Validation of UNF-ST&DARDS As-loaded safety analysis methods for BWR decay heat calculations

Progress in Nuclear Energy 143 (2022) 104042

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Progress in Nuclear Energy
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Research Paper

Validation of UNF-ST&DARDS As-loaded safety analysis methods for BWR
decay heat calculations☆,☆☆
Justin B. Clarity a, *, Henrik Liljenfeldt b, Kaushik Banerjee c, L. Paul Miller a
a

Oak Ridge National Laboratory, Nuclear Energy and Fuel Cycle Division, Oak Ridge, TN, USA
Noemi Analytics, Uppsala, Sweden
c
Pacific Northwest National Laboratory, Richland, WA, USA
b

A R T I C L E I N F O
Keywords:
Spent nuclear fuel
UNF-ST&DARDS
Decay heat
LWR

A novel assessment of the conservatism in the UNF-ST&DARDS decay heat calculations has been performed.
UNF-ST&DARDS is used to quantify the uncredited margin in safety analysis calculations for spent nuclear fuel
(SNF) storage, transportation, and disposal systems. The goal of the assembly-specific as-loaded safety analysis
approach in UNF-ST&DARDS is to determine the time-dependent realistic state of the SNF systems; however, it is

desirable to conservatively estimate safety analysis parameters, such as decay heat, for a given set of fuel
characteristics. The primary source of conservatism in the generic UNF-ST&DARDS assembly-specific as-loaded
analysis (also referred to as bounding within UNF-ST&DARDS) is the conservative assumptions of various reactor
operational parameters that attempt to envelop wide spectrum of reactor operating scenarios. The assessment in
this paper is necessary to demonstrate that sufficient decay heat conservatism is retained in the UNF-ST&DARDS
bounding as-loaded spent fuel analysis methodology. This paper also demonstrates the time dependent impact of
various parameters such as last cycle power on decay heat values. A comparison between the UNF-ST&DARDS
bounding decay heat calculations and calculations performed using a detailed description of the fuel assembly
operating histories, referred to as detailed calculations, was performed using recently acquired data. The data
used to perform this evaluation are from one set of 3019 assemblies from a US boiling water reactor (BWR) site
and one set of 2117 assemblies (952 8 × 8, and 1165 10 × 10) from a Swedish BWR reactor. Analyses of the US
data involved two sets of assumptions for the bounding calculations and produced two data sets. The first
analysis, in which the cycle-wise burnups were derived for the bounding calculations from the detailed data,
generated the derived data set; the second, in which the assumptions associated with incorporating US nuclear
fuel data survey (Form GC-859) data were included in the calculations for a subset of the same assemblies,
generated the GC-859 data set. When bounding assumptions were used, the average level of conservatism
(overestimation of decay heat) ranges between 9.0% and 17.7% for the derived data set, between 11.4% and
32.3% for the GC-859 data set, between 10.1% and 62.6% for the Swedish 8 × 8 fuel and between 8.3% and
44.7% for the Swedish 10 × 10 fuel. The level of conservatism and the scatter in the ratio between bounding and
detailed data increase significantly for the 100- and 200-year cases for derived US and Swedish data sets. The GC859 data set had large conservatisms in the early cooling times that initially shrank with time and then increased
for the 100-year and 200-year cooling times. These results show that, while UNF-ST&DARDS can be used to
calculate assembly decay heat based on assembly characteristics and operating history to identify potential
significant margins to the licensing basis decay heat calculations, the decay heats calculated by UNF-ST&DARDS

☆
Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US gov­
ernment retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable,
worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public
access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( />ss-plan).☆☆ Notice: This is a technical paper that does not take into account contractual limitations or obligations under the Standard Contract for Disposal of
Spent Nuclear Fuel and/or High-Level Radioactive Waste (Standard Contract) (10 CFR Part 961). To the extent discussions or recommendations in this paper conflict

with the provisions of the Standard Contract, the Standard Contract governs the obligations of the parties, and this paper in no manner supersedes, overrides, or
amends the Standard Contract.
* Corresponding author.
E-mail address: (J.B. Clarity).

/>Received 1 June 2021; Received in revised form 27 October 2021; Accepted 8 November 2021
Available online 25 November 2021
0149-1970/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( />

J.B. Clarity et al.

Progress in Nuclear Energy 143 (2022) 104042

are still conservative compared to more detailed calculations for the range of assemblies and operating condi­
tions assumptions evaluated in this study.

1. Introduction

analysis for subsequent use in thermal evaluation of SNF canisters in
their as-loaded configurations. The aim of this section is to provide
context for the application of the bounding decay heat analysis process
and a basis for comparison to the detailed decay heat analysis process
(Section 2.2). The decay heat calculational process is initiated by
providing the canister identifier and analysis date to UNF-ST&DARDS.
The canister identifier is used to look up all assembly identifiers asso­
ciated with the canister in the Unified Database (UDB). The assembly
identifiers are then used to look up the necessary Oak Ridge Isotope
Generation and Depletion Code (ORIGEN) reactor libraries (Gauld et al.,
2011), assembly average enrichments, burnups, discharge dates, and
assembly masses for each of the assemblies from the UDB. The assembly

type–specific ORIGEN libraries and irradiation information from the
discharge concentrations are then used to perform ORIGEN Assembly
Isotopics (ORIGAMI) depletion calculations to generate axial
segmented, node-wise, assembly-specific discharge nuclide concentra­
tions (Skutnik et al., 2015; Williams et al., 2020). UNF-ST&DARDS then
passes the discharge concentrations to the ORIGAMI decay calculation,
along with analysis-specific decay data necessary to produce decay heat
values for analysis. The decay heat information would then typically be
passed on to Coolant Boiling in Rod Arrays–Spent Fuel Storage
(COBRA-SFS) to perform canister-level thermal analysis to evaluate
quantities such as peak clad temperature. The thermal analysis calcu­
lations with COBRA-SFS are beyond the scope of this work but are dis­
cussed extensively in (Robb et al., 2017).
The ORIGAMI point depletion calculations that generate the
discharge nuclide concentrations use one-group cross-section libraries
generated with the Transport Rigor Implemented with the TRITON
sequence ((DeHart and Bowman, 2011), Sect. 3.1 (Rearden and Jessee,
2016)) using the NEWT lattice physics code and ENDF/B-VII.1 nuclear
data. Because the TRITON/NEWT calculations are relatively time
intensive, it is advantageous to use a set of prescribed modeling condi­
tions for operating history during the library generation process, thus
leaving only assembly type, enrichment, and burnup as the variables
available for the ORIGAMI calculation. The depletion assumptions used
in the TRITON calculations for UNF-ST&DARDS are discussed exten­
sively in Section II.D.3 of (Clarity et al., 2017) for BWR fuel and are
briefly reiterated in Section 2.4.2 to allow for comparison to the detailed
data presented here. Because they are required to accommodate all fuel
assemblies of a specific type, the depletion assumptions must be con­
servative. This work quantifies the conservatism of the bounding decay
heat calculations for BWR fuel assemblies. Fig. 1 provides a diagram of

the UNF-ST&DARDS bounding decay heat calculation process.

The dual-purpose canisters (DPCs) that are currently used for storage
and transportation of spent nuclear fuel (SNF) are designed and evalu­
ated for bounding (enveloping) characteristics such as fuel type, fuel
dimensions, initial enrichment, discharge burnup, and cooling time. The
bounding fuel characteristics for a system are used to establish upper
limits on safety analysis parameters such as decay heat, radiation source
terms, and canister keff values. Realistically, there are wide variations in
SNF assembly burnups, initial enrichments, and cooling times. There­
fore, dry storage systems are typically loaded with assemblies that
satisfy the bounding fuel characteristics defined in the licensing analysis
with some amount of unquantified and uncredited margin. The Used
Nuclear Fuel-Storage, Transportation & Disposal Analysis Resource and
Data System (UNF-ST&DARDS) is being developed to gain a better un­
derstanding of the true safety margins that exist for SNF canisters
(Banerjee et al., 2016; Lefebvre et al., 2017).
The work done with UNF-ST&DARDS to date provides estimates of
the margins associated with modeling accurate assembly enrichments,
burnups, and cooling times for thermal (Robb et al., 2017), criticality
(Clarity et al., 2017), shielding (Radulescu et al., 2017a), and contain­
ment (Radulescu et al., 2017b) analyses. However, due to the limited
detail associated with the available information, many assumptions with
regard to initial fuel composition, geometry, and operating history
remain in the UNF-ST&DARDS depletion and safety analysis method­
ology. Detailed fuel and operating history information from 3019 fuel
assemblies from two operating boiling water reactors (BWRs) at one US
site were obtained by ORNL. This paper also includes results for 2117
assemblies from one Swedish reactor. Analyses using Swedish data were
performed by a joint SKB, ORNL subcontractor (one of the authors of this

paper) using UNF-ST&DARDS. The Swedish data were not directly ob­
tained by ORNL. Calculations were performed for each assembly using
the typical UNF-ST&DARDS as-loaded margin assessment approach,
referred to here as bounding calculations, and with a new process capable
of modeling the fuel and operating history in full detail, referred to here
as detailed calculations.
Comparisons between the detailed and bounding calculations are
performed for decay heat in this work. Decay heat is an important input
to canister-level thermal analysis and is the primary driver of peak clad
temperature calculations (DeVoe et al., 2017) at an assembly level, as
well as a crucial parameter for repository design. This paper provides an
assessment of the amount of conservatism in the bounding calculations
relative to the detailed calculations as well as the operating history
parameters that are most highly correlated with the conservatism and
the nuclides that are most responsible for the differences.
This paper is organized as follows: Section 2 discusses the compu­
tational workflow of the bounding and detailed calculations. Section 3
contains analyses of the detailed data provided by the operating reactors
and comparisons of the assumptions used for the bounding calculations.
Section 4 documents the assembly decay heat calculations and compares
the detailed and bounding results, seeks to understand the drivers of the
differences, and looks at the nuclides that cause the differences. Section
5 presents the conclusions of this work and discusses future work needed
to further establish the conservatism of as-loaded analysis.

