ML22339A240

NUREG/IA-0529, Simulations of the Beavrs PWR with Scale and Parcs

ML22339A240
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Issue date:	12/31/2022
From:	Darnowski P, Pawluczyk M, Kirk Tien Office of Nuclear Regulatory Research, Warsaw Univ of Technology, Poland
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NUREG/IA-0529
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NUREG/IA-0529 Simulations of the BEAVRS PWR with SCALE and PARCS Prepared by:

Piotr Darnowski, Michal Pawluczyk Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Institute of Heat Engineering, Nowowiejska 21/25,00-665 Warsaw, Poland K. Tien Division of Systems Analysis Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 Manuscript Completed: December 2021 Date Published: December 2022 Prepared as part of The Agreement on Research Participation and Technical Exchange Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by U.S. Nuclear Regulatory Commission

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NUREG/IA-0529 Simulations of the BEAVRS PWR with SCALE and PARCS Prepared by:

Piotr Darnowski, Michal Pawluczyk Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Institute of Heat Engineering, Nowowiejska 21/25,00-665 Warsaw, Poland K. Tien Division of Systems Analysis Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 Manuscript Completed: December 2021 Date Published: December 2022 Prepared as part of The Agreement on Research Participation and Technical Exchange Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by U.S. Nuclear Regulatory Commission

ABSTRACT The first fuel cycle of the BEAVRS PWR benchmark was simulated and analyzed. Models were prepared using the SCALE package, TRITON depletion sequence and NEWT as a lattice physics solver. A set of branch and burnup calculations were prepared, and group constants in the form of PMAXS libraries were generated using GenPMAXS for PARCS nodal diffusion core simulator. The hot zero power reactor physics measurement data and hot full power data were used to perform model validation simulations for the 1st fuel cycle. The core inventories for the BOC and EOC were calculated on the basis of PARCS and TRITON results with a dedicated computer code and compared with ORIGEN-ARP point burnup calculations.

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FOREWORD This report is focused on the development of a PWR reactor model for SCALE/PARCS computer codes, model tests, validation and the core isotopic inventory estimation. It is based on the results obtained during research projects performed at the Institute of Heat Engineering at Warsaw University of Technology between 2015-2018.

The BEAVRS MIT PWR reactor based on the 1000MWe Westinghouse design was selected as a representative of a PWR type nuclear reactor due to publicly available data covering detailed reactor design and operational data.

Most of the research reported in this report was financed by the Polish nuclear regulatory body -

the National Atomic Energy Agency (PAA) in the framework of the project Calculation of Atomic Densities, Masses and Radioactive Activities of Fission Products for Selected Power Reactor Using Specialized Calculation Codes [1], under the contract: 13/2015/DBJ in 2015. Part of the work related to the core inventory predictions was performed in 2016 as a part of the project Assessment of the Main Steam Line Break of a Nuclear Power Plant with an EPR reactor financed by National Atomic Energy Agency under the contract 6/2016/DBJ [3].

Activities performed in 2017 were financed by the Faculty of Power and Aeronautical Engineering Dean Grant number 504/03264: Development of the novel core inventory calculation methodology for the PWR reactor. The computer infrastructure used to prepare this publication was provided by Information Platform TEWI Project which was funded by the European Union in the framework of the European Social Fund (2007-2013).

The authors wish to acknowledge the valuable cooperation and support from the National Atomic Energy Agency. The authors wish to express special thanks to Ernest Staro PhD and Szymon Suchcicki from PAA.

Finally, we would like to acknowledge Professor Tomasz Kozłowski for very fruitful discussions and his precious comments.

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TABLE OF CONTENTS ABSTRACT ................................................................................................................... iii FOREWORD ................................................................................................................... v TABLE OF CONTENTS................................................................................................ vii LIST OF FIGURES......................................................................................................... ix LIST OF TABLES .......................................................................................................... xi EXECUTIVE

SUMMARY

............................................................................................. xiii ABBREVIATIONS AND ACRONYMS .......................................................................... xv 1 INTRODUCTION ........................................................................................................ 1 2 MODELS AND SIMULATIONS .................................................................................. 3 2.1 The BEAVRS Core........................................................................................................3 2.2 SCALE/TRITON Models................................................................................................4 2.2.1 Critical Test Calculations ................................................................................7 2.2.2 Burnup Calculations .......................................................................................7 2.2.3 Branches ......................................................................................................10 2.2.4 Reflectors .....................................................................................................12 2.3 PARCS Models and Simulations .................................................................................13 2.3.1 Core Model ...................................................................................................13 2.3.2 Control Rods ................................................................................................14 2.4 ORIGEN-ARP Models .................................................................................................16 2.5 Core Inventory Calculation Methodology .....................................................................16 3 RESULTS AND DISCUSSION ................................................................................. 17 3.1 Group Constants Tests ...............................................................................................17 3.2 Fuel Assembly Burnup Calculations ............................................................................18 3.3 Benchmark Results .....................................................................................................25 3.3.1 Hot Zero Power Tests ..................................................................................25 3.3.2 Hot Full Power Operation .............................................................................31 3.4 Core Inventory Calculations ........................................................................................41 3.4.1 Initial Core State...........................................................................................41 3.4.2 Masses and Activities ...................................................................................41 3.4.3 Comparison of WUTBURN-PARCS-TRITON and ORIGEN-ARP ................. 45 4 CONCLUSIONS ....................................................................................................... 49 5 REFERENCES ......................................................................................................... 51 vii

LIST OF FIGURES Figure 2-1 The first fuel cycle core loading pattern. Numbers indicate the amount of burnable absorber borosilicate rods. The figure was taken from [7] .....................3 Figure 2-2 Axial reflector model ..........................................................................................12 Figure 2-3 Radial reflector model ........................................................................................12 Figure 2-4 Core map with assembly types. 1-9 fuel, 10 reflectors ....................................... 13 Figure 2-5 Core map with assemblies numbering from 1 to 193. 0 - number of an assembly ...........................................................................................................15 Figure 2-6 Core map with control banks (groups) numbering (1-9). 0 - assembly has no control rods. There are 24 Guide Tubes per assembly .................................. 15 Figure 3-1 Reactivity differences between 44g and 238g ( ).............................. 19 Figure 3-2 Infinite multiplication factor for FA01 assembly ..................................................20 Figure 3-3 Infinite multiplication factor for FA02 assembly ..................................................20 Figure 3-4 Infinite multiplication factor for FA03 assembly ..................................................21 Figure 3-5 Infinite multiplication factor for FA04 assembly ..................................................21 Figure 3-6 Infinite multiplication factor for FA05 assembly ..................................................22 Figure 3-7 Infinite multiplication factor for FA06 assembly ..................................................22 Figure 3-8 Infinite multiplication factor for FA07 assembly .................................................23 Figure 3-9 Infinite multiplication factor for FA08 assembly ..................................................23 Figure 3-10 Infinite multiplication factor for FA09 assembly ..................................................24 Figure 3-11 Average axial relative power calculated with PARCS for 213 D-bank withdrawn and 44 neutron groups compared with core averaged all detectors response ............................................................................................27 Figure 3-12 Average axial relative power calculated with PARCS for 213 D-bank withdrawn and 238 neutron groups compared with core averaged all detectors response ............................................................................................28 Figure 3-13 HZP detectors BEAVRS measurements compared with thermal flux distribution - tilt corrected for PMAX based on 44 groups ................................... 29 Figure 3-14 HZP detectors BEAVRS measurements compared with thermal flux distribution - tilt corrected for PMAX based on 238 groups ................................. 29 Figure 3-15 Core thermal flux radial distribution, relative difference between PARCS results with PMAXS based on 44 groups and 238 groups. Tilt corrected ........... 30 Figure 3-16 1/4th core radial power distribution calculated with PARCS and PMAX based on 44 groups ...........................................................................................30 Figure 3-17 1/4th core radial power distribution calculated with PARCS and PMAX based on 238 groups .........................................................................................30 Figure 3-18 Core power radial distribution, relative difference between results for PARCS with PMAXS generated with 44 groups and 238 groups ....................... 31 ix

Figure 3-19 Comparison of boron letdown curve vs EFPD available in BEAVRS specification Rev 1.0.1 and Rev 2.0.1 and critical boron concentration (core operating data) data as a function of exposure available in benchmark Rev 2.0.1...................................................................................................................32 Figure 3-20 Average boron concentration measurements for detectors data compared with boron letdown curve and core operating dataall data taken from BEAVRS. Operating Data and Boron letdown expressed in EFPD were recalculated to burnup .......................................................................................33 Figure 3-21 Boron letdown curve for cycle 1 as a function of EFPDs. The BEAVRS data compared with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results with 100% nominal power calculations and Xe&Sm equilibrium ............................................................................................34 Figure 3-22 Comparison of BEAVRS data expressed in burnup with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 100%

nominal power and equilibrium Xe/Sm with State-of-the-Art calculations for 100% full power with Serpent-ARES [11] ...........................................................34 Figure 3-23 Comparison of BEAVRS detectors and operating data with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 100%

nominal power, equilibrium and transient Xe/Sm................................................ 35 Figure 3-24 Comparison of BEAVRS detectors and operating data with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 75%

nominal power, equilibrium and transient Xe/Sm................................................36 Figure 3-25 Comparison of BEAVRS detectors and operating data with PARCS 44 &

238 neutron groups, 100% & 75% nominal power for equilibrium Xe/Sm ........... 37 Figure 3-26 Core average burnup as a function of effective full power time. BEAVRS data and PARCS results ....................................................................................38 Figure 3-27 Initial BEAVRS heavy metal (all uranium) masses radial distribution (in [g]).

Total mass: 81790749 grams .............................................................................41 Figure 3-28 Initial BEAVRS fissile (U-235) heavy metal masses radial distribution (in

[g]). Total mass: 1935560 grams........................................................................41 x

LIST OF TABLES Table 2-1 The basic core design data [7] .............................................................................4 Table 2-2 Fuel assembly data ..............................................................................................4 Table 2-3 BEAVRS cycle 1 fuel assemblies .........................................................................5 Table 2-4 Core operational data considered in calculations. HFP and HZP are reference states for branch calculations ...............................................................6 Table 2-5 Burnup sequence applied to all assemblies for 238 neutron groups and with detailed burnup calculations and without branches ..............................................8 Table 2-6 Fuel burnup sequence applied in branch calculations for assemblies without BAs ..........................................................................................................9 Table 2-7 Fuel burnup sequence applied in branch calculations for assemblies with BAs ....................................................................................................................10 Table 2-8 Branch sequence developed for Hot Full Power fuel cycle calculations ............. 11 Table 2-9 Branch sequence developed for Hot Zero Power Reactor Physics calculations ........................................................................................................11 Table 2-10 Thermal-hydraulics data for PARCS (CNTL & TH card) ..................................... 14 Table 2-11 Control banks data .............................................................................................16 Table 3-1 Comparison of the k-inf for 44 neutron groups in the HZP state for TRITON calculations, GenPMAXS results in PMAXS files and PARCS infinite homogenous core results ...................................................................................17 Table 3-2 Comparison of the k-inf for 238 neutron groups in the HZP state for TRITON calculations, GenPMAXS results in PMAXS files and PARCS infinite homogenous core results ...................................................................................18 Table 3-3 Differences between 44 and 238 groups for TRITON, PMAXS and infinite PARCS for HZP .................................................................................................18 Table 3-4 Beginning of cycle 1 hot zero power core physics for D-bank 213 steps withdrawn configuration .....................................................................................25 Table 3-5 Beginning of cycle 1 hot zero power core physics for All-Rods-Out (ARO) ......... 25 Table 3-6 Critical boron concentrations with inserted control banks for cycle 1 hot zero power tests ................................................................................................26 Table 3-7 Effective multiplication factor calculated for different control rod states with the BEAVRS values of boron concentration .......................................................26 Table 3-8 Comparison of Control Rod Bank Worth ............................................................26 Table 3-9 Comparison of PARCS critical boron concentration results with BEAVRS data. PARCS results are for Hot Full Power operation with 75% and 100%

nominal power ...................................................................................................39 Table 3-10 Comparison of the fuel burnup for BEAVRS and PARCS with 75% and 100% of nominal power......................................................................................40 xi

Table 3-11 Summary of masses and activities of the core at BOC and EOC calculated with WUTBURN. Total mass includes an oxide ..................................................42 Table 3-12 Mass balance in the TRITON PLT output files ..................................................43 Table 3-13 List of nuclides considered: Actinides, FP49 and FP200. ................................... 44 Table 3-14 Comparison of actinides inventory calculated with WUTBURN-PARCS and ORIGEN BEAVRS EOC (327.2 EFPDs) ............................................................46 Table 3-15 Comparison of fission products (FP49) inventory calculated with WUTBURN-PARCS and ORIGEN BEAVRS EOC (327.2 EFPDs) ..................... 47 xii

EXECUTIVE

SUMMARY

This report is focused on the development of a PWR reactor model for SCALE/PARCS computer codes, model tests, validation and the core isotopic inventory estimation. It is based on the results obtained during research projects performed at the Institute of Heat Engineering at Warsaw University of Technology between 2015-2018.

The BEAVRS MIT PWR reactor based on the 1000MWe Westinghouse design was selected as a representative of a PWR type nuclear reactor. What is more, the benchmark specification provides very detailed reactor design and operational data, and it was extensively studied worldwide by several organizations.

