, a second-cycle burnup 

gain of 18.72 GWd/MTHM, and a third-cycle burnup gain of 7.61 GWd/MTHM, as well as a 

discharge burnup of 48.19 GWd/MTHM. Therefore, the burnup gain for each cycle relative to the 

discharge burnup is 45.38% for the first cycle, 38.84% for the second cycle, and 15.77% for the 

third cycle. Assuming that each cycle of irradiation has the same cycle length, the power level per 

cycle relative to the average over all three cycles is 136.15% for the first cycle, 116.53% for the 

second cycle, and 47.33% for the third cycle. The depletion simulation for history OH-10 was 

constructed using these percentages and the same assembly average burnup at discharge as 

histories OH-1 through OH-9—45.2 GWd/MTHM. 

Table 3 Burnup characteristics derived from core-follow data 

Burnup

(GWD/MTHM)

First-cycle 

assemblies

Second-cycle 

assemblies

Third-cycle 

assemblies

Minimum 0 15.59 27.71

BOC Maximum 0 25.27 41.88

Mean 0 21.50 35.93

Minimum 16.62 34.44 37.44

EOC Maximum 24.58 44.85 48.44

Mean 21.87 40.22 43.53

Cycle burnupa 21.87 18.72 7.61

Burnup per cycleb (%) 45.38 38.84 15.77

Power level per cyclec (%) 136.15 116.53 47.33

a Cycle burnup was calculated as BBcccccc = 1

NNcccccc

∑ (BBii

EEEEEE − NNcccccc

ii=1 BBii

BB ), where i is index of assemblies in category cyc=1st, 2nd, or 3rd ; 

B is burnup; and Ncyc is the total number of assemblies in category cyc

b Burnup gain per cycle relative to discharge burnup (100%)

c Relative to average over all three cycles (sum over three cycles is 300% - number of cycles times 100%)
3-8

Figure 8 Burnup distribution at EOC for first-, second-, and third-cycle fuel assemblies 

 

3.2.4.2 Operating power histories from other sources

Detailed operating power history data are rare in publicly available references, and where 

available, they generally involve older assembly designs and operating cycles [15]. A literature 

search was performed to identify sources of detailed operating histories for assemblies irradiated 

for three reactor cycles, to use in consistent comparison with the operating histories OH-1 through 

OH-9 (Table 2). Although this literature search was largely unsuccessful, some resulting 

information is briefly summarized here and is deemed as potentially valuable for understanding 

operating data in the context of future BUC applications for BWR SNF.

Cycle-by-cycle assembly burnup data are available for 60 GE 7 × 7 assemblies irradiated in the 

Cooper and Monticello BWRs operated in the United States [15]. These assemblies were 

irradiated in the reactor from Cycle 1. Two of the assemblies were only irradiated during Cycles 1 

and 2, but the remaining assemblies were irradiated for 4, 5, or 6 cycles operated during 1974–

1982 for Cooper and 1971–1975 for Monticello. Given the old design, data for these assemblies 

are not typical of the majority of BWR assemblies now in storage, and they also differ from those 

now in operation.

Cycle-by-cycle assembly burnup data are available for 23 BWR assemblies irradiated at various

times between 1978 and 1992 in six different Swedish reactors [15]. These assemblies have 

unique designs: 8 × 8, 9 × 9, SVEA-64, and SVEA-100. They have been irradiated for 4 to 8 

cycles in the reactor, with most of them irradiated for more than 5 cycles. The power levels for the 

last irradiation cycles vary widely among these assemblies, depending on the assembly and 

reactor, ranging between 36% and 119% of the lifetime-averaged power.

Power history data of a GE14 assembly [16] irradiated between 2000 and 2005 in the Swedish 

Forsmark 3 reactor is illustrated in Figure 9. This assembly was irradiated for five cycles and had 

a power level of 53% during the last cycle. 
3-9

Figure 9 Power history for Forsmark 3 assembly 

The number of irradiation cycles for the BWR assemblies in the US GC-859 database [17] 

discharged from the reactor between 1969 and 2013 [18] is illustrated in Figure 10. This plot 

shows the number of assemblies as a function of the number of cycles for which they were 

irradiated in the reactor. This is illustrated for four assembly types (7 × 7, 8 × 8, 9 × 9, and 

10 × 10). The bar-style plot is color coded to indicate the years of assembly discharge between 

1969 and 2013. The most common number of cycles is three, while some fuel assemblies were 

irradiated for four or five cycles. However, the discharge burnup is the key parameter for BUC, not 

the total number of cycles. The results obtained for the assumed three-cycle history in this study 

would apply to a large extent to other multi-cycle histories if the discharge burnup is similar. While 

it is common to operate BWRs with fuel assemblies inserted for more than three cycles, the cycle 

length in this case would be shorter to maintain similar assembly discharge burnup values. As 

shown in the results to this study, there is very little impact to cask reactivity for varying the 

operating history (power level per cycle and downtime), so adding additional cycles that result in 

the same total discharge burnup will not result in significant changes to cask reactivity. 

1 2 3 4 5

0

20

40

60

80

100

120

140

160

Power level (%)

Cycle number
3-10

Figure 10 Number of irradiation cycles for BWR assemblies in the GC-859 database [17] 
3-11

Results 

Fuel Temperature 

The variation of the cask keff as a function of the fuel temperature used in the assembly depletion 

simulation is presented in Figure 11 for the AO isotope set and in Figure 12 for the AFP isotope 

set. The data in each figure are fitted with a linear least-squares fit line, which is plotted in green. 

Both AO and AFP results show trends that are well described by linear trend lines. In Figures 11

and 12, error bars have been omitted because the bars were smaller than the data markers 

themselves at ±0.0001 (10 pcm, 1 pcm = 10-5

). The legends in Figures 11 and 12 include the 

expression of the linear fit (with y as cask keff and x as temperature in K). The R2 parameter is also 

included in the legend. This parameter is a measure of the goodness of fit and varies between 0 

and 1, with a value close to 1 indicating a good fit.

Figure 11 Effect of fuel temperature on cask keff (AO isotope set) 

 
3-12

 

Figure 12 Effect of fuel temperature on cask keff (AFP isotope set) 

The calculated keff data illustrated in Figures 11 and 12 are listed in Table 4. This table also 

includes the keff differences in pcm relative to the nominal case. 

Table 4 Cask reactivity as a function of fuel temperature 

Temp.

(K)

AO AFP AO AFP

keff 1σa keff 1σ ∆keffb

(pcmc)

1σ

(pcm)

∆keff

(pcm)

1σ

(pcm)

596 0.82927 0.00010 0.72957 0.00010 -236 14 -219 14

696 0.83042 0.00010 0.73055 0.00010 -121 14 -121 14

796 0.83163 0.00010 0.73176 0.00010 0 0

896 0.83259 0.00010 0.73244 0.00010 96 14 68 14

996 0.83378 0.00010 0.73348 0.00010 215 14 172 14

1,096 0.83474 0.00010 0.73419 0.00010 311 14 243 14

1,196 0.83570 0.00010 0.73507 0.00010 407 14 332 14

1,296 0.83658 0.00010 0.73580 0.00010 495 14 404 14 a Standard deviation in keff as reported in the KENO output file b keff difference relative to the 796K nominal case c 1pcm = 0.00001

The effect of fuel temperature on cask reactivity is clearly linear over the temperature range 

studied: reactivity increases with increasing temperature, which is consistent with findings from 

previous studies [5,14]. The keff results listed in Table 4 are consistent with the expected physics 

behavior (e.g., resonance Doppler broadening increases with increasing temperature) and are 

driven by the change in isotopic composition of SNF as a function of temperature during depletion. 

As expected, the increase in cask keff with increasing fuel temperature is mainly due to actinides 

(major contributors 235U, 239Pu, 241Pu), as indicated by the small difference between ∆keff
3-13

calculated with the AO and AFP isotope sets for the same temperature. The magnitude of the 

cask reactivity increase is ~1.0 pcm/K for the AO set and ~0.9 pcm/K for the AFP set, based on 

the linear fits given in Figures 11 and 12.

The variation of the 235U and 239Pu number densities (in atoms/b-cm units) in all fuel rods as a 

function of the axial node and for temperatures considered in this study is illustrated in Figure 13. 

Figure 13 shows the 235U and 239Pu data corresponding to nominal, minimum, and maximum 

temperatures to facilitate understanding of the physics. Compared to the nominal case (796 K), 

when the temperature increases to 1,296 K, the discharge nodal-average 239Pu atomic density 

increases approximately 6–10%, depending on the node. The large step change in the 239Pu 

number density near 80 inches is due to the change from full to vanished lattice, which 

significantly changes the neutron spectrum due to the presence of empty lattice locations (more 

water moderator) in the vanished lattice. Other smaller variations in Figure 13 are due to the 

variations in the axial burnup profile. 