2.2. Detailed calculations
The detailed modeling process within UNF-ST&DARDS uses the most
accurate representation of the fuel and operational history possible
given the data available to estimate safety margins inherent in the
bounding calculation approach. The high-fidelity fuel and operational

history information is specified for each node of each assembly. The
combination of the unique fuel description and the unique operational
history for each fuel node requires that the roles of the library generation
and discharge calculation from the bounding UNF-ST&DARDS modeling
process be combined. Combining these roles significantly increases the
number of lattice physics calculations, making it desirable to execute the
lattice calculations more quickly. To accomplish this, the SCALE lattice
physics code Polaris is used for the discharge concentration portion of
the detailed calculations. Polaris is a relatively new module released in
SCALE 6.2 that provides 2D lattice physics analysis capability specif­
ically streamlined for light water reactor (LWR) fuel designs. A detailed

2. Methods
2.1. Bounding decay heat calculations with UNF-ST&DARDS
This section discusses the overall flow of information, codes, and
methods used by UNF-ST&DARDS to perform bounding decay heat
2


J.B. Clarity et al.

Progress in Nuclear Energy 143 (2022) 104042

description of Polaris methods and its calculational approach is provided
by Jessee et al. (Jessee and Wieselquistet al, 2014). As in TRI­
TON/NEWT, the Polaris lattice physics capability is based on multigroup
neutron transport coupled with the ORIGEN depletion/decay module for
time-dependent transmutation of depletion materials (Gauld et al.,
2011). The major differences between Polaris and TRITON/NEWT lie in
the resonance self-shielding and transport methods. Polaris employs the

embedded self-shielding method (ESSM) for resonance self-shielding
(Williams and Kim, 2012). For the transport calculation, Polaris em­
ploys the method of characteristics (MOC), which is sometimes referred
to as long characteristics. MOC solves the characteristic transport equa­
tion over a set of equally spaced particle tracks across the lattice ge­
ometry at prescribed angular quadratures. Polaris provides an
easy-to-use input format, allowing users to set up lattice models with
minimal input. Polaris has been tested extensively and found to perform
well for LWR fuel calculations (Mertyurek et al., 2018). The output of
the Polaris calculation is an F71 discharge composition file containing
pin-wise and node-wise data. The discharge composition data is stored
for future usage in the UDB.
The information used in the safety analysis models is prepared by
performing decay calculations with the composition information ob­
tained from the discharge composition data from the UDB using ORI­
GEN. The ENDF/B-VII.1 nuclear data library is used for both the Polaris
depletion calculations and the ORIGEN decay heat calculations. The
discharge composition data are combined with desired analysis data in a
manner similar to that used in the normal UNF-ST&DARDS analysis
calculations to generate isotopic number densities to generate decay
heats and other safety analysis inputs as desired. A diagram of the
detailed decay heat calculations is presented in Fig. 2. This method of
calculation was used for the detailed decay heat calculations using the
US data.

calculates isotopic concentrations, radiation source terms, and decay
heats for spent pressurized water reactor (PWR) and BWR fuel. Using the
detailed 3D power history from SIMULATE and isotopic inventories
from CASMO, the SNF code provides accurate answers for a variety of
calculations. SNF-calculated decay heats were compared with ORIGEN

calculations, decay heat standards and measured decay heats from the
Swedish interim spent fuel storage facility and were found to agree
closely (Beker et al., 2009; Børresen, 2004). The calculations performed
in 2004 (Børresen, 2004) that compared the SNF code with ORIGEN
show decay heat agreement within 0.1% between the two codes. For
comparison to the bounding and detailed processes in Figs. 1 and 2, the
detailed calculations using the direct method for importing
SNF-generated discharge nuclides is show in Fig. 3.
2.4. Potential sources of difference between the detailed and bounding
calculations
The UNF-ST&DARDS bounding analysis process needs to be flexible
enough to analyze a large portion of the SNF. This is done using infor­
mation in the UDB. The UDB is populated with widely available infor­
mation, such as information from the GC-859 fuel survey (Nuclear Fuel
Data Survey, 2012) and the fuel information available from the open
source literature. The expansive nature of the bounding analysis capa­
bility necessitates compromises on the modeling fidelity. Compromises
that have the potential to affect decay heat calculations include the use
of assembly type aliasing (using ORIGEN libraries from one assembly
design to represent a group of assembly designs), depletion conditions
such as moderator density and blade insertion, and in some cases
GC-859 data approximations such as approximated burnups and algo­
rithmically determined power histories. The following subsections
discuss each of these data and modeling differences within the context of
BWR fuel analysis.

2.3. Direct discharge import method

2.4.1. Fuel type aliasing
Many of the fuel designs are not explicitly modeled in the UNFST&DARDS bounding calculations because sufficient information is not

publicly available to build models for all assembly types. To model a
large variety of fuel, representative fuel assemblies are used in place of
detailed designs for the depletion models. The fuel type used for the US
fuel for which detailed information is available is the ATRIUM 10 fuel
design. Design information for the ATRIUM 10 fuel is not publicly
available. The fuel type aliased to ATRIUM 10 for the bounding calcu­
lations is the GE 14 fuel type. Additionally, the dominant lattice of the
GE 14 fuel assembly is used for depletion.
The ATRIUM 10 fuel assembly has a set of partial-length rods that
only extend part of the length of the assembly, leaving empty or vanished
locations in the upper portion of the assembly. A comparison of the
geometric representation of the ATRIUM 10 dominant lattice and the GE
14 lattice used for the bounding calculations is shown in Fig. 4. The
Swedish fuel assemblies all contain either 8 × 8 or 10 × 10 lattices of
unknown type (due to proprietary considerations, SKB did not disclose
the types of lattices to the author). The assemblies that have 8 × 8

Because many modern core simulators can give detailed discharge
nuclides, an import capability for discharge nuclides has been imple­
mented into UNF-ST&DARDS. For situations in which discharge (postirradiation with no cooling time) nuclide inventories are available from
core simulator results, core-monitoring software outputs, or previously
performed node-level calculations with other lattice physics codes, it is
possible to import results directly into the UDB. The results can then be
used for subsequent decay and safety analysis calculations. This is a
flexible method for gathering data to validate the UNF-ST&DARDS
bounding calculation input assumptions. Using this technique allows for
the detailed decay data and other downstream processes to be leveraged
without including all operating data. This method was used to collab­
orate with the Swedish Nuclear Fuel and Waste Management Company
(SKB).

The SNF code developed by Studsvik (SNF) was used by SKB to
determine the discharge nuclide concentrations that were subsequently
imported into the UDB and decayed using the UNF-ST&DARDS ORIGEN
calculations similar to those discussed in Section 2.2. The SNF code

Fig. 1. Bounding decay heat calculation process within UNF-ST&DARDS.
3


Progress in Nuclear Energy 143 (2022) 104042

J.B. Clarity et al.

Fig. 2. Analysis flow of UNF-ST&DARDS detailed decay heat calculations.

Fig. 3. Analysis flow of UNF-ST&DARDS detailed decay heat calculations using the direct discharge import method from the SNF code.

Fig. 4. Radial layout comparison between the ATRIUM 10 (left) and GE 14 (right) fuel assemblies.

lattices are aliased to an early-generation GE fuel design with a single
water rod; the assemblies that have 10 × 10 lattices are aliased to the GE
14 fuel design, as was done with the US ATRIUM 10 fuel.

Table 1
Summary of BWR depletion parameters.

2.4.2. Depletion Conditions
The BWR depletion parameters used for the BWR ORIGEN library
generation in the bounding analysis sequence are discussed extensively
in an article by Clarity et al. (2017) and are presented in Table 1. The

depletion parameters of the highest importance with regard to actinide
buildup, which affects long-term SNF decay heat, are moderator density
and control blade insertion, which are shown to be holistically conser­
vative for criticality calculations in (Clarity et al., 2017).

4

Parameter

Value

Fuel rod mixture
Fuel density (g/cm3)
Fuel temperature (K)
Moderator
temperature (K)
Moderator density (g/
cm3)
Absorber exposure

UO2
10.74
1200.00
560.70
0.30
Gd2O3 admixed with fuel pellets in a small number of rods
based on fuel type and full-length control blade exposure
throughout irradiation history

J.B. Clarity et al.

Progress in Nuclear Energy 143 (2022) 104042

2.4.3. GC-859 data approximations
For the US fuel, the GC-859 fuel survey information contains only the
final discharge burnup of the assembly and the cycles in which it was
irradiated. This information does not give any information with regard
to the temporal distribution that resulted in the final burnup of the fuel.
To perform the point depletion calculations, UNF-ST&DARDS distrib­
utes the burnup of the assembly according to the time over which each
cycle occurred, resulting in a constant power depletion. Common fuel
management strategies result in more burnup being accrued by fuel
during its first and/or second cycle of operation and less during the final
cycle in many cases. For the particular fuel used in this analysis, the
burnups are also rounded to the nearest gigawatt-day per metric ton of
uranium. The rounded values represent approximations in the data that
should be considered.

sometimes at reduced power. The integral values, VH, and nodal
burnup are useful because they are cumulative. The VH is the burnup
averaged void fraction over the assembly’s operational history to
that point in its life.
2. The second data format provided for the US plant is the control blade
insertion data, which is provided for several statepoints within a
cycle where the control blades are either inserted or removed. This
data was modeled as a histogram of bladed and unbladed portions of
each cycle for each node of each assembly. These histograms were
then combined with the assembly-wise end-of-cycle data to provide a
complete description of the depletion history of each node of each

assembly.
3.1.1. Derived and GC-859 data sets
UNF-ST&DARDS typically runs bounding calculations using data
available from the GC-859 fuel survey. The aim of this work is to
determine the level of conservatism inherent in the UNF-ST&DARDS
methods. These methods encompass both the operating history and fuel
modeling assumptions that are used in the depletion and safety analysis
modeling and the techniques used to process the assembly burnups into
UNF-ST&DARDS safety analysis inputs. The isolated impact of the
operating history assumptions was investigated by deriving bounding
data input from the detailed data available for the US fuel assemblies.
The bounding data for these calculations were derived by averaging the
enrichments and discharge burnups of each of the 25 nodes to determine
an assembly-averaged enrichment and burnup similar to what is pro­
vided in the GC-859 survey. In doing this, differences in total assembly
burnup and the burnup achieved in each cycle of operation, and hence
the specific power at which the fuel assembly was operated during that
cycle, are eliminated. For the remainder of this work, bounding calcu­
lations that are performed with data prepared in this manner are
referred to as the derived data set. Derived calculations are performed for
all 3019 fuel assemblies used in this work. The combined impact of UNFST&DARDS data-processing techniques and the operational history ef­
fect was assessed by using the GC-859 data provided for the assemblies.
Not all of the fuel for which detailed information is available have in­
formation available from the GC-859 fuel survey because some of the
fuel began operation after the latest available survey was completed
(2013). The data set for which GC-859 data are available contains a
1472 assembly subset of the derived data set and is referred to as the GC859 data set. The detailed calculations for both the derived data set and
the GC-859 data set use the same fuel and operating history assump­
tions, making the GC-859 detailed calculations simply a subset of the
derived data. A summary of what is included in the derived and GC-859

data sets is provided in Table 2.

