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AGR-3/4 Modeling and Transport Parameters

Outline AGR-3/4 experiment and objectives Description of AGR-3/4 modeling approach and inputs Source term (release from particles) Temperature profiles Diffusion through concentric rings Adsorption across gaps between rings Simplified Source Model and updated model results Reconstruction of fission product distributions from gamma tomography data

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE Advanced Gas Reactor Fuel Development and Qualification Program

Breakdown of the DOE Advanced Gas Reactor Fuel Development and Qualification Program. Including discussion topics on TRISO technology Status Circa 2000, New Production Reactor (NPR) Fuel Experience, Fuel Qualification, US DOE Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, Initial AGR Program Reference HTGR Design, Fuel Qualification Approach, Fuel Performance Modeling, Fuel Fabrication, Selected AGR-1, AGR-2, and AGR-5/6/7 Fuel Property Means, AGR Program TRISO Fuel Key Performance Data, Irradiation Performance: Fission Gas R/B, Irradiation Testing Results, Kernel and Coating Behavior During Irradiation, Locating and Studying Failed Particles Greatly Improves Understanding of Fuel Performance, Fission Product Release from UCO Fuel Compacts: AGR-1 and AGR-2 Examples, HTGR Accident Safety Testing of TRISO Fuel, Evaluating Behavior During D-LOFC Accidents, Safety Test Results for US UCO Fuel, Particle Failure Evaluation, Fuel Performance Summary, Ongoing Work and Outstanding Data Needs, Core Oxidation, Industry Engagement, and Coated-Particle-Fueled Reactor Concepts and Fuel Designs.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Efficient Failure Probability Calculations and Modeling Interface Debonding in TRISO Particles with BISON

This document constitutes completion of the NEAMS milestone, which is titled Demonstrate efficiency improvements in TRISO failure probability calculations and the effect of debonding on fission product transport in TRISO fuel particles in Bison . In this report we present the development of the following: (1) the anisotropic elasticity model of pyrolytic carbon and extended material models using the local coordinate system for aspherical particle geometry; (2) a capability of modeling interface debonding in TRISO particles; and (3) an efficient high-fidelity approach to calculate the failure probability of TRISO particles. Benchmark problems and AGR-2 tests are used to verify the models and demonstrate these new capabilities.

36 MATERIALS SCIENCE↗

Multi-scale fission product release model with comparison to AGR data

TRistructural ISOtropic (TRISO) particle fuel is central to several advanced, high-temperature reactor designs. Each particle consists of a fuel kernel encapsulated by three layers of carbon and ceramics that prevent the release of fission products and ensure physical integrity. Despite outstanding retention properties, fission product release has been observed from intact particles. To better understand and quantify fission product release from TRISO particles, a multiscale, mechanistic model of fission product transport is being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. Previous work focused on silver (Ag) transport and improved Ag release predictions. The work described in this report builds on this experience to better understand cesium (Cs) transport in silicon carbide (SiC), the main barrier to the release of fission products. Atomistic simulations provide bulk and grain boundary (GB) Cs diffusivities in SiC, which are used by phase field simulations in the mesoscale code Marmot to determine the temperature, microstructure, and irradiation-dependent Cs diffusivity at the mesoscale in SiC. This approach attributes the different temperature regimes experimentally observed for Cs diffusivities in SiC to a transition from bulk-dominated diffusivity at high temperatures to a GB-dominated regime at low temperatures, providing new insight. The multiscale, mechanistic effective diffusivity is then implemented in the fuel performance code BISON and further validated by comparing Cs release predictions from Advanced Gas Reactor (AGR)-1 and AGR-2 post-irradiation measurements. The new model improves BISON’s predictability. This document also reports improvements made on Ag transport modeling by accounting for different GB types having different diffusivities. Moreover, this report details preliminary efforts to model palladium (Pd) attack of the SiC at the mesoscale using a phase field approach. Pd attack and its impact on accelerated Ag transport remains a misunderstood phenomenon, and we use the model to demonstrate that the formation of lamellae that has been observed in experiments can be explained by the reaction of Pd with SiC to form alternating layers of graphite and Pd 2 Si. This effort aims to improve our understanding of the reaction and eventually provide a model for BISON to account for Pd penetration and its effects on fission product release.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing

The ability of tri-structural isotropic (TRISO) fuel to contain fission products is largely dictated by the quality of the manufacturing process, since most of the fission product release is expected to occur due to coating layer failure in a small number of particles containing defects. The Bison fuel performance code has capabilities to predict failure in individual particles, accounting for the presence of defects, and to apply statistical analysis methods to compute the probability of failure in a set of fuel particles. Bison has recently undergone significant development both to improve its physical representations of fuel particle behavior and to improve the efficiency of its statistical failure calculations. Physical model improvements include new capabilities to account for the pressure generated by fission gases on inner pyrolytic carbon (IPyC) crack surfaces and to use local material coordinate orientation to accurately incorporate the anisotropy in the material properties in aspherical particles. To improve statistical modeling efficiency, a direct integration approach which involves directly integrating the failure probability function associated with statistically varying parameters has been developed. The direct integration approach is much more efficient than the Monte Carlo (MC) schemes commonly employed, and allows Bison to directly run high-dimensional fuel performance models, which improves the accuracy of failure probability calculations. Finally, a set of benchmark problems is considered here to compare the MC and direct integration approaches, and a statistical failure analysis of compacts in the Advanced Gas Reactor (AGR)-2 experiments is performed using the direct integration approach.

36 MATERIALS SCIENCE↗

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Understanding Model Inadequacy in TRISO Nuclear Fuel Fission Products Release Models: Empirical and Mechanistic Approaches

The increasing use of tristructural isotropic (TRISO) particle fuel in both advanced and existing reactors necessitates a thorough evaluation of uncertainties and shortcomings in TRISO fission product release models. These inadequacies arise from the simplifications made in computational models compared to experimental data. Utilizing the BISON fuel performance code and experimental data from the Advanced Gas Reactor (AGR) program provides a unique chance to rigorously assess these inadequacies within a Bayesian uncertainty quantification (UQ) framework. This study contrasts the standard Bayesian framework with the Kennedy-O'Hagan (KOH) framework, which explicitly accounts for modeling inadequacies, in the context of UQ for TRISO silver release models. It examines both the traditional Arrhenius equation and a more advanced lower-length-scale (LLS)-informed model that incorporates microstructure information. The inverse UQ process applied to AGR-2 and AGR-3/4 datasets identified modeling inadequacy as the primary source of uncertainty, with experimental noise also being significant, while model parameter uncertainty was minimal. Both the Arrhenius and LLS-informed models showed similar levels of modeling inadequacy. For forward predictive UQ using the AGR-1 dataset, the KOH framework enhanced the accuracy and quality of quantified uncertainties by approximately 30% and 40%, respectively, compared to the standard Bayesian framework. This improvement was observed for both the Arrhenius and LLS-informed models. At the engineering scale, both models performed similarly, but the LLS-informed model outperformed the Arrhenius equation at the mesoscale. These findings underscore the importance of explicitly considering modeling inadequacy in the UQ process and highlight the need for ongoing refinement of physics-based models to address these shortcomings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Unpacking model inadequacy: The quantification of silver release from TRISO fuel by considering empirical and mechanistic approaches