Figure 13 Effect of fuel temperature on 235U and 239Pu in the non-Gd–bearing fuel pins 

3.3.1.1 Fuel temperature axial profile

The effect of the axial temperature distribution on cask reactivity is assessed by comparing fuel 

temperature profiles with uniform fuel temperatures constructed using the average temperature of 

the selected axial profiles. As previously stated, all the nodal fuel temperature data were averaged 

into cycle-average fuel temperature profiles for every fuel assembly, so every profile discussed in 

this section represented a cycle-averaged profile. The minimum (Min) and maximum (Max) 

average fuel temperature assemblies were selected and simulated using profiled and uniform 

axial fuel temperature distributions. These four temperature profiles, along with the cycle- and 

core-averaged fuel temperature profiles, are plotted in Figure 14. 
3-14

The difference in the calculated cask keff values comparing the Min Profile and Min Uniform results 

are 0.005% and -0.042% ∆keff for the AO and AFP isotope sets, respectively. The difference in the 

cask keff results for the Max Profile and Max Uniform are 0.113% and 0.037% ∆keff for the AO and 

AFP isotope sets, respectively. As expected, there is a larger impact from using a uniform 

temperature treatment for the maximum temperature case, as there is a larger variation in the fuel 

temperature as a function of axial position. The cask keff values are generally higher when a 

uniform axial temperature is used because the temperatures in the top nodes of the fuel assembly 

(of significant importance to cask reactivity) are higher than they are in the cases with nonuniform 

temperature profiles. This leads to increased plutonium production in the top nodes, slightly 

increasing cask keff. Overall, the impact of using uniform versus profiled axial fuel temperatures is 

very small, on the order of 0.1% ∆keff. Given this level of bias, as well as the direction of the bias, 

use of uniform axial fuel temperatures is conservative. 

Figure 14 Cycle-average fuel temperature profiles selected to analyze the effect of axial fuel 

temperature shape on cask reactivity 
3-15

Bypass Water Density 

The variation of the cask keff as a function of reduction in the bypass water density during the 

assembly depletion simulation is presented in Figure 15 for the AO isotope set and in Figure 16

for the AFP isotope set. For both AO and AFP isotope sets, keff varies linearly over the considered 

range of density reduction. The calculated keff data are presented in Table 5. 

Figure 15 Effect of bypass water density on cask keff (AO isotope set) 

Figure 16 Effect of bypass water density on cask keff (AFP isotope set) 
3-16

Table 5 Cask reactivity as function of bypass water density reduction 

Density

reduction

(%)

AO AFP AO AFP

keff 1σa keff 1σ ∆keffb

(pcmc)

1σ

(pcm)

∆keff

(pcm)

1σ

(pcm)

10 0.83897 0.00010 0.73679 0.00010 735 14 503 13

9 0.83806 0.00010 0.73595 0.00010 643 14 420 14

8 0.83745 0.00010 0.73560 0.00010 582 14 385 14

7 0.83664 0.00010 0.73485 0.00010 501 13 310 14

6 0.83598 0.00010 0.73458 0.00010 435 14 283 14

5 0.83516 0.00010 0.73400 0.00010 353 14 224 14

4 0.83449 0.00010 0.73353 0.00010 286 14 177 14

3 0.83393 0.00010 0.73285 0.00010 230 14 110 14

2 0.83319 0.00010 0.73246 0.00010 156 14 70 14

1 0.83227 0.00010 0.73216 0.00010 64 14 40 14

0 0.83163 0.00010 0.73176 0.00010 0 14 0 14 a Standard deviation in keff as reported in the KENO output file b keff difference relative to the nominal case (0% density reduction) c 1pcm = 0.00001

A large decrease in the density of the bypass water would lead to a significant hardening of the 

neutron spectrum based on the amount of water within the two large water rods at the center of 

the assembly and outside the assembly channel. Consequently, there will be an increase in the 

production of plutonium isotopes with decreasing bypass water density. The variation of the 235U 

and 239Pu atomic densities in the non-Gd–bearing fuel rods as a function of axial position is 

illustrated in Figure 17 for 0%, 5%, and 10% bypass flow density reduction. As seen in Figure 17, 

the impact on 239Pu content relative to the nominal case is large in both VAN and DOM lattice 

nodes. In the VAN lattice nodes, the spectrum differs from that in the DOM lattice nodes due to a 

combination of two effects: hardening due to less moderation (smaller coolant densities), and 

softening due to fewer fuel rods (larger neutron mean free path). The net effect is a hardening of 

the spectrum. Water density reduction in the large water rods at the center of the assembly and 

outside the assembly channel further impacts the neutron moderation in all nodes, with the actual 

impacts depending on the particular node environment and parameters (coolant density, burnup).

A 10% reduction in the bypass water density relative to its nominal value leads to an increase of 

the assembly average 239Pu content of ~7%. Consequently, it also leads to a significant increase 

in cask reactivity for the studied case. The actual bypass water density is not well known, but it is 

expected to be bounded by the 10% density reduction value. Even for an unlikely reduction in 

bypass water density of 10%, the impact on cask reactivity is significantly smaller than the effects 

of coolant density, axial burnup profile, or control blade usage [4]. Based on the results in this 

study, irrespective of the isotope set used in criticality calculations, the effect is clearly less than 

0.1% ∆keff for every 1% reduction in bypass water density.
3-17

Figure 17 Effect of bypass water density on 235U and 239Pu node-averaged atomic density 

Specific Power 

As discussed in Sect. 3.2.3, the specific power was changed by ±10% relative to the nominal 

case, while the irradiation times were adjusted to keep the discharge burnup the same. The 

impact of these variations on cask reactivity is summarized in Table 6 and illustrated in Figure 18. 

Data in Figure 18 are plotted with 1σ (statistical uncertainty in keff) error bars. The effect is 

extremely small for this magnitude of the specific power variation and not significantly higher than 

the statistical uncertainty (1σ) in the calculated cask keff. 

The direction and the magnitude of the change in cask reactivity are consistent with the expected 

behavior and results of previous studies [5,14]. Cask keff increases with higher specific power for 

the AO set due to the slight increase in the mass of plutonium isotopes. For example, increasing 

specific power by 10% results in an increase of less than 0.1% in the content of 235U and less than 

0.15% in the content of 239Pu in the considered assembly. Overall, the impacts are on the order of 

the 2-sigma uncertainty (28 pcm), indicating that there is very little impact on cask reactivity to 

varying specific power. The ±10% specific power used in this study is meant to test the sensitivity 

to inaccurately modeling the specific power. The results show that the specific power has a small 

effect on cask reactivity, although higher specific power may lead to slight increase in cask 

reactivity. Significant increases in assembly-specific power would require corresponding uprates 

to the core rated power; analysts should take care in correlating the core power with the time the 

assembly was in the core to generate an accurate estimate for the specific power. 
3-18

Table 6 Cask keff as function of change in specific power 

Specific 

power 

change

AO AFP AO AFP

keff 1σa keff 1σ ∆keffb

(pcmc)

1σ

(pcm)

∆keff

(pcm)

1σ

(pcm)

+10% 0.83196 0.00010 0.73173 0.00010 34 14 -3 14

0% 0.83163 0.00010 0.73176 0.00010 0 0

-10% 0.83138 0.00010 0.73153 0.00010 -25 14 -22 14 a Standard deviation in keff as reported in the KENO output file b keff difference relative to the nominal case (0% specific power change) c 1pcm = 0.00001

Figure 18 Effect of specific power on cask reactivity 

Operating History 

The variation of the cask keff for the operating histories listed in Table 2 is presented in Table 7. 

Figure 19 shows the impact in keff for each of the considered histories relative to history OH-1 

(which is characterized by 100% power level in each of the three cycles and no downtime

between cycles). In general, the trends of these results are similar to those identified in previous 

studies [14,19].
3-19

Table 7 Cask reactivity as function of operating history 

Operating 

History

AO AFP AO AFP

keff 1σa keff 1σ ∆keffb

(pcmc)

1σ

(pcm)

∆keff

(pcm)

1σ

(pcm)

OH-1 0.83163 0.00010 0.73176 0.00010 0 0 

OH-2 0.83170 0.00010 0.73154 0.00010 7 14 -21 14

OH-3 0.83099 0.00010 0.73092 0.00010 -63 14 -84 14

OH-4 0.83118 0.00010 0.73144 0.00010 -45 14 -31 14

OH-5 0.83100 0.00010 0.73155 0.00010 -63 13 -21 14

OH-6 0.83126 0.00010 0.73160 0.00010 -37 14 -16 14

OH-7 0.83189 0.00010 0.73170 0.00010 26 14 -6 14

OH-8 0.82987 0.00010 0.73043 0.00010 -175 14 -133 14

OH-9 0.83121 0.00010 0.73110 0.00010 -41 14 -66 14

OH-10 0.83083 0.00010 0.73138 0.00010 -80 14 -38 14 a Standard deviation in keff as reported in the KENO output file b keff difference relative to operating history OH-1 c 1pcm = 0.00001

History OH-1 results in the highest keff, within statistics. Relative to all other considered histories 

for either the AO or the AFP isotope sets, the differences in keff between OH-1 and other histories 

are either negative or statistically negligible (within two standard deviations). The only cases in 

which the difference is not negative (though the keff values are within two standard deviations) 

occur for histories OH-2 and OH-7 with the AO isotope set. 

Results for histories OH-1 and OH-2 are statistically equivalent, confirming that neglecting typical 

downtimes in depletion simulations do not impact cask reactivity, as previously noted [4]. 

Extended downtime later in an assembly’s irradiation history leads to lower cask keff for both AO 

and AFP isotope sets. This effect is mainly due to the decay of 241Pu (T1/2 = 14.4 yr), an actinide 

with significant effect on cask reactivity. The magnitude of the reactivity for the AO set is 

statistically similar (within 2σ) to that for the AFP isotope set. For example, for uniform power 

operation, an extended downtime before the last irradiation cycle (OH-3 vs. OH-1) leads to a cask 

keff decrease of 63 pcm (1σ=14 pcm) for the AO set and 84 pcm (1σ=14 pcm) for the AFP set. 