3. Data
This section discusses structure of the data used in the comparative
analysis between the bounding and detailed calculations for the US and
Swedish fuel. Statistical summaries of the important parameters are also
provided.
3.1. US data
The calculations performed for US fuel were based on data for a
single two-unit BWR site in the United States. The reactors at the site are
GE BWR Class 4 reactors with C-lattice cores. The C-lattice designation
indicates that the water gap is the same size on both sides of the fuel
assemblies. Each core contains 764 channeled fuel assemblies with an
active fuel length of 149.45 in. (modeled as 150 in.). The data contained
information for 3019 assemblies that were introduced in 5 cycles of
operation for each reactor (10 total cycles). Each fuel assembly was
followed through its full irradiation history, which includes consider­
ation of depletion of the fuel in an additional one to two cycles of
operation for each unit beyond the 10 cycles in which the fuel is intro­
duced. Each fuel assembly is of the Framatome ATRIUM-10 design and
contains 83 full-length rods, 8 part-length fuel rods, and one central
water channel occupying 9 fuel rod positions. Gadolinia (Gd2O3 blended
with UO2) rods are designed to control assembly axial and radial power
distribution and core reactivity. The fuel rods have natural uranium
blankets at the upper and lower ends.
Each core also contains 185 control blades. The control blades have a
cruciform cross section containing neutron absorber for reactivity con­
trol. The original equipment control blades contain boron carbide
powder in stainless steel tubes, and newer-generation control blades
contain a combination of boron carbide–filled tubes and solid hafnium

rods. Each of the blades can be inserted from the bottom of the core
between four adjacent fuel assemblies.
The fuel information for US fuel includes a complete specification of
the axial and radial layout of each assembly. The ATRIUM 10 fuel design
used for all US BWR cycles is provided. It is a modern BWR fuel assembly
categorized as multi-lattice according to the description provided in
Clarity et al. (2017). The fuel assembly specification designates which
lattices occupy each of the 25 nodes used in the Framatome core design
calculations. For each of the specified lattices, pin-wise fuel composi­
tions and radial orientations of the rods are provided.
Detailed operating history information is provided for the US BWR
cycles of interest in two formats.

3.1.2. Assembly burnup
The burnups of the US fuel assemblies in the derived data set ranged
Table 2
Comparison of the number of assemblies and input data for the derived and GC859 data sets.
Data Set

1. The first format is the assembly-wise end-of-cycle information,
including the axial node number, the nodal burnup, the instanta­
neous moderator density, the void history (VH), and the fuel tem­
perature. Because the end-of-cycle values are specified, the
instantaneous information—including the moderator density and
fuel temperature—is not representative of the assembly’s cumulative
behavior, particularly because the end-of cycle-statepoints are

Name

Derived

GC-859

Number of
Assemblies
Bounding
Calculation
Description

3019

1472 (subset of Derived set)

Detailed
Calculation
Description

5

Bounding operating history
Bounding operating history
assumptions with assembly
assumptions with assembly
enrichment, burnup and
enrichment and burnup from
cycle-wise burnup
GC-859 fuel survey and cycledistribution derived from
wise burnup distribution
detailed data.
constant power assumption.

Full axial and radial description of fuel geometry and
composition with time dependent operating conditions.


J.B. Clarity et al.

Progress in Nuclear Energy 143 (2022) 104042

from 33,312 to 51,628 MWd/MTU, with a mean and standard deviation
of 43,802 ± 3045 MWd/MTU. The GC-859 data set burnups range from
33,312 to 50,860 MWd/MTU with a mean and standard deviation of
43,922 ± 3209 MWd/MTU. Histograms of the assembly burnups for the
derived and GC-859 data sets are shown in Fig. 5. Based on examination
of the summary statistics and the histograms in Fig. 5, there are no gross
deviations in the assembly average burnups between the derived and
GC-859 data sets.
One source of potential deviations between the results of the detailed
and bounding calculations for the GC-859 data set is the difference be­
tween the burnup data provided in the GC-859 fuel survey and the
detailed fuel and operational information obtained for this work. The
declared burnups from the GC-859 data for the US BWR site evaluated in
this study are reported in integer numbers of GWd/MTU, such as 37 or
38 GWd/MTU. Fig. 6 provides a histogram of the differences between
the GC-859 assembly average burnups and the assembly average burn­
ups derived from the nodal data provided with the detailed data. The
difference in burnup was calculated by subtracting the detailed burnup
from the GC-859 burnup. The differences in burnup range between
− 142.0 and 1049.2 MWd/MTU, with a mean and standard deviation of
456.4 ± 304.9 MWd/MTU. The histogram in Fig. 6 indicates that the
burnup was rounded up for most of the assemblies in the GC-859 set for

this particular site.

Fig. 6. Difference in burnup between the GC-859 data and detailed information
using 1472 assemblies from GC-859 set.

burnup information, it is also important to understand the differences in
the operating history of the detailed data compared to the bounding
assumptions used in the UNF–ST&DARDS depletion method. The two
operating parameters with the largest impact on the neutron energy
spectrum during depletion and therefore the buildup of actinides in the
fuel are the moderator density and the presence of control blades during
depletion. As noted in Section 2.4.2, the control blades are modeled as
being present for the entirety of the depletion, and the moderator den­
sity is modeled as being 0.3 g/cm3 for the bounding calculations.
For the detailed calculations, the moderator density information
provided for the US fuel assemblies is the VH, which is calculated using
Eq. (1),
∑N ∑C
k=1
j=1 BUjk VFjk
VH = ∑N ∑C
(1)
k=1
j=1 BUjk

3.1.3. Moderator density and control blade insertion
In addition to understanding the fuel’s initial composition and

where BU is the cycle burnup of an axial node, VF is the instantaneous
void fraction, N is the number of nodes, C is the number of cycles.

The VH values were then converted to burnup averaged moderator
density using a liquid phase density of 0.743 g/cm3 and a vapor phase
density of 0.0353 g/cm3, corresponding to the values used from the
Polaris code. Conversion to burnup-average moderator density allows
for better comparison to the Swedish data. The measure of control rod
exposure used for this work is the bladed fraction (BF), which is calcu­
lated using Eq. (2),
∑N

k=1 BUk

BF =

∑C ∑S

1 if Bladed
i=1 CFijk { 0 if not Bladed
∑N ∑C
k=1
j=1 BUjk

j=1

(2)

where CF is the fraction of cycle burnup in a statepoint, and S is the
number of statepoints in a cycle.
The histograms of the moderator density and BF for the detailed data
for the assemblies in the Derived and GC-859 data sets are shown in
Fig. 7 and Fig. 8. Fig. 7 shows that the history-averaged moderator

density ranges between 0.366 and 0.508 g/cm3, with an average of
0.414 g/cm3 for the derived data set, and ranges between 0.372 and
0.508 g/cm3 with an average of 0.419 g/cm3 for the GC-859 data set.
Even at the lowest observed moderator density, the densities are higher
than the 0.3 g/cm3 value used in the bounding calculations. Fig. 8 shows
that the history-averaged BF ranges from 0 (in many cases) to 0.366 for
both the derived data and the GC-859 data. The average BF is 0.074 for
the derived data; the average BF for the GC-859 data is 0.075. These
values are substantially lower than the value of 1.0 assumed in the
bounding calculations. A lower moderator density and a higher fraction

Fig. 5. Distributions of assembly average burnups for the derived data set as­
semblies (top), and the GC-859 data set (bottom).
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Fig. 7. Distribution of moderator density for the derived data set (top), and the
GC-859 data set (bottom).

Fig. 8. Distribution of BF for the derived data set (top), and the GC-859 data
set (bottom).

of the assembly’s history being bladed will lead to a harder neutron
energy spectrum and therefore more actinide buildup at a given burnup.
This should lead to conservatism in decay heat calculations, particularly
at cooling times longer than five years. It is notable that there is little

difference in the appearance of the histograms for the derived and GC859 data set moderator density and BF values, indicating that the GC859 set it is likely to be an unbiased subset of the assemblies.

detailed and bounding analyses. To aid further discussion, the last cycle
specific power (LCP) for the Derived data set and the for the GC-859 data
set detailed and bounding calculations are provided in Fig. 9. There is
only one set of LCPs for bounding and detailed calculations for the
derived data set because the bounding cycle burnups and therefore
powers are calculated from the detailed data for the derived data set.
The LCPs in Fig. 9 range from 4.27 to 33.54 MW/MTU with an
average of 20.55 MW/MTU for the derived data set. They range from
4.27 to 32.90 MW/MTU with an average of 19.88 MW/MTU for the
detailed calculations in the GC-859 data set, and from 19.81 to 33.09
MW/MTU with an average of 26.57 MW/MTU for the bounding calcu­
lations. This shows that for the GC-859 data, there appears to be bias
toward higher specific powers in the bounding data due to the way that
data are processed upon import by UNF-ST&DARDS. There is also a
noticeable striping in GC-859 LCP values in the bottom of Fig. 9 due to
the rounding to the GC-859 reported burnups.
Equation (3) is used to provide a single-parameter descriptor of how
large the overprediction in the last cycle power is. The last cycle power
ratio (LCPR) is calculated by dividing the power in the last cycle of
operation for the bounding calculation by the power in the last cycle of
operation from the detailed data calculation. The LCPR parameter is
only applicable to the GC-859 data set because the derived data set

3.1.4. Last cycle power
Most of the safety analysis calculations performed by UNFST&DARDS are relatively insensitive to the temporal distribution of
burnup by the fuel assembly; however, a few short-lived nuclides (134Cs,
106
Rh, and 144Pr) that contribute to decay heat saturate with burnup and

are largely dependent on the assembly power level during the last
portion of the assemblies’ irradiation. These nuclides contribute to
decay heat over a relatively short time period following assembly
discharge (less than 10 years). If the power towards the end of the
irradiation is too low in the bounding calculations it could result in a
nonconservative estimate of the decay heat relative to the detailed cal­
culations. To investigate this the effect, the specific power level in the
last cycle of operation was calculated by dividing the burnup accrued in
the last cycle of operation by the length of the last cycle for both the
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Fig. 10. Distribution of LCPR values for the GC-859 data set.

