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Pathway To Low-Carbon Lignite Utilization; U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL) Cooperative Agreement No. DE-FE0024233

Utilities continue to investigate ways to decrease their carbon footprint. Carbon capture and storage (CCS) can enable existing power generation facilities to maintain operations and address carbon reduction. Subtask 2.1 – Pathway to Low-Carbon Lignite Utilization focused on several research areas in an effort to find ways to decrease the cost of capture across both precombustion and postcombustion platforms. Two postcombustion capture solvents were tested, one from CO 2 Solutions Inc. and one from ARCTECH, Inc. The CO 2 Solutions solvent had been evaluated previously, and the company had incorporated the concept of a rotating packed bed (RPB) to replace the traditional packed columns typically used. In the limited testing performed at the Energy & Environmental Research Center (EERC), no CO 2 reduction benefit was seen from the RPB; however, if the technology could be scaled up, it may introduce some savings in capital expense and overall system footprint. Rudimentary tests were conducted with the ARCTECH solvent to evaluate if it could be utilized in a spray tower configuration contactor and capture CO 2 , SO 2 , and NO x . This solvent after loading can be processed to make an additional product to filter wastewater, providing a second-tier usable product. Modeling of the RPB process for scaling to a 550-MW power system was also conducted. The reduced cost of RPB systems combined with a smaller footprint highlight the potential for reducing the cost of capturing CO 2 ; however, more extensive testing is needed to truly evaluate their potential for use at full scale. Hydrogen separation membranes from Commonwealth Scientific and Industrial Research Organisation (CSIRO) were evaluated through precombustion testing. These had also been previously tested and were improved by CSIRO for this test campaign. They are composed of vanadium alloy, which is less expensive than the palladium alloys that are typically used. Their performance was good, and they may be good candidates for medium-pressure gasifiers, but much more scale-up work is needed. Next-generation power cycles are currently being developed and show promise for high efficiency, and the utilization of supercritical CO 2 to drive a turbine could significantly increase cycle efficiency over traditional steam cycles. The EERC evaluated pressurized oxy-combustion technology from the standpoint of CO 2 purification. If impurities can be removed, the costs for CO 2 capture can be lowered significantly over postcombustion capture systems. Impurity removal consisted of a simple water scrubber referred to as the DeSNO x process. The process worked well, but corrosion management is crucial to its success. A model of this process was constructed. Finally, an integrated gasification combined-cycle (IGCC) system model, developed by the Massachusetts Institute of Technology (MIT), was modified to allow for the modeling of membrane systems in the IGCC process. This modified model was used to provide an assessment of the costs of membrane use at full scale. An economic estimation indicated a 14% reduction in cost for CO 2 separation over the SELEXOL™ process. This subtask was funded through the EERC–DOE Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal sponsors for this project were the North Dakota Industrial Commission, Basin Electric Power Cooperative, and Allete, Inc. (including BNI Coal and Minnesota Power).

24 POWER TRANSMISSION AND DISTRIBUTION↗

Technical Note: Dosimetric effects of couch position variability on treatment plan quality with an MRI-guided Co-60 radiation therapy machine

Purpose: Magnetic resonance imaging (MRI) guidance in radiation therapy brings real-time imaging and adaptive planning into the treatment vault where it can account for interfraction and intrafraction movement of soft tissue. The only commercially available MRI-guided radiation therapy device is a three-head {sup 60}Co and MRI system with an integrated treatment planning system (TPS). Couch attenuation of the beam of up to 20% is well modeled in the TPS. Variations in the patient’s day-to-day position introduce discrepancies in the actual couch attenuation as modeled in the treatment plan. For this reason, the authors’ institution avoids plans with beams that pass through or near the couch edges. This study investigates the effects of differential beam attenuation by the couch due to couch shifts in order to determine whether couch edge avoidance restrictions can be lifted. Couch shifts were simulated using a Monte Carlo treatment planning system and ion chamber measurements performed for validation. Methods: A total of 27 plans from 23 patients were investigated. Couch shifts of 1 and 2 cm were introduced in combinations of lateral and vertical directions to simulate patient position variations giving 16 shifted plans per reference plan. The 1 and 2 cm shifts were based on shifts recorded in 320 treatment fractions. Results: Following TG176 recommendations for measurement methods, couch attenuation measurements agreed with TPS modeled attenuation to within 2.1%. Planning target volume D95 changed less than 1% for 1 and 2 cm couch shifts in only the x-direction and less than 3% for all directions. Conclusions: Dosimetry of all plans tested was robust to couch shifts up to ±2 cm. In general, couch shifts resulted in clinically insignificant dosimetric deviations. It is conceivable that in certain cases with large systematic couch shifts and plans that are particularly sensitive to shifts, dosimetric changes might rise to a clinically significant level.