Therefore, these extended downtimes do not require explicit modeling for conservative estimates 

of cask reactivity.

The effect of extended downtime before the last irradiation cycle shows the same decreasing 

trend regardless of the power level history during irradiation. Moreover, the magnitude of the 

decrease is similar for the AO and AFP sets given the same power history, as seen in the values 

for OH-3 corresponding to the two isotope sets. Furthermore, the magnitude varies with the cycle 

down time. Operating histories OH-5 and OH-8 have the same power history (120% for the first 

two cycles and 60% for the last cycle), but their downtimes are much different before the last cycle 

(30d vs 720d). 
3-20

Figure 19 Effect of operating history on cask reactivity 

The decrease in keff due to extended downtime before the last cycle (OH-8 vs. OH-5) for both the 

AO and AFP sets is 112 pcm. The magnitude of the decrease is larger in this case than for the 

uniform power operation (OH-3 vs. OH-1) because more plutonium is produced during the first 

two cycles (higher burnup at the end of the first two cycles). The effect of the downtime is also

observed for operating histories OH-7 and OH-9, both of which have the same power history but 

different downtimes before the last cycle. Case OH-9 results in a decrease in reactivity of 67 pcm 

and 60 pcm compared to OH-7 for the AO and AFP isotope sets, respectively. The magnitude of 

the decrease is slightly less than that observed for uniform power operation (OH-3 vs OH-1), 

indicating once again that the magnitude of the effect depends on the power history. 

Operating histories OH-4 through OH-7 illustrate the effect of the power level variation during 

irradiation. They all have the same downtime, but they have different nonuniform power levels. 

The results indicate that the effect for the AFP isotope set is statistically negligible, within 2σ for all 

operating histories in this set compared to the reference history OH-1. However, if only the AO 

isotope set is considered, there is a small but clear effect on the power level in the last two cycles, 

especially in the last cycle. If the power in the last cycle is higher (OH-7), more plutonium is 

produced during this cycle, and there is less time for its fissile isotopes to undergo fission before 

assembly discharge. This results in increased plutonium content in the discharged assembly. For 

the AO isotope set, the keff value for OH-7 is 26 pcm higher than for OH-1. However, the two keff

values are within 2σ (1σ = 14 pcm).

The magnitude of the reactivity effects for the AO and AFP sets for history OH-7 are statistically 

the same (within 2σ). This is likely due to the interplay between the production and decay of those 

actinides and fission products with high impact on cask reactivity. If the power is higher in the last 

cycle, then not only does the quantity of actinides increase at discharge, but the quantity of the 
3-21

fission products also increases. This includes 155Eu, which decays with a half-life of 4.75 years to 

155Gd, a very strong neutron absorber. Therefore, there is an increase in 155Gd present in SNF at 

5-year cooling after discharge. In particular, the 155Gd assembly average atomic density for history

OH-7 at 5-year cooling is ~2% higher than the corresponding value for history OH-4.

Operating histories OH-8 and OH-9 are intended to illustrate the combined effect of the power 

level in the last cycle and the downtime preceding the last cycle. The combination of lower power 

levels during the last cycle and longer downtime preceding this cycle leads to the lowest cask keff

values, as observed in other studies [14]. 

Operating history OH-10 shows a decrease in reactivity relative to OH-1 for both isotope sets. For 

the AO set, the reactivity decrease is 80 pcm. For the AFP set, the decrease is smaller, at

38 pcm.

The results obtained for the ten operating histories considered indicate that the use of uniform 

power levels and no downtime between cycles is a suitable assumption. Case OH-7, has the

highest power level in the last cycle and typical downtime, and results in the highest cask 

reactivity. However, it provides results that are statistically the same as the uniform power and no 

downtime history.

Summary and Recommendations 

The assessments documented in this section are not fully comprehensive, as they are based on 

specific assembly and cask configurations, as well as a limited amount of available operating 

data. The calculated cask reactivity effects are determined for a single assembly average burnup 

(45.2 GWd/MTHM), but the variations illustrated here are expected to be similar for similar burnup 

values. Further analysis would be needed to apply these results to significantly different 

assembly-average burnup values. The established trends in cask reactivity with independent 

variations of the considered operating parameters are consistent with findings from other 

studies [5,14,19]. 

The directions and magnitudes of the impacts on cask reactivity are briefly summarized here for 

each reactor operating parameter assessed in this section. 

Fuel Temperature 

• Cask reactivity increases linearly with increasing fuel temperature, over the range of

596–1296 K for each of the AO and AFP isotope sets.

• The magnitude of the cask reactivity increase is slightly larger for the AO set than for the

AFP set at ~1.0 pcm/K for AO and ~0.9 pcm/K for AFP based on a linear fit in Figures 11

and 12.

• A bounding value in cask reactivity increase, irrespective of the isotope set used, is 0.12%

for every 100 K temperature increase based on data in Table 4.

• Use of the highest nodal-average fuel temperature in assembly depletion simulations will

lead to the conservative cask reactivity results.

Bypass Water Density 

• Cask reactivity increases with decreasing bypass water density for each of the AO and

AFP isotope sets.

• The magnitude of the cask reactivity increase is larger for the AO set than for the AFP set.
3-22

• Regardless of the isotope set used in criticality calculations, the cask reactivity increase is

less than 0.1% for every 1% reduction in bypass water density.

Specific Power 

• Cask reactivity increases with increasing specific power for the AO isotope set, but the

magnitude of the increase is very small: ~0.03% for 10% specific power increase based on

the data in Table 6.

• The cask reactivity effect for the AFP isotope set is negligible based on the data in

Table 6.

• BWR BUC analyses crediting only the AO isotope set that model a high, bounding specific

power during depletion result in the highest cask reactivities. For analyses using the AFP

isotope set, a reasonable specific power consistent with the expected depletion conditions

produces statistically equivalent cask reactivity to higher specific powers.

Operating History 

• Typical downtimes of ~30 days between cycles have a negligible impact on cask reactivity.

• Extended downtimes preceding an assembly’s last irradiation cycle before being

discharged leads to a decrease in cask keff values. The magnitude of the decrease is

similar for the AO and AFP sets.

• Cask reactivity is negligibly affected by the power level during the assembly’s last

irradiation cycle relative to the lifetime-average power. Cask keff slightly increases (within

2σ) with increasing power level during the last cycle for the AO set and is practically

unchanged for the AFP set (see Figure 19).

• An operating history with uniform power levels and no downtime between cycles provides

cask reactivity that is statistically equivalent to or higher than all other tested scenarios.

As expected, the results summarized here confirm that the impacts of the operating parameters 

under consideration are small relative to the impacts of control blade usage, axial coolant density, 

and axial burnup profile [4].
4-1

IMPACT OF ASSEMBLY-SPECIFIC CONDITIONS 

ON CASK REACTIVITY 

Background 

Axial burnup profile, axial coolant density profile, and control blade usage—the three research 

objectives previously categorized as high priorities [5]—were studied separately in 

NUREG/CR-7224 [4]. Each parameter was individually varied, while all the others were kept 

unchanged. In this study, the effect of the correlation of these parameters was investigated, as 

documented in this section. Assembly-specific conditions, also known as correlated parameters, 

are a set of conditions realistically experienced by an individual fuel assembly. For example, when 

the control blade is inserted, the assembly power, coolant density, and many other parameters all 

change accordingly. Modeling the assembly-specific conditions ensures that the operating 

parameters of interest are correlated. Previous studies [4] used uncorrelated data from different 

fuel assemblies that result in limiting cask reactivity estimates. The current work studies assemblyspecific conditions to (1) confirm that using uncorrelated but limiting values for all operating 

conditions leads to conservative cask reactivity and (2) to further understand the impact that 

modeling assembly-specific conditions has on cask reactivity. 

Using limiting values for the axial coolant density profile, burnup profile, control blade history, and 

other parameters will provide a conservative estimate of reactivity. However, simultaneous 

application of these limiting assumptions may be overly limiting. In reactor operation, it is unlikely 

that a fuel assembly would simultaneously experience a limiting control blade history (deeply 

inserted for long periods of time) and a limiting coolant density profile (low moderation due to high 

power and increased boiling). The impacts of using true operating data correlated between the 

various conditions are assessed in this section. 

To study the effect of the correlation of these parameters, some of the previously used basic 

assumptions are applied. The operating data employed in this study, which are the same as those 

used in NUREG/CR-7224 [4], are taken from a single cycle of simulated core-follow data from 

which nodal-averaged conditions are extracted. The conditions extracted for this study are the 

control blade history, power history (and resulting burnup profile), nodal coolant density, and nodal 

fuel temperature. The first three conditions were selected because they were identified as having 

the highest level of impact on fuel cask reactivity [4,5]. Fuel temperature was also included to 

identify potential impacts of using the assembly-specific axial fuel temperature profile. 

The main goals of this study are (1) to confirm the hypothesis that using individually limiting 

conditions selected from different fuel assemblies results in conservative cask reactivity estimates, 

and (2) to understand the range of possible cask reactivity estimates if assembly-specific 

conditions are used. 

Methodology 

Base Conditions 

The study of the effect of assembly-specific conditions requires that base conditions for all 

parameters of interest first be established. The base conditions for the coolant density profile and 

axial burnup profile were chosen to be the limiting conditions identified in NUREG/CR-7224 [4]. 

