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DOE OSTI2025

Deterministic High-Fidelity Neutronics Simulation of Pebble Bed Reactors Using Pebble Tracking Transport

The pebble tracking transport (PTT) algorithm offers a high-fidelity deterministic approach for neutron transport for pebble bed reactors (PBRs). This approach requires the mesh for the active-core region to consist exclusively of tetrahedral elements, where each node in the pebble-packing region represents a pebble centroid. This paper investigates the application of PTT for full-scale PBRs, considering both the isothermal and the temperature-dependent core conditions. Macroscopic cross sections are generated using Serpent 2 full-core eigenvalue simulations where pebbles are grouped into disjoint subsets using machine learning. To minimize the need for individual cross-section sets for each pebble in the core, K-means clustering is used to group pebbles by temperature and neutronic environment parameters. Here, we compare the multiplication factor and power rate distributions between PTT simulations using the Griffin reactor physics software and reference solutions from Serpent 2. Our analysis shows that a full-core, high-fidelity PTT calculation produces accurate results with minimal local (pebblewise) errors. Additionally, timing results indicate that PTT simulations converge rapidly on modern supercomputing platforms.

Griffin↗

DOE OSTI2026

ML-Based Pebble Power Reconstruction for Pebble Bed Reactor Analysis

Pebble power reconstruction has been explored to complement the conventional homogenized modeling approach in pebble bed reactor (PBR) analysis, as detailed heterogeneous geometry calculations are computationally expensive. The random distribution of pebble fuels within the core challenges the application of conventional pin power reconstruction methods. To address this, we introduce a machine learning approach based on the transformer model, composed of encoder and decoder layers, to estimate the flux and power form functions for reconstructing individual pebble neutron fluxes and powers. The homogeneous neutron flux distribution within each spectral zone (SZ) is obtained from finite element solutions of global diffusion or transport calculations. Verification tests demonstrate that the trained transformer model accurately predicts power form functions over a range of conditions, including variations in pebble enrichment, location, type, SZ size, and burnup. In particular, verification using a three-dimensional PBR benchmark with burned pebbles shows good agreement in heterogeneous pebble power distributions between Griffin and Serpent. These results highlight the potential of applying conventional pin power reconstruction approaches to PBR cores with randomly distributed pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

High-fidelity Pebble Bed Reactor Depletion Based on Pebble Tracking Transport in Griffin

The pebble tracking transport (PTT) method is a high-fidelity, heterogeneous deterministic transport technique for pebble bed reactor analysis. It discretizes the broad-group neutron transport equation in space and angle with the discontinuous finite element and the discrete ordinates method, and utilizes various solving techniques, including mesh sweeping and diffusion acceleration, to provide pebble- wise reaction rates. This work presents the extension of the PTT method to enable fuel depletion capability in the Griffin code. We discuss the implementation details of the PTT-based high-fidelity depletion where isotope inventory of all individual pebbles is tracked through pre-determined pebble flow paths in the core. The implementation is verified with a generic pebble bed reactor model. Some preliminary equilibrium core results are included. Future works are also discussed.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Burnup Monitoring for Pebble Bed Reactor Systems

A pebble burnup monitoring system is a required component for domestic reactor safety and safeguards applications associated with pebble bed reactors (PBRs). One of the main requirements of a PBR burnup monitoring system is that it needs to be capable of rapid measurements to assess the burnup of each individual pebble to determine whether to recirculate it in the reactor or discard it as spent fuel. This report considers three different approaches for a burnup monitoring system for pebbles discharged from the reactor core in a pebble bed modular reactor-400: • passive gamma spectrometry measurement, • passive neutron coincidence measurement, and • active neutron counter based on the differential die-away technique. Conceptual designs have been created for each of these detectors, and preliminary analysis has been performed using Monte Carlo N-Particle and Oak Ridge Isotope Generation code simulations. The advantages and practical limitations (e.g., high radiation background) of each system were identified. Simulations suggest that each of the three measurement techniques can be successfully employed to distinguish between pebbles based on their number of passes through the core and to quantify the burnup of pebbles.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Assessment of Self-interrogation Safeguards Signatures for Pebble Bed Reactor Fuel