Most of the research presented in this work was conducted in the framework of the research project for the Polish National Atomic Energy Agency (PAA): Calculation of Atomic Densities, Masses and Radioactive Activities of Fission Products for Selected Power Reactor Using Specialized Calculation Codes, which was performed in 2015 [1]. The main purpose of this project was to develop and test the methodology of detailed core inventory calculations for a Pressurized Water Reactor (PWR). The secondary purpose was to prepare and validate core models based on the BEAVRS MIT PWR Benchmark. Later research activities were focused on the BEAVRS benchmark and were conducted in 2016-2018 as a part of university research. Final outcomes related to the BEAVRS benchmark are reported in [2], and part of them are presented in the context of this report.

The analysis was performed for the BEAVRS first fuel cycle. Basic models for lattice physics simulations were prepared for nine assemblies using the SCALE 6.1.2 package for 44 and 238 neutron groups libraries (ENDF/B-V & ENDF/B-VII). The generated group constants were transferred to PMAXS format using the GenPMAXS code. The PMAXS files were applied to perform the full core simulations using the PARCS 3.2 core nodal simulator. The fuel cycle simulations covered full power (Hot Full Power - HFP) steady-state core operation and allowed to assess the ability of the code to simulate the fuel campaign. Additionally, the reactor physics calculations for Hot Zero Power (HZP) were performed to validate the model.

The obtained results for both HZP and HFP were in reasonable agreement with the benchmark data. Finally, core inventories for BOC and EOC were calculated using a novel methodology and the in-house developed code WUTBURN. Calculations were performed on the basis of TRITON and PARCS results and were compared with a point model developed with the ORIGEN-ARP. Core inventories obtained by a detailed PARCS simulations agreed reasonably with simplified ORIGEN model for the most important isotopes.

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ABBREVIATIONS AND ACRONYMS ARI All Rods In ARO All Rods Out BAF Bottom of Active Fuel BA Burnable Absorber BEAVRS Benchmark for Evaluation And Validation of Reactor Simulations BOC Beginning of Cycle BOL Beginning of Life BP Burnable Poison CR Control Rod CRGT Control Rods Guide Tube CRW Control Rod Worth EFPD Effective Full Power Days EOC End of Cycle EOL End of Life EPRI Electric Power Research Institute FA Fuel Assembly HZP Hot Zero Power HFP Hot Full Power ITC Instytut Techniki Cieplnej / Institute of Heat Engineering LWR Light Water Reactor LANL Los Alamos National Laboratories MOC Middle of Cycle MOX Mixed OXide MIT Massachusetts Institute of Technology ORNL Oak Ridge National Laboratories PAA Pastwowa Agencja Atomistyki / National Atomic Energy Agency PARCS Purdue Advanced Reactor Core Simulator PCM Per Cent Milirho (Per Cent Mille)

PCSR Pre-Construction Safety Report xv

PPM Parts Per Million PWR Pressurized Water Reactor TAF Top of Active Fuel US NRC US Nuclear Regulatory Commission US DOE US Department of Energy xvi

1 INTRODUCTION Detailed design analysis and proper safety analysis of nuclear reactors are fundamental for their safe and economical operation. One of the approaches to solve different challenges is to conduct appropriate neutronic and thermal-hydraulic calculations using modern computer codes. For this purpose, the core simulators such as PARCS, CRONOS or SIMULATE can be used allowing to compute the course of the fuel campaign, study core state during transients and accidents. This report is an example of the application of modern, state-of-the-art computational tools to study the fuel campaign.

The MIT Benchmark for Evaluation And Validation of Reactor Simulations (BEAVRS) was published in 2013 by the MIT Computational Reactor Physics Group [4]. It contains a very detailed design and (real) plant operational data for a 4-loop Westinghouse PWR type reactor core. The most recent revision 2.0.2 was published on April 11 2018 [5]. The earlier revision 2.0.1 was published on February 1, 2017 [6]. Basic models used to obtain the results presented in this report were finished in December 2015, and they are based on the Benchmark specification available at that time - revision 1.1.1 [7]. In 2016 minor modifications were introduced, and in 2017 additional updates were prepared, and the models were recalculated for the benefit of this report. Nevertheless, the models are still mainly based on the Benchmark revision 1.1.1. It should be highlighted, as there are important differences between revisions 2.0.2 and 1.1.1. This report is based on results obtained in 2017, and the alternative results for the updated PARCS model with modified reflector and different branches were reported in the 2019 paper [2]. The observed differences between these models are minor.

Alternative results are not presented in this report, to maintain consistency with results of the core inventory calculations, which were executed only for the model studied in this report.

The BEAVRS core models were developed and compared with available Hot Zero Power and first fuel cycle data. The approach is based on Lattice Physics calculations using a modular package SCALE and TRITON analysis sequence [8]. The purpose of the Lattice Physics calculations was to generate a library of group constants (PMAXS libraries) that could be used by the PARCS nodal-diffusion core simulator. The transport code performs criticality calculations with fuel burnup of a set of 2D fuel assembly models and series of the so-called branches. Branch sequences cover various core states: fuel and moderator temperatures, moderator densities, control rod states and different boric acid concentrations. Calculated constants are then converted by the GenPMAXS code into PMAXS format libraries which are readable by the core simulator. The Purdue Advanced Reactor Core Simulator (PARCS) was applied as the core nodal and fuel cycle simulator. In this study, only steady-state operation, i.e.

Hot Full Power or Hot Zero Power, was considered, hence a simple thermal-hydraulics module was applied, which is inherent to the PARCS code (PATHS code). It is also possible to apply advanced thermal-hydraulics codes such as RELAP or TRACE to perform more detailed simulations. However, in the case of this report, such an option was not used. An example of the mentioned calculation is available in [9].

The SCALE-PARCS two-step sequence was tested with BEAVRS data also in PHYSOR-2018, conference report which describes the University of Illinois at Urbana-Champaign research financed by US NRC [10]. Those results were performed with newer version of SCALE - 6.2.2.

In this work simulations were performed with SCALE version 6.1.2.

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2 MODELS AND SIMULATIONS 2.1 The BEAVRS Core The BEAVRS is a large PWR 4-loop Westinghouse nuclear reactor. The core loading pattern with fuel type and burnable absorbers configuration for the first cycle is presented in Figure 2-1, and the basic core data is presented in Table 2-1. Fuel assembly data and fuel details are presented in Table 2-2 and Table 2-3. Operating conditions for investigated core states are presented in Table 2-4.

The BEAVRS Benchmark specification is very detailed. It is likely the most detailed real PWR design data publicly available. However, models applied in this work are simplified in comparison to the level of details of the benchmark specification. A set of simplifications was applied, and it is because the main purpose of the project was to develop and test the methodology enabling the calculation of detailed core inventory, masses and activities.

Moreover, an important factor taken into account was the limited time frame of the main project.

What is more, model validation with the BEAVRS Benchmark was initially treated as a secondary goal. State-of-the-art benchmark calculations and extensive validation efforts are available in more recent publications [11]-[16] and in many earlier publications [17]-[21]. The alternative results for the BEAVRS model used in this work are also available in 2019 paper [2].

Figure 2-1 The first fuel cycle core loading pattern. Numbers indicate the amount of burnable absorber borosilicate rods. The figure was taken from [7]

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Table 2-1 The basic core design data [7]

Parameter Value Unit Electric power 1100 MWe Thermal power 3410 MWth Nominal pressure 15.51 MPa Core mass flow 61500 (incl. 5% bypass) tonnes/h Fuel (Cycle 1) UO2, 1.6%, 2.4%, 3.1% -

Initial mass of heavy metal (HM) 81.79 (Cycle 1) MT, metric tonnes, 1000kg Core average enrichment 2.36679  %

Specific power 41.6993 MWth/tHM 2.2 SCALE/TRITON Models The detailed fuel assembly design is based on benchmark Revision 1.1.1. [7]. Only crucial data are repeated in this report. The basic fuel assembly data is presented in Table 2-2. Nine fuel assemblies present during the first cycle were modelled in this exercise (Table 2-3).

Table 2-2 Fuel assembly data Parameter Value Unit Number of fuel assemblies 193 -

Fuel lattice 17x17 -

Active fuel column length 365.76 cm Fuel Assembly pitch 21.50364 cm Fuel rods pitch 1.25984 cm Number of fuel rods per assembly 264 -

Number of guide tubes 24 -

Number of instrumentation tubes 1 -

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Table 2-3 BEAVRS cycle 1 fuel assemblies Index Number Enrichment Number of BA rods Number of FA FA01 1 1.6% 0 65 FA02 2 2.4% 0 4 FA03 3 2.4% 12 28 FA04 4 2.4% 16 32 FA05 5 3.1% 0 32 FA06 6 3.1% 6 12 FA07 7 3.1% 15 4 FA08 8 3.1% 16 8 FA09 9 3.1% 20 8`

FA10 10 Reflector radial FA11 11 Reflector axial The two-dimensional fuel models were prepared for the SCALE/TRITON sequence for neutron transport with branches and fuel burnup. Nine fuel assembly (FA) models were characterized by different enrichment and population of burnable absorber (borosilicate glass) rods (BA), control rod guide tubes, central instrumentation tubes and control rods. As mentioned earlier some design details were simplified. Spacer grids were omitted during model preparation because of the necessity to perform separate transport calculations for all assemblies. Currently, the model includes only two types of the reflector.

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Table 2-4 Core operational data considered in calculations. HFP and HZP are reference states for branch calculations Parameter Hot Full Power (HFP) Hot Zero Power (HZP) Unit Pressure 15.5132 15.5132 MPa Moderator temperature 580 566.48 K Fuel temperature 900 600 K Other structures temperature 580 580 K Density of water without boric acid 0.711901 0.739860 g/cc Boron concentration 378 975 ppm Density of water with boric acid 0.712170 0.740582 g/cc The main Hot Full Power (Table 2-4) calculations were performed with boron concentration equal to the average boron concentration during cycle 1. It was calculated with the following equation:

1 Average Concentration = ()

Where: b - time of EOC, a - time of BOC, t - cycle time, f(t) - boron concentration evolution available in the benchmark specification. Average boron concentration between day 0 and 327 is equal to 378 ppm.

The Hot Zero Power conditions were used to perform zero power core physics simulations.

All the design data was applied in both TRITON and PARCS modelling. The HFP is the reference state for branches dedicated to fuel cycle calculations, and HZP is the reference state for a separate zero power branch.

There are two simplifications which are worth to be discussed. Burnable absorbers were burned without dividing rods into concentric rings. It is a common practice to divide the material into five to ten rings, especially for the fuel mixed with burnable absorbers [22]. In the case of BEAVRS PWR, the burnable absorbers are not mixed with the fuel and for simplicity - the multi-region option was not applied. Hence, borosilicate rods are burned homogenously.

The second important simplification assumes assembly-wise burnup. Hence, all fuel rods of the same kind, in a fuel assembly, are burned as one material. Those two issues are important and justify the potential reason for differences between the benchmark data and fuel cycle simulations. Otherwise, it should be highlighted that those simplifications should not affect the Hot Zero Power calculations.

Important differences exist between BEAVRS revision 1.1.1 and 2.0.1. The core axial geometry is different, and some material details are different. Especially, in rev 2.0.1 there are control rods with two absorbers AIC and B4C. Those features were not introduced in models used in this report. It has an impact on the control rods zero power validation calculations. It is worth mentioning that the control banks were not present in the core during the fuel cycle calculations because these were performed for constant full power operation without any outages (for 327 days).

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2.2.1 Critical Test Calculations Test calculations were performed to confirm the correctness of the group constants generation procedure (TRITON-GenPMAXS-PMAX-PARCS). Critical calculations were performed with TRITON for all fuel assembly types. Output files were processed with GenPMAXS to generate proper PMAXS files. The results were compared with the PARCS infinite homogenous core (reflective boundary conditions) model with one assembly type

[23]. Those calculations were performed for 44 and 238 groups in the HZP state with 975 ppm of boron.

2.2.2 Burnup Calculations The separate burnup calculations were performed without a branch sequence. Those were used to investigate the effect of nuclear library selection at the early stage of the research. Most of the calculations performed in this research were performed using the ENDF/B-V 44 group library, and it was necessary to assess what is the potential effect of the more recent ENDF/B-VII 238 group libraries. Application of 238 group libraries heavily increases the branch computational time in the TRITON sequence with NEWT transport calculations. Those test calculations were performed in Hot Full Power state with 378 ppm of boron. The burnup sequence, with fine depletion steps, was applied with 238 neutron groups and is presented in Table 2-5.

Later during the project, results without branches and for 238 groups with 378 ppm of boron were applied as a source of an isotopic assembly inventory. They were also applied in the dedicated core inventory prediction code WUTBURN described further in this report.

In the case of branch calculations with burnup, simulations were performed for both 44 and 238 neutron groups. Separate schemes were prepared for the fuel without burnable absorbers and for the fuel with burnable absorbers. The appropriate schemes are presented in Table 2-6 and Table 2-7.

In order to obtain Hot Zero Power, the results of a branch for the Beginning of Cycle core state with only one burnup step were applied.

7

Table 2-5 Burnup sequence applied to all assemblies for 238 neutron groups and with detailed burnup calculations and without branches Mid.