The limiting base burnup profile is challenging to define because it is a function of the assembly 

burnup and the isotope set used (AO or AFP). 
4-2

The base burnup profile was chosen based on the results presented in NUREG/CR-7224 [4]. The 

discharged assembly burnups cover a burnup range from 25 to 50 GWd/MTHM, so a profile that 

is limiting or near limiting over this entire range is desired. For conservatism, the models used in 

this study do not include natural uranium or low-enriched blankets. Tables 6.2 and 6.3 in 

NUREG/CR-7224 [4] present the top 10 most reactive profiles for a range of burnups for both the 

AO and AFP isotope sets. A review of these tables indicates that Profile 40 is limiting or near 

limiting for both isotope sets at all three burnups considered. For this reason, Profile 40 was 

selected as the base profile for the current study. 

The base control blade history uses fully withdrawn control blades during the entire irradiation

history because fully inserted control blades for the entire irradiation period is overly limiting 

compared to realistic control blade histories [4]. The base fuel temperature profile is the highest

time-averaged and spatially averaged temperature profile from the operating data. The base 

temperature profile is selected by averaging the temperature over the entire cycle for each node, 

resulting in a cycle-average profile. Then the cycle-average profiles are averaged axially, resulting 

in a single temperature value for each fuel assembly. The cycle-average profile with the highest 

axially averaged temperature is selected. 

Figure 20 plots the base conditions used in this study. The base burnup profile shown in Figure 20

is different than that used in previous studies [4], but the coolant density (void fraction) profile is 

the same as that used in Section 3 of this report and in NUREG/CR-7224 [4]. Each axial profile 

shown in Figure 20 is taken from a different fuel assembly, which is unrealistic, but it results in 

conservative estimates of cask reactivity. 

Figure 20 Base conditions used for the coolant void fraction, burnup, and fuel 

temperature axial profiles 

Assembly-Specific Conditions 

The assembly-specific conditions are obtained from the core-follow operating data. To study the 

impact of using assembly-specific conditions, an initial simulation is performed using only the base 

conditions for all considered parameters. All subsequent calculations use this baseline case as a 

reference to assess the impact of including the assembly-specific parameters of interest. To test 
4-3

the impact of including as-irradiated conditions, assembly-specific conditions are substituted for 

base conditions, and the cask’s keff results are compared to the base conditions. For example, to 

assess the impact of assembly-specific control blade insertion, the base condition of control 

blades removed for the entire irradiation is replaced with an actual control blade history from a 

specific assembly. When the assembly-specific conditions are applied, the axial shape and timedependence of these conditions are both simulated. 

Three fuel assemblies were chosen for analysis based on their control blade histories and are 

discussed in this section. Assembly 1 (A1) was chosen because it had the most limiting realistic 

control blade history as detailed in in NUREG/CR-7224 [4]. A1 contains two control blade 

insertions that were near full depth for a significant period of irradiation time. Assembly 2 (A2) was 

chosen because it had the most cumulative irradiation time where the control blade was inserted

(highest control blade history). Detailed control blade histories for A1 and A2 are provided in the 

results section. Assembly 3 (A3) was chosen as a control; A3 contains no control blade insertion, 

but it has one of the most limiting burnup profiles identified in NUREG/CR-7224 [4]. A3 will 

indicate whether the level of conservatism in the base conditions is due primarily to the burnup 

profile or the other operating conditions. 

The cycle-averaged coolant void fraction profiles, axial burnup profiles, and fuel temperature 

profiles for the base condition and assembly-specific conditions for A1, A2, and A3 are plotted in 

Figure 21. The burnup profiles in Figure 21 have been normalized to an assembly-averaged 

burnup of 25 GWd/MTHM. The burnup profile plot in Figure 21 (middle) shows that although the 

base and A3 burnup profiles were taken from different fuel assemblies, they are very similar. The 

burnup profiles for A1 and A2 have much higher burnups at the tops of the fuel assemblies than 

A3, which should result in lower cask reactivity for those two assemblies. The coolant void fraction 

profile plot in Figure 21 (left) shows that the base void profile has a higher exit void fraction (lower 

coolant density) than the three assembly-specific profiles, so the A1–A3 void profiles should result 

in lower cask reactivity compared to the base profile. 

Figure 21 Base and assembly-specific cycle-average conditions for the coolant void 

fraction, burnup, and fuel temperature axial profiles 
4-4

Five calculations are used for each selected assembly to assess the effects of the assemblyspecific conditions. Table 8 presents a summary of the sequence of these five consecutive 

calculations. In Table 8, the term base indicates that base conditions are used (as defined in 

Figure 20), while the term assembly indicates that assembly-specific conditions are used for that 

operating parameter. The first assembly-specific parameter applied is the control blade insertion. 

In subsequent calculations, additional conditions are changed one by one compared to the base 

case to ascertain the effect of correlating the operating conditions with control blade insertion. 

As identified in Table 8, case ID C uses the assembly-specific control blade history and base 

conditions for the coolant density, burnup profile, and fuel temperature. Case ID CV uses 

assembly-specific conditions for the control blade history and coolant density (void fraction), while 

base conditions are used for the burnup profile and fuel temperature. Likewise, case ID CVB uses 

assembly-specific conditions for the control blade history, coolant density, and burnup profile, 

while the base fuel temperature is used. Finally, case ID CVBT uses assembly-specific conditions 

for all parameters being tested. The assembly-specific conditions are added one by one to enable 

estimation of the individual effects of each condition rather than the effects of the total of all 

conditions. 

 Table 8 Summary of conditions used for correlated parameter calculations 

Case 

ID

Operating parameter

Control 

blade

Coolant 

density

Burnup 

profile

Fuel 

temperature

Base Base (out) Base Base Base

C Assembly Base Base Base

CV Assembly Assembly Base Base

CVB Assembly Assembly Assembly Base

CVBT Assembly Assembly Assembly Assembly

To model the control blade position as a function of irradiation time for a certain assembly, the 

irradiation time is divided into intervals that correspond to constant control blade position. Figures 

22 and 23 plot the control blade position as a function of time for assemblies A1 and A2, 

respectively. In Figure 22, the cycle has been divided into five time intervals in which the control 

blade is either fully withdrawn or inserted to some position as indicated by the gray and white

shading and circled numbers labeling each of the five different intervals. 

In the calculations that use assembly-specific conditions, both the axial- and time-dependence of 

the conditions are modeled. The actual operating data contain information on a finer timescale 

than the changes in control blade elevation. In the correlated parameter calculations, the 

conditions of interest (nodal coolant density, nodal power, and nodal fuel temperature) are 

averaged over each time period for which the control blade position is constant. For example, 

interval 2 of Figure 22 is divided into four different time subintervals, the boundaries for which are 

defined by the interval over which the control blade position is constant. In each of the four 

subintervals in time interval 2, time-averaged coolant density, nodal power, and fuel temperature 

are used for each axial node. In interval 2, the axial shape of the assembly-specific conditions is 

updated four times. The assembly-specific conditions are averaged over any interval during which 

the control blade position is constant. 
4-5

Figure 22 Control blade insertion depth as a function of time for assembly A1 

Figure 23 Control blade insertion depth as a function of time for assembly A1 

Two assembly-average discharge burnup values were chosen for analysis: 25 GWd/MTHM and 

50 GWd/MTHM. The low burnup value of 25 GWd/MTHM was chosen because it is at the upper 

limit of a typical single cycle-discharged fuel assembly. The higher burnup value of 50 

GWd/MTHM was chosen because it is a value more typical of a discharged fuel assembly. In 

each of the two discharge burnup cases, the operating data are applied over a single irradiation 

cycle that spans an irradiation time from BOL until the desired discharge burnup (25 or 50 

GWd/MTHM) is reached. This is done by modifying the cycle length while maintaining a certain 

power level to achieve a burnup of 25 GWd/MTHM and 50 GWd/MTHM. This approach differs 

from analyses in previous studies, which considered a three-cycle irradiation history. Assessing 

the impact of assembly-specific conditions over multiple cycles can be performed accurately only 

where data exist for multiple cycles, which is not the case here. Applying the same control blade 

history, power, and coolant density history for multiple cycles (as done in previous calculations for 

each of the three considered cycles) is likely inadequate for testing the impact of the correlation of 

the parameters. The results in Section 3 indicate that using no down time between cycles—or 

using one long cycle—has almost no impact on cask reactivity, so this assumption is deemed 

adequate for this study. 

Results 

To fully understand the results and impacts of the control blade insertion on assembly power and 

other parameters, the fuel assembly irradiation histories for A1 and A2 have been divided into 
4-6

time intervals that correspond to control blades being inserted or fully removed, as labeled in 

Figures 22 and 23. The other parameters of interest have been averaged over these time intervals

and plotted in Figures 24–28 for A1 and Figures 29–36 for A2. 

In Figures 22 and 23, which depict the control blade insertion depth as a function of time, gray 

shading used for time interval 1 indicates that the control blades are not inserted; while white 

shading used for interval 2 indicates that the control blades are inserted. The blue line indicates 

the axial position of the top of the control blade. These gray or white shaded regions in Figures 22

and 23 represent the time intervals for which operating data and results are averaged and labeled 

with identifying numbers. The actual calculations are performed on a finer timescale than the 

intervals indicated in the figures, as discussed in Section 4.2.2. For A3, plots like those shown for 

A1 and A2 in Figures 22–36 have been omitted, as A3 contains no control blade history, so there 

are no control blade changes to the plot.