3.2. Swedish data
Discharge nuclides from 2117 Swedish BWR assemblies were
generated using their full operational histories. The discharge nuclides
were imported by SKB staff using Studsvik’s SNF Code and were im­
ported into UNF-ST&DARDS for subsequent decay calculations using the
direct discharge import method described in Section 2.3. The calcula­
tions have undergone the quality assurance process that is performed as
part of the nuclear plants’ operation and core monitoring.
The data are from a single BWR unit and include data for both 8 × 8
and 10 × 10 types from multiple vendors; the specific fuel designs are
not known. The discharge dates for the fuel assemblies studied here
range from the 1989 to 2017. The assembly average burnups range

between 27,544 and 47,608 MWd/MTU, with an average and standard
deviation of 41,527 ± 2845 MWd/MTU. When the fuel was broken
down by the fuel type, burnups for the 8 × 8 fuel (952 assemblies)
ranged from 27,544 to 44,644 MWd/MTU with a mean and standard
deviation of 39,525 ± 2570 MWd/MTU, and burnups for the 10 × 10
fuel (1165 assemblies) ranged from 38,806 to 47,608 MWd/MTU with a
mean and standard deviation of 43,202 ± 1946 MWd/MTU. This in­
dicates that the 10 × 10 fuel generally achieved more burnup than the 8
× 8 fuel. A histogram of the Swedish data set burnups is shown in
Fig. 11.
Moderator densities were directly provided for the Swedish data. The
lifetime averaged moderator densities range from 0.404 to 0.594 g/cm3
with a mean and standard deviation of 0.490 ± 0.035 g/cm3. When
broken down by fuel type the 8 × 8 fuel assemblies had moderator
density ranging from 0.408 to 0.594 g/cm3 with a mean and standard
deviation of 0.500 ± 0.040 g/cm3 and the 10 × 10 fuel assemblies had
moderator densities ranging from 0.404 to 0.579 g/cm3 with a mean and
standard deviation of 0.489 ± 0.029 g/cm3. A histogram of the
moderator densities is provided in Fig. 12.
The values of BF were also directly taken from the core simulator
calculations. The values of BF ranged from 0.004 to 0.0.230 with a mean
and standard deviation of 0.046 ± 0.047 for the Swedish data set. When
considering the different fuel types the BF values for the 8 × 8 fuel as­
semblies ranged from 0.004 to 0.179 with a mean and standard devia­
tion of 0.028 ± 0.031 and the BF values for the 10 × 10 fuel assemblies
ranged 0.008 to 0.230 with a mean and standard deviation of 0.061 ±

Fig. 9. Distribution of LCP used for the derived data detailed and bounding
calculations (top), the GC-859 detailed calculations (middle), and the GC-859
bounding calculations (bottom).

calculates the cycle-wise bounding burnups from the detailed data and
would always result in an LCPR of 1.0.
LCPR =

LCPBounding
LCPDetailed

(3)

The LCPR values were calculated for all of the 1472 fuel assemblies
in the GC-859 data set. The LCPR values for the GC-859 data set range
from 0.860 to 5.022 with a mean and standard deviation of 1.704 ±
0.860. A histogram of the LCPR values is provided in Fig. 10. Based on an
examination of the results in Fig. 10, it is apparent that there are a
number of assemblies with LCPR values in the near vicinity of 1.0,
indicating that the algorithm used in UNF-ST&DARDS provides results
that are in good agreement with actual operation much of the time;
however, there are an also a large number of assemblies for which the
specific power is substantially overpredicted during the last cycle of
operation.
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Fig. 11. Distribution of assembly burnups for the Swedish data set.

Fig. 13. Distribution of BF values for the Swedish data set.

Fig. 14. Distribution of LCP values for the Swedish data set.

Fig. 12. Distribution of burnup averaged moderator densities for the Swedish
data set.

4.1. Derived US data set

0.052. A histogram of the values of BF for the Swedish data set are
provided in Fig. 13.
LCP values for the Swedish data set were derived from information
taken from core simulator values. The values of LCP range from 1.34 to
25.64 MW/MTU with a mean and standard deviation of 7.17 ± 4.57
MW/MTU. When the different fuel types were considered, the 8 × 8
assemblies had LCPs ranging from 1.34 to 23.27 MW/MTU with a mean
and standard deviation of 7.19 ± 5.30 MW/MTU and the 10 × 10 fuel
assemblies range from 1.78 to 25.65 MW/MTU with a mean and stan­
dard deviation of 7.15 ± 3.86 MW/MTU. This distribution of LCP values
for the Swedish data set is shown in Fig. 14.

An important input to thermal safety analysis of SNF for storage,
transportation, and disposal system design is decay heat. This section
presents an analysis of the impact of the operating histories on the decay
heat of discharged fuel assemblies. Calculations were performed for the
3019 fuel assemblies considered here using the bounding and detailed
analysis sequences available in UNF-ST&DARDS. Each assembly was
decayed to 1, 5, 10, 20, 100, and 200 years following assembly
discharge, and the decay heat was calculated.
The decay heat ratio (DHR) is used as a means of comparing the

detailed and bounding decay heats and was calculated by dividing the
bounding decay heat by the detailed decay heat as shown in Eq. (4). The
DHR is effectively the amount of conservatism in the bounding decay
heat. For example, a DHR of 1.35 would represent a 35% conservatism
in the bounding decay heat. The minimum, maximum, mean, and
standard deviation of the detailed and bounding decay heats and DHRs
for each cooling time are shown in Table 3 for the derived data set.
Additionally, the detailed and bounding decay heats are plotted as a

4. Results and discussion
This section presents the results of the bounding and detailed decay
heat calculations. The results of the US derived data set are discussed in
Section 4.1, the results of the US GC-859 data set are discussed in Section
4.2, and the results of the Swedish data set are discussed in Section 4.3.
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Table 3
Summary statistical comparison between the detailed decay heats and the derived bounding decay heats (watts).
Decay Time (years)
1
5
10
20
100
200

Detailed

Bounding

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

829.7
287.3
196.9
155.6
50.2
27.2

1535.8 ± 336.5
386.8 ± 29.1
270.8 ± 20.2
212.9 ± 15.9
68.1 ± 4.6
36.3 ± 2.3

2033.9
488.0
332.8
257.7
79.5
42.2

934.2
323.4
215.4
167.7
57.2
32.7

1669.5 ± 343.3
439.7 ± 32.7
300.5 ± 24.2
232.1 ± 19
76.3 ± 5.5
42.7 ± 2.9

2189.3
560

374.4
285.5
91.1
50.1

1.053
1.099
1.070
1.052
1.060
1.082

1.091 ±
1.137 ±
1.109 ±
1.090 ±
1.121 ±
1.177 ±

1.133
1.180
1.151
1.131
1.200
1.297

function of discharge burnup for the derived data in Fig. 15. The DHRs
for all of the decay times are plotted against the detailed decay heat in
Fig. 16.
DHR =

DHBounding
DHDetailed

DHR
0.018
0.015
0.015
0.016
0.032
0.048

all of the decay heats with burnup. It is also noticeable that there are two
distinct bands of decay heats with burnup, and the bands are most
distinct at low cooling time, merging to a single band at the later cooling
times. The presence of the two bands at low cooling time is likely due to
the multimodal nature of the LCP distribution that is apparent in top
portion of Fig. 9, where the top band is likely correlated with the higher
mode of Fig. 9 and the bottom band is likely due to the lower modes of
Fig. 9. The merging of the bands of decay heats is more pronounced for
the bounding data and occurs almost completely by 20 years of cooling
time. The detailed data merges over the first 20 years of decay time but
then shows more pronounced scatter for the 100- and 200-year cases.
The increase in scatter at longer cooling times is due to the dominance of
the actinides, which are more sensitive to variations in the neutron
energy spectrum during depletion at longer cooling times.

(4)

A few observations can be made when the detailed and derived

bounding data calculated decay heats in Table 3 and Figs. 15 and 16 are
examined. The first observation is that, in all cases, the bounding decay
heat is greater than the detailed decay heat in terms of the minimum,
maximum, and average values and by inspection of the burnupdependent plots. This confirms the conservatism associated with oper­
ating history assumptions made within the bounding sequence of UNFST&DARDS. For the derived data set, the average level of conservatism
ranges between 9.0% and 17.7%, with the conservatisms having an
approximate range about a mean of 8% between minimum and
maximum for decay times between 1 and 20 years. The level of
conservatism and the scatter in the DHR data increase significantly for
the 100- and 200-year cases.
The second observation is that there is a roughly linear behavior for

4.1.1. Irradiation parameter and nuclide contributions to variability of
decay heat for the derived data set
Correlations with operating history parameters and the individual
nuclide contributions to decay heat were examined to further investigate

Fig. 15. Detailed and derived bounding decay heats vs. burnup for 1, 5, 10, 20, 100, and 200 years of cooling time.
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Fig. 16. Decay heat ratio vs. detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the derived data set.