60 APPLIED LIFE SCIENCES↗

A Large Ensemble Global Dataset for Climate Impact Assessments

We present a self-consistent, large ensemble, high-resolution global dataset of long-term future climate, which accounts for the uncertainty in climate system response to anthropogenic emissions of greenhouse gases and in geographical patterns of climate change. The dataset is developed by applying an integrated spatial disaggregation (SD) - bias-correction (BC) method to climate projections from the MIT Integrated Global System Model (IGSM). Four emission scenarios are considered that represent energy and environmental policies and commitments of potential future pathways, namely, Reference, Paris Forever, Paris 2 °C and Paris 1.5 °C. The dataset contains nine key meteorological variables on a monthly scale from 2021 to 2100 at a spatial resolution of 0.5°x 0.5°, including precipitation, air temperature (mean, minimum and maximum), near-surface wind speed, shortwave and longwave radiation, specific humidity, and relative humidity. We demonstrate the dataset’s ability to represent climate-change responses across various regions of the globe. This dataset can be used to support regional-scale climate-related impact assessments of risk across different applications that include hydropower, water resources, ecosystem, agriculture, and sustainable development.

54 ENVIRONMENTAL SCIENCES↗

Giant increase of critical current density and vortex pinning in Mn doped K{sub x}Fe{sub 2−y}Se{sub 2} single crystals

We report a comparative study of the critical current density (J{sub c}) and vortex pinning among pure and Mn doped K{sub x}Fe{sub 2−y}Se{sub 2} single crystals. It is found that the J{sub c} values can be greatly improved by Mn doping and post-quenching treatment when comparing to pristine pure sample. In contrast to pure samples, an anomalous second magnetization peak (SMP) effect is observed in both 1% and 2% Mn doped samples at T = 3 K for H∥ab but not for H∥c. Referring to Dew-Hughes and Kramer's model, we performed scaling analyses of the vortex pinning force density vs magnetic field in 1% Mn doped and quenched pristine crystals. The results show that the normal point defects are the dominant pinning sources, which probably originate from the variations of intercalated K atoms. We propose that the large nonsuperconducting K-Mn-Se inclusions may contribute to the partial normal surface pinning and give rise to the anomalous SMP effect for H∥ab in Mn doped crystals. These results may facilitate further understanding of the superconductivity and vortex pinning in intercalated iron-selenides superconductors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Risks to Ecological Receptors Posed by Contaminants of Potential Concern in the Lower Three Runs Cooling Ponds and Canals

The upper portion of Lower Three Runs includes several ponds, reservoirs, and canals that were formerly used as a cooling system for nuclear production reactors. This area was divided into nine exposure areas (EAs) for the assessment of environmental contamination resulting from past reactor operations and other industrial processes. A tiered screening process identified several contaminants of potential concern including aluminum, cyanide, lead, manganese, mercury, DDD, DDE, and DDT. Risks posed by these contaminants to ecological receptors (river otter, belted kingfisher, raccoon, and blue heron) were assessed using contaminant exposure models that estimated contaminant intake resulting from ingestion of food, water, and sediment/ soil and compared these intakes with toxicity reference values (TRVs). The contaminant exposure models showed that the TRVs were not exceeded in the otter model, exceeded by aluminum in EA 7 (Pond 2 and associated canals) in the raccoon model, and exceeded by mercury in EAs 2, 3 (Pond B), 6 (Par Pond), and 8 (Ponds 4 and 5 and Canal to Pond C) in both the kingfisher and blue heron models. Hazard quotients (total exposure dose divided by the TRV) were 2.8 for aluminum and 1.7- 3.6 for mercury. The primary route of exposure for aluminum was the ingestion of soil, and the primary route of exposure for mercury was the ingestion of mercury contaminated fish. Elevated levels of mercury in fish were at least partly the result of the aerial deposition of mercury onto Lower Three Runs and its watershed. The atmospheric deposition of mercury creates pervasive contamination in fish throughout the Savannah River basin. Another possible source of mercury was the discharge of mercury contaminated Savannah River water into the Lower Three Runs cooling ponds and canals during previous years of reactor operation. This contamination originated from industries located upstream of the SRS. The aluminum exceedance for the raccoon was likely the result of naturally high aluminum levels in SRS soils rather than SRS operations. Aluminum exceedances have previously been observed in relatively undisturbed background locations as well as areas affected by SRS operations. Aluminum exceedances are more likely with the raccoon than the other receptors because it consumes more soil as a result of its feeding habits. Sensitivity analysis showed that model uncertainty can be reduced by adequate sampling of key variables (e.g., fish and sediments). Although sediment samples were collected from all EAs, fish samples were not collected from three EAs and some analytes (pesticides and cyanide) were not measured in fish. Water-to-fish concentration ratios were used to estimate contaminant levels in fish when direct measurements from fish were unavailable; however, such estimates are potentially less accurate than direct measurements.