In Figures 24–28 and 29–36, three operating condition subplots are included for each time 

interval: (1) axial coolant void profile (left), (2) specific power for the time interval and total 

accumulated burnup at the end of that time interval as a function of axial position (middle), and

(3) increase in 239Pu concentration during the time interval and the cumulative 239Pu concentration

at the end of the time interval as a function of axial position (right). Each operating history plot is

labeled in the top left corner, with the number of the time interval over which conditions are timeaveraged for plotting purposes. The red dashed line in the operating history plots corresponds to

the time-averaged control blade tip location for that interval.

As shown in Figures 24–28, when the control blade is inserted during irradiation, a relatively small 

impact is observed on the axial void profile. The exit void fraction for step 1 (Figure 24) is 86%, 

and then it drops only to 77% when the blade is inserted in step 2 (Figure 25). The exit void 

fraction then increases to 87% for step 3 (Figure 26) when the blade is removed, and then it 

decreases to 78% in step 4 (Figure 27) when the blade is inserted again. This indicates that near 

full-depth control blade insertion shifts the exit void fraction on the order of 10%, while the impact 

on the power density is much larger than 10%. 

The effect of control blade insertion on the axial power shape is more pronounced than the void 

profile, as observed in step 2 (Figure 25). In step 2, the control blade is inserted to approximately 

3⁄4 of full depth, pushing additional power to the top of the fuel assembly. Then when the control 

blade is removed in step 3 (Figure 26), the axial power shape becomes significantly bottompeaked because power has been suppressed for an amount of time in that location. At step 5

(Figure 28), most of the fissile material has been consumed at the bottom of the fuel assembly, 

and power is shifted to the top of the fuel assembly, leading to increased plutonium production in 

that portion of the fuel assembly. 

For A2 (Figures 29–36), the impact of control blade insertion on the axial power profile and axial 

burnup profile is much more apparent than for A1. For A2, the control blade is inserted to ~50% 

full depth, much less than in A1, resulting in significant changes to the axial power shape. In A1, 

the control blade is inserted to near full-depth, causing a significant change in the magnitude, but 

little change in the shape of the power density. Similar to A1, insertion of the control blade in A2 

has a relatively small impact on the exit void fraction—generally less than 10% when comparing 

steps with the blade inserted to those with the blade removed. 
4-7

Figure 24 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu 

concentration as a function of time for A1 during time interval 1 

Figure 25 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu 

concentration as a function of time for A1 during time interval 2 

Figure 26 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu 

concentration as a function of time for A1 during time interval 3 
4-8

Figure 27 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu 

concentration as a function of time for A1 during time interval 4 

Figure 28 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu 

concentration as a function of time for A1 during time interval 5 

Figure 29 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 1 
4-9

Figure 30 Axial coolant void profile, axial-specific power and burnup profile, and axial 

239Pu concentration as a function of time for A2 during time interval 2 

Figure 31 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 3 

Figure 32 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 4 
4-10

Figure 33 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 5 

Figure 34 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 6 

Figure 35 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 7 
4-11

Figure 36 Axial coolant void profile, axial-specific power and burnup profile, and axial 239Pu 

concentration as a function of time for A2 during time interval 8 

The effect of assembly-specific conditions on cask reactivity is presented in Tables 9 and 10 for 

the AO and AFP isotope sets at an assembly average discharge burnup of 25 GWd/MTHM. 

These tables contain cask keff values for the five tested cases: base, C, CV, CVB, and CVBT for 

A1, A2, and A3, as well as differences in cask keff relative to the base case (∆keff). The ∆keff values 

have been plotted in Figure 37 for the AO and AFP isotope sets. The dashed lines in this figure 

indicate the base case reactivity (∆keff is zero). As discussed in Section 4.2.1, the base cases 

assumed limiting conditions and control blades completely withdrawn. Any data above this 

dashed line represent an increase in cask reactivity above the base conditions; likewise, any data 

below the dashed line represent a decrease in cask reactivity relative to the base conditions. 

For A1 and A2, use of the assembly-specific control blade history (C cases) results in a relatively 

small impact on cask reactivity of less than 1% ∆keff for both the AO and AFP isotope sets. 

Although these studies are slightly different than those previously documented, this result aligns 

well with the results in NUREG/CR-7224 [4], indicating an impact of less than 1% on cask 

reactivity for realistic control blade usage. 

The addition of the assembly-specific coolant density profile to the assembly-specific control blade 

history results in a reduction in reactivity for all cases, although the magnitude of the reduction 

depends largely on the assembly-specific coolant density profile itself. The reduction in reactivity 

when comparing C to CV is larger (~500 pcm, or 0.5% ∆keff) for A2 than for the other two 

assemblies. This is primarily caused by a less limiting coolant density profile (shown in Figure 21) 

for A2 compared to A1 and A3. Overall, using the assembly-specific control blade and coolant 

density data results in small impacts to cask reactivity. 

As shown in Figure 37, the largest impact to cask reactivity for the assemblies with control blade 

insertion is clearly the addition of the assembly-specific burnup profile. The magnitude of the 

impact of the burnup profile varies for each fuel assembly. For the rodded assemblies (A1 and 

A2), the burnup profile is worth 2–3% ∆keff at 25 GWd/MTHM (comparing CV to CVB). Control 

blade insertion alone does not have a significant impact on reactivity, but the presence of the 

control blade during irradiation has a relatively significant impact on the burnup profile. Because 

control blades in BWRs are inserted from the bottom of the assembly, the power and therefore the 

burnup profile tend to be more top-peaked during periods of control blade insertion. This leads to 

a reduction in fissile 235U in the upper portion of the fuel assembly, resulting in a large impact 
4-12

compared to one of the limiting burnup profiles. Control blade usage tends to result in less limiting 

burnup profiles than the cases with no control blade insertion. 

For all cases, the impact of including fuel temperature is very small compared to the inclusion of 

the other three operating conditions. This is expected from the results in Section 3.3.1, which 

show that the impact of fuel temperature on cask reactivity is on the order of ~1 pcm/K. Section 

3.3.1 also shows that the effect of the fuel temperature profile on cask reactivity is small. Overall, 

the impact of including the fuel temperature in the assembly-specific conditions study is very small 

compared to the other parameters considered. 

The results for A3 are significantly different than the results for A1 and A2. This is largely due to 

the difference in the operating history for A3 compared to the operating histories for A1 and A2. 

A1 and A2 were specifically chosen because their operating histories contain significant control 

blade insertion, leading to changes to other assembly-specific conditions. A3 was chosen 

because it has no control blade insertion and had one of the more limiting burnup profiles. 

Because A3 has no control blade insertion, there is little impact to using the assembly-specific 

conditions for that fuel assembly. However, cask reactivity is slightly lowered by using the 

assembly-specific conditions for A3, which is primarily due to a less limiting coolant density profile. 

The magnitude of the reduction in cask reactivity for A3 is much smaller than that obtained for A1 

or A2. 

Table 9 Cask reactivity data for the AO isotope set at 25 GWd/MTHM 

Case ID A1 keffa A2 keffa A3 keffa A1 ∆keffb A2 ∆keffb A3 ∆keffb

Base 0.89955 0.89955 0.89955 0.00% 0.00% 0.00%

C 0.90316 0.90111 0.89963 0.36% 0.16% 0.01%

CV 0.90122 0.89714 0.89688 0.17% -0.24% -0.27%

CVB 0.88050 0.86472 0.89773 -1.91% -3.48% -0.18%

CVBT 0.88030 0.86516 0.89720 -1.93% -3.44% -0.24% a Standard deviation is 0.00010 for keff and 0.00014 for ∆keff in all cases b ∆keff relative to base

Table 10 Cask reactivity data for the AFP isotope set at 25 GWd/MTHM 

Case ID A1 keffa A2 keffa A3 keffa A1 ∆keffb A2 ∆keffb A3 ∆keffb

Base 0.81705 0.81705 0.81705 0.00% 0.00% 0.00%

C 0.82116 0.82304 0.81691 0.41% 0.60% -0.01%

CV 0.81969 0.81793 0.81499 0.26% 0.09% -0.21%

CVB 0.80992 0.80042 0.81488 -0.71% -1.66% -0.22%

CVBT 0.80964 0.79965 0.81415 -0.74% -1.74% -0.29% a Standard deviation is 0.00010 for keff and 0.00014 for ∆keff in all cases b ∆keff relative to base
4-13

Figure 37 Cask ∆keff values for the AO (left) and AFP (right) isotope sets at an assembly 

average discharge burnup of 25 GWd/MTHM 

The effect of assembly-specific conditions on cask reactivity can be found in Tables 11 and 12 for 

the AO and AFP isotope sets at an assembly average discharge burnup of 50 GWd/MTHM. 

These two tables contain cask keff values, as well as the difference in keff (∆keff) relative to the base 

case. Figure 38 plots ∆keff values for the four tested cases at an assembly average discharge 

burnup of 50 GWd/MTHM. The C and CV cases have ∆keff values similar to those of the 25 

GWd/MTHM cases, but the impact of the burnup profile is much greater for the 50 GWd/MTHM 

cases than for the 25 GWd/MTHM cases. The greater impact of the burnup profile compared to 

the other parameters is due to the more top-peaked fission density axial profiles for the 50 

GWd/MTHM cases, as discussed below. Note that in these studies, full-length fuel without natural 

uranium blankets were modeled, so the impact of the burnup profile and other parameters would 

change, depending on the assumptions used to model the fuel assembly. 

