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

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.

Progress in Nuclear Energy 143 (2022) 104042

Available online 25 November 2021

Research Paper

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

Justin B Claritya,*, Henrik Liljenfeldtb, Kaushik Banerjeec, L Paul Millera

aOak Ridge National Laboratory, Nuclear Energy and Fuel Cycle Division, Oak Ridge, TN, USA

bNoemi Analytics, Uppsala, Sweden

cPacific Northwest National Laboratory, Richland, WA, USA

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 GC-

859 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

gov-ernment retains and the publisher, by accepting the article for publication, acknowledges that the US govgov-ernment 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 (http://energy.gov/downloads/doe-public-acce 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: clarityjb@ornl.gov (J.B Clarity)

Contents lists available at ScienceDirect Progress in Nuclear Energy

https://doi.org/10.1016/j.pnucene.2021.104042

Received 1 June 2021; Received in revised form 27 October 2021; Accepted 8 November 2021

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

condi-1 Introduction

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 k eff 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 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

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 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

exten-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

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

2.3 Direct discharge import method

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 (post-

irradiation 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

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

2.4.1 Fuel type aliasing

Many of the fuel designs are not explicitly modeled in the UNF- ST&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

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

J.B Clarity et al

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

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)

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

Table 1

Summary of BWR depletion parameters

Parameter Value Fuel rod mixture UO2 Fuel density (g/cm 3 ) 10.74 Fuel temperature (K) 1200.00 Moderator

temperature (K) 560.70 Moderator density (g/

cm 3 ) 0.30 Absorber exposure Gd2O3 admixed with fuel pellets in a small number of rods

based on fuel type and full-length control blade exposure throughout irradiation history

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

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 orientacomposi-tions of the rods are provided

Detailed operating history information is provided for the US BWR

cycles of interest in two formats

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

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 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

pro-referred to as the derived data set Derived calculations are performed for

all 3019 fuel assemblies used in this work The combined impact of UNF- ST&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 GC-

859 data set The detailed calculations for both the derived data set and

the GC-859 data set use the same fuel and operating history 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

Calculation Description

Bounding operating history assumptions with assembly enrichment, burnup and cycle-wise burnup distribution derived from detailed data

Bounding operating history assumptions with assembly enrichment and burnup from GC-859 fuel survey and cycle- wise burnup distribution constant power assumption Detailed

Calculation Description

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

J.B Clarity et al

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

3.1.3 Moderator density and control blade insertion

In addition to understanding the fuel’s initial composition and

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

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)

Fig 6 Difference in burnup between the GC-859 data and detailed information

using 1472 assemblies from GC-859 set

Progress in Nuclear Energy 143 (2022) 104042

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 GC-

859 data set moderator density and BF values, indicating that the GC-

859 set it is likely to be an unbiased subset of the assemblies

3.1.4 Last cycle power

Most of the safety analysis calculations performed by UNF-

ST&DARDS are relatively insensitive to the temporal distribution of

burnup by the fuel assembly; however, a few short-lived nuclides (134Cs,

106Rh, 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

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

Fig 7 Distribution of moderator density for the derived data set (top), and the

J.B Clarity et al

calculates the cycle-wise bounding burnups from the detailed data and

would always result in an LCPR of 1.0

LCPR = LCP Bounding

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

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)

Fig 10 Distribution of LCPR values for the GC-859 data set

Progress in Nuclear Energy 143 (2022) 104042

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

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

4.1 Derived US data set

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

Fig 11 Distribution of assembly burnups for the Swedish data set

Fig 12 Distribution of burnup averaged moderator densities 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

J.B Clarity et al

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 = DH Bounding

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 burnup-

dependent plots This confirms the conservatism associated with

oper-ating history assumptions made within the bounding sequence of UNF-

ST&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

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

4.1.1 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

Table 3

Summary statistical comparison between the detailed decay heats and the derived bounding decay heats (watts)

Progress in Nuclear Energy 143 (2022) 104042

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 cycle-

wise 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

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

Table 4

Nuclides used for decay heat investigations

Actinides Fission Products

241 Am, 243 Am, 242 Cm, 244 Cm, 238 Pu,

239 Pu, 240 Pu and 241 Pu

144 Ce, 134 Cs, 137 Cs ( 137 Cs + 137m Ba), 154 Eu,

144 Pr, 106 Rh, and 90 Sr ( 90 Sr + 90 Y) Fig 17 Correlation coefficient between detailed decay heat and LCP, VH, BF,

and the sum of VH and BF by cooling time

J.B Clarity et al

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 short-

lived 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

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