Bayesian calibration of irradiated graphite property models under high temperatures
Source abstract
Abstract
Abstract Graphite under high temperatures and irradiation is central to advanced reactors. We develop a Bayesian calibration framework for graphite property models that explicitly represents model-data mismatch via a Gaussian-process discrepancy. The approach propagates uncertainty from parameters, experimental noise, and model form, with a hierarchical variance structure to capture group and cross-group noise. Using two predictive models across five grades (IG-110, NBG-18, PCEA, NBG-17, 2114) and four properties-irradiation-induced dimension change, creep, Young’s modulus change ratio, and coefficient of thermal expansion change ratio-we obtain average predictive-error reductions of 54%, 65%, 17%, and 17% when discrepancy is included. We illustrate engineering impact with a multiphysics model of a very-high-temperature reactor prismatic reflector brick, analyzing stresses under high fluence and temperature. Accounting for model discrepancy markedly improves predictive accuracy and provides a robust basis for reliable graphite component design in advanced reactors.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Graphite, nuclear technology, radiation studies · Nuclear reactor physics and engineering · Radiative Heat Transfer Studies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (44)
Show source-provided references
1. Scarlat, R. O. et al. Design and licensing strategies for the fluoride-salt-cooled, high-temperature reactor (FHR) technology. Prog. Nucl. Energy 77, 406–420 (2014).10.1016/j.pnucene.2014.07.002 ↗
2. Arregui-Mena, J. D. et al. A review of finite element method models for nuclear graphite applications. Arch. Comput. Methods Eng. 27, 331–350 (2020).10.1007/s11831-018-09310-y ↗
3. Price, D., Roskoff, N., Radaideh, M. I. & Kochunas, B. Thermal modeling of an eVinciTM-like heat pipe microreactor using OpenFOAM. Nucl. Eng. Des. 415, 112709 (2023).10.1016/j.nucengdes.2023.112709 ↗
4. Prithivirajan, V. Examining graphite degradation in molten salt environments: A chemical, physical, and material analysis. Tech. Rep. TLR-RES/DE/REB-2024-14, Idaho National Laboratory https://www.nrc.gov/docs/ML2423/ML24236A722.pdf (2024).10.2172/2474875 ↗
5. Lan, T., Peng, X., FengSheng & Tan, W. Seismic modeling and simulation of the graphite core in gas-cooled micro-reactor. Nucl. Eng. Des. 431, 113714 (2025).10.1016/j.nucengdes.2024.113714 ↗
6. Srinivasan, M. Design and manufacture of graphite components for 21st century small modular reactors. Nucl. Eng. Des. 386, 111568 (2022).10.1016/j.nucengdes.2021.111568 ↗
7. Metcalfe, M. Damage tolerance in the graphite cores of UK power reactors and implications for new build. Nucl. Eng. Des. 406, 112237 (2023).10.1016/j.nucengdes.2023.112237 ↗
8. Windes, W. E., Rohrbaugh, D. T., Swank, W. D. & Cottle, D. L. AGC-3 specimen post-irradiation examination data package report. Tech. Rep. INL/EXT-17-43823, Idaho National Laboratory (2017).10.2172/1468625 ↗
9. Campbell, A. A., Katoh, Y., Snead, M. A. & Takizawa, K. Property changes of G347A graphite due to neutron irradiation. Carbon 109, 860–873 (2016).10.1016/j.carbon.2016.08.042 ↗
10. Heijna, M., de Groot, S. & Vreeling, J. A. Comparison of irradiation behaviour of HTR graphite grades. J. Nucl. Mater. 492, 148–156 (2017).10.1016/j.jnucmat.2017.05.012 ↗
11. Srinivasan, M., Marsden, B., von Lensa, W., Cronise, L. & Turk, R. Appendices to the assessment of graphite properties and degradation, including source dependence. Tech. Rep. TLR/RES/DE/REB-2021-08, U.S. Nuclear Regulatory Commission (2021).
12. Bajpai, P., Prithivirajan, V., Munday, L. B., Singh, G. & Spencer, B. W. Development of graphite thermal and mechanical modeling capabilities in Grizzly. Tech. Rep. INL/RPT-24-78905, Idaho National Laboratory, Idaho Falls, ID (2024).10.2172/2403365 ↗
13. Davies, M. A. & Bradford, M. A revised description of graphite irradiation induced creep. J. Nucl. Mater. 381, 39–45 (2008).10.1016/j.jnucmat.2008.07.019 ↗
14. Saitta, M., Johannes van Zanten, F. & Baylis, S. Physics informed graphite material model. In Pressure Vessels and Piping Conference, V001T01A041 (American Society of Mechanical Engineers, 2024).10.1115/PVP2024-123396 ↗
15. Dhulipala, S. L. N., Simon, P. C. A., Demkowicz, P. A., Hirschhorn, J. A. & Novascone, S. R. Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches. J. Nucl. Mater. 610, 155795 (2025).10.1016/j.jnucmat.2025.155795 ↗
16. Kennedy, M. C. & O’Hagan, A. Bayesian calibration of computer models. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 63, 425–464 (2001).10.1111/1467-9868.00294 ↗
17. Dhulipala, S. L. N., Bajpai, P., Singh, G. & Spencer, B. W. Bayesian calibration of nuclear graphite property models accounting for model inadequacy and impacts on component performance. Tech. Rep. INL/RPT-25-86883, Idaho National Laboratory, Idaho Falls, ID United States (2025).
