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Insights into Methodologies and Stochastic Optimization of Thermal Energy Storage-Coupled Advanced Reactor Systems: A Comparison of Methods for Accessing Long-Term Sub-System Sizing Adequacy

This paper investigates the potential of coupling Thermal Energy Storage (TES) with Advanced Reactors (ARs) to address uncertainties posed by climate change in deep decarbonized power systems. The TES Use-case Team at Idaho National Laboratory (INL) has examined the potential of storing thermal energy from ARs during low demand periods and optimizing discharge during peak-priced hours, in both steady-state and transient conditions. Building on this groundwork, this study bridges the gaps in optimal sizing of the sub-system of TES-coupled AR systems using Risk Analysis Virtual Environment (RAVEN) and Holistic Energy Resource Optimization Network (HERON), INL?s framework for grid optimization. By applying this framework, we present statistically-robust optimal charge, discharge including balance of plant (BOP), and storage sizing for the High-Temperature Gas-Cooled Reactor (HTGR) with 203 MWth output. To this end, we generated synthetic price samples for 30 years using 2018 ? 2021 real-time market data from ERCOT, PJM and MISO. Our results reveals that the TES-coupled HTGR system is highly effective in maximizing revenue from electricity sales. We observed a substantial increase of 40 % in ERCOT and a noteworthy 15 % increase in PJM and MISO when compared to the conventional BOP without TES. This improvement is achieved through regionally-tailored sub-system sizing, which ranges from 398 to 416 MWth for the discharge system and 610 to 1029 MWth for the TES. We find that the average electricity price directly impacts the overall economics, while price volatility influences storage size. Additional sensitivity analyses were performed to access the impact of key assumptions on system economics and sizing, differentiating the optimization window (i.e., 24 ? 219 hours of chronological observations) and by imposing storage continuity condition in tracking TES cycles. We observed that at the 120-hour of the optimization window, a reasonable balance between computation time and accuracy was achieved. Our analysis also highlights the significance of conducting multi-day cycle analysis (> 120-hour) for TES to capture interaction between electricity prices and storage dynamics, providing a comprehensive understanding of TES behavior that AR developers should integrate into their plant designs.

25 ENERGY STORAGE↗

Dynamic Monte Carlo Transient Analysis with Thermal-Hydraulic Feedback by McCARD/CUPID

The reactor core transient analysis requires neutronics calculations with the thermal-hydraulic (TH) feedback. Recently the dynamic Monte Carlo (DMC) neutron transport algorithm controlling delayed neutron precursors was developed and successfully applied for core transient problems with help of a sub-channel code. In the Seoul National University Monte Carlo (MC) code, McCARD, a DMC scheme for the core transient analysis has been implemented by coupling with a computational fluid dynamics code, CUPID using the TCP/IP socket communication. In the McCARD/CUPID transient calculations, temperature-dependent cross sections are produced by a built-in on-the-fly Doppler broadening (OTF DB) module. This paper presents McCARD/CUPID transient analysis results for a triangular unit cell problem in the IAEA coordinated research project (CRP) benchmark on the high temperature gas cooled reactor (HTGR) uncertainty analysis. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of the spatial self-shielding impact for TRISO-based nuclear fuel depletion

Reactor physics analyses of nuclear cores with nuclear fuel concepts containing tristructural isotropic (TRISO) particles, such as pebbles or compact fuel elements, rely on various degrees of simplification to keep these highly heterogeneous problems computationally tractable. One such limitation regards the level of spatial discretization employed during burnup calculations, where traditionally only a limited number of spatial zones are modeled at the full core level and assume that the spectrum is constant within the fuel elements and TRISO particles in this depletion zone. This type of assumption neglects the impact of spatial self-shielding effect within the kernels (microscale level) as well as within the compact or pebbles (mesoscale level). Furthermore, the Monte Carlo code Serpent 2 contains many relevant features for efficiently modeling this type of geometry, including a collision-based domain decomposition intended for very large burnup calculations, which we leveraged for this work to quantify the impact of capturing neutron flux variations occurring at the micro- and mesoscale level on a series of high-temperature gas-cooled reactor fuel element depletion problems. While spatial self-shielding is observed at both scales, with differences from a volume-averaged burnup of ±7% within the kernels and ±2% between TRISO particles within the fuel element, the conjugated effect on nuclide inventories and multiplication factor are negligible, hence confirming that assuming a single average spectrum value may be sufficient for most applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Machine learning from RANS and LES to inform coarse grid simulations

Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. In conclusion, the performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Microwave-induced selective decomposition of cellulose: Computational and experimental mechanistic study

Understanding microwave-material interactions will help facilitate the utilization of microwave technology in gasification and renewable energy production. In this study, cellulose was used as a model compound to simulate the organic matter in biomass, and its catalytic decomposition under a microwave (MW) field was studied to identify structural changes from the reaction. The study was conducted using a MW source coupled to a fixed-bed gas-flow reactor, mass spectroscopic, and Fourier transform infrared spectroscopy post-reaction analysis. Zeolite 13X was chosen as a microwave absorber to study the catalytic enhancement of the decomposition of cellulose. Density functional theory (DFT) was used to gain insights into the molecular transformations occurring in the presence of a static electric field, which was used to simulate the electric field component of the microwave electromagnetic radiation. Theoretical calculations demonstrated that both the positive and negative portion of the electric field interact with the permanent dipoles of the cellulose effecting the decomposition through the glycosidic bond breaking mechanism. The theoretical result was verified using infrared spectroscopic analysis of the pure cellulose during microwave heating. The theoretical calculations suggest only the positive electric field component may be active for the cellulose decomposition in the presence of Zeolite 13X. Physically mixing Zeolite 13X with the cellulose led to a significant enhancement in the decomposition rate of the glycosidic bond. Zeolite 13X enhanced the glycosidic O-C decomposition at lower MW power (lower temperatures), whereas the O-H functional group required higher MW power (higher temperature) for its decomposition. The DFT study coupled with the reaction studies revealed that the electric field polarizability is dependent upon both the direction and the orientation of the cellulose. Gas products revealed that applying 250 W of MW power led to the production of CO, H 2 , along with some CO 2 , CH 4 , and benzene at 305 °C. Finally, reaction under 500, 750, and 1000 W of power at constant temperature (305 °C) revealed that higher power led to the complete decomposition of cellulose to mostly CO, H 2 , and CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Steam Gasification Rates of Three Bituminous Coal Chars in an Entrained-Flow Reactor at Pressurized Conditions

Three bituminous coal chars (Illinois #6, Utah Skyline, and Pittsburgh #8) were gasified separately at total pressures of 10 and 15 atm in an entrained-flow reactor using gas temperatures up to 1830 K and particle residence times <240 ms. The experiments were performed at conditions where the majority of particle mass release was due to H 2 O gasification, although select experiments were performed at conditions where significant mass release was due to gasification by both H 2 O and CO 2 . The measured coal data we recorded were fit to three char gasification models including a simple first-order global model, as well as the CCK N and CCK models that stem from the CBK model. The optimal kinetic parameters for each of the three models are reported, and the steam reactivity of the coal chars at the studied conditions is as follows: Pittsburgh #8 > Utah Skyline > Illinois #6.

01 COAL, LIGNITE, AND PEAT↗

Pronghorn

Pronghorn is designed as a multi-dimensional coarse-mesh conjugate heat transfer simulator (tightly coupled fluid and solid phase heat transfer) for nuclear reactor core applications. Pronghorn’s design philosophy of is that: 1. The tool will be agnostic of reactor concept, including VHTRs, SFRs, FHRs, and LWRs. 2. Must be higher fidelity than traditional nuclear systems/safety analysis (0D-1D). 3. Avoid lower-length scale phenomena, such as boundary layer theory, i.e., rely on closure relations. 4. Apply mixture theory (homogenization) wherever possible. 5. Conserve mass and energy (solve all physics on single mesh). 6. Must be easily coupled to both MOOSE-based and external physics applications. 7. Does not require a super computer. Thus, Pronghorn’s algorithmic philosophy is to resolve large scale flow features and model lower-length scale phenomena, such as boundary layers. The coarse mesh approach for lower-length scale modeling is to develop a multi-component multi-phase homogenization of solid and liquid phases into a mixture formulation inside a finite element. For example, a pebble bed core is represented as a two-phase mixture of coolant and fuel pebbles, where the fuel phase is stationary. Thus, the solid phase exerts a drag force on the fluid phase, composed of form and viscous drag, and both phases exchange internal energy through conduction and convective heat transfer. For Pronghorn, the volume fraction of fluid can vary in space, but not in time. Pronghorn has been validated against the VHTR PBMR400 benchmark problems, used for rod ejection simulations have been conducted for thermal-fluids/neutronics for both pebble-bed and prismatic gas-cooled reactors and simple thermal-neutronics coupled LWR benchmark problems. Pronghorn flow models cover a wide range of transient and steady flow conditions, including, porous fluid flow, compressible flow, and nearly incompressible, thermally expansive flow. The physics can be solved in three-dimensional Cartesian coordinates and two-dimensional cylindrical (r-z) coordinates.