Specific power Day Day Interval Burnup Burnp step Burnup Step MWth/tHM EFPD EFPD EFPD GWd/tHM GWd/tHM 0 41.699 0 0 0 0.0 0.00 1 41.699 1 1 0.5 0.0 0.04 2 41.699 6 5 3.5 0.3 0.21 3 41.699 16 10 11 0.7 0.42 4 41.699 26 10 21 1.1 0.42 5 41.699 41 15 33.5 1.7 0.63 6 41.699 56 15 48.5 2.3 0.63 7 41.699 71 15 63.5 3.0 0.63 8 41.699 96 25 83.5 4.0 1.04 9 41.699 121 25 108.5 5.0 1.04 10 41.699 146 25 133.5 6.1 1.04 11 41.699 176 30 161 7.3 1.25 12 41.699 206 30 191 8.6 1.25 13 41.699 236 30 221 9.8 1.25 14 41.699 266 30 251 11.1 1.25 15 41.699 296 30 281 12.3 1.25 16 41.699 326 30 311 13.6 1.25 17 41.699 356 30 341 14.8 1.25 18 41.699 386 30 371 16.1 1.25 19 41.699 416 30 401 17.3 1.25 20 41.699 446 30 431 18.6 1.25 21 41.699 476 30 461 19.8 1.25 22 41.699 506 30 491 21.1 1.25 23 41.699 536 30 521 22.4 1.25 24 41.699 566 30 551 23.6 1.25 25 41.699 596 30 581 24.9 1.25 26 41.699 626 30 611 26.1 1.25 27 41.699 656 30 641 27.4 1.25 28 41.699 686 30 671 28.6 1.25 29 41.699 716 30 701 29.9 1.25 30 41.699 746 30 731 31.1 1.25 31 41.699 776 30 761 32.4 1.25 32 41.699 806 30 791 33.6 1.25 33 41.699 836 30 821 34.9 1.25 34 41.699 866 30 851 36.1 1.25 35 41.699 896 30 881 37.4 1.25 36 41.699 926 30 911 38.6 1.25 37 41.699 956 30 941 39.9 1.25 38 41.699 986 30 971 41.1 1.25 39 41.699 1016 30 1001 42.4 1.25 40 41.699 1046 30 1031 43.6 1.25 41 41.699 1076 30 1061 44.9 1.25 42 41.699 1106 30 1091 46.1 1.25 8

Table 2-6 Fuel burnup sequence applied in branch calculations for assemblies without BAs Specific power Day Day Interval Mid. Burnup Burnup Burnp step Step MWth/tHM EFPD EFPD EFPD GWd/tHM GWd/tHM 0 41.699 0 0 0 0.00 0.00 1 41.699 5 5 2.5 0.10 0.21 2 41.699 20 15 12.5 0.52 0.63 3 41.699 45 25 32.5 1.36 1.04 4 41.699 70 25 57.5 2.40 1.04 5 41.699 95 25 82.5 3.44 1.04 6 41.699 120 25 107.5 4.48 1.04 7 41.699 145 25 132.5 5.53 1.04 8 41.699 170 25 157.5 6.57 1.04 9 41.699 195 25 182.5 7.61 1.04 10 41.699 255 60 225 9.38 2.50 11 41.699 315 60 285 11.88 2.50 12 41.699 375 60 345 14.39 2.50 13 41.699 435 60 405 16.89 2.50 14 41.699 495 60 465 19.39 2.50 15 41.699 555 60 525 21.89 2.50 16 41.699 615 60 585 24.39 2.50 17 41.699 675 60 645 26.90 2.50 18 41.699 735 60 705 29.40 2.50 19 41.699 795 60 765 31.90 2.50 20 41.699 855 60 825 34.40 2.50 21 41.699 915 60 885 36.90 2.50 22 41.699 975 60 945 39.41 2.50 23 41.699 1035 60 1005 41.91 2.50 24 41.699 1095 60 1065 44.41 2.50 9

Table 2-7 Fuel burnup sequence applied in branch calculations for assemblies with BAs Specific power Day Day Interval Mid. Burnup Burnup Burnp step Step MWth/tHM EFPD EFPD EFPD GWd/tHM GWd/tHM 0 41.699 0 0 0 0 0 1 41.699 5 5 2.5 0.10 0.21 2 41.699 20 15 12.5 0.52 0.63 3 41.699 45 25 32.5 1.36 1.04 4 41.699 70 25 57.5 2.40 1.04 5 41.699 95 25 82.5 3.44 1.04 6 41.699 120 25 107.5 4.48 1.04 7 41.699 145 25 132.5 5.53 1.04 8 41.699 170 25 157.5 6.57 1.04 9 41.699 195 25 182.5 7.61 1.04 10 41.699 235 40 215 8.97 1.67 11 41.699 275 40 255 10.63 1.67 12 41.699 315 40 295 12.30 1.67 13 41.699 355 40 335 13.97 1.67 14 41.699 395 40 375 15.64 1.67 15 41.699 435 40 415 17.31 1.67 16 41.699 475 40 455 18.97 1.67 17 41.699 515 40 495 20.64 1.67 18 41.699 555 40 535 22.31 1.67 19 41.699 595 40 575 23.98 1.67 20 41.699 635 40 615 25.64 1.67 21 41.699 675 40 655 27.31 1.67 22 41.699 715 40 695 28.98 1.67 23 41.699 755 40 735 30.65 1.67 24 41.699 795 40 775 32.32 1.67 25 41.699 835 40 815 33.98 1.67 26 41.699 875 40 855 35.65 1.67 27 41.699 915 40 895 37.32 1.67 28 41.699 955 40 935 38.99 1.67 29 41.699 995 40 975 40.66 1.67 30 41.699 1035 40 1015 42.32 1.67 31 41.699 1075 40 1055 43.99 1.67 2.2.3 Branches Several different branch (about 10) configurations were developed and tested. In this report, only the final versions are included and presented in Tables 2-8 and 2-9. Branches are orthogonal, and it was possible to generate PMAXS files with GenPMAXS [23].

Branch recommendations were applied described in references [23], [24]. Nevertheless, branch sequence preparations were difficult, and the calculations were time-consuming. Hence, the learning curve based on subsequent user errors or shortcomings had a low slope. Worth mentioning, from the time perspective Authors admit that the applied branches are too complex and they could have been simplified.

In the case of basic branch sequence calculations, the core was in steady-state HFP for all considered operation states, and transient calculations were not taken into account. In the case of the HFP calculations, the reference state corresponded to the nominal HFP state.

Similarly, in case of the branch sequence dedicated to HZP calculations, the reference case corresponded to the base HZP state.

10

Table 2-8 Branch sequence developed for Hot Full Power fuel cycle calculations Moderator Boron Fuel Moderator Number Control Rods density concentration temperature temperature Units [1-in, 0-out] [g/cc] [ppm] [K] [K]

0 0 0.71 378 900 580 1 0 0.74 378 900 580 2 1 0.71 378 900 580 3 1 0.74 378 900 580 4 0 0.71 0 900 580 5 0 0.74 0 900 580 6 1 0.71 0 900 580 7 1 0.74 0 900 580 8 0 0.71 756 900 580 9 0 0.74 756 900 580 10 1 0.71 756 900 580 11 1 0.74 756 900 580 12 0 0.69 378 900 580 13 1 0.69 378 900 580 14 0 0.69 0 900 580 15 1 0.69 0 900 580 16 0 0.69 756 900 580 17 1 0.69 756 900 580 Table 2-9 Branch sequence developed for Hot Zero Power Reactor Physics calculations Moderator Boron Fuel Moderator Number Control Rods density concentration temperature temperature Units [1-in, 0-out] [g/cc] [ppm] [K] [K]

0 0 0.74 975 566 566 1 0 0.71 975 566 566 2 1 0.74 975 566 566 3 1 0.71 975 566 566 4 0 0.74 1500 566 566 5 0 0.71 1500 566 566 6 1 0.74 1500 566 566 7 1 0.71 1500 566 566 8 0 0.74 0 566 566 9 0 0.71 0 566 566 10 1 0.74 0 566 566 11 1 0.71 0 566 566 12 0 0.71 975 900 566 13 1 0.71 975 900 566 14 0 0.71 1500 900 566 15 1 0.71 1500 900 566 16 0 0.71 0 900 566 17 1 0.71 0 900 566 18 0 0.74 975 900 566 19 1 0.74 975 900 566 20 0 0.74 1500 900 566 21 1 0.74 1500 900 566 22 0 0.74 0 900 566 23 1 0.74 0 900 566 11

2.2.4 Reflectors Two reflector models were developed by applying the methodology described in [23]. The first model was aimed at covering the axial (top and bottom) reflectors. The second one was used for the radial reflector. The reflectors are presented in Figure 2-2 and 2-3. Two versions of those models were calculated, one with 378 ppm borated water and the second with 975 ppm. Calculations were performed with 238 neutron groups, and PMAXS libraries were generated as input for PARCS.

The first model was based on the FA01 fuel assembly and an added region with a homogenous mixture of water, steel, cladding, helium and boron. The mixture material inventory was characterized by the volume fractions corresponding to the FA01 assembly geometry. The fuel was exchanged with helium. It was assumed for simplicity that the top and bottom reflectors are the same.

Figure 2-2 Axial reflector model Figure 2-3 Radial reflector model The radial reflector model was based on FA05, which is one of the most common assemblies at the core-periphery. It comprises a standard FA05 assembly model and an additional zone with the same dimensions but filled with a steel barrel, water zone and reactor vessel.

12

2.3 PARCS Models and Simulations 2.3.1 Core Model The core model was developed for the PARCS v3.2 code. It was composed of 20 active core axial levels and two additional axial levels, one for the upper and one for the lower reflector. A radial nodalization applies typical approach with one node per one fuel assembly. The core map with assembly types is presented in Figure 2-4. The PARCS model with thermal-hydraulic and geometrical details are presented in Table 2-10. The map with the assembly numbering is presented in Figure 2-5.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 10 10 10 10 10 10 10 10 10 2 10 10 10 5 6 5 6 5 6 5 10 10 10 3 10 10 5 5 8 1 9 1 9 1 8 5 5 10 10 4 10 5 7 4 1 4 1 4 1 4 1 4 7 5 10 5 10 10 5 4 2 4 1 3 1 3 1 4 2 4 5 10 10 6 10 5 8 1 4 1 3 1 3 1 3 1 4 1 8 5 10 DUMMY 7 10 6 1 4 1 3 1 3 1 3 1 3 1 4 1 6 10 10 REFLECTOR 8 10 5 9 1 3 1 3 1 4 1 3 1 3 1 9 5 10 1 FA 1 1.60% 00BA 9 10 6 1 4 1 3 1 4 1 4 1 3 1 4 1 6 10 2 FA 2 2.40% 00BA 10 10 5 9 1 3 1 3 1 4 1 3 1 3 1 9 5 10 3 FA 3 2.40% 12BA 11 10 6 1 4 1 3 1 3 1 3 1 3 1 4 1 6 10 4 FA 4 2.40% 16BA 12 10 5 8 1 4 1 3 1 3 1 3 1 4 1 8 5 10 5 FA 5 3.10% 0BA 13 10 10 5 4 2 4 1 3 1 3 1 4 2 4 5 10 10 6 FA 6 3.10% 6BA 14 10 5 7 4 1 4 1 4 1 4 1 4 7 5 10 7 FA 7 3.10% 15BA 15 10 10 5 5 8 1 9 1 9 1 8 5 5 10 10 8 FA 8 3.10% 16BA 16 10 10 10 5 6 5 6 5 6 5 10 10 10 9 FA 9 3.10% 20BA 17 10 10 10 10 10 10 10 10 10 Figure 2-4 Core map with assembly types. 1-9 fuel, 10 reflectors The axial geometry arrangement is simplified. The main part of the model comprises an active core height with 20 levels extending between Bottom of Active Fuel (BAF) and Top of Active Fuel (TAF). All 20 levels have the same length equal to 18.288 cm (total sum is 365.76 cm). The structures below and above were assumed to be part of the axial reflector model. A simple model based on top axial data was applied using the same PMAXS libraries for both the bottom and top reflector. The length of the top and bottom reflector node is equal to the fuel assembly pitch. Several other simplifications were taken into account: an assumption was made that instrumentation tubes, guide tubes and burnable absorbers have the same length as the active core.

13

Table 2-10 Thermal-hydraulics data for PARCS (CNTL & TH card)

HZP (HOT ZERO HFP (HOT FULL Parameter Units POWER) POWER)

Reactor Power MWth 25 (0.73%) 3411 (100%)

Initial boron concentration ppm 975.00 378 Moderator temperature °C 293.33 306.85 Fuel temperature °C 293.33 626.85 Assembly power (nominal) MWth 17.6735 Assembly pitch cm 21.50364 Pellet radius mm 3.9218 Clad outer radius mm 4.572 Clad thickness mm 0.5715 Guide tube outer radius mm 6.0198 Moderator density 1 g/cm3 0.739860 0.711901 Gap conductance W/m2K 10000 (default)

Gamma heating fraction [-] 0.01 (assumed)

Coolant mass flow per FA, reduced by 5% due to kg/s 84.0889 bypass flow Comparing the model used in this project with the design reported in the benchmark revision 1.1.1

[7] some differences are visible. First, borosilicate glass (burnable absorber) rods are shorter than fuel rods. In the PARCS model, it was assumed that they have equal length. According to [7],

there is a 5.08 cm difference between the bottom of the active fuel and BA rods. Moreover, in [7],

there is a different geometry of the guide tubes above and at the dashpot. Similarly, burnable poison geometry and control rods geometry above and below dashpot are different. Moreover, spacer grids were not considered in the model. All the above mentioned details may have a potential impact on the neutronics. Without a detailed investigation, it is impossible to assess it.

Some interesting considerations are available in [11], [12].

2.3.2 Control Rods The control rod banks pattern applied in the PARCS model is presented in Figure 2-6 and described in Table 2-11. There are nine different control banks, four are dedicated to operational reactivity manipulation (A, B, C, D), and five are shutdown banks (SA, SB, SC, SD, SE). One control rod step corresponds to 1.58173 cm, and there are 228 steps with a total length of 360.634 cm, where the 228th step value is the control rod fully removed and step no. 0 is for the full rod insertion. The full insertion position is located 30.492 cm above the bottom plane of the model.