18. Bradford, M. R. & Steer, A. G. A structurally-based model of irradiated graphite properties. J. Nucl. Mater. 381, 137–144 (2008).10.1016/j.jnucmat.2008.07.040 ↗
19. Hoffman, M. D. & Gelman, A. The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15, 1593–1623 (2014).
20. Béghein, P., Berlioux, G., du Mesnildot, B., Hiltmann, F. & Melin, M. NBG-17–An improved graphite grade for HTRs and VHTRs. Nucl. Eng. Des. 251, 146–149 (2012).10.1016/j.nucengdes.2011.10.060 ↗
21. Arendt, P. D., Apley, D. W. & Che, W. Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability. ASME J. Mech. Des. 134, 100908 (2012).10.1115/1.4007390 ↗
22. MacCallum, R. C. & O’Hagan, A. Advances in modeling model discrepancy: Comment on Wu and Browne. Psychometrika 80, 601–607 (2015).10.1007/s11336-015-9452-2 ↗
23. Maupin, K. A. & Swiler, L. P. Model discrepancy calibration across experimental settings. Reliab. Eng. Syst. Saf. 200, 106818 (2020).10.1016/j.ress.2020.106818 ↗
24. White, A. & Mahadevan, S. Discrepancy modeling for model calibration with multivariate output. Int. J. Uncertain. Quantification 13, 1–23 (2023).10.1615/Int.J.UncertaintyQuantification.2023044543 ↗
25. Spencer, B. W. et al. Grizzly and BlackBear: Structural component aging simulation codes. Nucl. Technol. 207, 981–1003 (2021).10.1080/00295450.2020.1868278 ↗
26. Giudicelli, G. et al. 3.0-MOOSE: Enabling massively parallel multiphysics simulations. SoftwareX 26, 101690 (2024).10.1016/j.softx.2024.101690 ↗
27. American Society of Mecahnical Engineers. Section III. Rules for Construction of Nuclear Facility Components. Division 5. High Temperature Reactors. Tech. Rep. ASME BPVC.III.5-2023, ASME Boiler and Pressure Vessel Code (2023).
28. Campbell, A. A. & Katoh, Y. Summary report on effects of irradiation on material IG-110 – prepared for Toyo Tanso Co., Ltd. Tech. Rep. ORNL/TM-2017/705, Oak Ridge National Laboratory (ORNL), Oak Ridge, TN, United States (2017).10.2172/1483188 ↗
29. Vreeling, J., Wouters, O. & Van der Laan, J. Graphite irradiation testing for htr technology at the high flux reactor in petten. J. Nucl. Mater. 381, 68–75 (2008).10.1016/j.jnucmat.2008.07.041 ↗
30. Campbell, A. A. & Burchell, T. D. Radiation effects in graphite. In Konings, R. J. & Stoller, R. E. (eds.) Comprehensive Nuclear Materials, 398–436 (Elsevier, Oxford, 2020), second edition edn.10.1016/B978-0-12-803581-8.12055-7 ↗
31. Haag, G. Properties of ATR-2E graphite and property changes due to fast neutron irradiation. Tech. Rep. 4183, Institut für Sicherheitsforschung und Reaktortechnik, Jülich, Germany https://juser.fz-juelich.de/record/49235/files/Juel_4183_Haag.pdf (2005).
32. Shibata, T. et al. Draft of standard for graphite core components in high-temperature gas-cooled reactor. Technical Report JAEA-Research 2009-042, Japan Atomic Energy Agency (2010).
33. Windes, W., Swank, W. D., Rohrbaugh, D. & Lord, J. AGC-2 graphite preirradiation data analysis report. Tech. Rep. INL/EXT-13-28612, Idaho National Laboratory, Idaho Falls, ID, United States (2013).10.2172/1088408 ↗
34. Kelly, B. T. & Foreman, A. J. E. The theory of irradiation creep in reactor graphite – The dislocation pinning-unpinning model. Carbon 12, 151–158 (1974).10.1016/0008-6223(74)90021-9 ↗
35. Martin, D. & Henson, R. The scattering of long wavelength neutrons by defects in neutron-irradiated graphite. Philos. Mag. 9, 659–672 (1964).10.1080/14786436408211878 ↗
36. Kelly, B. T., Martin, W. H. & Nettley, P. Dimensional changes in pyrolytic graphite under fast-neutron irradiation. Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 260, 37–49 (1966).
37. Rasmussen, C. E. Gaussian Processes in Machine Learning (Springer Berlin Heidelberg, 2004).10.7551/mitpress/3206.001.0001 ↗
38. Neal, R. M. Handbook of Markov chain Monte Carlo, chap. MCMC using Hamiltonian dynamics (Chapman and Hall/CRC, 2011).10.1201/b10905-6 ↗
39. Bingham, E. et al. Pyro: Deep Universal Probabilistic Programming. J. Mach. Learn. Res. 20, 1–6 (2019).
40. General Atomics. Gas turbine-modular helium reactor (GT-MHR) conceptual design description report. GA Proj. 7658, 910720 (1996).
41. MacDonald, P. E. et al. NGNP point design-results of the initial neutronics and thermal-hydraulic assessments during FY-03, Rev. 1. Tech. Rep., Idaho National Laboratory, Idaho Falls, ID (United States) (2003).
42. Sterbentz, J. W. Calculated neutron and gamma-ray spectra across the prismatic very high temperature reactor core. In Reactor Dosimetry State of the Art 2008, 596–606 (World Scientific, 2009).10.1142/9789814271110_0074 ↗
43. Maruyama, T., Kaito, T., Onose, S. & Shibahara, I. Change in physical properties of high density isotropic graphites irradiated in the ‘JOYO’ fast reactor. J. Nucl. Mater. 225, 267–272 (1995).10.1016/0022-3115(95)00051-8 ↗
44. Bratton, R. Modeling mechanical behavior of a prismatic replaceable reflector block. Tech. Rep. INL/EXT-09-15868, Idaho National Laboratory, Idaho Falls, ID (2009).