Table 11 Cask reactivity data for the AO isotope set at 50 GWd/MTHM 

Case ID A1 keffa A2 keffa A3 keffa A1 ∆keffb A2 ∆keffb A3 ∆keffb

Base 0.83834 0.83834 0.83834 0.00% 0.00% 0.00%

C 0.84310 0.83919 0.83824 0.48% 0.08% -0.01%

CV 0.84022 0.83334 0.83389 0.19% -0.50% -0.44%

CVB 0.79733 0.77012 0.83364 -4.10% -6.82% -0.47%

CVBT 0.79754 0.77073 0.83288 -4.08% -6.76% -0.55% a Standard deviation is 0.00010 for keff and 0.00014 for ∆keff in all cases b ∆keff relative to base
4-14

Table 12 Cask reactivity data for the AFP isotope set at 50 GWd/MTHM 

Case D A1 keffa A2 keffa A3 keffa A1 ∆keffb A2 ∆keffb A3 ∆keffb

Base 0.76000 0.76000 0.76000 0.00% 0.00% 0.00%

C 0.76547 0.76126 0.75999 0.55% 0.13% 0.00%

CV 0.76242 0.75545 0.75569 0.24% -0.46% -0.43%

CVB 0.71189 0.68802 0.75531 -4.81% -7.20% -0.47%

CVBT 0.71154 0.68877 0.75445 -4.85% -7.12% -0.55% a Standard deviation is 0.00010 for keff and 0.00014 for ∆keff in all cases b ∆keff relative to base

Figure 38 Cask ∆keff values for the AO (left) and AFP (right) isotope sets at an assembly 

average discharge burnup of 50 GWd/MTHM 

The shapes of the curves in Figure 38 are similar to those in Figure 37, but the impact of the 

assembly-specific conditions is significantly greater at assembly average burnups of 50 

GWd/MTHM than at 25 GWd/MTHM. Specifically, the impact of adding the assembly-specific 

burnup profile is more significant at 50 than at 25 GWd/MTHM. This is caused by the shape of the 

axial fission distribution at 25 GWd/MTHM, which is less top-peaked than at 50 GWd/MTHM. 

Plots of the axial fission distributions for the CVBT cases for the AO and AFP isotope sets at 25 

and 50 GWd/MTHM are shown in Figure 39. As discussed in this and previous reports, the fission 

density distribution in the top axial portion of the fuel assembly plays a major role in cask 

reactivity. The more top-peaked the distribution is, the higher the impact of the burnup profile on 

cask reactivity [4]. The cases considered here have a less top-peaked fission distribution at 25 

GWd/MTHM compared to that for 50 GWd/MTHM, so the importance of the assembly-specific 

burnup profile is lessened for the lower burnup. 

Figure 40 plots the base burnup profile and the assembly-specific burnup profile for A1, as well as 

the relative burnup difference as a function of axial position. The relative burnup difference for 

each axial position is calculated as the absolute value of the difference between 1.0 and the ratio 

of the burnup values at that position for the assembly-specific and base profiles (equation given 

on the plot). As shown in the figure, the base burnup profile has much lower burnup values at the 

top of the fuel assembly compared to those in the A1 assembly profile. Correlating that with the 

more top-peaked fission distribution at 50 GWd/MTHM as shown in Figure 39 indicates that the 
4-15

impact of the burnup profile for the higher burnup is primarily due to the large difference in the 

burnup profiles at the top of the fuel assembly. The relative burnup difference is plotted rather than 

the absolute difference because high burnup regions in the axial middle of the assembly have a 

relatively small impact on cask reactivity compared to the low burnup axial top regions. The same 

absolute burnup difference is worth more in terms of cask reactivity at the top than in the middle of 

the assembly. Plotting the relative difference in burnup provides a better indication of the impact 

that burnup difference will have on cask reactivity. Figure 40 clearly illustrates that the top portion 

of the fuel assembly is very important for cask reactivity, and it highlights the importance of the 

axial fission distribution. 

The less top-peaked fission density distribution at 25 GWd/MTHM is a result of the combined 

impact of the increased residual 235U in the middle axial regions of the fuel assembly, the lower 

concentration of 239Pu at the top of the assembly, and the higher concentration of residual 

gadolinium in the top of the fuel assembly. Figure 41 shows the 235

U, 239Pu, and 155Gd 

concentration plotted as a function of axial position for assembly A1. 

The distribution of the 235U concentration as a function of axial position follows an inverse shape of 

the burnup profile: it has higher concentrations for lower burnup regions and lower concentrations 

for higher burnup regions. At both 25 and 50 GWd/MTHM, the 235U concentration is higher at the 

axial ends of the fuel assembly than in the middle portions of the fuel assembly. Comparing the 

239Pu concentration as a function of axial position for the two selected burnups (Figure 41, middle) 

reveals that the 50 GWd/MTHM burnup results in higher plutonium concentrations in the top axial 

portion of the assembly. For the gadolinium BA, the 25 GWd/MTHM case results in higher 155Gd 

concentrations in the top and bottom of the assembly due to the lower burnup at the ends of the 

fuel assembly. 

The fission distribution for the AO isotope set (Figure 39, left), which does not contain gadolinium, 

shows that the 50 GWd/MTHM case is more top-peaked than the 25 GWd/MTHM case. However, 

it is clear that the gadolinium has an impact at 25 GWd/MTHM, as seen by comparing the fission 

distributions for the AO and AFP isotope sets in Figure 39. The AFP fission distribution is clearly 

less top-peaked than the AO fission distribution at 25 GWd/MTHM. 
4-16

Figure 39 Axial fission distribution for assembly A1 CVBT case at assembly average 

discharge burnup values of 25 and 50 GWd/MTHM for the AO and AFP 

isotope sets 
4-17

Figure 40 Comparison of the base burnup profile and assembly-specific burnup profile 

for A1 

Figure 41 235U (left), 239Pu (middle), and 155Gd (right) concentration for A1 CVBT case at 25 

and 50 GWd/MTHM 
4-18

Comparing the 235U, 239Pu, and 155Gd isotopic concentrations at the two burnup values indicates 

why the fission density distributions are more top-peaked at 50 GWd/MTHM than at 25 

GWd/MTHM, but it does not explain why there is such a significant difference when using the 

assembly-specific burnup profile instead of the base profile. To understand why the base burnup 

profile results in a higher cask keff value than the assembly-specific profiles, the 235U and 239Pu 

concentrations for A1, using the base and the assembly-specific burnup profiles, have been 

plotted in Figure 42 at the assembly-average burnup of 50 GWd/MTHM. The difference in 235U 

remaining when using the two burnup profiles, base vs. assembly-specific, is the primary reason 

that the base burnup profile results in high cask reactivity when compared to the assemblyspecific burnup profile. As shown in Figure 42, the assembly-specific burnup profile results in a 

slightly higher plutonium concentration at the top of the assembly than the base burnup profile, but 

a lower 235U concentration. 

Figure 42 235U (left), 239Pu (right), assembly A1 using the base and assembly-specific 

burnup profiles at 50 GWd/MTHM 

The results for A1 and A2 indicate that using assembly-specific conditions results in lower cask 

reactivity than the base conditions; however, the level of reactivity reduction is largely dependent 

on the individual fuel assembly. The reactivity reduction compared to the base conditions for A1 

and A2 is relatively large, as the burnup distribution’s shape, which is influenced by control blade 

usage, is less limiting than the base burnup profile. Namely, control blade insertion leads to higher 

relative burnups in the top portion of the fuel assembly, which leads to lower cask reactivity. The 

impact of the real control blade histories when considered separately from other parameters has a 

relatively small impact on cask reactivity, but when the impact on the burnup profile caused by 

control blade usage is considered, the overall impact on reactivity is much larger. 
4-19

With respect to the addition of the burnup profile to the assembly-specific conditions, A3 is an 

outlier compared to A1 and A2. There is no impact to A3 with addition of the assembly-specific 

control blade history because A3 contains no control blade insertion. There is almost no impact 

from the addition of the assembly-specific burnup profile for A3, whereas for A1 and A2, the 

addition of the assembly-specific profile has a very significant impact on cask reactivity, up to 7% 

∆keff. This is almost entirely caused by assembly A3 having a burnup profile nearly identical to the 

chosen limiting base burnup profile. However, results for A3 contain important information. First, 

A3 further highlights the importance of selection of the axial burnup profile. A3 also indicates that 

the effect of assembly-specific conditions is rather small when there is little control blade insertion 

and when other parameters are near limiting conditions. A3 indicates that using assembly-specific 

conditions still results in lower cask reactivity compared to the base conditions, but the magnitude 

of this reactivity reduction is small. Addition of all tested assembly-specific conditions for A3 leads 

to a difference in cask reactivity of less than ~0.5% ∆keff compared to the base case. 

The results of the assembly-specific conditions study show that the burnup profile has the largest 

impact on cask reactivity for the test parameters. In this particular study, unlike in 

NUREG/CR-7224 [4], the assemblies were not binned into similar EOC burnup bins. The limiting 

burnup profile and the data from A3 were taken from a first-cycle (low-burnup) fuel assembly. 

Comparing assembly-specific conditions for similar discharge burnup values would lessen the 

effect of the assembly-specific conditions because the base burnup profile and the profiles from 

tested assemblies would be much more similar than they are in this study. 

Summary and Recommendations 

The impact of assembly-specific conditions was studied by performing detailed depletion 

calculations using assembly-specific operating conditions for control blade history, axial coolant 

density profile, axial burnup profile, and axial fuel temperature profile and performing follow-on fuel 

cask criticality calculations using the depleted fuel isotopics. The results obtained are compared to 

similar calculations that use limiting base conditions rather than assembly-specific conditions. 