Increasing adoption of the proposed tristructural isotropic (TRISO) particle fuel for both advanced and existing reactors makes it critical to assess and address any uncertainties and inadequacies of TRISO fission product release models. Model inadequacy stems from simplifications made to the computational model when compared to the experiments. The modeling and simulation efforts conducted using the BISON fuel performance code, along with the experimental campaigns carried out under the Advanced Gas Reactor Fuel Development and Qualification Program, afford a unique opportunity to conduct a rigorous modeling inadequacy assessment within the Bayesian uncertainty quantification (UQ) framework. Here, this study compares the standard Bayesian framework against the Kennedy-O'Hagan (KOH) framework, which explicitly represents modeling inadequacy, in regard to UQ for TRISO silver release models. For this purpose, both the traditional Arrhenius equation fitted to experimental data and the more advanced lower-length-scale (LLS)-informed model, which considers microstructure information, are independently considered. Applying the inverse UQ process on the AGR-2 and -3/4 datasets revealed modeling inadequacy to be the most dominant source of uncertainty. Experimental noise uncertainty is also significant; however, model parameter uncertainty can be considered negligible. Interestingly, both the Arrhenius equation and the LLS-informed model demonstrated similar levels of modeling inadequacy. For the forward predictive UQ, the KOH framework improved both the accuracy and quality of quantified uncertainties in comparison to the standard Bayesian framework. This is true for both the Arrhenius equation and the LLS-informed model. In comparing these modeling approaches, both demonstrated similar performance at the engineering scale, while the LLS-informed model expectedly outperformed the Arrhenius equation at the mesoscale. These conclusions highlight the importance of explicitly accounting for modeling inadequacy in the UQ process, and reinforce the need for continuous refinement of physics-based models in order to address the modeling inadequacy.

Advanced reactors↗

Assessment of buffer-IPyC thermomechanical debonding behavior using new experimental strength data in BISON

TRIstructural ISOtropic (TRISO) fuel is a nuclear fuel commonly used in High Temperature Gas-cooled Reactors (HTGRs). A single sub-millimeter-diameter TRISO fuel particle consists of a spherical fuel kernel surrounded by four coating layers: a low-density pyrocarbon buffer layer, an inner pyrolytic carbon (IPyC) layer, a silicon carbide (SiC) layer, and an outer pyrolytic carbon (OPyC) layer. The kernel is commonly made of UO2 or a mixture of uranium carbide and uranium oxide (UCO). During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. Not all irradiated particles will experience buffer-IPyC gap formation. The debonding may be partial, or it may be nearly total. However, from post-irradiation examination of UCO TRISO fuels irradiated as part of the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, it was concluded that partial buffer-IPyC debonding was the most common type of buffer-IPyC interaction. To predict TRISO thermomechanical performance, multi-physics models have been built that are being continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for 1D, 2D, and 3D TRISO particle simulations. This code is used to calculate fuel temperature, kernel swelling, buffer densification, thermal and irradiation creep, fracture, and fission gas production and release. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated AGR TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. That observation is also implemented in the TRISO interface debonding model. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fission product distribution in irradiated safety-tested and as-irradiated AGR-2 TRISO particles

In this work, two tristructural isotropic (TRISO)-coated nuclear fuel particles were examined by electron probe microanalysis (EPMA) as part of the Advanced Gas Reactor program. The compacts’ average irradiation temperatures ranged from approximately 1260 to 1290 °C. One particle was examined in the as-irradiated condition, while the other was subject to 1600 °C post-irradiation safety testing. This study was undertaken to test a newly-developed EPMA technique to determine fission product masses in TRISO particles on a layer-by-layer basis, and to compare fission product distributions between an as-irradiated and safety-tested particle. Fission product concentration profiles were collected along two radii in each particle, with measured concentrations used to compute the fission product mass in each TRISO particle layer. These measured masses were then compared to those predicted from ORIGEN modeling calculations. Data collected from these measurements show that for these two particles, masses determined via EPMA were within ± 20% of the calculated masses for the rare-earth elements, Mo, Zr, Cs, I, and Pd. Elements that tend to be less homogeneously distributed include Sr, Te, Eu, Ag, and possibly Ba. Measured Ag masses differed by more than 40% from the calculated mass. Lanthanides other than Eu remain primarily within the fuel kernel in the as-irradiated particle but in the safety-tested particle these element masses were divided approximately equally between the kernel and kernel periphery. In both particles, the majority of Sr and Eu accumulated in the carbon-rich kernel periphery, although in the safety-tested particle, Sr and Eu accumulated farther from the fuel kernel than occurred with irradiation alone. A greater mass fraction of mobile elements, such as Cs and I accumulated in the buffer and IPyC in the safety-tested particle as compared to the as-irradiated particle. When fully developed and tested, this mass balance approach to TRISO particle analysis has the potential to provide insight into fuel behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Summary Report of the FY24 DOE Contributions to the GIF VHTR CMVB