The BAF plane is located 21.42 cm above the bottom plane, and TAF is 387.18 cm above the bottom of the model.

1 moderator density without boron.

14

R P N M L K J H G F E D C B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 2 3 4 5 6 7 2 2 8 9 10 11 12 13 14 15 16 17 18 3 3 19 20 21 22 23 24 25 26 27 28 29 30 31 4 4 32 33 34 35 36 37 38 39 40 41 42 43 44 5 5 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 6 6 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 7 7 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 8 8 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 9 9 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 10 10 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 11 11 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 12 12 150 151 152 153 154 155 156 157 158 159 160 161 162 13 13 163 164 165 166 167 168 169 170 171 172 173 174 175 14 14 176 177 178 179 180 181 182 183 184 185 186 15 15 187 188 189 190 191 192 193 Figure 2-5 Core map with assemblies numbering from 1 to 193. 0 - number of an assembly 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 BANK NO NO SPIDERS GT/BANK 3 0 0 0 5 0 2 0 3 0 2 0 5 0 0 0 1 4-A x 4 96 4 0 0 0 0 8 0 6 0 6 0 7 0 0 0 0 2 8-B x 8 192 5 0 0 5 0 4 0 0 0 9 0 0 0 4 0 5 0 0 3 8-C x 8 192 6 0 0 0 7 0 0 0 0 0 0 0 0 0 8 0 0 0 4 5-D x 5 120 7 0 0 2 0 0 0 3 0 1 0 3 0 0 0 2 0 0 5 8-SA x 8 192 8 0 0 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 6 8-SB x 8 192 9 0 0 3 0 9 0 1 0 4 0 1 0 9 0 3 0 0 7 4-SC x 4 96 10 0 0 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 8 4-SD x 4 96 11 0 0 2 0 0 0 3 0 1 0 3 0 0 0 2 0 0 9 4-SE x 4 96 12 0 0 0 8 0 0 0 0 0 0 0 0 0 7 0 0 0 53 1272 13 0 0 5 0 4 0 0 0 9 0 0 0 4 0 5 0 0 14 0 0 0 0 7 0 6 0 6 0 8 0 0 0 0 15 0 0 0 5 0 2 0 3 0 2 0 5 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 Figure 2-6 Core map with control banks (groups) numbering (1-9). 0 - assembly has no control rods. There are 24 Guide Tubes per assembly 15

Table 2-11 Control banks data Number Designation No. of assemblies Total number of rods in group 1 A 4 96 2 B 8 192 3 C 8 192 4 D 5 120 5 SA 8 192 6 SB 8 192 7 SC 4 96 8 SD 4 96 9 SE 4 96 SUM - 53 1272 2.4 ORIGEN-ARP Models The model of a fuel assembly with enrichment equal to the core average (2.36679%) was prepared for the ORIGEN-ARP (it uses ORIGEN-S) module in the SCALE package. The template model was applied, which is based on a default Westinghouse 17x17 assembly with 238 groups PWR cross-section libraries available in ORIGEN-ARP/SCALE package distribution. The design of the assemblies is very similar to the BEAVRS assembly design.

Final results are compared with the detailed 3D calculations in Section 3.3.

2.5 Core Inventory Calculation Methodology A special in-house computer code WUTBURN was developed to calculate detailed PWR core inventory using the PARCS simulator. The code processes SCALE/TRITON (and ORIGEN-S which is part of the TRITON sequence) burnup results for 2D assemblies. Output files contain detailed fuel assembly isotopic inventory as a function of burnup (irradiation time).

Next, the code imports the PARCS core simulator output with spatial and temporal burnup 3D distribution for a given fuel cycle. In the next step, the code processes (interpolates and/or extrapolates) those distributions into detailed spatial-temporal core isotopic inventory based on TRITON results. It assumes that the burnup and the isotopic inventory are directly dependent during the full power operation for the cycle without outages. It was not tested for different power history, nor other changing conditions and this approach may not be applicable in general. This issue needs to be tested in future research.

16

3 RESULTS AND DISCUSSION 3.1 Group Constants Tests In order to perform test calculations with PARCS, a model of the infinite homogenous core with reflective boundary conditions was applied. Eighteen calculations were performed, each for a single type of fuel assembly, no reflector and 44 or 238 neutron groups. Xenon and Samarium calculations and thermal-hydraulics feedbacks were turned off. A comparison of results with corresponding TRITON eigenvalues and PMAXS eigenvalues is presented in Table 3-1. All calculations were performed in order to test the group constants transfer process between TRITON-GenPMAXS-PARCS. The results are presented in Table 3-2 and Table 3-3. The observed differences are negligible (smaller than 1pcm), and it can be concluded that the methodology works properly.

Table 3-1 Comparison of the k-inf for 44 neutron groups in the HZP state for TRITON calculations, GenPMAXS results in PMAXS files and PARCS infinite homogenous core results Result Result TRITON-PMAX PARCS infinite PARCS-TRITON PARCS-PMAX

1. FA TRITON PMAXS difference [pcm] homogenous difference [pcm] difference [pcm]

• .out FA1 0.98732521 0.98732567 0.05 0.98732500 -0.02 -0.07 FA2 1.12834879 1.12834907 0.02 1.12835000 0.10 0.07 FA3 1.00598419 1.00598454 0.03 1.00598500 0.08 0.05 FA4 0.96793802 0.96793830 0.03 0.96793900 0.10 0.07 FA5 1.20964318 1.20964336 0.01 1.20964500 0.12 0.11 FA6 1.15330786 1.15330803 0.01 1.15331200 0.31 0.30 FA7 1.06958646 1.06958652 0.01 1.06958600 -0.04 -0.05 FA8 1.05518859 1.05518866 0.01 1.05517900 -0.86 -0.87 FA9 1.01968210 1.01968241 0.03 1.01968600 0.38 0.35 A comparison between 44 and 238 groups is presented in Table 3-4. Large differences were observed with values as high as 330-450 pcm. In consequence, the models were compared and reviewed. The only differences between the models observed were related to nuclear libraries applied with different neutron groups (ENDF-V and ENDF-VII) and isotopes available in those libraries. It is worth mentioning that the solution is for HZP, hence there is no burnup influence the present.

Assembly isotopic composition slightly varies in the case of the model with 44 groups and 238 groups. Many isotopes present in the air (Ar), borosilicate glass (Si), Inconel (Si, Cr, Fe, Ni),

steel (Cr, Si, Fe, Ni) and Zircalloy-4 (Cr, Fe) were not available in 44 group libraries in an explicit form as in 238 libraries and as described in the benchmark. Only natural mixture compositions are available, and those were applied in the 44-group case. It was not expected to receive such a difference due only to this type of material exchange. It is possible that those differences were 17

caused by self-shielding effects, but it would require further investigation. The results of the fuel burnup presented in the next sub-chapter may suggest such a conclusion.

Table 3-2 Comparison of the k-inf for 238 neutron groups in the HZP state for TRITON calculations, GenPMAXS results in PMAXS files and PARCS infinite homogenous core results Result Result TRITON-PMAX PARCS infinite PARCS-TRITON PARCS-PMAX

1. FA TRITON PMAXS difference [pcm] homogenous difference [pcm] difference [pcm]

• .out FA1 0.99173526 0.99173260 -0.27 0.99173300 -0.23 0.04 FA2 1.13322188 1.13321912 -0.21 1.13321700 -0.38 -0.17 FA3 1.00986990 1.00986755 -0.23 1.00986500 -0.48 -0.25 FA4 0.97153058 0.97152811 -0.26 0.97152400 -0.70 -0.44 FA5 1.21465760 1.21465433 -0.22 1.21465100 -0.45 -0.23 FA6 1.15787893 1.15787625 -0.20 1.15787500 -0.29 -0.09 FA7 1.07351946 1.07351720 -0.20 1.07352000 0.05 0.24 FA8 1.05898940 1.05898714 -0.20 1.05897700 -1.11 -0.90 FA9 1.02322324 1.02322078 -0.23 1.02322000 -0.31 -0.07 Table 3-3 Differences between 44 and 238 groups for TRITON, PMAXS and infinite PARCS for HZP TRITON difference v44- PMAXS difference v44- PARCS Infinite Homogenous difference v44-

1. FA v238 [pcm] v238 [pcm] v238 [pcm]

FA1 -450.39 -450.07 -450.18 FA2 -381.11 -380.87 -380.63 FA3 -382.48 -382.22 -381.92 FA4 -382.03 -381.74 -381.23 FA5 -341.28 -341.05 -340.71 FA6 -342.30 -342.09 -341.70 FA7 -342.53 -342.33 -342.62 FA8 -340.14 -339.93 -339.89 FA9 -339.40 -339.13 -338.71 3.2 Fuel Assembly Burnup Calculations Fuel assembly burnup calculations were performed using 44 and 238 groups neutron cross-sections data libraries. The final PARCS calculations for the fuel cycle were performed with both 44 and 238 libraries, but initially, the 44 groups library was applied. Thus, the main purpose of the comparison was to estimate what was the difference between 238 groups and 44 groups results as a function of the burnup.

18

Reactivity differences between 44 groups and 238 groups are presented in Figure 3-1. It is possible to conclude that there are significant differences in terms of reactivity for all assemblies. Initially, the reactivity for the case with 44 groups is smaller by about 500 pcm in comparison to 238 groups. Deviation gradually decreases with burnup at various rates. The smallest difference <50 pcm at the end of burnup was observed for FA06, FA07, FA08, FA09, characterized by the highest enrichment and large BA inventory. The largest difference (~300 pcm) was observed for FA01, characterized by the lowest enrichment and no BAs. Comparison of eigenvalue results for every assembly is presented in Figures 3-2 to Figure 3-10.

It can be concluded that the application of 44 group libraries in comparison to 238 groups for fuel cycle calculations should reduce reactivity at the BOL (BOC in the case of Cycle 1) by less than 500 pcm (~50 ppm of boron). The maximum BEAVRS burnup at the end of the first cycle was lower than 20 GWd/tHM with an average equal to 13 GWd/tHM. Hence, underprediction of the core reactivity in comparison to 238 group case is expected for the first cycle. The results of the fuel cycle calculations presented in Section 3 are in good agreement with these predictions.

It is worth mentioning that the burnup calculations were performed with the constant flux option for Burnable Absorbers. In principle, this option is important when fuel is mixed with burnable absorbers. It is of less importance for BEAVRS because burnable absorbers are not mixed with the fuel. In these tests, the relative difference between 44 and 238 was a figure of merit, so the eventual difference was of less importance. Similar calculations were performed in the earlier stage of the project for burnup without constant flux burning, and observed differences were similar to those presented in Figure 3-1.

Figure 3-1 Reactivity differences between 44g and 238g ( )

19

Figure 3-2 Infinite multiplication factor for FA01 assembly Figure 3-3 Infinite multiplication factor for FA02 assembly 20

Figure 3-4 Infinite multiplication factor for FA03 assembly Figure 3-5 Infinite multiplication factor for FA04 assembly 21

Figure 3-6 Infinite multiplication factor for FA05 assembly Figure 3-7 Infinite multiplication factor for FA06 assembly 22

Figure 3-8 Infinite multiplication factor for FA07 assembly Figure 3-9 Infinite multiplication factor for FA08 assembly 23

Figure 3-10 Infinite multiplication factor for FA09 assembly 24

3.3 Benchmark Results 3.3.1 Hot Zero Power Tests In order to validate the model, Hot Zero Power state at the BOC (it is also BOL) was modelled.

The core power is equal to 25 MWth, and water contains 975 ppm of boron (see Table 2-10). Calculations were performed for conditions without the Xe/Sm - a clean core (PARCS card: XE_SM 0 0 0 0) with active thermal-hydraulic feedbacks. The HZP state was characterized by slightly inserted D-bank control rods, 213 steps position (228 - full withdrawn) as it is described in the Benchmark specification. For comparison, some states were simulated for ARO (All-Rods-Out).

Table 3-4 and Table 3-5 present a comparison between the BEAVRS data and results for 44 and 238 neutron groups for critical boron concentration and eigenvalue with 975 ppm. The difference between PARCS with 238 groups is large but acceptable ~200 pcm and substantially large ~720 pcm for 44 groups. In the case of critical boron calculations differences are ~20 ppm and ~60 ppm of boron respectively.

In comparison to the literature, the obtained results suggest that the model demands further improvements, see [11]-[16] and [17]-[21]. One of the potential reasons for this discrepancy is reflector modelling. It was observed that the reflector model has a quite large impact on the final results. Applying different reflector models, critical boron concentrations were obtained with variations as high as 15-20 ppm for both HZP and HFP calculations.

It might be significant because the reflector model applied in this work is simplified in comparison to some models described in the literature. What is more, the axial structure of the model is simplified, and spacer grids were not considered. Those issues should be solved in future research.

Differences between results for 44 groups and 238 groups results are relatively large, ~500 pcm for eigenvalue or ~40 ppm for boron. The difference between 44 and 238 groups was discussed in the previous sub-chapter. Minor differences are observed between the state with D-bank slightly inserted and ARO state.

