General Pebble Bed Reactor with Stochastic Analyses

Contact: Zachary M. Prince, [email protected]

Purpose and Background

This 200MWth General Pebble Bed Reactor (GPBR200) model is the latest iteration of a series of pebble-bed high-temperature gas reactor (HTGR) models developed at Idaho National Laboratory (INL) using MOOSE-based applications. These models are primarily meant as a testing ground for multiphysics, optimization, and stochastic methods for PBRs, some also serving as verification benchmarks. An in-depth description of the latest iteration can be found in Prince et al. (2024). It is recommended to read this paper before continuing in the exposition here.

The purpose of this exposition is to show how to perform multiphysics simulations of PBRs and stochastic analyses of reactors, in general, with MOOSE-based applications. This is done by presenting and explaining the inputs that perform:

Equilibrium-core neutronics and depletion using Griffin Wang et al. (2025)
Thermal-hydraulics simulation using weakly-compressible finite-volume fluids and finite-volume heat conduction with Pronghorn Novak et al. (2021)
Pebble and particle thermomechanics with Bison Williamson et al. (2021)
Multi-scale physics coupling using MOOSE MultiApps Giudicelli et al. (2024)
Surrogate modeling and sensitivity analysis using the MOOSE stochastic tools module Slaughter et al. (2023)

Brief Geometry and Property Description

The GPBR200 model is 2D axisymmetric geometry shown in Figure 1. The mesh shown was generated using a custom MOOSE MeshGenerator, not currently available publicly. The relevant properties of the model are shown in Table 1. Note that these are "nominal" property values, where some of them will be varied as part of the stochastic analyses.

Figure 1: Geometric diagram of GPBR200 model.

Table 1: Nominal properties of GPBR200 model.

Property	Value	Unit
Power	200	MW
Core radius	1.2	m
Core height	8.93	m
Pebble diameter	6	cm
TRISO filling factor	9.34	%
Fuel kernel composition	UCO	–
Fuel kernel diameter	0.425	mm
Fuel enrichment	15.5	%wt
Discharge rate	1.5	pebbles/min
Discharge limit	147.6	MWd/kg
He mass flow rate	64.3	kg/s
He inlet temperature	260	°C
He outlet pressure	5.8	MPa
RCCS temperature	70	°C

Outline

The remainder of this model description dives deeply into the inputs and a presentation of results, which are mostly showcased in Prince et al. (2024).

References

Guillaume Giudicelli, Alexander Lindsay, Logan Harbour, Casey Icenhour, Mengnan Li, Joshua E. Hansel, Peter German, Patrick Behne, Oana Marin, Roy H. Stogner, Jason M. Miller, Daniel Schwen, Yaqi Wang, Lynn Munday, Sebastian Schunert, Benjamin W. Spencer, Dewen Yushu, Antonio Recuero, Zachary M. Prince, Max Nezdyur, Tianchen Hu, Yinbin Miao, Yeon Sang Jung, Christopher Matthews, April Novak, Brandon Langley, Timothy Truster, Nuno Nobre, Brian Alger, David Andrš, Fande Kong, Robert Carlsen, Andrew E. Slaughter, John W. Peterson, Derek Gaston, and Cody Permann. 3.0 - MOOSE: enabling massively parallel multiphysics simulations. SoftwareX, 26:101690, 2024. URL: https://www.sciencedirect.com/science/article/pii/S235271102400061X, doi:https://doi.org/10.1016/j.softx.2024.101690.

@article{giudicelli2024moose,
    author = "Giudicelli, Guillaume and Lindsay, Alexander and Harbour, Logan and Icenhour, Casey and Li, Mengnan and Hansel, Joshua E. and German, Peter and Behne, Patrick and Marin, Oana and Stogner, Roy H. and Miller, Jason M. and Schwen, Daniel and Wang, Yaqi and Munday, Lynn and Schunert, Sebastian and Spencer, Benjamin W. and Yushu, Dewen and Recuero, Antonio and Prince, Zachary M. and Nezdyur, Max and Hu, Tianchen and Miao, Yinbin and Jung, Yeon Sang and Matthews, Christopher and Novak, April and Langley, Brandon and Truster, Timothy and Nobre, Nuno and Alger, Brian and Andr{\v{s}}, David and Kong, Fande and Carlsen, Robert and Slaughter, Andrew E. and Peterson, John W. and Gaston, Derek and Permann, Cody",
    title = "3.0 - {MOOSE}: Enabling massively parallel multiphysics simulations",
    year = "2024",
    journal = "{SoftwareX}",
    volume = "26",
    pages = "101690",
    issn = "2352-7110",
    doi = "https://doi.org/10.1016/j.softx.2024.101690",
    url = "https://www.sciencedirect.com/science/article/pii/S235271102400061X",
    keywords = "Framework, Finite-element, Finite-volume, Parallel, Multiphysics, Multiscale"
}

A.J. Novak, R.W. Carlsen, S. Schunert, P. Balestra, D. Reger, R.N. Slaybaugh, and R.C. Martineau. Pronghorn: a multidimensional coarse-mesh application for advanced reactor thermal hydraulics. Nuclear Technology, 207:1015–1046, 2021. URL: https://www.tandfonline.com/doi/full/10.1080/00295450.2020.1825307, doi:https://doi.org/10.1080/00295450.2020.1825307.

