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Assessment of ORIGEN Reactor Library Development for Pebble-Bed Reactors Based on the PBMR-400 Benchmark

This report provides an evaluation of present SCALE capabilities for modeling depletion of pebble-bed reactor systems, using the PBMR-400 benchmark as a test case. A specific aim of this work is to understand the system characteristics required to generate production-quality reactor data libraries for rapid depletion calculations with ORIGEN. This report includes a discussion of present SCALE capabilities for modeling doubly heterogeneous fuels, prior SCALE work modeling pebble bed–type reactors, and a detailed neutronic analysis of the PBMR-400 core for both fresh and equilibrium-composition core conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Griffin/Pronghorn PBMR-400 Benchmark Results [Slides]

Content Overview: 1) Pronghorn & Griffin, MOOSE based applications overview: Codes capabilities description & MOOSE ecosystem overiew; Current research activities and synergies with other projects; Different multiphysics coupling scheme description. 2) PBMR-400 Benchmark: OECD NEA Benchmark and Pronghorn/Griffin models description; Standalone NK Ex1 and TH Ex2 Results description; Coupled Steady state Ex3; Results analysis for Transiet Ex4a (100-40-100 Load Following) & Ex3 (Protected PLOFC). 3) Conclusions $ Future steps.

97 MATHEMATICS AND COMPUTING↗

Coupling of Pronghorn and RELAP-7 for a Pebble Bed Reactor

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling and Simulation of Fuel Burnup in Pebble Bed Reactors

Modeling and simulation of fuel burnup plays important roles in reactor design, operation, safety, and security as well as nuclear material control and accounting (MC&A) [1]. This task is uniquely challenging for pebble bed reactors (PBR) because the pebbles are continuously added and recycled into the reactor core, and their paths through the core are random. To address this problem, we present two simulation models in this paper. Brookhaven National Laboratory (BNL) developed a simple lattice model of a PBR in Serpent software to generate used pebble isotopic concentrations. The benefit of using Serpent software in this specific application is that it helps streamline the data generation process without having to use too many independent software codes in combination to achieve a simple task. For example, transport, burnup and zero power decay can be implemented in a single pass. Three-dimensional core models were developed using Serpent to simulate the burnup process of 5 subject pebbles starting from fresh till they reach nearly target burnup, with each pebble placed in one of the five artificially designated radial channels to capture the changing neutron spectra along the core radius. Equilibrium isotopic concentrations were assumed in all other pebbles in the core. To provide a verification for the Serpent isotope transmutation and decay results, Oak Ridge National Laboratory (ORNL) performed simple SCALE/ORIGEN calculations using the average neutron spectra calculated by Serpent for each of the 5 pebbles. The 252-group neutron spectra from Serpent were then used by ORIGEN to produce the one-group library for depletion and decay calculations. The isotopic concentrations of a few nuclides of interest and neutron and gamma source terms produced from the ORIGEN calculations were compared with the ones from the Serpent calculations. The model simulated in this work was based on the Pebble Bed Modular Reactor (PBMR)-400 design because many data needed for the simulation such as core power profiles, fuel and reflector temperatures, and equilibrium core composition are publicly available. In this paper, we will compare the results between these two approaches and benchmark the results against a set of well-established simulation results for PBMR-400.