Table 3-4 Beginning of cycle 1 hot zero power core physics for D-bank 213 steps withdrawn configuration Parameter Units BEAVRS v44 v238 Crit. Boron Conc. @ keff= 1, D-bank: 213 steps [ppm] 975.0 915 958 Difference to BEAVRS [ppm] 0 -60 -17 k-eff @ 975ppm, D-bank: 213 steps [-] 1.00000 0.99284 0.99796 Reactivity @ 975 ppm, D-bank: 213 steps [pcm] 0 -721 -205 Table 3-5 Beginning of cycle 1 hot zero power core physics for All-Rods-Out (ARO)

Parameter Units BEAVRS v44 v238 Crit. Boron Conc. @ keff= 1, ARO [ppm] 975.0 917 960 Difference to BEAVRS [ppm] 0 -58 -15 K-eff @ 975ppm, ARO [-] 1.00000 0.99288 0.99799 Reactivity @ 975 ppm ARO [pcm] 0 -718 -202 25

Table 3-6 Critical boron concentrations with inserted control banks for cycle 1 hot zero power tests Critical Boron Concentration [ppm]

Parameter BEAVRS v44 groups Difference v238 groups Difference ARO 975 917 -58 960 -15 D in 902 849 -53 896 -7 C,D in 810 739 -72 798 -12 A,B,C,D in 686 585 -102 657 -29 A,B,C,D,SE,SD,SC in 508 379 -130 472 -36 Critical boron concentrations for different control banks insertion states were calculated, and the results are presented in Table 3-6. The results for 238 neutron groups case are more consistent with the benchmark results. The highest difference for 238 groups was ~40 ppm, and for 44 groups it was ~130 ppm. The 238 results are within 50 ppm, industrial standard [25].

Similar results, however for eigenvalues with boron concentrations fixed to the BEAVRS value are presented in Table 3-7. The values presented in Table 3-6 and 3-7 show that the 238 group results are better in terms of benchmark results. What is interesting, heavily rodded configurations are characterized by the largest differences.

Table 3-7 Effective multiplication factor calculated for different control rod states with the BEAVRS values of boron concentration Boron Effective Multiplication Factor, [-]

Parameter Concentration, BEAVRS v44 groups Difference, [pcm] v238 groups Difference, [pcm]

[ppm]

ARO 975 1.00000 0.99288 -718 0.99799 -202 D in 902 1.00000 0.99354 -650 0.99921 -79 C,D in 810 1.00000 0.99144 -864 0.99856 -145 A,B,C,D in 686 1.00000 0.98778 -1237 0.99648 -353 A,B,C,D,SE,SD,SC in 508 1.00000 0.98459 -1565 0.99575 -427 Control Rod Bank Worth (CRW) calculations for the BEAVRS, 44 and 238 groups are compared in Table 3-8. Those were calculated assuming constant boron inventory equal to 975 ppm. The largest difference for 44 groups was ~230 pcm (~20% of CRW), and in the case of 238 groups, it was 174 pcms (~30%). In this case, there is no rule to judge which case is better as both are characterized by similar deviations. The lowest difference was 4 pcm (0.38%)

and 26 pcm (3.25%) for 44 and 238 groups respectively.

Table 3-8 Comparison of Control Rod Bank Worth Control Rod Bank Worths [pcm]

Parameter all@ 975ppm boron BEAVRS v44 groups Difference v238 groups Difference D in 788 822 34 762 -26 C with D in 1203 1295 92 1149 -54 B with D,C in 1171 1399 228 1302 131 A with D, C, B in 548 451 -97 374 -174 SE with D, C,B, A in 461 386 -75 342 -119 SD with D, C, B, A, SE in 772 816 44 745 -27 SC with D, C, B, A, SE, SD in 1099 1103 4 973 -126 26

Figures 3-11 and 3-12 compare radially averaged axial response of all BEAVRS core detectors compared with radially averaged axial power profile and average thermal neutron flux profile calculated with PARCS for 44 and 238 neutron groups with D-bank 213 steps state.

The results are consistent with a small deviation at the bottom of the core and imply reflector improvements. Moreover, it is possible to observe the lack of spacer grid flux depressions.

Figure 3-11 Average axial relative power calculated with PARCS for 213 D-bank withdrawn and 44 neutron groups compared with core averaged all detectors response 27

Figure 3-12 Average axial relative power calculated with PARCS for 213 D-bank withdrawn and 238 neutron groups compared with core averaged all detectors response The radial distribution of the thermal neutron flux results for 44 and 238 groups are presented in Figure 3-13 and 3-14. Those are compared with detectors measurements after tilt corrections introduced in benchmark Rev 2.0.1. All differences between both calculations are less than 11% for 44 groups and 10% for 238 groups. Figure 3-15 presents the relative percentage difference between results. Acceptable agreement was observed.

I has to be mentioned that in [2], by mistake, the radial power and radial flux maps were presented for the reflector model studied in this report.

28

H G F E D C B A 0.917 0.750 1.050 0.919 1.152 0.932 1.293 0.818 8 0.779 1.065 0.940 1.147 0.935 1.264 0.778

-3.8 -1.4 -2.3 0.5 -0.3 2.3 5.1 0.750 1.000 0.883 1.136 0.958 1.203 0.901 0.851 9 0.779 1.011 0.897 1.143 0.974 1.168 0.873 0.815

-3.8 -1.1 -1.5 -0.6 -1.6 3.0 3.2 4.4 1.050 0.883 1.129 0.965 1.201 0.963 1.275 0.759 10 1.065 0.897 1.138 0.968 1.212 0.984 1.242 0.728

-1.4 -1.5 -0.8 -0.3 -0.9 -2.2 2.7 4.2 0.919 1.137 0.965 1.245 1.029 1.341 0.915 0.596 11 0.940 1.143 0.968 1.249 1.307 0.584

-2.2 -0.5 -0.3 -0.4 2.6 2.0 1.154 0.959 1.201 1.029 1.357 1.121 0.947 12 1.147 0.974 1.212 1.343 1.196 0.958 0.6 -1.5 -0.9 1.0 -6.3 -1.1 0.933 1.205 0.964 1.342 1.121 0.945 0.660 13 0.935 1.168 0.984 1.307 1.196 0.852 0.702

-0.2 3.1 -2.1 2.7 -6.2 10.9 -5.9 1.295 0.903 1.277 0.916 0.947 0.660 14 1.264 0.873 1.242 0.958 0.702 2.5 3.4 2.8 -1.1 -5.9 0.820 0.854 0.760 0.597 PARCS v44 15 0.778 0.815 0.728 0.584 BEAVRS 5.4 4.8 4.4 2.3 Diff. %

Figure 3-13 HZP detectors BEAVRS measurements compared with thermal flux distribution - tilt corrected for PMAX based on 44 groups H G F E D C B A 0.914 0.705 1.051 0.881 1.173 0.905 1.350 0.822 8 0.779 1.065 0.940 1.147 0.935 1.264 0.778

-9.5 -1.3 -6.3 2.2 -3.2 6.8 5.6 0.705 0.999 0.842 1.146 0.928 1.240 0.857 0.865 9 0.779 1.011 0.897 1.143 0.974 1.168 0.873 0.815

-9.5 -1.2 -6.1 0.3 -4.7 6.2 -1.8 6.1 1.052 0.842 1.137 0.930 1.227 0.938 1.337 0.765 10 1.065 0.897 1.138 0.968 1.212 0.984 1.242 0.728

-1.2 -6.1 -0.1 -4.0 1.3 -4.7 7.6 5.1 0.881 1.147 0.930 1.268 0.995 1.394 0.887 0.616 11 0.940 1.143 0.968 1.249 1.307 0.584

-6.3 0.4 -4.0 1.6 6.7 5.4 1.174 0.929 1.228 0.996 1.365 1.101 0.963 12 1.147 0.974 1.212 1.343 1.196 0.958 2.3 -4.6 1.3 1.6 -7.9 0.5 0.906 1.242 0.939 1.395 1.101 0.917 0.682 13 0.935 1.168 0.984 1.307 1.196 0.852 0.702

-3.1 6.3 -4.6 6.7 -7.9 7.7 -2.8 1.353 0.859 1.339 0.888 0.963 0.683 14 1.264 0.873 1.242 0.958 0.702 7.1 -1.6 7.8 0.5 -2.8 0.825 0.868 0.767 0.617 PARCS v238 15 0.778 0.815 0.728 0.584 BEAVRS 6.0 6.5 5.3 5.6 Diff. %

Figure 3-14 HZP detectors BEAVRS measurements compared with thermal flux distribution - tilt corrected for PMAX based on 238 groups 29

H G F E D C B A 8 -0.30 -5.93 0.12 -4.15 1.77 -2.86 4.45 0.49 9 -5.93 -0.10 -4.61 0.88 -3.16 3.07 -4.88 1.64 10 0.20 -4.63 0.67 -3.67 2.23 -2.60 4.80 0.80 11 -4.20 0.91 -3.69 1.92 -3.27 3.94 -3.10 3.33 12 1.76 -3.15 2.21 -3.20 0.55 -1.78 1.63 13 -2.91 3.05 -2.55 3.94 -1.80 -2.93 3.29 14 4.47 -4.87 4.80 -3.15 1.64 3.37 15 0.62 1.63 0.87 3.28 Figure 3-15 Core thermal flux radial distribution, relative difference between PARCS results with PMAXS based on 44 groups and 238 groups. Tilt corrected H G F E D C B A 8 0.6975 0.78255 0.7983 0.9599 0.8763 0.97305 0.98635 1.0619 9 0.7826 0.76067 0.92265 0.86398 1.0015 0.91605 1.1603 1.1095 10 0.7985 0.9228 0.85842 1.0082 0.91305 1.0051 0.97305 0.98522 11 0.9604 0.86438 1.0085 0.94663 1.0763 1.0217 1.1809 0.77935 12 0.87705 1.0023 0.9136 1.0766 1.4323 1.1802 1.2339 13 0.9745 0.91727 1.0061 1.0224 1.1804 1.2286 0.86325 14 0.98835 1.1628 0.97447 1.1822 1.2344 0.86323 15 1.0644 1.1133 0.98707 0.78097 Figure 3-16 1/4th core radial power distribution calculated with PARCS and PMAX based on 44 groups H G F E D C B A 8 0.6684 0.7519 0.7685 0.9319 0.8569 0.9651 0.9908 1.0938 9 0.7519 0.7305 0.8912 0.8381 0.9825 0.9077 1.1671 1.1429 10 0.7687 0.8914 0.8305 0.9838 0.897 1.0008 0.9803 1.0173 11 0.9325 0.8386 0.9841 0.9275 1.0647 1.0207 1.198 0.8152 12 0.8578 0.9834 0.8976 1.065 1.4271 1.1857 1.2714 13 0.9668 0.9091 1.002 1.0214 1.1859 1.2465 0.9039 14 0.9931 1.1699 0.982 1.1995 1.2721 0.9039 15 1.0968 1.1473 1.0195 0.8171 Figure 3-17 1/4th core radial power distribution calculated with PARCS and PMAX based on 238 groups 30

Radial power distributions calculated by PARCS for a quarter of the core are presented in Figure 3-16 and 3-17. Relative differences between 44 and 238 groups are presented in Figure 3-18.

Largest differences were observed in the central and peripheral part of the core.

H G F E D C B A 8 -4.17 -3.92 -3.73 -2.92 -2.21 -0.82 0.45 3.00 9 -3.92 -3.97 -3.41 -3.00 -1.90 -0.91 0.59 3.01 10 -3.73 -3.40 -3.25 -2.42 -1.76 -0.43 0.75 3.26 11 -2.91 -2.98 -2.42 -2.02 -1.08 -0.10 1.45 4.60 12 -2.19 -1.89 -1.75 -1.08 -0.36 0.47 3.04 13 -0.79 -0.89 -0.41 -0.10 0.47 1.46 4.71 14 0.48 0.61 0.77 1.46 3.05 4.71 15 3.04 3.05 3.29 4.63 Figure 3-18 Core power radial distribution, relative difference between results for PARCS with PMAXS generated with 44 groups and 238 groups 3.3.2 Hot Full Power Operation A comparison of SCALE/PARCS results and BEAVRS fuel cycle data is presented in this sub-chapter [7]. The BEAVRS boron letdown curve as a function of effective time at full power (EFPD

- Effective Full Power Days) is available in Table 21 and Figure 53 in Benchmark Revision 1.1.1 (in [7]). The same data is available in Figure 59 and Table 24 in Benchmark Revision 2.0.1 (in

[6]).

What is important, benchmark Rev 2.0.1 contains an additional Table 25 [6] (not present in [7])

with core operating data as a function of exposure expressed in EFPD. The data is different from Table 24 in [6], and it may introduce some confusion. It is worth mentioning that in the benchmark 2.0.1, there is no explicit discussion about a detailed difference between both datasets.

Nevertheless, it may be considered that the boron letdown curve represents core excess reactivity expressed in boron concentration for full power operation with all control rods withdrawn.

Otherwise, operating data is for variable conditions - inlet temperature, bank D position and power. These two datasets are compared in Figure 3-20. The boron letdown curve is treated as reference data as it was present in the original specification. What is more, calculations presented in this work were performed only for constant power operation. For operating data, one can observe high initial reactivity which is due to the low power at the initial core operation and higher Xe/Sm concentration.

31

Figure 3-19 Comparison of boron letdown curve vs EFPD available in BEAVRS specification Rev 1.0.1 and Rev 2.0.1 and critical boron concentration (core operating data) data as a function of exposure available in benchmark Rev 2.0.1 The third dataset (it is an average boron concentration) represented by green points on Figure 3-21, may be derived from spreadsheets with detector measurements delivered with the Benchmark specification. The boron concentrations are expressed as a function of fuel burnup.

Figure 3-21 compares this set with two other curves in terms of burnup, where time was recalculated assuming constant power 3411 MWth and mass 81.791 tHM.

32

Figure 3-20 Average boron concentration measurements for detectors data compared with boron letdown curve and core operating dataall data taken from BEAVRS. Operating Data and Boron letdown expressed in EFPD were recalculated to burnup Figure 3-22 presents the calculated boron letdown curve as a function of the effective time at full power compared with the BEAVRS data. The PARCS model was run at hot full power for the whole simulation time with equilibrium Xenon and Samarium (PARCS card: XE_SM 1 1 1 1) and all control rods removed.