the causes of the conservatism in the bounding decay heats relative to
the detailed decay heats. The derived data set is examined first because
the differences associated with processing the GC-859 data into cyclewise burnups are not included in this data set. The operating parame­

ters considered for the decay heat evaluation are VH, BF, the sum of VH
and BF (VH + BF), and LCP. VH is used rather than moderator density
because it is positively correlated with increases in decay heat, as is BF,
so the sum of the two numbers results in a potentially meaningful metric
for assessing the combined effect of operational parameters on the
neutron energy spectrum. The nuclides considered in the evaluation are
listed in Table 4. For simplicity, the decay heat from 137mBa is combined
with the decay heat from 137Cs, and the decay heat from 90Y is combined
with the decay heat from 90Sr because the latter nuclides are short lived
and are in secular equilibrium with the former nuclides. For all cooling
times of the detailed and bounding calculations, this set of nuclides was
sufficient to capture more than 95% of the total assembly decay heat.
For cooling times greater than 1 year, these nuclides capture more than
99% of the total assembly decay heat.
A correlation analysis was performed on the detailed decay heats, the
bounding decay heats, and the DHRs to investigate the operating pa­
rameters that most heavily influence the conservatism in decay heat
calculations. It is widely known that decay heat at a constant cooling
time is strongly influenced by burnup. Because burnup is explicitly
accounted for in UNF-ST&DARDS calculations and the goal is to deter­
mine what factors lead to the conservatism discussed in Section 4.1, it is
desirable to remove burnup as variable from the analysis. To control for
burnup, a linear fit of the detailed and bounding decay heats was per­
formed as a function of assembly average burnup, and the residual decay
heat about the trend line was calculated by subtracting the fitted values
from each of the explicitly calculated assembly decay heats. The re­
siduals were not calculated for the DHR values because the detailed and
bounding decay heats are calculated at the same burnup. The Pearson

correlation coefficient was then calculated for the detailed decay heat

residuals, the bounding decay heat residuals, and the DHR values with
the LCP, VH, BF, and VH + BF variables for each of the cooling times
considered here. The correlation coefficients are shown in Fig. 17.
Fig. 18, and Fig. 19 for the detailed decay heat residuals, the
bounding decay heat residuals, and the DHRs, respectively. The corre­
lation coefficient inherently ranges from − 1 to 1 and the color coding in
Fig. 17 through 19 shades values closer to one in red and values closer to
negative one in blue, with values near zero being lighter shades of each
color.
It is apparent from an examination of the correlations for the detailed
decay heat residuals in Fig. 17 that there is a strong correlation between
the decay heat residuals and LCP and VH with the strength of the cor­
relations varying based on the cooling time considered. The correlation
between the decay heat residuals and LCP is 0.996 and 0.975 at 1 year
and 5 years of cooling time, respectively, representing a nearly perfect
linear relationship. The correlation drops to 0.725 at 10 years of cooling
time and to values that are approximately 0.6 for the higher cooling
times. This indicates that at short cooling times the variation in the

Table 4
Nuclides used for decay heat investigations.
Actinides
241

243

Fission Products
242

244

Am, Am, Cm, Cm,
Pu, 240Pu and 241Pu

239

238

Pu,

144
144

Ce, 134Cs, 137Cs (137Cs + 137mBa),
Pr, 106Rh, and 90Sr (90Sr + 90Y)

154

Eu,

Fig. 17. Correlation coefficient between detailed decay heat and LCP, VH, BF,
and the sum of VH and BF by cooling time.
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residuals and BF.

It is apparent from an examination of the correlations for the
bounding decay heat residuals in Fig. 18 that again there is a strong
correlation between the bounding decay heat residuals and LCP for the
1-year and 5-year cases. Because the high correlation was present in the
1- and 5-year cases for the detailed calculations and the cycle-wise
burnups for each assembly were calculated based on the average of
the nodal information used for the detailed calculations, it is logical that
the same correlations would be present in the bounding calculations.
Also, there are mild correlations between the bounding decay heat re­
siduals and VH and VH + BF. The correlations are likely a result of the
cross correlation between VH and LCP, like what was noted for the
detailed decay heat residuals. No other strong correlations were
observed for the bounding decay heat residuals. This is expected because
the depletion conditions for the bounding calculations are fixed based on
the assumptions discussed in Section 2.4.2, and little variability should
be expected outside total burnup and the temporal burnup distribution.
The correlations for the DHR values with the operating parameters
shown in Fig. 19 indicate negative correlations to the same parameters
as the detailed decay heat residuals, namely, LCP, and VH. It is intuitive
that the DHR would be negatively correlated with VH because VH causes
the detailed decay heat to skew high for a given burnup, and the
bounding decay heat is insensitive to it, so the ratio of bounding decay
heat to detailed decay heat should trend negatively with increasing VH.
The negative correlation between LCP and DHR is less intuitive because
both the bounding and detailed decay heat residuals had positive cor­
relations with LCP. There is a correlation coefficient of 0.999 between
the bounding and detailed decay heats at 1 year of cooling time, indi­
cating that the negative correlation is possibly due to the bounding
decay heats and detailed decay heats having different sensitivities to
LCP.

The change in individual nuclide decay heat between the bounding
and detailed calculations vs. DHR is plotted in Fig. 20 for all of the
cooling times analyzed here. The data in the upper left portion of Fig. 20
indicate that the primary nuclides contributing positively to the
conservatism in the bounding calculations in the 1-year cooling time
case are 134Cs, 244Cm, 106Rh, and 238Pu, with 90Sr and 144Pr contributing
negatively to the conservatism between the two sets of calculations. The
increased decay heat contributions of 244Cm, 134Cs, and 238Pu in the
bounding calculations relative to the detailed calculations are due to the
harder neutron energy spectrum. The decreased decay heat contribu­
tions of 90Sr and 144Pr in the bounding calculations relative to the
detailed calculations are due to the lower 239Pu/235U fission ratio
associated with a softer energy spectrum during the detailed depletion
calculations. The fission yields of 90Sr and 144Pr are lower from 239Pu
than from 235U. The data in the upper right portion of Fig. 20 show that a
similar set of nuclides contribute to the conservatism in the bounding
calculations in the 5-year case. For the five-year case, the negative
contribution of 144Pr and the positive contribution of 106Rh have
virtually disappeared, and the positive contribution of 134Cs has
decreased relative to 244Cm because of the short half-life of 134Cs. By 10
years, the conservatism in the decay heat calculations is due almost
entirely to 244Cm; the effect of 134Cs has dropped out completely. The
20-year case begins to show relatively increased contributions of 241Am,
which is the primary driver of the conservatism in the 100- and 200-year
cases.

Fig. 18. Correlation coefficient between bounding decay heat and LCP, VH, BF,
and the sum of VH and BF for the derived data set.

Fig. 19. Correlation coefficient between DHR and LCP, VH, BF, and the sum of

VH and BF for the derived data set.

specific power of the fuel explains the variation in the detailed decay
heat that is not due to burnup variation. The correlation between VH and
the detailed decay heat residuals is strongest for the 100 year (0.900)
and 200 year (0.880) of cooling time cases and gradually drops off with
decreasing cooling time to a value of 0.612 for the 1-year case. The
strong correlation between VH and the residual decay heat for the
detailed calculations is expected due to the impact of increased VH on
the actinide source term, which dominates decay heat at longer cooling
times.
Correlations between input variables can sometimes affect the cor­
relations between the outputs. The correlation between the inputs LCP
and VH is 0.602 for the derived data set. This correlation is logical
because assemblies that experience higher specific powers during
operation result in larger enthalpy rises in coolant and therefore higher
void fractions; however, the correlation between LCP and VH is limited
because LCP only considers the last cycle of operation, to which shortlived nuclides are sensitive. The cross correlation between LCP and
VH is responsible for the correlations between LCP and the decay heat
residuals at high cooling times and VH and the decay heat residuals at
short cooling times. A moderate correlation between BF and residual
decay heat was also observed for the 100-year case (0.553) and 200-year
cases (0.559), although the correlation between the VH + BF and the
detailed decay heat residuals is slightly smaller than the correlation on
VH alone. The correlation between BF and VH is 0.311 and likely does
not explain the moderate correlation between the detailed decay heat

4.2. GC-859 US decay heat
This section discusses the decay heat results for the 1472 assemblies
for which GC-859 survey data were available. Comparison of those data

to the data found in Section 4.1 allows for insight into the effect that the
GC-859 data processing has on conservatism of the UNF-ST&DARDS
decay heat calculations in addition to the impact of the operating history
effects. Each assembly was decayed to 1, 5, 10, 20, 100, and 200 years
following assembly discharge, and the decay heat was calculated. Like
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Fig. 20. Nuclide decay heat changes vs. DHR for the derived data set.

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the derived data set, the DHR values were also calculated for each as­
sembly using Eq. (4).
The minimum, maximum, mean, and standard deviation of the
detailed and bounding decay heats and DHRs for each cooling time are
shown in Table 5 for the GC-859 data set. Additionally, the detailed and
bounding decay heats are plotted as a function of discharge burnup (as
calculated from the detailed data) for the GC-859 data in Fig. 21. The
DHRs for all of the decay times are plotted against the detailed decay
heat in Fig. 22.

Four observations were made based on an examination of the
detailed and GC-859 bounding data calculated decay heats in Table 5,
Figs. 21, and Fig. 22. The first observation is that, in all cases, the
bounding decay heat is greater than the detailed decay heat in terms of
the minimum, maximum, and average values and by inspection of the
burnup-dependent plots. This confirms the conservatism associated with
operating-history assumptions made within the bounding sequence of
UNF-ST&DARDS as well as with the algorithm used to process the GC859 burnup data into cycle-wise burnups for depletion calculations
(discussed in Section 2.4.3. For the GC-859 data set, the average level of
conservatism ranges between 11.4% and 32.3%, with the conservatisms
having a widely varied range about mean for all decay times. The level
of conservatism and the scatter in the data are largest for the 1-year case
(32.3% ± 24.4%), and they decrease progressively, reaching a minimum
at the 20-year case (11.4% ± 2.4%), at which point they increase for the
100-year (14.6% ± 3.3%) and 200-year (20.5% ± 4.9%) cases. The high
level of conservatism and the scatter in the data at low cooling times,
which are larger than were observed with the derived data set, are
caused by variation in the power level of the last cycle introduced by the
algorithm that assigns cycle-wise burnups based on the GC-859
discharge burnup declarations. The higher degrees of conservatism
and scatter in the data for the longer cooling times are likely due to the
conservatism in the depletion parameter assumptions, like what was
observed in the derived data set.
The second observation is that there is a roughly linear behavior for
both the detailed and bounding the decay heats with burnup across all
decay times. It is also noticeable that both the detailed and bounding
decay heats have two distinct bands, which are most distinct at low
cooling time. For the bounding decay heat, the bands merge to a single
band by 10-year case and remain merged through the 200-year case. The
detailed data bands merge over the first 20 years of decay time but have

increased scatter for the 100- and 200-year cases. The increase in scatter
at longer cooling times is due to the dominance of the actinides, which
are more sensitive to variations in the neutron energy spectrum during
depletion at longer cooling times. The burnup-dependent behavior of
the plots is similar to those of the detailed data set shown in Fig. 15.
The third observation is that there is a “stairstep” behavior to the
bounding data when plotted against the burnups derived from the
detailed data. The stairstep behavior results from the GC-859 burnups
having been rounded to the nearest 1000 MWd/MTU when reported by
the plant staff responsible for completing the GC-859 survey. This in­
troduces an additional source of uncertainty into the calculated decay
heats, but it appears to be insignificant in comparison to the overall
behavior of the data.
The fourth observation is that the approximations used to process the