Dim, Odera↗

Modeling and Simulation of Fuel Burnup in Pebble Bed Reactors

Modeling and simulation of fuel burnup plays important roles in reactor design, operation, safety, and security as well as nuclear material control and accounting (MC&A) [1]. This task is uniquely challenging for pebble bed reactors (PBR) because the pebbles are continuously added and recycled into the reactor core, and their paths through the core are random. To address this problem, we present two simulation models in this paper. Brookhaven National Laboratory (BNL) developed a simple lattice model of a PBR in Serpent software to generate used pebble isotopic concentrations. The benefit of using Serpent software in this specific application is that it helps streamline the data generation process without having to use too many independent software codes in combination to achieve a simple task. For example, transport, burnup and zero power decay can be implemented in a single pass. Three-dimensional core models were developed using Serpent to simulate the burnup process of five subject pebbles starting from fresh till they reach nearly target burnup, with each pebble placed in one of the five artificially designated radial channels to capture the changing neutron spectra along the core radius. Equilibrium isotopic concentrations were assumed in all other pebbles in the core. To provide a verification for the Serpent isotope transmutation and decay results, Oak Ridge National Laboratory (ORNL) performed simple SCALE/ORIGEN calculations using the average neutron spectra calculated by Serpent for each of the five pebbles. The 252-group neutron spectra from Serpent were then used by ORIGEN to produce the one-group library for depletion and decay calculations. The isotopic concentrations of a few nuclides of interest and neutron and gamma source terms produced from the ORIGEN calculations were compared with the ones from the Serpent calculations. The model simulated in this work was based on the Pebble Bed Modular Reactor (PBMR)-400 design because many data needed for the simulation such as core power profiles, fuel and reflector temperatures, and equilibrium core composition are publicly available. In this paper, we will compare the results between these two approaches and benchmark the results against a set of well-established simulation results for PBMR-400.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

NRC Multiphysics Analysis Capability Deployment (FY2020--Part 3)

This report details progress and activities of Idaho National Laboratory (INL) on the NRC project ”Development and Modeling Support for Advanced Non-Light Water Reactors.” The tasks completed for this report are as follows: First, Task 2c: Explicit modeling of pebble transient temperature response. In this simulation, the PBMR-400 reactor experiences a 20 second power ramp from 100% to 150% power. This is followed by a similar reduction in the power back to 100%. Several multiscale pebble coupling approaches are tested with one pebble per mesh element in the active core region. The results show good conservation behavior and the stability of the coupling. Next, Extended scope part 1: An assessment of the computational efficiency of the DFEM heat transfer solver shows good scalability. The DFEM solver is a factor of 4 more expensive in solution time than the FEM solver for heat transfer problems due to the increased number of degrees of freedom. Nonetheless, the DFEM approach provides the user with the flexibility to model gap heat transfer problems. Then Extended scope part 2: the GapHeatTransferInterfaceMaterial was improved to give the user increased flexibility with the modeling of heat transfer through gaps with the DFEM solver. A number of gap parameters can now be coupled both through functions and variables. Finally, Extended scope part 3: demonstration of how the gap width between hexagonal fuel cells can be calculated during a heat up transient and used in the GapHeat- TransferInterface model. A full domain DFEM model with gap expansion is coupled to a SubApp that models the thermal expansion of the base plate. The results show the expected physical behavior, although have not been fully bench- marked at this point in time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Conceptual design study of neutron detectors for safeguards measurement of an irradiated pebble

Nuclear material control and accounting (MC&A) of pebble-bed reactors (PBRs) is challenging because a PBR utilizes hundreds of thousands of identical, unmarked pebbles that are continuously recirculated through the core. To develop tools that enable the implementation of international safeguards, especially in the context of MC&A of spent pebbles, we designed and simulated three neutron detection concepts to determine fissile content in individual pebbles: a differential die-away (DDA) detector, a californium interrogation prompt neutron (CIPN) detector, and a passive neutron albedo reactivity (PNAR) detector using Monte Carlo calculations. Burnup calculations were performed on the spent pebbles from the PBMR-400 classic PBR. The varying neutron and gamma source terms, and isotopic compositions in the spent pebbles calculated at various burnup levels were used in the neutron detector models. DDA was found to be sensitive to the number of passes a pebble has had through the core and to the fissile content contained in a spent pebble. Optimization in the DDA design further increased the neutron count rates and thus reduced counting uncertainty. Meanwhile, passive neutron counting using the same detector body could distinguish pebbles with different numbers of passes, but its response was dominated by neutron-emitting actinides and was not sensitive to fissile content. On the other hand, the PNAR technique was not viable for a single pebble but performed reasonably for a 27-pebble array, which suggested potential use for verification measurements of containers filled with 27 or more spent pebbles.