A good agreement between PARCS with 238 neutron groups and BEAVRS boron letdown curve was observed. There is a visible difference at the end of the cycle (>250 EFPDs), but it is 20 ppm of boron (Figure 3-22). A difference between PARCS 44 group boron letdown curve and reference BEAVRS dataset is about ~60 ppm of boron in the beginning, and it slowly decreases at the end of the cycle to ~20 ppm. The discussion presented in Section 3.1 and 3.2 concluded that at the beginning of the cycle an up to 50 ppm underprediction for 44 groups is expected and in fact, it was observed.

A comparison of results expressed in terms of burnup for 44 and 238 neutron groups with the State-of-the-Art results obtained by Finnish VTT using SERPENT-ARES is presented in Figure 3-23. It was also discussed in [2]. The SERPENT code was used for lattice physics, and ARES was used as a nodal simulator [11]. Above 250 EFPDs, the SERPENT-ARES results are more consistent with the BEAVRS boron letdown curve than PARCS 238 group results, and it is the only substantial difference. The reason for this difference was not explained.

33

Figure 3-21 Boron letdown curve for cycle 1 as a function of EFPDs. The BEAVRS data compared with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results with 100% nominal power calculations and Xe&Sm equilibrium Figure 3-22 Comparison of BEAVRS data expressed in burnup with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 100% nominal power and equilibrium Xe/Sm with State-of-the-Art calculations for 100% full power with Serpent-ARES [11]

34

The results with transient Xenon & Samarium calculations (PARCS card: XE_SM 2 2 2 2) for 100 % nominal power are presented and compared with non-transient results, core operational and detectors data in Figure 3-24.

Figure 3-23 Comparison of BEAVRS detectors and operating data with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 100%

nominal power, equilibrium and transient Xe/Sm 35

Figure 3-24 Comparison of BEAVRS detectors and operating data with PARCS using PMAXS libraries based on 44 and 238 neutron groups. Results for 75%

nominal power, equilibrium and transient Xe/Sm In the next step, simulations were performed for the core power equal to about 75% of nominal power. The capacity factor was equal to ~57% for the BEAVRS 1st cycle; however, when outages are not considered, the average core power is about ~75%. This approach was applied in the literature [13], [15], [26]. A comparison of PARCS 75% nominal power results for 44 and 238 groups, equilibrium and transient Xe & Sm with the BEAVRS operational and detectors data is presented in Figure 3-25. The transient results are presented in Figure 3-24 and 3-25. A difference is visible at the beginning of the cycle, due to the initial xenon transient and also due to the power manoeuvring and subsequent Xe&Sm transients, which are not reproduced by constant power calculations.

Additionally, all constant power equilibrium results are compared with all available datasets in Figure 3-26 and Table 3-9. It is possible to observe that PARCS 75% calculations predict higher boron concentration. It is expected that it is mainly due to lower Xenon equilibrium concentrations and possibly due to the change in the Doppler effect. Reduced power causes less equilibrium Xenon concentration and lower core temperatures which lead to reduced Doppler negative reactivity defect. In consequence, more boron is necessary to suppress excess reactivity to reach the critical state.

36

Figure 3-25 Comparison of BEAVRS detectors and operating data with PARCS 44 & 238 neutron groups, 100% & 75% nominal power for equilibrium Xe/Sm What can be observed, for the 238 neutron groups, the application of a 75% power calculations does not provide a solution which is more consistent with operational data when comparing with 100% power results. It can be assessed that results are inconclusive, but it can be postulated that 100% power simulation is more appropriate in this case.

In general, the obtained results for 238 neutron groups are acceptable from the point of view of the report and scope of the studied model. We expect that the 238 neutron groups results are better and more trustable. It demands special caution, as is possible to observe that the 44 groups results in some cases seem to be more consistent with some benchmark results.

However, it is a matter of luck, and 44 groups results should not be considered as more accurate. It was shown for HZP that 44 group results are in general underpredicted.

We believe that in further research, the addition of more detailed reflector and spacer grids may play a crucial role in the refinement of results. It was indicated in our other research with the Monte Carlo AP1000 model that spacer grids are important [27]. In the paper [28] it can be found that the presence of spacer grids can remove even up to 400 pcm, in the case of small PWR core and it can correspond even up to 40 ppm of boron. In consequence, it is expected that refined results with spacer grids will reduce core reactivity.

The results for the BEAVRS with power manoeuvring and comparison with detectors are reported and discussed in [2]. These newer results were obtained with the changed model and are not repeated in this report.

The comparison between BEAVRS average burnup and calculated burnup is presented in Figure 3-27 and Table 3-10.

37

Figure 3-26 Core average burnup as a function of effective full power time. BEAVRS data and PARCS results 38

Table 3-9 Comparison of PARCS critical boron concentration results with BEAVRS data. PARCS results are for Hot Full Power operation with 75% and 100%

nominal power BEAVRS Data Rev 1.1.1 BEAVRS Rev 2.0.1 Core PARCS v44 100% NP. PARCS v44 75% NP. PARCS v238 100% NP. PARCS v238 75% NP.

Boron letdown curve operating data

[EFPD] [ppm] [EFPD] [ppm] [EFPD] [ppm] [DAYS] [ppm] [DAYS] [ppm] [DAYS] [ppm]

0 - 0 709 0 565 0 583 0 612 0 630 4 599 6 674 4 545 4 558 4 594 4 608 11 610 21 609 6 547 6 560 6 596 6 609 16 614 25 598 11 554 11 564 11 601 11 613 22 621 36 596 16 562 16 570 16 608 16 617 31 638 52 590 21 570 21 576 21 615 21 622 36 610 80 556 22 571 22 577 22 616 22 624 52 623 110 494 25 574 25 581 25 619 25 627 69 598 140 437 31 576 31 588 31 620 31 632 85 569 144 476 36 577 36 590 36 620 36 634 96 559 150 416 52 570 52 592 52 611 52 635 110 533 156 404 69 551 69 587 69 591 69 627 124 506 180 352 80 536 80 579 80 575 80 619 141 471 220 258 85 528 85 575 85 568 85 615 144 461 235 218 96 510 96 565 96 550 96 604 152 457 266 140 110 485 110 550 110 525 110 589 164 415 296 58 124 459 124 533 124 499 124 573 174 394 310 49 140 428 140 513 140 468 140 552 177 384 326 31 141 426 141 511 141 466 141 551 180 384 327 29 144 420 144 508 144 460 144 547 190 367 150 407 150 500 150 448 150 539 204 322 152 403 152 497 152 444 152 536 214 296 156 395 156 491 156 435 156 531 219 286 164 378 164 480 164 419 164 520 225 270 174 357 174 466 174 397 174 506 228 270 177 350 184 452 177 391 184 491 248 207 180 344 194 437 180 384 194 477 271 149 190 322 204 421 190 362 204 462 295 72 204 290 214 406 204 331 214 446 326 0 214 266 224 390 214 307 224 431 327 0 219 255 234 374 219 296 234 415 220 252 244 358 220 293 244 398 225 240 254 341 225 281 254 382 228 233 264 325 228 274 264 365 235 216 274 308 235 257 274 348 248 184 284 290 248 225 284 331 266 139 294 273 266 180 294 314 271 126 304 255 271 167 304 296 295 63 314 237 295 105 314 278 296 61 324 218 296 102 324 260 310 24 334 200 310 65 334 241 326 -19 344 181 326 23 344 223 327 -22 354 162 327 20 354 204 364 143 364 185 374 124 374 166 384 105 384 146 394 85 394 127 404 65 404 107 414 46 414 87 424 26 424 68 434 6 434 48 444 -14 444 28 449 -24 449 18 39

Table 3-10 Comparison of the fuel burnup for BEAVRS and PARCS with 75% and 100%

of nominal power BEAVRS Data Rev 1.1.1 PARCS v44 100% NP. PARCS v44 75% NP. PARCS v238 100% NP. PARCS v44 75% NP.

Boron letdown curve EFPD [GWd/tHM] [EFPD] [GWd/tHM] [DAYS] [GWd/tHM] [DAYS] [GWd/tHM] [DAYS] [GWd/tHM]

0 0 0 0 0 0 0 0 0 0 4 0.17 4 0.165 4 0.124 4 0.165 4 0.124 11 0.453 6 0.248 6 0.186 6 0.248 6 0.186 16 0.659 11 0.455 11 0.341 11 0.455 11 0.341 22 0.921 16 0.662 16 0.496 16 0.662 16 0.496 31 1.296 21 0.869 21 0.652 21 0.869 21 0.652 36 1.499 22 0.91 22 0.683 22 0.91 22 0.683 52 2.157 25 1.034 25 0.776 25 1.034 25 0.776 69 2.898 31 1.282 31 0.962 31 1.282 31 0.962 85 3.564 36 1.489 36 1.117 36 1.489 36 1.117 96 3.999 52 2.151 52 1.613 52 2.151 52 1.613 110 4.58 69 2.855 69 2.141 69 2.855 69 2.141 124 5.159 80 3.31 80 2.482 80 3.31 80 2.482 141 5.874 85 3.516 85 2.637 85 3.516 85 2.637 144 5.998 96 3.972 96 2.979 96 3.972 96 2.979 152 6.337 110 4.551 110 3.413 110 4.551 110 3.413 164 6.862 124 5.13 124 3.847 124 5.13 124 3.847 174 7.274 140 5.792 140 4.344 140 5.792 140 4.344 177 7.39 141 5.833 141 4.375 141 5.833 141 4.375 180 7.51 144 5.957 144 4.468 144 5.957 144 4.468 190 7.93 150 6.205 150 4.654 150 6.205 150 4.654 204 8.49 152 6.288 152 4.716 152 6.288 152 4.716 214 8.941 156 6.454 156 4.84 156 6.454 156 4.84 219 9.148 164 6.785 164 5.089 164 6.785 164 5.089 225 9.37 174 7.198 174 5.399 174 7.198 174 5.399 228 9.501 177 7.322 184 5.709 177 7.322 184 5.709 248 10.338 180 7.447 194 6.019 180 7.447 194 6.019 271 11.293 190 7.86 204 6.33 190 7.86 204 6.33 295 12.305 204 8.439 214 6.64 204 8.439 214 6.64 326 13.598 214 8.853 224 6.95 214 8.853 224 6.95 327 219 9.06 234 7.26 219 9.06 234 7.26 220 9.101 244 7.571 220 9.101 244 7.571 225 9.308 254 7.881 225 9.308 254 7.881 228 9.432 264 8.191 228 9.432 264 8.191 235 9.722 274 8.502 235 9.722 274 8.502 248 10.26 284 8.812 248 10.26 284 8.812 266 11.004 294 9.122 266 11.004 294 9.122 271 11.211 304 9.432 271 11.211 304 9.432 295 12.204 314 9.743 295 12.204 314 9.743 296 12.246 324 10.053 296 12.246 324 10.053 310 12.825 334 10.363 310 12.825 334 10.363 326 13.487 344 10.673 326 13.487 344 10.673 327 13.528 354 10.984 327 13.528 354 10.984 364 11.294 364 11.294 374 11.604 374 11.604 384 11.915 384 11.915 394 12.225 394 12.225 404 12.535 404 12.535 414 12.845 414 12.845 424 13.156 424 13.156 434 13.466 434 13.466 444 13.776 444 13.776 449 13.931 449 13.931 40

3.4 Core Inventory Calculations 3.4.1 Initial Core State Initial heavy metal masses and fissile heavy metal masses available in Benchmark specification are presented in Figure 3-28 and 3-29 respectively. These data were input to the WUTBURN computer code.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 422352 422860 420911 424112 423798 421004 423404 2 421693 425885 420794 424618 425904 423343 425033 424776 420730 424800 424937 3 424427 422588 424014 425338 421148 424409 423810 424241 423535 424543 424180 424170 424193 4 425671 421881 421257 424261 424555 424468 422511 423025 423810 421801 424406 421871 422216 5 423062 422784 423101 425262 424742 421432 425512 423653 423622 423695 424255 424911 424615 420894 424944 6 422801 423297 424140 423693 424150 423746 424294 424642 424373 424865 423596 424399 423086 425287 420716 7 426100 425103 425284 423907 423764 424555 423432 421497 424759 421380 421655 424181 422483 425899 426067 8 424656 423857 424883 424198 424256 424044 423016 423849 423952 421443 423553 425152 424345 423432 424475 9 425240 420685 425421 424072 425410 422699 424375 422875 421474 423216 423530 422222 424595 425449 425874 10 422084 424630 424268 425652 424950 424649 424281 424615 423211 424117 423784 424412 424891 424324 425803 11 421775 423052 424275 422201 421625 423288 424993 424072 425181 424105 426061 424304 424941 424062 420801 12 423471 424620 424551 423639 424956 424165 425265 424361 425283 420485 423100 421583 422104 13 422419 422582 425089 424023 423244 421347 422934 424788 421755 423910 424783 423048 423343 14 425319 425657 424050 422255 424730 424688 426234 424904 424243 424281 421975 15 424459 424116 421853 425788 423030 424964 423782 Figure 3-27 Initial BEAVRS heavy metal (all uranium) masses radial distribution (in [g]).