GC-859 data into the bounding calculations introduce additional
conservatism relative to the derived data set at short cooling times. This
is evidenced by the DHR values being larger for the GC-859 data set than
for the derived data set at each decay time considered. This increase is
shown by the much larger variation in the 1-yr cooled data in Fig. 22 in
comparison to Fig. 16. The increase in the conservatism is most notable
for the early cooling time, as is expected because short-lived nuclides are
most sensitive to temporal burnup distribution.
4.2.1. Irradiation parameter and nuclide contributions to variability of
decay heat for GC-859 data set
Correlations with operating history parameters and the individual
nuclide contributions to decay heat differences were examined to
further investigate the causes of the conservatism in the bounding decay
heats relative to the detailed decay heats for the GC-859 data set. The
same operating parameters that were considered for the derived data set

were used here, namely, VH, BF, VH + BF, and LCP. In the same manner
as was done for the derived data set, a linear fit of the detailed and
bounding decay heats as a function of fuel burnup was performed, and
the residual decay heats about the trend line were calculated by sub­
tracting the fitted values from each of the explicitly calculated assembly
decay heats. The residuals were not calculated for the DHR values
because the detailed and bounding decay heats are calculated at the
same burnup. The Pearson correlation coefficient was then calculated
between the detailed decay heat residuals, the bounding decay heat
residuals, and the DHR values, with the LCP, VH, BF, and VH + BF for
each of the cooling times considered here. The LCP values used here are
different for the detailed data (middle portion of Fig. 9), the bounding
data (bottom portion of Fig. 9), and the DHR (LCPR values in Fig. 10).
The correlation coefficients are shown in Fig. 23, Fig. 24, and Fig. 25 for
the detailed decay heat residuals, the bounding decay heat residuals,
and the DHRs. The same color shading scheme as is discussed in Section
4.1.1 is applied here for the correlation shading. The nuclide contribu­
tion analysis was performed in the same manner as was discussed in
Section 4.1.1.
It is apparent from an examination of the correlations for the detailed
decay heats in Fig. 23 that there is a strong correlation between the
decay heat residuals and LCP and VH; the strength of the correlations
varies based on the cooling time considered. The correlation coefficients
between the decay heat residuals and LCP is 0.996 and 0.975 at 1 year
and 5 years of cooling time, respectively, representing a nearly perfect
linear relationship. The correlation drops to 0.727 at 10 years of cooling
time and to values that are approximately 0.6 for the higher cooling
times. This indicates that at short cooling times the variation in the
specific power of the fuel explains the variation in the detailed decay
heat that is not due to burnup variation. The correlation between VH and

the detailed decay heat residuals is strongest for the 100-year (0.900)
and 200-year (0.871) cooling time cases. It gradually drops off with
decreasing cooling time to a value of 0.576 for the 1-year case. The
strong correlation between VH and the residual decay heat for the
detailed calculations is expected, due to the impact of increased VH on
the actinide source term, which dominates decay heat at longer cooling
times. The correlation between LCP and VH is 0.574 for the detailed
calculations. The cross correlation is responsible for the higher-than-

Table 5
Summary statistical comparison between the detailed decay heats and the GC-859 bounding decay heats (watts).
Decay Time (years)
1
5
10
20
100
200

Detailed

Bounding

DHR

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

878.6
287.3
196.9
155.6
50.2
27.2

1513.2 ± 340.7
386.3 ± 28.9
271.2 ± 20.8
213.2 ± 16.5
68.0 ± 4.7
36.2 ± 2.3

2033.9
464.7
322.8

252.3
78.1
41.0

1470.6
337.2
221.7
172.0
58.5
33.5

1926.0 ± 163.5
466.7 ± 37.0
310.0 ± 27.6
237.7 ± 20.9
78.0 ± 6.1
43.7 ± 3.1

2249.5
543.0
377.0
284.9
90.6
50.1

1.037
1.108
1.080
1.063
1.085

1.125

1.323 ±
1.209 ±
1.142 ±
1.114 ±
1.146 ±
1.205 ±

1.892
1.343
1.207
1.167
1.231
1.328

14

0.244
0.063
0.026
0.021
0.033
0.049


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Progress in Nuclear Energy 143 (2022) 104042

Fig. 21. Detailed and GC-859 bounding decay heats vs. burnup for 1, 5, 10, 20, 100, and 200 years of cooling time.

Fig. 22. Decay heat ratio vs. detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the GC-859 data set.

expected correlations of LCP at long cooling times and VH at short
cooling times. A moderate correlation between BF and residual decay
heat was also observed for the 100-year (0.525) and 200-year cases

(0.538) although the correlation between the VH + BF and the residual
decay heat produced a correlation slightly smaller than the correlation
on VH alone. The correlation between BF and VH is 0.328 and likely
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does not explain this effect alone. All of the correlation results are
similar to what was seen for the Derived data set, which is expected since
these assemblies are merely a subset for the detailed calculations.
It is apparent from an examination of the correlations for the
bounding decay heat residuals in Fig. 24 that again there is a strong
correlation (0.971) between the bounding decay heat residuals and LCP
for the 1-year case and significant but less strong correlation (0.791) for
the 5-year case. There is a mild correlation significant correlation be­
tween the VH and the bounding decay heat residuals for the 1-year and
5-year cases with values of 0.787 and 0.783. They are likely due to the
cross correlation of VH and LCP of 0.838 for the bounding calculations.
There is a mild correlation between the decay heat residuals and the VH

+ BF in the 1-year and 5-year cases; however, that correlation is also
likely a result of the same cross correlation, however, diluted by the
addition of BF. No other strong correlations were observed for the
bounding decay heat residuals. That finding is important because the
depletion conditions are fixed based on the assumptions discussed in
Section 2.4.2, and little variability should be expected outside of total
burnup and the temporal burnup distribution.
The correlations for the DHR values with the operating parameters
are shown Fig. 25. The correlation between LCPR and DHR was stron­
gest for the 1-year case, incrementally dropping off for subsequent years.
This is similar to the observations for both the detailed and bounding
decay heat residuals, although the decrease in the DHR correlation with
increased cooling time is more subtle than was observed with the either
the detailed or bounding decay heat residuals. The correlation between
the DHR values and the difference in burnup between the detailed values
and the GC-859 reported values (ΔBU) is minimal with the exception of
the 10-year and 20-year cases. For those cases moderate correlations of
0.454 and 0.491 were observed. The 10-year and 20-year cooling times
are dominated by changes in 244Cm, which is known to be highly sen­
sitive to differences in burnup. Strong negative correlations of DHR to
VH with cooling time were observed to increase progressively as well;
the strongest correlations occurred at the higher cooling times. This is
logical because detailed decay heat is preferentially increased with
increased VH, and the bounding decay heats are insensitive to it, thus
resulting in decreased margins at higher values of VH. There is moderate
negative correlation between DHR and BF for the 100-year and 200-year
cases and a progressively increasing in magnitude negative correlation
for the VH + BF across cooling times that is largely due to the VH
component.
The change in individual nuclide decay heat between the bounding

and detailed calculations is plotted vs. DHR in Fig. 26 for all of the
cooling times analyzed here. The data in the upper left portion of Fig. 26
indicate that the primary nuclides contributing positively to the
conservatism in the bounding calculations in the 1-year cooling time
case are 106Rh, 144Pr, and 134Cs, with additional positive contributions
from 244Cm and 242Cm and a negative contribution from 90Sr. The
increased decay heat contributions of 244Cm, 242Cm, and 238Pu in the
bounding calculations relative to the detailed calculations are due to the
harder neutron energy spectrum. The decreased decay heat contribution
of 90Sr in the bounding calculations relative to the detailed calculations
is due to the lower 239Pu/235U fission ratio associated with a softer en­
ergy spectrum during the detailed depletion calculations. The increases
in 106Rh and 144Pr decay heats in the bounding vs. detailed calculations
are primarily due to the increase in LCP for the bounding cases. The
contribution for 144Pr to the derived data set was negative because of the
shift in the 239Pu/235U fission ratio; however, the shift is smaller than the
effect of the increased LCP values for the GC-859 data set. Some dif­
ferences in 144Pr decay heat are negative for the GC-859 data set in cases
where the LCPR values are near 1. The increase in the 134Cs contribution
is due to a combination of the harder spectrum and increased LCP for the
bounding calculations. The data in the upper right portion of Fig. 26
show that the nuclides contributing to the conservatism in the bounding
calculations in the 5-year case are primarily 244Cm and 134Cs. For the 5year case, the contribution of 144Pr has virtually disappeared, and the

Fig. 23. Correlation coefficients between detailed decay heat and LCP, VH, BF,
and the sum of VH and BF for the GC-859 data set.

Fig. 24. Correlation coefficients between bounding decay heat and LCP, VH,
BF, and the sum of VH and BF for the GC-859 data set.

Fig. 25. Correlation coefficient between DHR and LCPR, ΔBU, VH, BF, and the
sum of VH and BF for the GC-859 data set.

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Fig. 26. Nuclide decay heat changes leading to total decay heat changes for 1, 5, 10, 20, 100 and 200 years of cooling time between GC-859 and detailed data.