CIPN↗

Evaluation of PBR Spent Fuel Criticality and Dose Rate Compliance for Storage and Transportation

Spent tri-structural isotropic (TRISO)–based fuels have a strong track record in storage and transportation without documented incidents. This work seeks to reduce uncertainty to aid in more informed spent fuel management of TRISO-based fuels by modeling both fresh and spent pebble bed reactor (PBR) fuel and comparing the results to the regulatory standards from 10 CFR 71. SCALE was used for all modeling due to it having fast and accurate methods for handling PBR fuel modeling, as well as having an efficient method for shielding calculations in monaco with automated variance reduction using importance calculations (MAVRIC), which utilizes the consistent adjoint-driven importance sampling (CADIS) and the forward-weighted consistent adjoint-driven importance sampling (FW-CADIS) methods. KENO-VI was used for all criticality calculations, TSUNAMI was used for uncertainty quantification on k-effective, TRITON and the Oak Ridge isotope generation code (ORIGEN) were both used for depletion of the fuel, and MAVRIC was used for shielding calculations. For criticality assessments, this study focused on the requirement that the value of the neutron multiplication factor, k-effective (k-eff), would not exceed a peak value of 0.95, including uncertainty, with 95% confidence. Criticality was initially examined by modeling fresh fuel from three different designs—HTR-10 fuel, PBMR-400 fuel, and demonstration fuel representative of a TRISO-fueled modern high-temperature gas reactor (HTGR) design, henceforth referred to as Demo HTGR—and placing them into various sized containers with conditions described in 10 CFR 71 to quantify the peak k-eff state. When the peak value of 0.95 k-eff was exceeded, mitigation methods were examined in those scenarios. Burnup credit, pebble displacement in areas of strong neutron multiplication, and random pebble replacement using pebbles of various compositions and replacement fractions were examined. In summary, the criticality of PBR fuels can be well accounted for by restricting container size, taking credit for burnup, or by displacing/replacing pebbles. Uncertainty of the k-eff due to nuclear data uncertainties was recorded at ~0.6644%Δk/k, or roughly 664% mil (pcm). The nuclear data–induced uncertainty was relatively small and should not require significant modification in the design to be accounted for. Revisions to the evaluated nuclear data file values have been shown to have a larger impact than nuclear data–induced uncertainty. For dose rate aspects, U.S. Nuclear Regulatory Commission regulations require a maximum dose rate of 10 millirem per hour (mrem/h) at 2 meters. In examining the dose rate behavior of spent PBR fuel, the representative Demo HTGR fuel was modeled exclusively due to it possessing the highest target burnup of the examined fuels. Equilibrium cycle modeling methods were used to produce a higher-fidelity discharge isotopic composition than simple assumptions, such as reflected pebbles. The discharge composition was used as a source term in the fixed-source transport shielding calculations, and dose rates were calculated at 2 m for the shortest possible cooling time. The low concentration of fuel material led to dose rates that were in line with regulatory limits, despite the high burnup when compared to traditional light water reactor fuels. In conclusion, the methods employed in this study would require more work to further verify and validate and are limited to the criticality and dose rate analyses performed.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Rapid depletion analysis of flowing-pebble reactor systems at equilibrium using SCALE

Several high-temperature gas-cooled reactor concepts (and more recently, salt-cooled designs such as the fluoride salt-cooled high-temperature reactor) feature core designs employing continuously circulating fuel pebbles. These reactor designs permit both continuous online refueling of fuel elements as well as higher overall achievable discharge burnups. However, rapid calculation of time-dependent fuel isotopic inventories proves challenging for this class of dynamic systems with current analysis tools. While iterative approaches employing coupled neutron transport have been developed to solve this issue, rapid depletion analysis techniques are needed to calculate time-dependent inventories for individual pebbles and batches (and thus the construction of full- core inventory at equilibrium). We propose a depletion analysis strategy for this type of system for cores at equilibrium. Drawing upon previous neutronic analysis of the PBMR-400 equilibrium core, we demonstrate the viability of developing collapsed one-group cross section libraries suitable for performing rapid depletion analyses with SCALE. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MELCOR Accident Progression and Source Term Demonstration Calculations for a HTGR