Total mass: 81790749 grams 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 13092 13118 13082 13134 13121 13280 13084 2 13265 13193 13073 6826 13192 6793 13158 6817 13039 13159 13163 3 13146 13124 10131 6828 10132 6824 10136 6834 10162 6843 10156 13119 13136 4 13187 10131 10112 10159 6819 10163 6778 10162 6823 10123 10169 10124 13097 5 13099 13107 6785 10201 6849 10140 6859 10164 6839 10149 6837 10202 6829 13253 13162 6 13119 6826 10176 6822 10166 6824 10208 6822 10207 6872 10170 6848 10146 6846 13030 7 13196 13163 6870 10139 6831 10169 6834 10187 6831 10157 6786 10210 6783 13198 13160 8 13155 6827 10175 6854 10154 6818 10153 6823 10177 6782 10191 6833 10192 6792 13142 9 13172 13284 6872 10153 6872 10153 6824 10143 6782 10180 6836 10147 6849 13182 13192 10 13071 6827 10175 6843 10200 6832 10221 6825 10156 6837 10167 6847 10221 6852 13186 11 13100 13116 6852 10199 6792 10149 6847 10157 6847 10174 6882 10181 6844 13129 13069 12 13111 10163 10155 10192 6839 10176 6865 10148 6862 10097 10150 10130 13159 13 13108 13101 10199 6813 10138 6753 10150 6847 10118 6809 10202 13127 13140 14 13149 13183 13133 6776 13157 6836 13199 6840 13137 13124 13192 15 13147 13121 13063 13194 13097 13164 13111 Figure 3-28 Initial BEAVRS fissile (U-235) heavy metal masses radial distribution (in [g]).

Total mass: 1935560 grams 3.4.2 Masses and Activities A summary of core masses and activities for actinides and fission products is presented in Table 3-11 for the BOC (fresh fuel) and EOC (after 327 EFPDs). Results were obtained with WUTBURN tool. Most of the actinides available in ORIGEN were selected and are listed in Table 3-13. All available uranium, plutonium, neptunium, americium, curium and californium isotopes were 41

investigated as well as two sets of fission products. The first called FP49 is the list of 49 fission products applicable to source term analysis (see Table 3-13). The list is based on the EPR reactor source terms described in PSA Level 2 UK EPR PCSR Chapter 15.4 [29]. The second list, FP200, contains 200 arbitrary selected isotopes and is presented in Table 3-13. Those were selected during initial analysis based on 200 isotopes with the highest activity for FA01 burned to about 45 GWd/tHM.

Table 3-11 Summary of masses and activities of the core at BOC and EOC calculated with WUTBURN. Total mass includes an oxide Core State BOC EOC Parameter MASS ACTIVITY MASS ACTIVITY Unit KG Ci KG Ci ACTINIDES URANIUM 81771.346 1.27376E+02 80148.379 2.03379E+09 NEPTUNIUM 0.000 0.000 17.793 1.99612E+09 PLUTONIUM 0.000 0.000 458.752 1.22548E+07 AMERICIUM 0.000 0.000 1.418 2.82742E+06 CURIUM 0.000 0.000 0.257 4.23605E+05 CALIFORNIUM 0.000 0.000 8.103E-11 8.61230E-06 OTHER 0.000 0.000 1.626E-04 6.01750E-04 U+Pu/MA/TRU U+PU 81771.346 1.27376E+02 80607.131 2.04605E+09 MA 0.000 0.000 19.469 1.99938E+09 TRU 0.000 0.000 478.221 2.01163E+09 FISSION PRODUCTS FP49 0.000 0.000 131.433 4.46329E+09 FP200 0.000 0.000 67.476 1.51116E+10 TOTAL SUM ACTINIDES 81771.346 0.000 80626.600 4.04542E+09 SUM ACT+FP49 81771.346 0.000 80758.032 8.50871E+09 SUM ACT+FP200 81771.346 0.000 80694.076 1.91570E+10 TOTAL 93157.333 1.27378E+02 93157.333 1.99690E+10 Analyzing the results in Table 3-11, it is possible to conclude that at the end of the 1st cycle (EOC) actinides and FP200 consist of most of the core mass and almost 96% of core activity. Actinides and FP49 is only about 42.6% of the total core activity and what is remarkable has a higher mass than actinides plus FP200 (higher mass does not mean higher activity). The actinides activity is only 20.3% of the total core activity at the core shutdown.

In the left part of Table 3-11, the core mass balance obtained with WUTBURN after numerical tests of the code for the BOC is presented. About 19.4 kg deviation in heavy metal (uranium) mass was observed (sum of U235, U238 and U234) in comparison to the sum of input data (Figure 3-28). Fissile mass difference (U-235) is about 0.043 kg (43 grams); hence it is a minor difference (Figure 3-29). There are two potential sources of those differences, which are discussed below.

The first: heavy metal core masses are evaluated by WUTBRUN based on TRITON results. The data are generated and stored in PLT (Origen code, OPUS module) files where masses of all actinides are normalized to one ton of Heavy Metal (or MTU). It was observed that the mass balance at the BOC (fresh core) does not sum up to 1 ton (1000 kg), even if all available actinides were considered (see Table 3-13). There is a small deviation, and it is the main source of difference in the heavy metal balance. The mass balance based on PLT files for all nine assembly 42

types at the BOC (fresh fuel) calculated by TRITON sequence is presented in Table 3-12.

There is a small deviation - uranium mass is equal to about ~999.7 kg instead of 1000 kg.

Table 3-12 summarizes these differences for all assemblies and for the whole core, the deviation is equal to about -19.4016 kg. It is very close to WUTBRUN calculated difference of -19.4032 kg. The difference between both deviations is about 1.4 grams. Hence, the agreement can be assessed as very good.

Table 3-12 Mass balance in the TRITON PLT output files ACTINIDE MASS CORE MASS: 81.790749 ASSEMBLY TYPE KG/TONNE NO OF Fas KG/CORE FA01 999.7288 65 27538.63667 FA02 999.792 4 1694.792467 FA03 999.792 28 11863.54727 FA04 999.792 32 13558.33973 FA05 999.7681 32 13558.01562 FA06 999.7681 12 5084.255859 FA07 999.7681 4 1694.751953 FA08 999.7681 8 3389.503906 FA09 999.7681 8 3389.503906 TOTAL 193 81771.34739 DIFFERENCE -19.40161324 The second: another potential source of deviation has roots in the fissile mass balance. The code in its basic version uses detailed heavy metal masses (all uranium isotopes) described in the benchmark as a reference mass. It does not use detailed fissile-only (U-235) mass balance. Further in the process, the code calculates mass fractions of the normalized metal isotope masses stored in PLT files. Then it recalculates every single assembly using its heavy metal total mass. Therefore, calculated fractional masses are based on PLT files.

Furthermore, PLT files are the same for all assemblies of the same type. Analyzing Figure 3-29, it is possible to notice that there are mass deviations in fissile mass even for assemblies of the same type. It is also an issue for the total heavy metal mass. In consequence, a small deviation in fissile mass is produced (~grams). Moreover, a small influence on the total heavy metal may be anticipated because the same assembly with different uranium masses will, in general burn differently. The fissile mass difference is not an effect of the first issue described in the previous paragraph. It was attempted to normalize all assembly masses to one ton to correct PLT files based input data. In consequence, total fissile mass deviation increased ten times to about 400 grams. Hence, it was concluded that the difference was probably due to the application of the same PLT files for every assembly. The next sub-chapter presents WUTBURN code preliminary verification with one point ORIGEN calculations.

43

Table 3-13 List of nuclides considered: Actinides, FP49 and FP200 ACTINIDES FP49 FP200 1 'u230' 1 'kr85' 1 'i134' 65 'i131' 133 'y98m' 2 'u231' 2 'kr85m' 2 'xe133' 66 'pr145' 134 'cs143' 3 'u232' 3 'kr87' 3 'i135' 67 'nb102' 135 'pr149' 4 'u233' 4 'kr88' 4 'i133' 68 'mo105' 136 'ru106' 5 'u234' 5 'xe133' 5 'mo99' 69 'ba144' 137 'te136' 6 'u235' 6 'xe135' 6 'cs138' 70 'nb103' 138 'rh105m' 7 'u236' 7 'i131' 7 'xe137' 71 'zr101' 139 'pd109' 8 'u237' 8 'i132' 8 'nb100' 72 'rb91' 140 'ag109m' 9 'u238' 9 'i133' 9 'ba139' 73 'la145' 141 'br87' 10 'u239' 10 'i134' 10 'mo101' 74 'te135' 142 'xe135m' 11 'u240' 11 'i135' 11 'cs139' 75 'i137' 143 'xe141' 12 'u241' 12 'te127' 12 'te134' 76 'y91' 144 'sb129' 13 'np235' 13 'te127m' 13 'nb101' 77 'te131' 145 'te129' 14 'np236' 14 'te129' 14 'tc103' 78 'y96' 146 'sb130m' 15 'np237' 15 'te129m' 15 'tc101' 79 'tc106' 147 'rh109' 16 'np238' 16 'te131m' 16 'ba140' 80 'rb92' 148 'la147' 17 'np239' 17 'te132' 17 'nb98' 81 'y97' 149 'xe135' 18 'np240' 18 'sr89' 18 'tc102' 82 'te133m' 150 'sb130' 19 'np241' 19 'sr90' 19 'xe138' 83 'sr96' 151 'ru109' 20 'pu236' 20 'sr91' 20 'mo102' 84 'ce146' 152 'br86' 21 'pu237' 21 'sr92' 21 'mo103' 85 'pr146' 153 'br88' 22 'pu238' 22 'mo99' 22 'zr98' 86 'xe140' 154 'kr92' 23 'pu239' 23 'rh105' 23 'la140' 87 'ce144' 155 'nb104' 24 'pu240' 24 'ru103' 24 'zr99' 88 'sb131' 156 'tc100' 25 'pu241' 25 'ru105' 25 'nb99' 89 'pr144' 157 'pr150' 26 'pu242' 26 'ru106' 26 'nb97' 90 'i136' 158 'ce149' 27 'pu243' 27 'rb86' 27 'zr97' 91 'rb89' 159 'i134m' 28 'pu244' 28 'cs134' 28 'zr100' 92 'rb90' 160 'tc108' 29 'pu245' 29 'cs136' 29 'ba141' 93 'sr89' 161 'y100' 30 'pu246' 30 'cs137' 30 'ru103' 94 'cs142' 162 'sb132m' 31 'am239' 31 'ba139' 31 'la141' 95 'kr90' 163 'br85' 32 'am240' 32 'ba140' 32 'tc99m' 96 'kr89' 164 'kr85m' 33 'am241' 33 'la140' 33 'ce141' 97 'rb93' 165 'mo107' 34 'am242m' 34 'la141' 34 'y95' 98 'sb132' 166 'br89' 35 'am242' 35 'la142' 35 'la142' 99 'ru107' 167 'nb104m' 36 'am243' 36 'nb95' 36 'ce143' 100 'rh107' 168 'i139' 37 'am244' 37 'nd147' 37 'ba142' 101 'y98' 169 'nd151' 38 'am244m' 38 'pr143' 38 'i132' 102 'pr147' 170 'ba146' 39 'am245' 39 'y90' 39 'rh103m' 103 'nd147' 171 'sr98' 40 'am246' 40 'y91' 40 'pr143' 104 'y99' 172 'pm151' 41 'cm241' 41 'y92' 41 'la143' 105 'ce147' 173 'rb95' 42 'cm242' 42 'y93' 42 'tc104' 106 'y96m' 174 'nb105' 43 'cm243' 43 'zr95' 43 'cs140' 107 'sb133' 175 'la146m' 44 'cm244' 44 'zr97' 44 'zr95' 108 'zr102' 176 'sn132' 45 'cm245' 45 'ce141' 45 'y94' 109 'mo106' 177 'zr103' 46 'cm246' 46 'ce143' 46 'te132' 110 'y91m' 178 'se85' 47 'cm247' 47 'ce144' 47 'mo104' 111 'rb88' 179 'se86' 48 'cm248' 48 'sb127' 48 'y93' 112 'kr88' 180 'sn130' 49 'cm249' 49 'sb129' 49 'ba143' 113 'tc107' 181 'nb99m' 50 'cm250' 50 'sr93' 114 'pm149' 182 'br84' 51 'cm251' 51 'sr94' 115 'rh106' 183 'se84' 52 'cf249' 52 'la144' 116 'i138' 184 'sn129' 53 'cf250' 53 'nb95' 117 'rh104' 185 'eu156' 54 'cf251' 54 'tc105' 118 'kr91' 186 'rb90m' 55 'cf252' 55 'xe139' 119 'i136m' 187 'sn130m' 56 'cf253' 56 'ru105' 120 'pr148' 188 'nb100m' 57 'cf254' 57 'cs141' 121 'y97m' 189 'sb128' 58 'cf255' 58 'te133' 122 'ba145' 190 'te131m' 59 'ra226' 59 'sr95' 123 'rh108' 191 'pr151' 60 'ra228' 60 'y92' 124 'ru108' 192 'sn128' 61 'ac227' 61 'sr92' 125 'kr87' 193 'pm152' 62 'th229' 62 'rh105' 126 'ce148' 194 'nd152' 63 'th230' 63 'ce145' 127 'sr97' 195 'rh110' 64 'th232' 64 'sr91' 128 'la146' 196 'ru110' 129 'nb102m' 197 'sn131' 130 'rb94' 198 'pm148' 131 'nd149' 199 'ce150' 132 'sm153' 200 'cs144' 44

3.4.3 Comparison of WUTBURN-PARCS-TRITON and ORIGEN-ARP The WUTBURN-PARCS-TRITON methodology to calculate the core inventory was compared with the results of simple single assembly point-wise calculations using the ORIGEN-ARP module of the SCALE package. The Westinghouse 17x17 fuel assembly default ORIGEN-ARP data was applied with fuel enrichment equal to the BEAVRS average enrichment. All masses were recalculated to the total core mass.