New reactor designs, such as pebble-bed reactors, present challenges for the safeguarding of fissile material. Due to the multi-pass fuel circulation design and the non-uniform path a pebble may traverse through a pebble-bed reactor, there will be variations in the irradiation history of spent fuel pebbles. The standard approach of estimating actinide quantities based on fission gamma spectra or neutron emission paired with depletion modeling may yield uncertainties too large for safeguards and material accountancy. This project investigated, through modeling and experimentation, the potential of neutron self-interrogation of spent fuel pebbles as an innovative method to implement materials accountability. As an example, our feasibility studies indicate that the mass of U-235, U-238, Pu-239 and Pu-241 can be predicted to 4.1, 0.86, 13 and 13 % accuracy, respectively, when measuring 100 closely packed end-of-life spent fuel pebbles over approximately 12 days using a 4π counting geometry.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗

DOE OSTI2025

Parameter Study of the Running-In Process for the Generic Pebble Bed Reactor (GPBR200)

The run-in period of a pebble bed reactor is complex and difficult to model given significant heterogeneity in core composition, power, and temperature. While it is understood that the initial composition of the core should eventually result in the same equilibrium core composition, the approach to equilibrium can vary significantly depending on factors such as start-up fuel enrichment and power ramp rate. To explore this, a high-fidelity model of the General Pebble Bed Reactor was used to vary power ramp schemes and start-up core compositions. It was found that both the initial core composition and power ramp rate had a significant impact on the flow rate of pebbles during early time steps, with higher ramp rates and low enrichment resulting in non-physical flow rates. Power ramp rate alone was found to dictated maximum pebble power peaking observed during the run-in process, with higher ramp rates resulting in greater peak pebble powers. Start-up fuel enrichment and power ramp were found to both impact total fuel consumption, although the impact of start-up fuel enrichment was generally secondary to ramp rate.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy

This report describes how to produce reference solutions for the equilibrium core search of pebble bed reactors using the pyrates Python library. The pyrates library uses the kugelpy methodology to perform running-in calculations to reach an equilibrium core. This approach relies on full-core Monte Carlo neutron transport calculations and the shifting of fuel pebble inventory through the reactor to simulate pebble movement in the core from one step to the next of a running-in scenario. In addition to the use of Serpent for the Monte Carlo neutron transport calculations, as part of this work, updates for the use of the Shift Monte Carlo code were integrated into the official pyrates GitHub repository. Comparisons of running-in simulations for a generic pebble bed reactor produced by using pyrates with Serpent and Shift are shown. Although consistent trends are shown between the use of the two Monte Carlo codes, the limiting factor in either calculation is the computation time due to the need to perform several hundred full-core neutron transport calculations before an equilibrium core is reached.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Numerical Method Improvements in Griffin for Pebble Bed Reactors with a Focus on the Computation of Burnup

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Multiphysics Running-In Simulations for Pebble-Bed Reactors with Griffin

Griffin, a Multiphysics Object-Oriented Simulation Environment (MOOSE)–based application targeting transient modeling of advanced reactors, has been used recently to model pebble-bed reactors (PBRs). The modeling effort has focused thus far on equilibrium core calculations. A new capability to simulate the running-in phase of PBR operation has been added to Griffin. This work demonstrates the new capability with a coupled multiphysics running-in simulation. Griffin computes power densities in the core at each time step of the running-in simulation and passes these to Pronghorn, which models fluid flow and heat transfer to calculate pebble surface temperatures. These surface temperatures are used along with the power densities in a heat conduction model to compute average fuel and moderator temperatures, which are passed back to Griffin and accounted for with temperature-dependent cross sections. This work also describes a novel methodology for determining appropriate pebble feed rates and control rod positioning during the running-in simulation. Furthermore, the RZ-geometry model used in this work requires minimal computational resources and can be used for optimization and uncertainty studies in future works.