MELCOR is an integrated thermal hydraulics, accident progression, and source term code for reactor safety analysis that has been developed at Sandia National Laboratories for the United States Nuclear Regulatory Commission (NRC) since the early 1980s. Though MELCOR originated as a light water reactor (LWR) code, development and modernization efforts over the past decades have expanded its application scope to include non-LWR reactor concepts. Current MELCOR development efforts include providing the NRC with the analytical capabilities to support regulatory readiness for licensing non-LWR technologies under Strategy 2 of the NRC's near-term Implementation Action Plans. Beginning with the Next Generation Nuclear Project (NGNP), MELCOR ha s undergone a range of enhancements to provide analytical capabilities for modeling the spectrum of advanced non-LWR concepts. This report describes the generic plant model developed to demonstrate MELCOR capabilities to perform high-temperature gas reactor (HTGR) safety evaluations. The generic plant model is based on publicly available PMBR-400 design information. For plant aspects (e.g., reactor building size and leak rate) that are not described in the PBMR-400 references, the analysts made assumptions needed to construct a MELCOR full-plant model. The HTGR model uses a TRi-structural ISOtropic (TRISO)-particle fuel pebble-bed reactor with a primary system rejecting heat to a recuperative heat exchange r. Surrounding the reactor vessel is a reactor cavity contained within a confinement room cooled by the Reactor Cavity Cooling System (RCCS). Example calculations are performed to show the plant response and MELCOR capabilities to characterize a range of accident conditions. The accidents selected for evaluation consider a range of degraded and failed modes of operation for key safety functions providing reactivity control, primary system heat removal and reactor vessel decay heat removal, and confinement cooling.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling of a Generic Pebble Bed High-temperature Gas-cooled Reactor (PB-HTGR) with SAM

This report presents the modeling of the core of a generic pebble-bed reactor (PBR) at the system level using the System Analysis Module (SAM) code. This work is an extension of a previous work by the authors (Ooi et al. (2021)) that used the so-called 2-D ring model approach to model the PBMR-400. With the new approach, the pebble bed of the reactor is modeled with multiple PBCoreChannel components with spherical heat structures which allows the code to calculate thermal fluid parameters with built-in closure relations. The new core-channel approach is an improvement to the 2-D ring model approach as it does not introduce geometric distortions to the model and thus reduces the uncertainties of the predictions. In addition to thermal fluid simulations, point kinetics (PKE) are included to the model. Simulations are performed under a steady-state normal operation condition and a load-following transient scenario. This particular transient scenario is chosen as it tests both the thermal fluid and neutronics aspects of the model. The predicted results from both the steady-state and transient scenarios are compared with the results by Stew- art et al. (2021) who performed similar simulations with a Griffin-Pronghorn coupled tool. Despite the differences between the codes, with SAM being a system-analysis code and Pronghorn being a porous-medium code, both sets of results compare favorably. The over- all profiles and trends of the predicted temperatures and reactivities from the SAM and Griffin/Pronghorn simulations are similar, with some differences in their predicted values. The first part of the report covers the significance of a relatively fast-running approach that is capable of modeling the pebble bed reactor at the system-level while simultaneously capturing the radial thermal behavior of the core. Then, the modeling approach used in this work is discussed in details. Lastly, the results and comparisons with the Griffin/Pronghorn simulation are presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Finite Volume Discretization of the Euler Equations in Pronghorn

Modeling flow and heat transfer in high temperature gas reactors (HTGR) requires the ability to model a wide range of flow speeds from slow (natural convection), to intermediate (forced-flow conditions), to supersonic regimes (depressurization) for a wide range of geometries including the pebble bed, upper and lower plenum, and risers. In previous work, Pronghorn has effectively modeled low-to-medium speed flows in scenarios such as the one described in the two-dimensional PBMR-400 benchmark, using its finite-element-based streamline-upwind Petrov-Galerkin (SUPG) stabilized implementation of the Euler equations. However, limitations of this method become apparent when dealing with more complicated geometries (e.g. imposing slip boundary conditions at nodes belonging to two different boundaries) and when gas speeds are fast enough for shocks and supersonic flow to occur. For these problems, the finite-element-based solver lacks robustness and is plagued by slow iterative convergence or even divergence. In order to address these challenges, the Pronghorn code at INL has been updated with new, modified versions of its original equations. The new Pronghorn models are built on the finite volume method with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver based numerical flux method, which (1) allows imposing slip boundary conditions much more robustly and (2) performs well for a wide range of flow speeds. The finite-volume-based flow solver will form the basis for a robust coarse-mesh thermal-hydraulics capability in Pronghorn.