Martineau, RichardC.↗

Examining Graphite Degradation in Molten Salt Environments: A Chemical, Physical, and Material Analysis

Molten-salt reactors (MSRs) are Generation IV nuclear reactors that use liquid salt as a coolant and/or fuel. In several MSR designs, graphite serves as a moderator and/or reflector. However, due to limited experimental data and operational experience, our understanding of graphite behavior in molten salt environments remains incomplete. This report aims to identify the degradation mechanisms of nuclear graphite in MSRs, detail the mechanisms of each factor, and provide an initial assessment of their impact on the structural integrity of graphite components. This assessment is based on an extensive literature review and insights from subject matter experts. Furthermore, given the limited data, a modeling strategy using existing Grizzly software is proposed for a more thorough analysis where appropriate. Additionally, it presents mitigation strategies where applicable. The report covers physical degradation mechanisms such as infiltration, erosion, and abrasion, as well as chemical degradation mechanisms including fluorination, intercalation, corrosion, and oxidation. Molten salt can infiltrate the porous structure of graphite, leading to several detrimental effects. Entrapment of fissile products within the graphite pores can cause radiation damage and could pose challenges in the handling and disposal of contaminated components. The differential thermal expansion between the infiltrated salt and graphite, along with internal stress from pressurized molten salt and volumetric heating, can compromise the structural integrity of graphite. To mitigate these effects, employing ultra-fine graphite grades and applying sealants and coatings are effective strategies. A computational model based on coupled solid mechanics and heat transfer phenomena could be used to predict the internal stresses using Grizzly software. In pebble-bed MSRs, graphite fuel pebbles can cause abrasion against reactor components due to friction and wear. The severity of wear is influenced by various factors such as temperature, environment, and the presence of lubricants. Tribological studies reveal that higher temperatures and molten salt environments, such as FLiBe, significantly reduce wear rates compared to dry conditions. Additionally, the chemical composition of the salt can further optimize graphite's tribological performance. Long-term wear effects can be modeled by incorporating surface defects into the geometry and predict stresses under thermal and radiation effects using Grizzly software. Chemical degradation of graphite in a molten salt environment can occur through fluorination and intercalation. Fluorination can occur via replacement of hydrogen or oxygen atoms, or at the active sites, but does not cause structural degradation. Intercalation, on the other hand, can lead to exfoliation, where layers of graphite separate and peel away, damaging the graphite. Protective coatings can enhance graphite's resistance to intercalation. Graphite generally exhibits good chemical stability in molten salt environments, though it can corrode under specific conditions, particularly in the presence of impurities or oxidants. Studies have shown that protective coatings, such as plasma-sprayed partially stabilized zirconia (PSZ), can effectively prevent such degradation. Corrosion behavior varies significantly with different graphite grades and coating applications, underscoring the need for detailed studies on uncoated and coated graphite to understand and mitigate corrosion mechanisms in MSRs. Research indicates that the presence of oxidants and impurities can accelerate graphite degradation in molten salts, making it essential to explore acceptable impurity limits. Oxidation is another critical degradation mechanism, leading to weight loss and structural damage due to the formation of CO and CO 2 from the reaction of carbon atoms with oxygen. This process creates new porosity and compromises graphite's integrity. While extensive research on graphite oxidation has been conducted for gas-cooled reactors, studies specific to MSRs are limited. Findings from the coal industry suggest that molten alkali metal salts can significantly accelerate graphite oxidation, a hypothesis worth exploring for fluoride salts in MSRs. Understanding oxidation behavior in MSRs is vital for developing protective measures. The analysis of post-irradiated graphite from the MSRE experiment demonstrated exceptional chemical compatibility with molten fluoride salt, suggesting that the extent of chemical attack on graphite largely depends on the salt's infiltration capability. Therefore, the use of ultra-fine grade graphite could help mitigate chemical degradation effects. Existing oxidation modeling capabilities in Grizzly, which use reaction-diffusion equations to model graphite-air interactions, could be adapted to simulate the chemical degradation effects of graphite in molten salt environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Validation of the Fast and Thermal Neutron Flux Profiles in the Advanced Test Reactor for the AGR-3/4 Experiment