Actinides inventories are compared in Table 3-14. The FP49 fission products are compared in Table 3-15. In the case of analyzed actinides, a low deviation was observed for actinides characterized by high mass. For U-235 the difference is about +4.5%, in the case of U-238 the mass difference is only 0.021%. For the most abundant plutonium isotopes, the difference is less than 6%. Higher differences were observed for other isotopes which are produced in much smaller concentrations. The highest difference was observed for Ra-228, and it was almost 100-fold - but the mass is less than 1E-14 kg. At those mass concentrations, numerical errors are expected to be substantial. In the case of FP49, a very good agreement was observed with an average difference of less than 3% in comparison to ORIGEN-ARP. The highest difference of -56% was observed for Te127m.

The results obtained in the framework of this simple average model and detailed 3D model are remarkable and allows us to conclude that the WUTBURN code provides physically reasonable results. However, it is only a preliminary test, and the code demands further testing. It is recommended to perform ORIGEN calculations for separate assembly types. It is also recommended to create ORIGEN cross-section libraries specially designed for BEAVRS assemblies to perform more detailed code testing. It will be a topic of further research.

45

Table 3-14 Comparison of actinides inventory calculated with WUTBURN-PARCS and ORIGEN BEAVRS EOC (327.2 EFPDs)

MASS ACTINIDES PARCS ORIGEN RATIO Number Nuclide KG KG PARCS/ORIGEN 1 'u230' 4.4052854E-13 1.3421862E-14 32.82172 2 'u231' 1.3012209E-12 8.9151916E-13 1.45955 3 'u232' 2.2089210E-06 1.9433482E-06 1.13666 4 'u233' 9.9550677E-05 6.6880295E-05 1.48849 5 'u234' 1.2347887E+01 1.2096852E+01 1.02075 6 'u235' 1.0388829E+03 9.9457551E+02 1.04455 7 'u236' 1.5255466E+02 1.6325434E+02 0.93446 8 'u237' 4.7721504E-01 5.2853182E-01 0.90291 9 'u238' 7.8944056E+04 7.8960789E+04 0.99979 10 'u239' 5.9455377E-02 5.7572508E-02 1.03270 11 'u240' 8.7387631E-16 1.8934558E-15 0.46152 12 'u241' 3.8787142E-19 0.0000000E+00 N/A 13 'np235' 4.3571819E-08 1.1630645E-07 0.37463 14 'np236' 3.4982844E-06 2.3457587E-06 1.49132 15 'np237' 9.1976006E+00 9.6594875E+00 0.95218 16 'np238' 3.3756301E-02 3.7083926E-02 0.91027 17 'np239' 8.5619155E+00 8.3099401E+00 1.03032 18 'np240' 1.2273932E-04 3.0565203E-04 0.40157 19 'np241' 7.8756663E-12 0.0000000E+00 N/A 20 'pu236' 1.6429491E-05 5.5552277E-06 2.95748 21 'pu237' 2.9937137E-06 2.6639247E-06 1.12380 22 'pu238' 1.4206956E+00 1.4436067E+00 0.98413 23 'pu239' 3.1679814E+02 3.3108895E+02 0.95684 24 'pu240' 9.1010254E+01 8.6452822E+01 1.05272 25 'pu241' 4.0887041E+01 4.6702518E+01 0.87548 26 'pu242' 8.6326368E+00 7.6703364E+00 1.12546 27 'pu243' 3.0531338E-03 2.6966410E-03 1.13220 28 'pu244' 4.4843606E-05 9.5858758E-05 0.46781 29 'pu245' 2.8754061E-09 6.3592307E-09 0.45216 30 'pu246' 1.2836952E-21 5.6918182E-11 2.26E-11 31 'am239' 2.2441620E-11 4.1615133E-11 0.53927 32 'am240' 2.0740215E-08 1.8255695E-08 1.13610 33 'am241' 5.1353807E-01 5.0759339E-01 1.01171 34 'am242m' 5.2251162E-03 1.6570806E-03 3.15321 35 'am242' 1.8972656E-03 8.2935819E-03 0.22876 36 'am243' 8.9770495E-01 6.4663766E-01 1.38827 37 'am244' 6.3616942E-05 6.8172589E-04 0.09332 38 'am244m' 4.0848710E-05 0.0000000E+00 N/A 39 'am245' 5.6136807E-10 1.2415836E-09 0.45214 40 'am246' 3.7118583E-17 1.4223411E-13 0.00026 41 'cm241' 6.9289503E-09 3.8196280E-09 1.81404 42 'cm242' 1.2477869E-01 9.0215196E-02 1.38312 43 'cm243' 1.3205646E-03 9.2996082E-04 1.42002 44 'cm244' 1.2716745E-01 6.8491573E-02 1.85669 45 'cm245' 3.7837909E-03 1.1319840E-03 3.34262 46 'cm246' 2.0766391E-04 4.0069288E-05 5.18262 47 'cm247' 9.6405459E-07 1.4166158E-07 6.80534 48 'cm248' 2.6850844E-08 3.1129559E-09 8.62551 49 'cm249' 4.1360327E-13 3.8785173E-14 10.66395 50 'cm250' 2.9143636E-15 3.4409368E-16 8.46968 51 'cm251' 8.7522642E-20 1.4427888E-21 60.66213 52 'cf249' 9.3389807E-12 7.6016322E-13 12.28549 53 'cf250' 5.2529782E-11 2.1093834E-12 24.90291 54 'cf251' 1.4303822E-11 7.1599622E-13 19.97751 55 'cf252' 4.8453891E-12 1.6153673E-13 29.99559 56 'cf253' 7.1916018E-15 1.8484709E-16 38.90568 57 'cf254' 1.3467597E-17 4.7062397E-18 2.86165 58 'cf255' 2.0468442E-23 7.8903536E-24 2.59411 59 'ra226' 1.3054279E-10 1.2849327E-10 1.01595 60 'ra228' 3.2864460E-15 3.5448111E-17 92.71146 61 'ac227' 2.9698429E-11 2.0913895E-11 1.42003 62 'th229' 1.5162723E-09 1.4386993E-09 1.05392 63 'th230' 2.9053748E-05 3.0221682E-05 0.96135 64 'th232' 1.3356362E-04 2.3809287E-06 56.09728 46

Table 3-15 Comparison of fission products (FP49) inventory calculated with WUTBURN-PARCS and ORIGEN BEAVRS EOC (327.2 EFPDs)

MASS FP49 PARCS ORIGEN RATIO Number Nuclide KG KG PARCS/ORIGEN 1 'kr85' 9.6673061E-01 9.7658154E-01 0.98991 2 'kr85m' 3.1082497E-03 3.0687889E-03 1.01286 3 'kr87' 1.7923912E-03 1.7683160E-03 1.01361 4 'kr88' 5.3462898E-03 5.3679269E-03 0.99597 5 'xe133' 1.0153191E+00 9.7576364E-01 1.04054 6 'xe135' 1.3553764E-02 1.4084367E-02 0.96233 7 'i131' 7.4154428E-01 7.4036986E-01 1.00159 8 'i132' 1.3044805E-02 1.2939296E-02 1.00815 9 'i133' 1.6738750E-01 1.6816178E-01 0.99540 10 'i134' 7.9873905E-03 8.0277620E-03 0.99497 11 'i135' 5.1073743E-02 5.1168293E-02 0.99815 12 'te127' 2.9090578E-03 2.9567356E-03 0.98387 13 'te127m' 5.1652698E-02 1.1892375E-01 0.43433 14 'te129' 1.1514733E-03 1.1360735E-03 1.01356 15 'te129m' 1.3329411E-01 1.4869558E-01 0.89642 16 'te131m' 2.4047774E-02 2.2361591E-02 1.07541 17 'te132' 4.2453858E-01 4.3283664E-01 0.98083 18 'sr89' 3.2099013E+00 3.3051642E+00 0.97118 19 'sr90' 1.9695861E+01 2.0333180E+01 0.96866 20 'sr91' 3.2715901E-02 3.2454569E-02 1.00805 21 'sr92' 9.9785517E-03 9.9539342E-03 1.00247 22 'mo99' 3.5933279E-01 3.5987930E-01 0.99848 23 'rh105' 9.2842643E-02 9.7412782E-02 0.95308 24 'ru103' 4.0931322E+00 4.1844147E+00 0.97819 25 'ru105' 1.3605784E-02 1.3708130E-02 0.99253 26 'ru106' 6.7818028E+00 6.7313786E+00 1.00749 27 'rb86' 7.7806285E-04 7.6907841E-04 1.01168 28 'cs134' 2.3275780E+00 2.1200162E+00 1.09791 29 'cs136' 2.2139311E-02 2.7563482E-02 0.80321 30 'cs137' 4.1244224E+01 4.2359429E+01 0.97367 31 'ba139' 1.0377830E-02 1.0591902E-02 0.97979 32 'ba140' 2.2312488E+00 2.2451561E+00 0.99381 33 'la140' 2.9782403E-01 3.0957798E-01 0.96203 34 'la141' 2.7236682E-02 2.7228140E-02 1.00031 35 'la142' 1.0253835E-02 1.0264739E-02 0.99894 36 'nb95' 3.6977357E+00 3.9627618E+00 0.93312 37 'nd147' 7.3641734E-01 7.5239310E-01 0.97877 38 'pr143' 2.1554245E+00 2.0987506E+00 1.02700 39 'y90' 5.1833710E-03 5.5257830E-03 0.93803 40 'y91' 4.8158165E+00 5.0268594E+00 0.95802 41 'y92' 1.3191980E-02 1.3160132E-02 1.00242 42 'y93' 4.2882394E-02 4.2490294E-02 1.00923 43 'zr95' 7.0927939E+00 7.3783435E+00 0.96130 44 'zr97' 8.2019923E-02 8.3262982E-02 0.98507 45 'ce141' 5.3459145E+00 5.4546251E+00 0.98007 46 'ce143' 2.1854922E-01 2.1870846E-01 0.99927 47 'ce144' 2.3105185E+01 2.4226420E+01 0.95372 48 'sb127' 3.1546621E-02 3.0606098E-02 1.03073 49 'sb129' 4.6043033E-03 4.6187236E-03 0.99688 47

4 CONCLUSIONS The BEAVRS Westinghouse 4-loop PWR reactor model was developed and tested.

Detailed lattice physics calculations with fuel burnup and branches were performed using SCALE 6.1.2 and TRITON sequence. Group constants libraries were prepared for the core nodal simulator PARCS 3.2. Hot Zero Power core physics and Hot Full Power operation simulations for the 1st fuel cycle were performed using the PARCS core simulator.

The Hot Zero Power results are characterized by some deviation in comparison to the BEAVRS Benchmark measurement data. Critical boron concentrations and eigenvalues for 44 and 238 groups are considered as satisfactory in the scope of this work. The 238 neutron groups results are considered as substantially better than 44 groups. Calculated control rod worth values are satisfactory. Detector measurements were compared with neutron thermal fluxes, and the results were consistent.

The Hot Full Power fuel cycle results for 238 groups are in very good agreement with the available BEAVRS data. Otherwise, about 50-60 ppm of boron deviation at the BOC was observed for 44 groups calculations and was decreasing with the fuel cycle progression. Nevertheless, 238 groups results are considered as more appropriate.

One can conclude that the presented models may be improved. Especially, reflector modelling demands special attention in future research. It is recommended to add spacer grid modelling and test multiregional burnup for Burnable Poisons. Fuel was burned assembly-wise, and detailed pin-wise calculations are considered in the future. Moreover, updating the model to be consistent with the BEAVRS Rev 2.0.2 specification may be a reasonable choice.

The new branch for HFP operation should be developed. Moreover, branches for HZP and HFP should be merged. Authors believe that the applied branches are not perfect, and more reasonable branches could have been developed.

In the calculations, the older SCALE 6.1.2 was applied, and it is recommended to use the newer SCALE 6.2 with TRITON or the new POLARIS transport solver. It is also customary to use newer PARCS versions.

A special computer code WUTBURN was developed to calculate detailed 3D core inventory using PARCS. The code predicts initial core mass with high accuracy. WUTBURN was initially verified, and the results were compared with ORIGEN for a single Westinghouse 17x17 assembly which is available in the ORIGEN-ARP package. The results obtained agreed for the most important actinides and were in good agreement for 49 (FP49) selected fission products. The presented methodology, after detailed research, might be applied as a support calculation approach during the core inventory calculation studies. However, the code demands further testing; it is recommended to perform ORIGEN-S calculations for separate assemblies. It is also recommended to create ORIGEN-S cross-sections libraries specially designed for the BEAVRS core to perform more detailed code testing.

49

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NUREG/IA-0529 Simulations of the BEAVRS PWR with SCALE and PARCS December 2022 Piotr Darnowski Technical Michał Pawluczyk Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Institute of Heat Engineering, Nowowiejska 21/25,00-665 Warsaw, Poland Division of Systems Analysis Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 K. Tien The first fuel cycle of the BEAVRS PWR benchmark was simulated and analyzed. Models were prepared using the SCALE package, TRITON depletion sequence and NEWT as a lattice physics solver. A set of branch and burnup calculations were prepared, and group constants in the form of PMAXS libraries were generated using GenPMAXS for PARCS nodal diffusion core simulator. The hot zero power reactor physics measurement data and hot full power data were used to perform model validation simulations for the 1st fuel cycle. The core inventories for the BOC and EOC were calculated on the basis of PARCS and TRITON results with a dedicated computer code and compared with ORIGEN-ARP point burnup calculations.

BEAVRS benchmark, core inventory calculations, burnup calculations, PARCS, SCALE, TRITON, computer code WUTBURN

NUREG/IA-0529 Simulations of the BEAVRS PWR with SCALE and PARCS December 2022