54 ENVIRONMENTAL SCIENCES↗

Assessment of Pump Coastdown and Reactor Protection Scram Delays during Station Blackout Conditions

This report presents an assessment of the impact of pump coastdown time and reactor protection scram delays for the Versatile Test Reactor (VTR) during Protected Station Blackout (PSBO) conditions. While previous simulations for the VTR assumed centrifugal pumps in the primary system, the current pre-conceptual design uses electromagnetic (EM) pumps. Because there is uncertainty as to what the parameters of the EM pump design will be, this report focuses on the impact of the flow coastdown and the reactor protection scram delay, not on the needs of the pump design. PSBO transient simulations were performed using the SAS4A/SASSYS-1 fast reactor safety analysis code (version 5.2.3). The model used in the simulations is based on the FY18 SAS4A/SASSYS-1 model. A change to the model was made to replace the centrifugal pump model with an electromagnetic pump model with a motor generator as a coastdown mechanism. The results of the PSBO transient simulations were assessed against the criteria used in Reference 2 with an additional 50°C for conservatism to account for uncertainties. The results show that as the delay before scramming the rods increases, the moment of inertia of the coastdown mechanism must increase to satisfy the criteria. By increasing the moment of inertia to extend the flow coastdown, temperatures can be kept below the desired limits with reactor protection scram delays between 3 and 10 seconds.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

3D spherical functional expansion tallies in Serpent 2 Monte Carlo code

This work extends the application of functional expansion tallies to 3D spherical geometries. The 3D Zernike polynomials are set as an orthonormal polynomials basis for the functional reconstruction. The study describes the construction of the complete set of polynomials, a natural expansion of the spherical harmonics polynomials where 3D Zernike moments can be evaluated as a linear combination of the geometrical moments. The 3D Zernike polynomials formulation and the computational approach implemented in Serpent 2 are presented and tested through the Godiva model from the ICSBEP criticality benchmark test cases. The implementation results are in agreement with a reference solution described in a fine-resolution mesh, enhancing also the performance and memory demand. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Conservation Voltage Reduction (CVR) via Two-Timescale Control in Unbalanced Power Distribution Systems

Voltage control devices are employed in power distribution systems to reduce the power consumption by operating the system closer to the lower acceptable voltage limits; this technique is called conservation voltage reduction (CVR). The different modes of operation for system’s legacy devices (with binary control) and new devices (e.g. smart inverters with continuous control) coupled with variable photovoltaic (PV) generation results in voltage fluctuations which makes it challenging to achieve CVR objective. This paper presents a two-timescale control of feeder’s voltage control devices to achieve CVR that includes (1)a centralized controller operating in a slower time-scale to coordinate voltage control devices across the feeder and (2) local controllers operating in a faster timescale to mitigate voltage fluctuations due to PV variability. The centralized controller utilizes a three-phase optimal power flow model to obtain the decision variables for both legacy devices and smart inverters. The local controllers operate smart inverters to minimize voltage fluctuations and restore nodal voltages to their reference values by adjusting the reactive power support. The proposed approach is validated using the IEEE-123 bus (medium-size) and R3-12.47-2 (large-size) feeders. It is demonstrated that the proposed approach is effective in achieving the CVR objective for unbalanced distribution systems.