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contribution of 106Rh is significantly lessened. For the 10-year case, the
conservatism in the decay heat calculations is largely due to 244Cm. The
effect of 134Cs lessened significantly, and there is a minor contribution
from 238Pu. The 20-year case begins to show relatively increased con­
tributions of 238Pu and 241Am, and the conservatism in the 100- and 200year cases is mostly driven by 241Am.
While there are remarkable differences in the data from the derived
data set in the 1-year case and 5-year cases that increase the conserva­
tism, it is notable that most of these difference are minimized by the 10
years of cooling time. This indicates that the impact of the GC-859 dataprocessing algorithm on decay heat is likely limited to the first 10 years
of cooling time.

calculations, the 8 × 8 fuel has higher decay heat values at a given
burnup than the 10 × 10 fuel. The different lattice types have different
geometric characteristics as well as time periods during which they were
irradiated. Although specific details of the designs are not available for
either fuel type, the 8 × 8 fuel designs represent an earlier generation of
BWR fuel design, which in general did not use part-length rods and made
more limited use of water rods in the lattices than did 10 × 10 fuel, so it
is reasonable to expect a harder neutron spectrum during irradiation for
the 8 × 8 fuel. The earlier operation of the 8 × 8 fuel is also possibly
correlated with operation of the reactor at lower overall power levels,
although the moderator densities in Fig. 12 and the LCP values in Fig. 14
are similar between the two lattice types.
4.3.1. Irradiation parameter and nuclide contributions to variability of
decay heat for the Swedish data set
To further investigate the causes of the conservatism in the bounding
decay heats relative to the detailed decay heats for the Swedish data set,
correlations with operating history parameters and the individual
nuclide contributions to decay heat differences are examined for both
the 8 × 8 and 10 × 10 fuel assemblies. The same operating parameters
that were considered for both US data sets (i.e., VH, BF, the VH + BF,
and LCP) were used. In the same manner as was done for the both US
data sets, a linear fit of the detailed and bounding decay heats as a
function of fuel burnup was performed, and the residual decay heats
about the trend line were calculated by subtracting the fitted values
from each of the explicitly calculated assembly decay heats. The Pearson
correlation coefficient was then calculated between the detailed decay
heat residuals, the bounding decay heat residuals, and the DHR values,
with each of LCP, VH, BF, and VH + BF for each of the cooling times
considered here. It was reported that cycle-wise burnups for the
bounding calculations were taken from the SNF code data, so the LCP

values are the same for the detailed and bounding calculations as was
the case for the derived US data set. The correlation coefficients are
shown in Fig. 29, Fig. 30, and Fig. 31 for the detailed decay heat re­
siduals, the bounding decay heat residuals, and the DHRs, respectively.
The left half of each figure contains the data for the 8 × 8 fuel; the right
half of the figure contains the data for the 10 × 10 fuel. The same color
scheme as is discussed in Section 4.1.1 is applied the figures for the
correlation shading. The nuclide contribution analysis was performed in
the same manner as was discussed in Section 4.1.1. The results of the
nuclide analysis are shown in Fig. 32 for the 8 × 8 fuel and in Fig. 33 for
the 10 × 10 fuel.
It is apparent from an examination of the correlations for the detailed
decay heat residuals in Fig. 29 that there is a strong correlation between
the decay heat residuals and LCP and VH for the 8 × 8 fuel and that the
strength of the correlations vary based on the cooling time considered.
The correlation coefficients between the decay heat residuals and LCP
are 0.903 and 0.790 at 1 year and 5 years of cooling time, indicating a
very strong linear relationship. The correlation drops to 0.615 at 10
years of cooling time and mildly declines over the remainder of the
decay times to a value of 0.445 at 200 years. The cross correlation be­
tween LCP and VH is 0.471 and is likely responsible for the correlation
between the detailed decay heat residuals and LCP at longer cooling
times for the 8 × 8 fuel. There is a strong and relatively constant with

4.3. Swedish decay heat data
Bounding and detailed assembly discharge calculations and subse­
quent decay calculations were performed for the 2117 Swedish BWR
fuel assemblies, and the decay heat was calculated for post-irradiation
cooling times of 1, 5, 10, 20, 100, and 200 years. The DHR was calcu­
lated by dividing the bounding decay heat by the detailed decay heat, as

shown in Eq. (4). Investigation of the results showed that there were
marked differences in the behavior of the 8 × 8 fuel (952 assemblies)
and 10 × 10 fuel (1165 assemblies), so it was decided to treat those fuel
types independently. The minimum, maximum, mean, and standard
deviation of the decay heats and DHRs for each cooling time are shown
in Table 6 for the 8 × 8 fuel and in Table 7 for the 10 × 10 fuel. Addi­
tionally, the detailed and bounding decay heats are plotted as a function
of burnup for the Swedish BWR data in Fig. 27, and the DHRs are plotted
against the detailed decay heat in Fig. 28. In each figure the 8 × 8 and
10 × 10 fuel assemblies are indicated by separate colors.
A couple of observations were made when the calculated decay heats
in Tables 6 and 7 and Fig. 27 were examined. The first observation is
that, in all cases, the bounding decay heat is greater than the detailed
decay heat in terms of the minimum, maximum, and average values and
by inspection of the burnup-dependent plots. This confirms the conser­
vatism associated with operating history assumptions made within the
bounding sequence of UNF-ST&DARDS for the Swedish data set
regardless of fuel type. The DHR data in Tables 6 and 7 and Fig. 28, show
that the average level of conservatism ranges between 10.1% and 62.6%
for the 8 × 8 fuel and 8.3%–44.7% for the 10 × 10 fuel, depending on
decay time, with the conservatisms varying relatively widely about the
mean for each decay time. The level of conservatism and the scatter in
the DHR data within each lattice type increase significantly with
increasing decay time and are markedly increased for the 100- and 200year cases compared with the shorter decay times. This information is
shown in Fig. 28.
The second observation is that the behavior is roughly linear for all of
the decay heats with burnup within each of the fuel types for cooling
times considered except 1 year, which is heavily scattered due to vari­
ations in LCP. It is also noticeable that there are two distinct bands of
decay heats with burnup (Fig. 27), and the bands become increasingly

distinct with increasing cooling time (Figs. 27 and 28). The bands are
related to the Swedish BWR data set, which is composed of data for 8 × 8
and 10 × 10 fuel assemblies. For both the detailed and bounding

Table 6
Summary statistical comparison between the Swedish 8 × 8 fuel assembly detailed and the bounding decay heats (watts).
Decay Time (years)
1
5
10
20
100
200

Detailed

Bounding

DHR

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

482.3
228.8
162.5
128.2
41.9
23.6

940.5 ± 267.2
316.3 ± 40.8
232.8 ± 23.3
183 ± 17.1
56.8 ± 4.8
30.4 ± 2.4

1668.2
427.4
290.3
223.1
68.2
36.4

550.6

266.6
181.6
143.6
54.5
33.5

1032.7 ± 282.9
374.4 ± 46.0
280.1 ± 28.1
222.3 ± 21.2
81.9 ± 7.0
49.5 ± 3.9

1815.4
492.8
343.2
266.7
94.8
56.3

1.005
1.123
1.117
1.120
1.300
1.419

1.101 ± 0.020
1.185 ± 0.013
1.203 ± 0.013

1.215 ± 0.016
1.441 ± 0.036
1.626 ± 0.052

1.212
1.214
1.234
1.253
1.529
1.761

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Table 7
Summary statistical comparison between the Swedish 10 × 10 fuel assembly detailed and the bounding decay heats (watts).
Decay Time (years)
1
5
10
20
100
200

Detailed

Bounding

DHR

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

Min.

Mean ± σ

Max.

547.5
268.2
212.6
168.2
50.2
26.1

975.3 ± 189.9

332.1 ± 24.3
243 ± 13.3
189.9 ± 9.7
56.7 ± 2.6
29.5 ± 1.3

1770.3
415.1
282.0
216.4
63.6
32.8

600.1
312.7
246.9
196.5
66.7
38.3

1055.1 ± 200
383.4 ± 27.1
284.4 ± 15.7
222.8 ± 11.6
74.6 ± 3.4
42.7 ± 1.7

1867.3
470.3
325.1

252.2
82.5
46.5

1.011
1.114
1.129
1.128
1.242
1.328

1.083 ±
1.155 ±
1.170 ±
1.174 ±
1.316 ±
1.447 ±

1.133
1.201
1.211
1.213
1.384
1.551

0.021
0.012
0.011
0.012
0.024

0.037

Fig. 27. Swedish detailed and bounding decay heats vs. burnup for 1, 5, 10, 20, 100, and 200 years of cooling time.

respect to decay time correlation between VH and the detailed decay
heat residuals of approximately 0.8 for the 8 × 8 fuel. A strong corre­
lation between the residuals and VH is expected at longer cooling times,
however, the correlation at short cooling times is unexpected and is too
high to be explained by the cross correlation between VH and LCP. It is
not understood why the VH correlation is invariant with time. The 8 × 8
detailed decay heat residuals show virtually no correlation with BF, and
the correlation with the VH + BF is slightly lower in magnitude than the
correlation between the residuals and VH as was observed in the US Data
sets.
The correlations for the 10 × 10 fuel detailed decay heat residuals
with LCP are somewhat reduced in comparison to the 8 × 8 fuel at one
year (0.796) and five (0.656) years of cooling time but are still strong.
The 10 × 10 fuel detailed decay heat residuals correlation with LCP also
drops off more steeply than with decay time after 5 years than the 8 × 8
fuel correlation does because the cross correlation between LCP and VH
is only 0.060, which is logical, given the lack of influence of LCP on
decay heat after the first 5 years. The correlation between 10 × 10 fuel
detailed decay heat residuals and VH was lower than the correlation

observed with the maximum value of 0.537 occurring for the 10-year
case. Because VH primarily influences the actinide compositions, it
was expected that the correlation would grow with time, but it did not. It
is not currently understood why the correlation of the 10 × 10 fuel
detailed decay heat residuals with VH is lower for the Swedish data set
than the correlations for the other data sets and why it does not grow

with time, although it is possible it is a result of there being multiple fuel
designs considered in the data set. The detailed decay heat residuals
show a moderate correlation with BF for 100-year and 200-year cases.
The correlation of the VH + BF is greater than that for either VH or BF
individually for the 100-year and 200-year cases and indicates that there
may be some synergy between these two variables for the 10 × 10 fuel.
The correlation between the residuals and the VH + BF increases
consistently with decay time.
It is apparent from an examination of the correlations for the
bounding decay heat residuals in Fig. 30 that both the 8 × 8 and 10 × 10
fuel have 1-year and 5-year correlations with LCP that are similar to
what was observed in the detailed decay heat residuals. This correlation
is expected because the LCP values for bounding calculations should be
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Fig. 28. Decay heat ratio vs. detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the Swedish data set.

Fig. 29. Correlation coefficients between detailed decay heat residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set.