The assessments documented in this section are not comprehensive; they are based on specific 

assembly and cask configurations and a limited amount of available operating data. The studies 

herein are provided to enhance understanding of important impacts on cask reactivity rather than 

indicating a procedure for performing BWR BUC analysis. 

The primary conclusions from the assembly-specific conditions study are (1) that individually 

limiting depletion conditions chosen from different fuel assemblies results in conservative cask 

reactivity estimates when compared to using assembly-specific data for all depletion conditions, 

and (2) that the magnitude of the reduction in cask reactivity due to the assembly-specific 

conditions is highly dependent on the individual fuel assembly chosen.

The directions and magnitudes of the impacts on cask reactivity are summarized here for the 

correlation of the control blade, axial coolant density, axial burnup profile, and axial fuel 

temperature profile. 

• Use of the assembly-specific burnup profile has the most significant impact on cask

reactivity, which is consistent with previous findings [4]. The impact varies significantly

according to the assembly being considered.

• Control blade insertion during operation impacts the axial shape of the axial coolant

density and burnup profile. Insertion of the control blade to near full-depth tends to impact
4-20

the magnitude of the axial coolant density and burnup profiles, shifting the entire curve to a 

lower value rather than modifying the axial shape of these profiles. Insertion of the control 

blade to depths of 75% or less results in significant changes to the axial power shape, 

leading to changes in the burnup profile. Insertion of the control blade results in a 

reduction in the exit coolant density of ~10% or less during the time that the control blade 

is inserted. 

• Consistent with previous results [4], use of assembly-specific control blade history

increases reactivity relative to a control blades-out assumption. The magnitude of this

effect varies with the control blade history, but it is generally less than 1% ∆keff.

• Addition of the assembly-specific coolant density profile to the assembly-specific control

blade history reduces cask reactivity. The magnitude of this reduction is highly dependent

on the assembly-specific coolant density profile.

• Simulating assembly-specific conditions results in reduced cask reactivity compared to the

base case that uses a control-blades out assumption and limiting values for the coolant

density and axial burnup profile. The magnitude of the reduction in cask reactivity varies

for each assembly, and it would also depend on the penalty taken for using the controlblades-out assumption.

• The cask reactivity reduction that was observed by performing depletion calculations with

assembly-specific conditions ranges from ~0.50% ∆keff to more than 7% ∆keff, depending

on the assembly and the assembly-specific conditions.
5-1

CONCLUSIONS 

Continuing the work documented in NUREG/CR-7224 [4] on extended BWR BUC, this report 

documents the impacts of operating parameters used in assembly depletion calculations on SNF

cask reactivity. The main conclusions from NUREG/CR-7224 are included in this section to 

provide a basis for comparing previous results and the results documented in this report. This 

report quantifies the individual effects of fuel temperature, bypass coolant density, power density, 

and operating history on cask reactivity. Additionally, it quantifies the impact that correlation of 

operating parameters for depletion simulations has on cask reactivity. 

These conclusions are drawn from a relatively limited range of data because the core-follow data 

set used for these investigations represents a single cycle from a single reactor. 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 studies 

were only readily available from one source. Additional work should be performed to demonstrate 

wider applicability of the conclusions drawn here. 

Summary of Previous Studies 

Axial coolant density distributions 

Details of the axial coolant density profile analyses are presented in NUREG/CR-7224, 

Section 4 [4]. The axial coolant 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. A summary of the impacts of axial coolant density distributions is as follows:

• A cycle-averaged coolant density can be used in each node of an axial coolant density

profile for depletion calculations with an appropriate penalty for conservatism.

• Based on the previous analysis [4], a reactivity penalty of 0.25% Δkeff may be sufficient to

cover potential differences between detailed and cycle average coolant density treatments

in depletion calculations.

• A limiting axial coolant density profile will have low moderator densities in the top nodes of

the assembly.

• Use of average coolant densities determined from consideration of multiple assemblies or

multiple axial nodes will result in reactivity underprediction.

• A single coolant density value can be used conservatively in all nodes only if it is lower

than the coolant densities in all nodes of the assemblies to be placed in the cask.

Control blade usage 

The details of the control blade usage analyses are presented in NUREG/CR-7224, Section 5 [4]. 

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 expected as the control blades must

be inserted more than 50% into the core for an extended period before they have a noticeable 

effect. A summary of the impacts of control blade usage is as follows:

• 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, which increases cask reactivity by 4.3% ∆keff. The limiting case for
5-2

the AO isotope set—full control blade insertion for the entire depletion—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.

• 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.

Axial burnup profiles 

The details of the axial burnup profile analyses are presented in NUREG/CR-7224, Section 6 [4]. 

Axial burnup profiles can have a significant impact on cask keff and must be treated appropriately 

to ensure conservative analysis results. The selection of the axial burnup profile has the largest 

impact on cask reactivity of any tested parameter. A summary of the impacts of the axial burnup 

profile is as follows:

• The range of cask keff values resulting from the profiles used in this study was as large as

7.6% ∆keff.

• 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-inch natural blankets.

• Distributed burnup profiles must be considered for extended BWR BUC. End effects of up

to 12.7% ∆keff were identified.

• 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.

• 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.

Operating Parameters 

The impacts of operating parameters (fuel temperature, bypass coolant density, power density, 

and operating history) are relatively small compared to the impacts observed for previous studies 

of coolant density, control blade history, and axial burnup profile [4]. While these impacts are 

small, care should still be taken when modeling these conditions. 

Note that the individual effects of operating parameters were determined for a single assembly’s 

average burnup (45.2 GWd/MTHM); therefore, this study does not quantify burnup dependence 

on these effects. However, the established trends in cask reactivity with independent variations of 

the considered operating parameters are consistent with findings from other studies. 

Fuel temperature 

• Cask reactivity increases with increasing fuel temperature due to increased plutonium

production.

• Fuel temperature impact is ~0.10% keff and ~0.09% keff per 100 K for the AO and AFP

isotope sets, respectively.
5-3

• Using the highest pellet-averaged fuel temperature for all fuel will result in a conservative

cask reactivity estimate.

Bypass water density 

• Cask reactivity increases with decreasing bypass water density due to increased

plutonium production in these cases.

• Cask reactivity increase is less than 0.1% keff for every 1% reduction in bypass water

density for both isotope sets.

• Additional data are needed to know the amount by which the bypass moderator density

can change under normal operating conditions. Using bypass moderator densities higher

than the saturated liquid water density should be avoided to ensure conservatism.

Specific power 

• Calculations show that cask reactivity increases with increasing specific power, but the

magnitude of the increase in cask reactivity is very small—on the order of the uncertainty

of the calculations themselves.

Operating history 

• Typical downtimes (~30 days between cycles) have a negligible impact on cask reactivity.

Extended downtimes preceding an assembly’s last irradiation cycle before being

discharged lead to decreases in cask keff values.

• Cask reactivity is negligibly affected by the power level during assembly’s last irradiation

cycle relative to the lifetime average power. Cask keff slightly increases (within 2σ) with

increasing power level during the last cycle for the AO set and is practically unchanged for

the AFP set.

Assembly-Specific Conditions 

The impacts of the correlation of major operating conditions, coolant density profile (void 

profile), control blade history, and axial burnup profile vary with each fuel assembly. Using 

limiting conditions for the coolant density profile, control blade history, and axial burnup profile 

will result in conservative cask reactivities compared to the use of assembly-specific conditions. 

The impacts of assembly-specific conditions were evaluated for 25 and 50 GWd/MTHM 

assembly average discharge burnups. The assembly-specific conditions were studied for three 

different assemblies. The results obtained using these three assemblies are unlikely to bound all 

possibilities for all reactors. Additional research is needed using multiple cycles of data from 

additional reactors to fully assess the impacts of assembly-specific conditions. 

• Cask reactivity is reduced by using assembly-specific conditions compared to limiting

conditions for the major operating conditions. The magnitude of this reactivity reduction

ranges from ~0.50% ∆keff to more than 7% ∆keff depending on the assembly and

assembly-specific conditions included.

• Using the assembly-specific burnup profile has the most significant impact on cask

reactivity, which is consistent with previous findings. The impact varies significantly

according to the assembly selected.

• The impact of assembly-specific conditions on cask reactivity is greatest for assemblies

with significant control blade insertion. Use of the control blade during operation changes
5-4

the axial shape of the coolant density and burnup profile. Insertion of the control blade

leads to less limiting coolant density and burnup axial profiles. 

• The impacts of assembly-specific conditions on cask reactivity are greater for high

discharge burnups than for low discharge burnups.

The results from previous studies [4] and the studies documented in this report all indicate 

that the axial burnup profile has the greatest impact on cask reactivity of any studied 

parameter. The significant impact to cask reactivity is due to the top-peaked axial fission 

distribution in BWR spent fuel casks combined with the low-burnup axial top portion of BWR 

fuel assemblies. The next largest impact on cask reactivity is the axial coolant density 

distribution. Limiting coolant density distributions have low coolant density at the top of the 

fuel assembly, leading to increased plutonium production. The impact of realistic control 

blade histories is relatively minor because few assemblies experience near full-depth control 

blade insertion for significant periods of irradiation. The impact of modeling assembly-specific 

conditions that are correlated can provide cask reactivity reductions, but the magnitude of the 

reduction varies significantly with each fuel assembly. The impacts of fuel temperature, 

bypass coolant density, power density, and operating history are all relatively small compared 

to the other studied parameters. 