The AGR-3/4 experiment was designed to irradiate TRISO particle fuel in the Advanced Test Reactor (ATR) at the Idaho National Laboratory. Temperature control of the test capsules containing the TRISO particles was important since the goal was to measure diffusion rates of fission product elements through graphite as a function of temperature. During the experiment, differences were observed between temperatures measured by the thermocouples and temperatures calculated with the thermal analysis model. To rule out the possibility that the used ATR driver fuel elements were the root cause of these temperature differences, an experiment was devised to measure the axial fast and thermal neutron flux profiles in the northeast flux trap containing the AGR-3/4 experiment. An important input parameter to the thermal analysis model was the calculated compact heat rates from the MCNP physics model. To verify these calculated heat rates were consistent with the ATR driver fuel element loading and operating lobe power, axial flux wires were inserted into ATR northeast flux trap. The measured fast and thermal neutron axial flux profiles derived from the flux wire activation showed excellent agreement with the calculated flux profiles. This agreement dispelled any concerns that the used ATR fuel elements in the northeast lobe might have introduced unusual axial flux variation. In addition, the agreement provided a validation basis for the physics calculation, specifically, (1) MCNP physics model, (2) Monte Carlo depletion methodology, (3) method used to load the ATR driver fuel, and (4) ATR measured lobe power data used in the calculation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Micromechanical response of SiC-OPyC layers in TRISO fuel particles

Tristructural isotropic (TRISO)–coated particle fuel is a proposed fuel for multiple advanced reactor concepts. The performance of the particle depends on whether the silicon carbide (SiC) layer remains intact to prevent the release of metallic and gaseous fission products. Mechanical fracture of the SiC layer is a potential failure mode under various fuel configurations and operating environments, including the potential transmission of matrix-originating cracks through TRISO particles. Furthermore, this study uses instrumented indentation techniques on cross-sectioned surrogate particles to examine the mechanical stability of the critical interface between SiC and the outer pyrolytic carbon (OPyC) layer. The observed behavior at the interface is rationalized by examining the radially dependent fracture behavior of the SiC layer and performing a numerical analysis to quantify the residual stresses that develop during the processing and cross-sectioning of the as-fabricated particle. Characterizing the SiC-OPyC interface of surrogate TRISO particles using nanoindentation provides unique insight into the interface's room-temperature residual stress and mechanical stability. The modeling efforts were used to investigate the experimental procedure further, and the results are presented herein to validate this fuel form's potential mechanical failure modes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Molten Salt Reactor Engineering Study for Off-Gas Management

In previous work published by the current team, the waste processing and waste form options were summarized for molten salt reactors (MSR) (Riley et al., 2018b; Riley et al., 2019). The primary types of waste from an MSR are summarized in Figure S1 and include (1) off-gas streams, (2) salt waste streams, (3) separated salt streams, (4) metal waste streams, (5) carbon waste streams, (6) decommissioning and decontaminating (D&D) waste streams, and (7) operating waste streams, or those that are generated from maintenance procedures. The primary focus of this report will be on management of the off-gas stream as it represents the pressure boundary for fuel-salt MSRs and, thus, is required for fission product confinement during reactor operation and reduction of the source term during a reactor accident.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Determining the minimum required uranium carbide content for HTGR UCO fuel kernels