Griffin↗

DOE OSTI2025

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the Fluoride-Cooled High-Temperature Pebble-Bed Reactor reference plant models for the United States Nuclear Regulatory Commission. These models, developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, serve as the foundation for the future development of detailed design evaluation models based on license applications. BlueCRAB is the code suite proposed for non-light-water reactor systems safety analyses, and it incorporates various simulation tools developed by the Nuclear Energy Advance Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of this work is to assess the level of readiness of BlueCRAB for modeling fluoride-cooled high-temperature pebble-bed reactors. We first developed numerical models in BlueCRAB that include the key physics for this technology, ensuring an adequate level of fidelity for modeling the core performance during accident scenarios. This was followed by simulation of transient scenarios, two loss-of-forced-cooling events (one protected and one unprotected), and two control rod withdrawal events (one delayed and one prompt supercritical reactivity insertion). The analysis includes comparisons between the 2-D thermal fluid porous media models in Pronghorn and SAM, comparisons between coupled Pronghorn-Griffin and coupled SAM-Griffin models for two loss-of-forced cooling events and one control rod withdrawal event, and comparisons between SAM single-solve and domain-overlapping approaches for multi-scale thermal fluid coupling. In addition, we performed comparisons between 3-D, 2-D, and 0-D neutronic models for the two control rod withdrawal scenarios with Pronghorn-Griffin. The results show that the BlueCRAB models led to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields such as the neutron flux, power, temperatures, densities, pressures, and velocities are all within the expected ranges, and their distributions can be explained from the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. The simulations demonstrate that there are differences between the various levels of fidelity, and it is advisable to have flexible tools that can cover the breadth and depth of needs that may arise in future technical evaluations. We believe that BlueCRAB’s capabilities represent a significant asset for confirmatory analyses aimed at resolving important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE

This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Nuclear Data Impact Assessment for the HTR-10 Pebble-Bed Reactor Using SCALE

The HTR-10 was used as a representative pebble-bed high-temperature gas-cooled reactor in this assessment of nuclear data’s impact on important reactor and spent fuel metrics, including safety-related quantities such as the effective multiplication factor (k eff ), temperature reactivity feedback, spent fuel inventory, and decay heat. Using the SCALE code system tools and ENDF/B-VII.1 nuclear data libraries, we quantify the effect of nuclear data uncertainties on these key performance metrics for both fresh fuel and equilibrium core configurations. For reactor core key parameters, important contributors to uncertainty include reactions of 235 U [$\bar{v}$, fission, (n, γ)], 238 U [elastic, (n, γ)], and graphite [elastic, (n, γ)]. Additional important contributors for the equilibrium core include reactions of higher actinides ( 239 Pu, 240 Pu) and fission products ( 135 Xe, 149 Sm). For spent fuel analysis, most nuclide inventory uncertainties remain below 5%. Higher uncertainties up to 11% are being observed for minor actinides like 243 Am and 244 Cm. Additionally, fission product uncertainties in 155 Eu and 155 Gd, of 25% and 23% respectively, are also significant and have implications for burnup credit applications. 110m Ag also shows high uncertainty of up to 11%, mainly due to fission product yield uncertainties. Decay heat relative uncertainties remain below 0.6% up to 10 years’ cooling time after fuel discharge. The highest relative uncertainty of 1.5% occurs at 500 years of cooling; however, because the decay heat value is very low at that time, the absolute uncertainty is not significant. This work demonstrates that extending assessments beyond fresh fuel k eff to include irradiated cores, nuclide inventories, and decay heat is essential in understanding the behavior of uncertainties as a function of fuel burnup and can support improvements of safety margins and spent fuel management.

Nuclear data impact↗

DOE OSTI2025

PSA 2025 Presentation: "Modeling and Sensitivity Analysis of a Generation IV Pebble Bed Reactor Using MELCOR 2.2"

Accompanying the advancement of reactor technologies is the need for computational modeling and simulation to predict their behavior under normal operating conditions and accident scenarios. New Generation IV reactor designs which employ non-conventional fuel have a particular need for modeling the behavior and release of radionuclides and other material from the fuel. In this work, MELCOR version 2.2, a system-level safety and accident scenario code developed by Sandia National Laboratories, was used to model a 200-MWth pebble bed modular reactor and calculate the inventories of circulating and deposited graphite, metal dust, and elemental components released from the fuel elements. A base case modeling the reactor under standard operating conditions was calculated using MELCOR and the inventories were extrapolated to 30 years of operation time using a logarithmic regression fit. A sensitivity analysis was also performed in which several key parameters for the base case model were modified to explore the effect of these changes on the inventories calculated by MELCOR. A set of transient scenario simulations for a depressurized loss of forced cooling (DLOFC) accident were also performed. The results of the sensitivity analysis and transient simulations are reported and discussed in relation to the modeling techniques used for this study.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Scoping Analysis of Pebble-Bed Reactors for the Destruction of the Transuranic Inventory of LWR Spent Nuclear Fuel