Table 13 provides a brief summary of the parameters studied to date, as presented in 

NUREG/CR-7224 [4] and in this document. Each parameter is summarized by indicating the 

direction and magnitude that its variation has on cask reactivity. Based on the direction and 

magnitude, each parameter is labeled high, medium, or low impact. Table 13 provides the 

most basic summary of each parameter. More detailed information, including burnup 

dependence, changes due to isotope set, etc., can be found in NUREG/CR-7224 and 

Sections 3 and 4 of this document. 
Table 13 Summary of the impact of studied parameters on cask reactivity 

Parameter Impact Physics Basis Direction of variation Magnitude Co

Burnup axial profile High Lower burnup is more 

reactive due to increased 

residual fissile content 

(

235U) of the fuel

Lower burnup in top 

axial portion of the 

assembly leads to higher 

cask keff

Variation up to 7.6% Δ keff

for the tested profiles

Di

us

un

be 

bu

Coolant density axial profile Medium Lower coolant density 

leads to harder neutron 

spectra, resulting in 

increased plutonium 

production

Low coolant density in 

the top axial portion of 

the assembly leads to 

higher cask keff

Axially uniform density 

corresponding to 40% void 

fraction yields 

nonconservative cask 

reactivity up to 10% Δ keff

Ax

de

ch

al

Control blade insertion Medium Control blade insertion 

leads to harder neutron 

spectra, resulting in 

increased plutonium 

production

Control blades inserted 

deeply into the core, late 

in life, for long periods of 

time result in high cask 

keff

~0.6% Δ keff increase due 

to control blade history 

for the tested assemblies 

Co

th

al

re

Assembly-specific conditions Medium Variation of assembly 

power, due to the control 

blade or other factors, 

affects the burnup 

distribution, coolant 

density, fuel temperature, 

etc. 

Use of assembly-specific 

conditions lowers cask 

reactivity compared to 

individually limiting 

conditions for all other 

parameters

Decrease in keff ranging 

from 0.5% to more than 

7% for the tested 

assemblies

In

te

co

bu

lim

Fuel temperature Low Higher fuel temperature 

leads to increased 238U 

absorption resonance 

widths, resulting in 

increased plutonium 

production

High fuel temperatures 

lead to high cask keff

~0.1% Δ keff for every 100 

K increase in fuel 

temperature

No

5-5
Table13 Summary of the impact of studied parameters on cask reactivity (continued) 

Parameter Impact Physics Basis Direction of variation Magnitude Co

Bypass flow density Low Lower moderator density 

leads to harder neutron 

spectra, resulting in 

increased plutonium 

production

Decreased bypass flow 

density results in higher 

cask keff

~0.1% Δ keff for every 1% 

reduction in bypass flow 

density

No 

if 

th

du

Specific power Low Increases in power density 

lead to less time for 

radioactive nuclides to 

decay during operation

Increasing specific power 

tends to increase cask 

keff

Very small, on the order of 

the calculation 

uncertainty

Li

fo

AF

Operating history Low Operating history affects 

the spent fuel 

compositions by changing 

the rates at which fission 

products and other 

actinides are generated or 

consumed

Increased power near 

the end of operation 

tends to increase cask 

keff, typical downtimes 

(~30 days) have a 

negligible impact on cask 

keff

Very small, on the order of 

the calculation 

uncertainty

No

5-6
6-1

REFERENCES 

[1] US Code of Federal Regulations Title 10, “Energy,” US Nuclear Regulatory

Commission, Washington, DC (2017).

[2] Division of Spent Fuel Storage and Transportation, Interim Staff Guidance – 8,

Revision 3, Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in

Transportation 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, Tennessee (April 2015).

[4] W. J. Marshall, B. J. Ade, S. M. Bowman, and J. S. Martinez, Axial Moderator Density

Distributions, Control Blade Usage, and Axial Burnup Distributions for Extended BWR

Burnup Credit, NUREG/CR-7224 (ORNL/TM-2015/544), prepared for the US Nuclear

Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, Tennessee

(August 2016).

[5] 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/CR-7158 (ORNL/TM-2012/261), prepared for the US Nuclear Regulatory

Commission by Oak Ridge National Laboratory, Oak Ridge, Tennessee

(February 2013).

[6] SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis

and Design, ORNL/TM-2005/39, Version 6.2.1, Oak Ridge National Laboratory, Oak

Ridge, Tenn. (August 2016). Available from Radiation Safety Information Computational

Center at Oak Ridge National Laboratory as CCC-834.

[7] M. D. DeHart and S. M. Bowman, “Reactor Physics Methods and Analysis Capabilities

in SCALE,” Nuclear Technology, 174(2) (May 2011): 196–213.

[8] 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, Tennessee

(November 2012).

[9] I. C. Gauld, G. Radulescu, G. Ilas, B. D. Murphy, M. L. Williams, and D. Wiarda,

“Isotopic Depletion and Decay Methods and Analysis Capabilities in SCALE,” Nuclear

Technology, 174(2) (May 2011): 169–195.

[10] I. C. Gauld, M. T. Pigni, and G. Ilas, "Validation and Testing of ENDF/B-VII Decay

Data,” Nuclear Data Sheets 120 (2014): 33–36.

[11] 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).

[12] D. E. Mueller, J. M. Scaglione, J. C. Wagner, and S. M. Bowman, Computational

Benchmark for Estimated Reactivity Margin from Fission Products and Minor Actinides
6-2

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, 

Tennessee (February 2013).

[13] D. P. Henderson, Summary Report of Commercial Reactor Criticality Data for LaSalle

Unit 1, B00000000-01717-5705-00138 REV 00, Civilian Radioactive Waste

Management System M&O Contractor (September 1999).

[14] J. C. Wagner, M. D. DeHart, and B. L. Broadhead, Investigation of Burnup Credit

Modeling Issues Associated with BWR Fuel, ORNL/TM-1999/193, Oak Ridge National

Laboratory, Oak Ridge, Tennessee (October 2000).

[15] I. C. Gauld, G. Ilas, B. D. Murphy and C. F. Weber, Validation of SCALE 5 for Decay

Heat Predictions of LWR Spent Fuel, NUREG/CR-6972, prepared for the US Nuclear

Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge,

Tennessee (2010).

[16] J. S. Martinez, B. J. Ade, S. M. Bowman, I. C. Gauld, G. Ilas, B. J. Marshall, “Impact of

Modeling Choices on Inventory and In-Cask Criticality Calculations for Forsmark3 BWR

Spent Fuel,” CD Proceedings, International Conference on Nuclear Criticality Safety

ICNC’15, Charlotte, NC, USA (September 2015).

[17] US Energy Information Administration, Form GC-859, "Nuclear Fuel Data

Survey" (2013).

[18] J. Hu, J. L. Peterson, I. C. Gauld, and S. M. Bowman, US Commercial Spent Nuclear

Fuel Assembly Characteristics 1968–2013, NUREG/CR (ORNL/TM-2015/619),

prepared for the US Nuclear Regulatory Commission by Oak Ridge National

Laboratory, Oak Ridge, Tennessee (in progress).

[19] C. V. Parks, M. D. DeHart, and J. C. Wagner, Review and Prioritization of Technical

Issues Related to Burnup Credit for LWR Fuel, NUREG/CR-6665 (ORNL/TM1999/303), prepared for the US Nuclear Regulatory Commission by Oak Ridge National

Laboratory, Oak Ridge, Tennessee (February 2000).
NUREG/CR-7240 

ORNL/TM-2017/46

Brian J. Ade, William (B.J.) Marshall, Germina Ilas, Benjamin Betzler, Stephen 

M. Bowman

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

1 Bethel Valley Road

Oak Ridge, TN 37831-6170

M. Aissa, NRC Project Manager

Impact of Operating Parameters on Extended BWR Burnup Credit

Division of System Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555-0001

NUREG/CR-7240 indicates that there are several parameters of medium importance to BWR burnup credit (BUC), 

including fuel temperature, operating history, specific power, and bypass water density. A summary of the effect of 

each of these parameters is provided in this report. In addition, the correlation of various operating parameters is 

studied here. Because BWRs use control blades during operation, there can be significant changes to the local axial 

power shape, coolant density profile, and other parameters when the blades are inserted. Previous studies separately 

examined the reactor operating parameters that impact fuel cask reactivity. The previous studies identified limiting 

conditions for fuel cask reactivity or the direction of trends with cask reactivity. However, simultaneously using limiting 

conditions for all parameters may be unrealistic. When the control blades are inserted deeply into the reactor (a limiting 

condition), the power is reduced, and the void fraction decreases (a less limiting condition). This study identifies the 

impacts of using assembly-specific conditions for the control blade history, coolant density profile, burnup profile, and 

fuel temperature profile. Cask reactivity is reduced by using assembly-specific operating conditions versus combining 

limiting conditions for the individual parameters of interest, but the magnitude of the reactivity reduction varies based on 

each assembly and its operating conditions. Finally, a summary of the present studies is presented within the context of 

the previous studies cited above. The conclusions summarize the technical basis for extended BWR burnup credit as a 

result of the past and present studies.

burnup credit

BWR

spent fuel

control blades

burnup profiles

moderator density

fuel temperature

correlated parameters

assembly-specific conditions

 January 2018

Technical



NUREG/CR-7240 Impact of Operating Parameters on Extended BWR Burnup Credit January 2018