97 MATHEMATICS AND COMPUTING↗

NRC Multiphysics Analysis Capability Deployment FY21: Part 3

This report details the progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” The deliverables completed for this report are: Deliverable 1c: the capability to model gas mixtures was added to Pronghorn. A test problem mimicking the conditions achieved in a depressurized loss of forced cooling (DLOFC) event was solved with both RELAP-5 and Pronghorn. Pronghorn employed a finite vol ume method with the Kurganov-Tadmor discretization. The comparison between the mass fraction spatial profiles computed with RELAP-5 and Pronghorn clearly shows the presence of numerical artifacts (i.e., overly diffusive behavior at low Mach numbers). We confirmed that the problem disappears at higher Mach numbers. We recommend future work on the implementation of a low Mach finite volume formulation to better treat low Mach number problems. Deliverable 2a: we demonstrated two approaches to model the radiation/conduction/natural convection heat transfer across a stagnant gas for the PBMR-400 design using Pronghorn. The first approach is based on the net radiation method, which relies on the computation of view factors with the Multiphysics Object-Oriented Simulation Environment (MOOSE) ray tracing capability. The second method is a traditional thermal resistance approach. The test problems include both 2D and 3D geometries. In all cases, the results show very good agreement during a DLOFC transient. This confirms that the faster thermal resistance method produces solutions that are equivalent to the net radiation method for this geometry. Deliverable 3d: we demonstrated the use of the advection kernel for the delayed neutron precursor equation in Griffin with a 2D MSFR model. The results appear physical but further verification is recommended. We also recommend the addition of conjugate heat transfer to compute the temperatures and model the thermomechanic behavior of the reflectors and other structures. Significant memory and performance issues were encountered in the 3D axisymmetric model. Future work is recommended in this area. Task 8g: this task allows multidimensional MOOSE applications to be coupled to system codes (RELAP-7 and SAM). We implemented a faster multiphysics iteration coupling algorithm, which provides an overall 6× acceleration of the 3D-1D coupling of the core multidi- mensional fluid flow solver and the 1D primary and secondary loop model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NRC Multiphysics Analysis Capability Deployment FY2020: Part 3

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Sup- port for Advanced Non-Light Water Reactors.” The tasks completed for this report are: Task2c: Explicit modeling of pebble transient temperature response. In this simulation, the 400 MWth Pebble-Bed Modular Reactor (PBMR) design, PBMR- 400, experiences a 20-second power ramp from 100% to 150% power. This is followed by a similar reduction in the power back to 100%. Several multiscale pebble coupling approaches are tested with one pebble per mesh element in the active core region. The results show good conservation behavior and the stability of the coupling.; Extended scope part 1: An assessment of the computational efficiency of the Discontinuous Finite Element Method (DFEM) heat transfer solver shows good scalability. The DFEM solver is a factor of 4 more expensive in solution time than the Finite Element Method (FEM) solver for heat transfer problems due to the increased number of degrees of freedom. Nonetheless, the DFEM approach provides the user with the flexibility to model gap heat transfer problems.; Extended scope part 2: The GapHeatTransferInterfaceMaterial was improved to give the user increased flexibility with the modeling of heat transfer through gaps with the DFEM solver. A number of gap parameters can now be coupled both through functions and variables.; Extended scope part 3: Demonstration of how the gap width between hexagonal fuel cells can be calculated during a heat-up transient and used in the GapHeatTransferInterface model. A full-domain DFEM model with gap expansion is coupled to a SubApp that models the thermal expansion of the base plate. The results show the expected physical behavior, although have not been fully bench-marked at this point in time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