The Generation-IV Forum (GIF) Very-High-Temperature Reactor-Computational Methods Validation and Benchmark (VHTR-CMVB) initiative, involving organizations from Korea Atomic Energy Research Institute (KAERI) (South Korea), Institute of Nuclear and New Energy Technology of Tsinghua University (INET) (China), U.S. Department of Energy (DOE) (U.S.), Joint Research Centre (JRC) (Europe), and Japan Atomic Energy Agency (JAEA) (Japan), is dedicated to the verification and validation of tools for High-Temperature Gas-Cooled Reactors (HTGRs) analysis, using data shared by Computational Methods Validation and Benchmark (CMVB) signatories. For FY24, the US DOE CMVB has committed to several critical activities. Under WP1, led by the US, the integration of the High Temperature Gas Cooled Reactor - Pebble-Bed Module (HTR-PM) Phenomena Identification and Ranking Table (PIRT) into the comparative PIRT is progressing, with a new draft of the comparison tables issued earlier this year and currently being utilized by INET for their contribution. Neutronic validation efforts under WP3 include the preparation of the burnup analysis benchmark, preliminary calculations, and the development of reference models and results. In WP2, a validation exercise for hot gas mixing in the lower plenum of HTR-PM is in progress, using experimental data from INET (China) to validate modeling approaches. A model of the experimental facility has been developed using StarCCM+, with initial calculations slated for presentation at the GIF CMVB meeting this fall. Another WP2 activity focuses on validating numerical models for air-cooled Reactor Cavity Cooling System (RCCS) with experimental data from the Wisconsin Madison RCCS facility. A high-fidelity model, developed using NEK-RS, is currently being validated with available data from a low power forced convection test. These efforts are aimed at enhancing and confirming the accuracy of HTGR analysis tools, ensuring their alignment with experimental data and regulatory requirements.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of XCT for Matrix Density Measurement of Particle Fuel Forms

Particle fuel forms generally consist of a dispersion of fuel, such as tristructural isotropic (TRISO) particles, within a refractory matrix (e.g., graphite or silicon carbide). The density of matrix materials for particle fuel forms is of interest for modeling fuel form strength and thermal properties and may be specified as a quality control parameter, depending on reactor design. Some of the uncertainty associated with traditional, manual approaches can be eliminated by performing x-ray computed tomography (XCT) on the fuel forms and applying image processing methods to generate a precise count of the number of particles. This also removes the need to include determination of particle count within each individual fuel form during fabrication. Unfortunately, reconstruction artifacts from high-Z uranium-bearing kernels prevent accurate measurement of individual particle volumes using this approach, so the use of mean particle mass and volume are still necessary for computation of average fuel form matrix density. This method of using XCT to count particles in individual fuel form for determination of average matrix density was applied to three archived compacts from the Advanced Gas Reactor Fuel Development and Qualification (AGR)-1 campaign, four archived compacts with uranium carbide/uranium oxide (UCO) TRISO from the AGR-2 campaign, and three archived UO 2 -TRISO compacts from the AGR-2 campaign. The resulting density values were compared with those previously reported, showing slight changes due to uncertainties in the previously used number of particles in each of these cylindrical, graphite matrix compacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