With the forecasted increase in the construction and operation of nuclear reactors, there will be a corresponding increase in the quantity of spent nuclear fuel (SNF) that requires long-term storage. In SNF, transuranic isotopes contribute the most to the long-term radiotoxicity of the fuel and pose a proliferation risk. One option that has been explored to address these issues is the removal of the transuranic isotopes from SNF and the conversion of these isotopes into transuranic fuel (TRU fuel). Here, this work sought to determine how effective a micro-modular Pebble-Bed High-Temperature Gas-Cooled Reactor (PB-HTGR); the 10-MW High Temperature Gas-cooled Test Reactor (HTR-10); and a salt-cooled small-modular pebble-bed reactor (PBR), i.e. the generic Fluoride-cooled High-temperature Reactor (gFHR), are at reducing the inventory of transuranic isotopes while still maintaining the intrinsic safety features of the PBR designs, such as negative temperature coefficients of reactivity. Optimized pebble designs utilizing TRU fuel were found for both reactors through the adjustment for the packing fraction of fuel in each pebble. The Axial Zone Equilibrium Modeling (A-ZEM) method was used in this work to help select the optimized pebble design. Once an optimized pebble design was selected and an equilibrium model was produced, the results from the deep burn (DB) HTR-10 and gFHR designs were compared to the results of two models from the literature. While both the DB gFHR and the DB HTR-10 were able to reduce the weapons-usable transuranic inventory, the performance of these reactors did not match that of the small-modular PB-HTGRs in the literature. Therefore, a need was identified for further refinement of the gFHR design using TRU fuel, as the results for this model were more promising than those of the DB HTR-10, which was strongly limited by the high leakage intrinsic to micro-modular PB-HTGRs.

Transuranic fuel↗

DOE OSTI2025

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the pebble-bed high-temperature gas-cooled reactor (PB-HTGR) reference plant models for the United States Nuclear Regulatory Commission. These models serve as the foundation for the future development of detailed design evaluation models based on license applications. The reference plant models have been developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, which is the code suite proposed for non-light-water reactor systems safety analysis. It incorporates various simulation tools developed by the Nuclear Energy Advanced Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of the work that was performed was to assess BlueCRAB’s level of readiness for modeling a PB-HTGR. To do so, we first developed numerical models in BlueCRAB that include the key physics for this technology to ensure an adequate level of fidelity for modeling PB-HTGR core performance and for performing multiphysics simulations for equilibrium core conditions and different accident scenarios. Then we simulated transient scenarios, including depressurized and pressurized loss of forced cooling accidents, over-cooling, and control rod withdrawal events with delayed and prompt supercritical reactivity insertions. The analysis in this report includes comparisons of the 2D thermal fluid porous media models in Pronghorn and SAM, and comparisons of coupled SAM/Griffin/SAM and coupled Pronghorn/Griffin for depressurized and pressurized loss of forced cooling, over-cooling, and control rod withdrawal events. In addition, we compare 3D, 2D, and 0D/PKE neutronic models for the two control rod withdrawal scenarios with coupled Pronghorn/Griffin. The comparisons show that the BlueCRAB models lead to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields, such as neutron flux, power, temperature, density, pressure, and velocity, are within the expected ranges, and their distributions can be explained by the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. This work further highlights the need for flexible tools with various levels of fidelity to cover the breadth and depth of needs that may arise in future technical evaluations of the PB-HTGR. We believe that the BlueCRAB capabilities will be a significant asset for confirmatory analyses in order to resolve important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

New capabilities for rapid depletion analysis of pebble-bed reactors in SCALE

The SCALE Leap-In for Cores at Equilibrium (SLICE) method leverages capabilities available in the SCALE modeling and simulation suite to facilitate rapid estimation of equilibrium core inventories for flowing-pebble reactor systems in support of a variety of fuel cycle applications. New capabilities that compliment the SLICE method have been developed for the ORIGAMI interface to ORIGEN in SCALE to facilitate rapid depletion calculations for flowing-pebble systems. New features include a more generalized and flexible means of specifying interpolation dimensions, the ability to evaluate pebbles moving through user-defined “axial zones” in each of the pebble’s multiple passes through the core, and the treatment of differential velocities across radial channels (representing both pebble-to-pebble and wall-to-pebble friction effects). ORIGAMI thus provides an efficient user interface to define a pebble’s path and irradiation histories of its multiple passes through the core to calculate the pebble’s time-dependent inventories, which can be useful in various applications domains such as safeguards, criticality safety, and disposal analyses. The consistency of new ORIGAMI approach was verified against the solution obtained using the SLICE method with ORIGEN-ARP, showing excellent agreement.

Skutnik, Steven E. [Oak Ridge National Laboratory ↗