Fig. 30. Correlation coefficients between bounding decay heat residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set.

the same as those in detailed calculations such as the derived US data
set. The LCP correlations tail off significantly with increasing decay
time, as is expected. For the 8 × 8 fuel, this indicates that the detailed
decay heat residual correlations for the longer cooled cases were likely a

result of the cross correlation with VH. The correlation of the 8 × 8 fuel

bounding residuals with VH is higher than would be expected at early
cooling times because the depletion conditions are invariant to opera­
tional history. This is likely partially a result of the cross correlation with
LCP. The 10 × 10 fuel shows no strong correlations with VH, as is ex­
pected. Neither fuel type shows any significant correlation with BF. The
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Fig. 31. Correlation coefficients between DHR residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set.

correlation of the 8 × 8 fuel with the VH + BF appears to be a result of
the VH component, which is partially explained by the cross correlation
with LCP. The 10 × 10 fuel shows no significant correlation with VH +
BF.
It is apparent from an examination of the correlations of DHR with
the operating history parameters in Fig. 31 that DHR is most highly
correlated with VH and the sum of VH + BF for both fuel categories. The
8 × 8 fuel correlation VH is highest at for the 5-year case but otherwise
ranges between − 0.46 and − 0.61 and increases gradually over the 20year to 200-year cases. It is non-physical that the correlation would be
so high in the 5-year case and decreased in later years. There is currently
no explanation for this. The same behavior is observed for the VH + BF;
however, the correlations are slightly more negative. It is logical that VH
and the VH + BF would be negatively correlated with DHR because they
would cause an increase in the detailed decay heat and no change in the

bounding decay heat. The correlation of DHR with VH for the 10 × 10
fuel is larger in magnitude than it was for the 8× 8 fuel, although the 5year case still seem higher than it should be. The correlations of DHR
with BF and the VH + BF increase in magnitude smoothly with decay
time.
The change in individual nuclide decay heat between the bounding
and detailed calculations is plotted vs. DHR for the 8 × 8 fuel in Fig. 32.
The data in the upper left portion of Fig. 32 indicates that the primary
nuclides contributing positively to the conservatism in the bounding
calculations in the 1-year cooling time case are 244Cm, 134Cs, 242Cm, and
238
Pu and negative contributions are from 90Sr and 144Pr. The increased
decay heat contributions of 244Cm, 134Cs, 242Cm, and 238Pu in the
bounding calculations relative to the detailed calculations are due to the
harder neutron energy spectrum. The decreased decay heat contribu­
tions of 90Sr and 144Pr in the bounding calculations relative to the
detailed calculations are due to the lower 239Pu/235U fission ratio. The
fission yields of 90Sr and 144Pr are lower from 239Pu than from 235U. The
5-year nuclide contributions in the upper right corner of Fig. 32 shows
that the dominant positive contributions are from 244Cm and 238Pu with
a negative contribution from 90Sr. The same nuclides the 5-year case
remain major contributors to the conservatism in the decay heat through
the 20-year case with increasing contributions from 241Am over time.
241
Am is the dominant driver of decay heat conservatism in the 100-year
and 200-year cases, with 238Pu contributing in the 100-year case.
The change in individual nuclide decay heat between the bounding
and detailed calculations is plotted vs. DHR for the 10 × 10 fuel in
Fig. 33. The nuclide decay heat results for the 10 × 10 fuel look quali­
tatively similar to the results for the 8 × 8 fuel, showing that same nu­
clides primarily contribute to conservatism at the same time periods in a

qualitative manner. It appears that the differences between the detailed
and bounding actinide decay heats are somewhat smaller in many in­
stances for the 10 × 10 fuel, driving the smaller DHR values in com­
parison to the 8 × 8 fuel.
The cycle-wise burnups and therefore power histories for the
Swedish data are derived from the detailed information. Therefore,

comparison to the derived US data is most appropriate. In comparison to
the derived US data, the changes in actinide contributions between the
detailed and bounding calculations are qualitatively similar to the
Swedish data set but higher in magnitude for both fuel types. It is likely
that the magnitude differs because the overall moderator densities
experienced by Swedish fuel (average of 0.489 g/cm3) were higher than
those experienced by the US fuel (average of 0.414 g/cm3). There are
also differences in the short-lived fission products in the 1-year and 5year decay time results because of the differences between the LCP
values between the data sets; the US data have significantly higher LCP
values (average of 20.55 MW/MTU) than the Swedish data (7.17 MW/
MTU). The higher LCP values experienced by the US fuel exacerbate any
decay heat differences induced by changes in neutron energy spectrum
or fission yield between the bounding and detailed calculations.
5. Conclusions and future work
Licensing evaluations for SNF storage, transportation, and disposal
systems are typically performed using bounding operating history as­
sumptions and canister contents. The canister contents are assumed to
be limiting in an attempt to envelop maximum possible loading varia­
tions in comparison to their actual loading. The UNF-ST&DARDS tool
has been designed to analyze SNF systems so that the margin to the
licensing basis can be characterized and used to inform decision making.
Although the aim of as-loaded analysis is to take credit for the actual fuel
type, burnup, enrichment, and cooling time associated with assemblies

loaded in the SNF systems, it is desired that some level of conservatism
associated with the depletion conditions be retained for safety analysis
work.
This paper examines the level of conservatism in the UNFST&DARDS bounding assembly-specific decay heat calculations. A
comparison between the UNF-ST&DARDS bounding decay heat calcu­
lations and calculations using a detailed description of the operating
histories of several fuel assemblies was performed using recently ac­
quired data. The data used to perform the evaluation were one set of
3019 assemblies from a US twin-reactor site and one set of 2117 as­
semblies for a Swedish reactor. The US data set was analyzed using two
different sets of assumptions. The first analysis derived the cycle-wise
burnups for the bounding calculations from the detailed data, referred
to as the “derived data set”; the second analysis was based on the as­
sumptions associated with incorporating GC-859 data in UNFST&DARDS, where the cycle-wise burnup is derived from the average
discharge burnups and cycle lengths assuming constant power (referred
to as the “GC-859 data set”). For each data set the decay heat values
were calculated for all assemblies using the detailed and bounding
analysis pipelines, and the results were compared. For each data set, the
bounding and detailed decay heats were compared with one another as a
function of burnup, and DHRs were calculated by dividing the bounding
decay heat by the detailed decay heat. Additionally, correlations be­
tween the various operating history parameters and the bounding and
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Fig. 32. Nuclide decay heat changes vs. DHR for the 8 × 8 Swedish fuel.

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Fig. 33. Nuclide decay heat changes vs. DHR for the 10 × 10 Swedish fuel.

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detailed decay heat residuals and DHR values were examined, as were
the nuclide contributions to decay heat conservatism.
The derived US data set compared decay heats calculated using the
detailed analysis pipeline to bounding decay heats using axially aver­
aged burnups developed from the detailed data. An important conclu­
sion of this work is that for the derived data set, the average level of
conservatism ranges between 9.0% and 17.7%; the conservatisms have
an approximate range about the mean of 8% between minimum and
maximum for decay times between 1 and 20 years. The level of
conservatism and the scatter in the data increase significantly for the
100- and 200-year cases. The conservatisms for the derived data set are
most highly correlated with LCP in the 1-year and 5-year cases and most
highly correlated with VH at longer cooling times. Differences in shortlived fission products contribute significantly to the conservatism in the

1-year and 5-year cases; 244Cm contributed significantly to the conser­
vatism over the first 20 years of cooling time, and 241Am significantly
contributed to the conservatism in the 100-year and 200-year cases.
The GC-859 US data set compared decay heat values calculated using
the detailed analysis pipeline to bounding decay heat values calculated
using assembly burnups from the GC-859 data collection process for the
1472 assembly subset of the derived data set for which the GC-859 in­
formation was available. The primary difference in the bounding cal­
culations between the GC-859 data set and the derived data set is that
the assembly average burnups were rounded up to the nearest 1000
MWd/MTU in most cases in the values report to GC-859 survey and that
the cycle-wise burnup distribution was developed using the algorithm
that UNF-ST&DARDS uses to process the GC-859 data. For the GC-859
data set, the average level of conservatism ranges between 11.4% and
32.3%. The level of conservatism and the scatter in the data are largest
for the 1-year case and decrease progressively, reaching minimums at
the 20-year case, at which point they increase for the 100-year and 200year cases. An important conclusion arising from this data set is the
processing of the GC-859 discharge burnups into cycle-wise burnups
adds significant additional conservatism to the 1-year and 5-years
cooled cases, however, the additional conservatism declines signifi­
cantly beginning with the 10-years cooled case. Strong correlations are
shown between the LCPR and DHR for the 1-year and 5-year cases, and
strong correlations are found with VH for the 100-year and 200-year
cases. The same nuclides as were discussed for the derived data set
contributed to the difference. Additional contributions are expected to
come from the short-lived fission products in the 1-year and 5-year
cases.
The Swedish data set provided for a comparison of the detailed decay
heats calculated using the inventory of nuclide compositions imported
from core simulator models and decayed using the UNF-ST&DARDS

detailed pipeline with bounding decay heats calculated using the cyclewise burnups from the SNF Code. Little is known about the character­
istics of the fuel designs; however, the number of rods in the lattice of the
fuel assemblies was disclosed, and the data set was divided into two
subsets: 8 × 8 fuel and 10 × 10 fuel. The average level of conservatism
ranges between 10.1% and 62.6% for the 8 × 8 fuel and 8.3%–44.7% for
the 10 × 10 fuel, depending on decay time. Unlike that of the US data
sets, the level of conservatism for the Swedish data sets increased
monotonically across all decay times. The nuclide results for both
Swedish data subsets indicated that the substantially lower last cycle
power likely limited the contribution of the short-lived nuclides to the
conservatism in early cooling time cases. There was also more conser­
vatism in the longer cooling time cases because the Swedish fuel was
operated at a substantially higher moderator density, which results in a

more pronounced difference between the detailed and bounding calcu­
lation actinide compositions.
Future work in this area should focus on expanding the amount of
fuel and variety of fuel designs considered as well as the variety of an­
alyses. This work represents an investigation of the conservatism of
decay heat calculations for BWR fuel from two sites. The conservatism of
decay heat should be investigated for a broader range of fuel types and
reactors to confirm that these results apply broadly. Many other types of
analyses such as criticality, dose rate and thermal analyses must be
performed to demonstrate the safety of SNF. Additional investigations of
the conservatism of the operating history assumptions within UNFST&DARDS will be performed for criticality, dose rate and thermal an­
alyses will be performed. A companion paper, which covers criticality
safety of BWR SNF systems, is forthcoming. These types of analyses
should also be performed for PWR fuel assemblies as well to determine
whether similar conclusions can be drawn. Additionally, validations of
the predictions of reactor physics codes such as Polaris and criticality

codes such as KENO must be performed by comparison to measured
data. Analysis sequences within UNF–S&TDARDS are currently being
developed to address these validation needs as well.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgment
The work was sponsored the US Department of Energy, Office of
Nuclear Energy, Integrated Waste Management Program.
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