@article{novak2021Pronghorn,
    author = "Novak, A.J. and Carlsen, R.W. and Schunert, S. and Balestra, P. and Reger, D. and Slaybaugh, R.N. and Martineau, R.C.",
    title = "{Pronghorn}: A Multidimensional Coarse-Mesh Application for Advanced Reactor Thermal Hydraulics",
    year = "2021",
    volume = "207",
    issue = "7",
    pages = "1015--1046",
    journal = "{Nuclear Technology}",
    doi = "https://doi.org/10.1080/00295450.2020.1825307",
    url = "https://www.tandfonline.com/doi/full/10.1080/00295450.2020.1825307",
    keywords = "Pronghorn, pebble bed reactor, MOOSE"
}

Zachary M. Prince, Paolo Balestra, Javier Ortensi, Sebastian Schunert, Olin Calvin, Joshua T. Hanophy, Kun Mo, and Gerhard Strydom. Sensitivity analysis, surrogate modeling, and optimization of pebble-bed reactors considering normal and accident conditions. Nuclear Engineering and Design, 428:113466, 2024. doi:https://doi.org/10.1016/j.nucengdes.2024.113466.

@article{prince2024Sensitivity,
    author = "Prince, Zachary M. and Balestra, Paolo and Ortensi, Javier and Schunert, Sebastian and Calvin, Olin and Hanophy, Joshua T. and Mo, Kun and Strydom, Gerhard",
    title = "Sensitivity analysis, surrogate modeling, and optimization of pebble-bed reactors considering normal and accident conditions",
    journal = "Nuclear Engineering and Design",
    volume = "428",
    pages = "113466",
    year = "2024",
    issn = "0029-5493",
    doi = "https://doi.org/10.1016/j.nucengdes.2024.113466"
}

Andrew E Slaughter, Zachary M Prince, Peter German, Ian Halvic, Wen Jiang, Benjamin W Spencer, Somayajulu L N Dhulipala, and Derek R Gaston. MOOSE Stochastic Tools: A module for performing parallel, memory-efficient in situ stochastic simulations. SoftwareX, 22:101345, 2023. doi:10.1016/j.softx.2023.101345.

@article{Slaughter2023,
    author = "Slaughter, Andrew E and Prince, Zachary M and German, Peter and Halvic, Ian and Jiang, Wen and Spencer, Benjamin W and Dhulipala, Somayajulu L N and Gaston, Derek R",
    doi = "10.1016/j.softx.2023.101345",
    issn = "2352-7110",
    journal = "SoftwareX",
    keywords = "MOOSE,Multiphysics,Parallel,Stochastic",
    pages = "101345",
    title = "{MOOSE Stochastic Tools: A module for performing parallel, memory-efficient in situ stochastic simulations}",
    volume = "22",
    year = "2023"
}

Yaqi Wang, Zachary M. Prince, Hansol Park, Olin W. Calvin, Namjae Choi, Yeon Sang Jung, Sebastian Schunert, Shikhar Kumar, Joshua T. Hanophy, Vincent M. Labouré, Changho Lee, Javier Ortensi, Logan H. Harbour, and Jackson R. Harter. Griffin: a moose-based reactor physics application for multiphysics simulation of advanced nuclear reactors. Annals of Nuclear Energy, 211:110917, 2025. URL: https://www.sciencedirect.com/science/article/pii/S0306454924005802, doi:https://doi.org/10.1016/j.anucene.2024.110917.

@article{wang2025Griffin,
    author = "Wang, Yaqi and Prince, Zachary M. and Park, Hansol and Calvin, Olin W. and Choi, Namjae and Jung, Yeon Sang and Schunert, Sebastian and Kumar, Shikhar and Hanophy, Joshua T. and Labouré, Vincent M. and Lee, Changho and Ortensi, Javier and Harbour, Logan H. and Harter, Jackson R.",
    title = "Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors",
    journal = "Annals of Nuclear Energy",
    volume = "211",
    pages = "110917",
    year = "2025",
    issn = "0306-4549",
    doi = "https://doi.org/10.1016/j.anucene.2024.110917",
    url = "https://www.sciencedirect.com/science/article/pii/S0306454924005802",
    keywords = "Griffin, MOOSE, Radiation transport, Multiphysics, Reactor analysis"
}

Richard L. Williamson, Jason D. Hales, Stephen R. Novascone, Giovanni Pastore, Kyle A. Gamble, Benjamin W. Spencer, Wen Jiang, Stephanie A. Pitts, Albert Casagranda, Daniel Schwen, Adam X. Zabriskie, Aysenur Toptan, Russell Gardner, Christoper Matthews, Wenfeng Liu, and Hailong Chen. Bison: a flexible code for advanced simulation of the performance of multiple nuclear fuel forms. Nuclear Technology, 207(7):1–27, 2021. URL: https://doi.org/10.1080/00295450.2020.1836940, doi:10.1080/00295450.2020.1836940.

@article{BISON,
    author = "Williamson, Richard L. and Hales, Jason D. and Novascone, Stephen R. and Pastore, Giovanni and Gamble, Kyle A. and Spencer, Benjamin W. and Jiang, Wen and Pitts, Stephanie A. and Casagranda, Albert and Schwen, Daniel and Zabriskie, Adam X. and Toptan, Aysenur and Gardner, Russell and Matthews, Christoper and Liu, Wenfeng and Chen, Hailong",
    title = "BISON: A Flexible Code for Advanced Simulation of the Performance of Multiple Nuclear Fuel Forms",
    journal = "Nuclear Technology",
    volume = "207",
    number = "7",
    pages = "1-27",
    year = "2021",
    publisher = "Taylor \& Francis",
    doi = "10.1080/00295450.2020.1836940",
    URL = "https://doi.org/10.1080/00295450.2020.1836940"
}

Purpose and Background
Brief Geometry and Property Description
Outline
References