There are three important failure mechanisms that must be controlled in high-temperature gas-cooled reactor (HTGR) fuel for certain higher burnup applications are SiC layer rupture, SiC corrosion by CO, and coating compromise from kernel migration. All are related to high CO pressures stemming from free O generated when uranium present as UO 2 fissions and the O is not subsequently bound by other elements. Furthermore, in the HTGR UCO kernel design, CO buildup from excess O is controlled by the inclusion of additional uranium in the form of a carbide, UC x . An approach for determining the minimum UC x content to ensure negligible CO formation was developed and demonstrated using CALPHAD models and the Serpent 2 reactor physics and depletion analysis tool. Our results are intended to be more accurate than previous estimates by including more nuclear and chemical factors, in particular the effect of transmutation products on the oxygen distribution as the fuel kernel composition evolves with burnup.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Numerical study of air ingress transition to natural circulation in a high temperature helium loop

Here, the generation-IV high temperature gas cooled reactors (HTGRs) are designed with many passive safety features, one of which is the ability to passively remove heat under a loss of coolant accident (LOCA). However, several common reactor designs do not prevent against a large break in the coolant system and may therefore experience a depressurized LOCA. This would lead to air entering into the reactor system via several potential modes of ingress: diffusion, gravity currents, and natural circulation. At the onset of a LOCA, the initial rate of air ingress is expected to be very slow because it is governed by molecular diffusion. However, after several hours, natural circulation would commence, thus, bringing the air into the reactor system at a much higher rate. As a consequence, air ingress would cause the high temperature graphite matrix to oxidize, leading to its thermal degradation and decreased passive heat (decay) removal capability. Therefore, it is essential to understand the transition of air ingress from molecular diffusion to natural circulation in an HTGR system. This paper presents results from a computational fluid dynamics (CFD) model to study the air ingress transition behavior. These results are validated against an h-shaped high temperature helium loop experiment. Details are provided to quantitatively predict the transition time from molecular diffusion to natural circulation.

42 ENGINEERING↗

In-situ microstructure observation of oxidized SiC layer in surrogate TRISO fuel particles under krypton ion irradiation

In accidental scenarios of high temperature gas-cooled reactors, both oxidation of and irradiation to the SiC layer in tri-structural-isotropic (TRISO) fuel particles can change the microstructure and integrity of the fuel elements. Here, in the present study, microstructure and defect evolution in the oxidized SiC layer of surrogate TRISO fuel particles under 1.2 MeV krypton ion irradiation was observed by in-situ transmission electron microscopy. The SiC layers oxidized in water vapor at 1200 °C were irradiated azt room temperature and 800 °C and at damage levels of 0.28–11.2 dpa, respectively. SiC and SiO 2 were found to still be in their crystal structures at the damage level of 11.2 dpa at 800 °C, while SiC was observed to have been amorphized at only 0.56 dpa irradiation at room temperature. The defect number density at 800 °C was an order of magnitude lower than that in the sample irradiated at room temperature. Also, crystalline SiO 2 had higher radiation resistance compared to SiC. A defect reaction rate theory was utilized to understand the fundamental defect evolution process and irradiation resistance difference.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

In-situ TEM study of Kr ion irradiation tolerance of SiFeOC nanocomposite

Here, in this work, ion irradiation of polymer derived SiFeOC nanocomposite was carried out using 1.2 MeV Kr ions at room temperature and 600°C. The starting composite was composed of Fe 3 Si, SiC, SiOC, SiO 2 , and graphitic C. In-situ TEM investigations show uniform distribution of nano-crystalline Fe 3 Si and SiC phases in the amorphous SiOC matrix. During ion irradiation, the SiOC bulk microstructure and interfaces between Fe 3 Si or SiC crystallites and the SiOC matrix remain defect-free and demonstrate outstanding ion irradiation resistance. At room temperature, the crystalline domains are stable up to 2 dpa. At 600°C, Fe 3 Si crystallites are more stable than SiC; SiC crystallites are stable up to 4 dpa while the Fe 3 Si crystallites are stable up to 10 dpa. These crystallites also coalescence and amorphize simultaneously during ion irradiation. The exceptional tolerance to defect formation and irradiation of the SiFeOC nanocomposite provides important guidance to developing irradiation resistant fuels for advanced gas cooled reactors.

36 MATERIALS SCIENCE↗