optimal control, distributed generation, fluctuati↗

Mechanistic nuclear fuel performance modeling of uranium nitride

Uranium mononitride (UN) is a nuclear fuel candidate for advanced reactor designs and an alternative being considered for light water reactors due to its higher thermal conductivity and uranium density than UO 2 . As with any nuclear fuel, swelling and fission gas release are important factors for safety, while also being some of the hardest phenomena to predict with a high degree of confidence. Getting a grasp on the gas swelling behavior and release is crucial to lower the barrier for UN utilization. An accelerated swelling rate at high temperatures observed experimentally, sometimes referred to as “breakaway swelling,” further complicates the prediction of fuel performance of UN. A mechanistic model has been developed using a multiscale approach to describe the intragranular and intergranular fission gas behavior. Lower-length-scale calculations have been employed to inform models of the gas and self-diffusion behavior, resolution rate, and bubble shape. Leveraging previous work on high burnup UO 2 , two populations of intragranular bubbles are considered; small bulk bubbles and larger bubbles located along dislocations. The dislocation bubbles were found to be crucial to the overall swelling behavior, and the breakaway swelling transition was associated with the transition in the gas atom diffusion mechanism from an irradiation-induced athermal diffusion regime at lower temperatures to an intrinsic thermal equilibrium regime at higher temperatures, accelerating the growth of the dislocation bubbles. Similarly, the threshold for fission gas release was associated with the grain boundary vacancy diffusivity surpassing the gas atom diffusivity at sufficiently high temperatures, allowing the over-pressurized grain boundary bubble to grow in size and interconnect. Using thermo-mechanical models with the fission gas model, two integral fuel pin assessment cases were simulated. Finally, this work demonstrates the ability of a multiscale approach to accelerate the understanding of advanced fuel forms when experimental data is limited.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

On Degeneracies in Retrievals of Exoplanetary Transmission Spectra

Accurate estimations of atmospheric properties of exoplanets from transmission spectra require the understanding of degeneracies between model parameters and observations that can resolve them. We conduct a systematic investigation of such degeneracies using a combination of detailed atmospheric retrievals and a range of model assumptions, focusing on H{sub 2}-rich atmospheres. As a case study, we consider the well-studied hot Jupiter HD 209458 b. We perform extensive retrievals with models ranging from simple isothermal and isobaric atmospheres to those with full pressure–temperature profiles, inhomogeneous cloud/haze coverage, multiple-molecular species, and data in the optical–infrared wavelengths. Our study reveals four key insights. First, we find that a combination of models with minimal assumptions and broadband transmission spectra with current facilities allows precise estimates of chemical abundances. In particular, high-precision optical and infrared spectra, along with models including variable cloud coverage and prominent opacity sources, with Na and K being important in the optical, provide joint constraints on cloud/haze properties and chemical abundances. Second, we show that the degeneracy between planetary radius and its reference pressure is well characterized and has little effect on abundance estimates, contrary to previous claims using semi-analytic models. Third, collision-induced absorption due to H{sub 2}–H{sub 2} and H{sub 2}–He interactions plays a critical role in correctly estimating atmospheric abundances. Finally, our results highlight the inadequacy of simplified semi-analytic models with isobaric assumptions for reliable retrievals of transmission spectra. Transmission spectra obtained with current facilities such as the Hubble Space Telescope and Very Large Telescope can provide strong constraints on atmospheric abundances of exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗

Topology and burning rates of turbulent, lean, H 2 /air flames

Improved understanding of turbulent flames characterized by negative consumption speed-based Markstein lengths is necessary to develop better models for turbulent lean combustion of high hydrogen content fuels. In this paper we investigate the topology and burning rates of turbulent, lean (φ = 0.31), H 2 /air flames obtained from a recently published DNS database (Aspden et al., 2011). We calculate local flame front curvatures, strain rates, thicknesses, and burning velocities and compare these values to reference quantities obtained from stretched laminar flames computed numerically in three model geometrical configurations-a counterflow twin flame, a tubular counterflow flame and an expanding cylindrical flame. We compare and contrast the DNS with these model laminar flame calculations, and show both where they closely correlate with each other, as well as where they do not. These results in the latter case are shown to result from non-flamelet behaviors, unsteady effects, and curvature-strain correlations. These insights are derived from comparisons conditioned on different topological features, such as portions of the flame front with a spherical/cylindrical shape, the leading edge of the flame, and portions of the flame front with low mean curvature. We also show that reference time scales vary appreciably over the flame, and characterizing the relative values of fluid mechanic and kinetic time scales by a single value leads to erroneous conclusions. For example, there is a two order of magnitude decrease in chemical time scales at the leading edge of the front relative to its unstretched value. In conclusion, for this reason, the leading edge of the front quite closely tracks quasi-steady calculations, even in the lowest Damköhler number case, Da F ~0.005

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SU-E-T-665: Radiochromic Film Quenching Effect Reduction for Proton Beam Dosimetry

Purpose: Depending on the useful dose range in which radiochromic films operate, number of different radiochromic film models have been designed. The impact of different film models on quenching effect for percent depth dose (PDD) measurements in proton beams has been investigated. Methods: Calibrated PTW Markus ionization chamber was used to measure PDD and beam output for 26.5 MeV protons produced by CS30 cyclotron. An aluminum cylinder was added in front of the beam exit serving as a radiation shutter. The measured signal was normalized to a monitor chamber reading and subsequently scaled by ratio of water-to-air stopping powers at given depth, while the effective depth of measurements was scaled by ratios of material-to-water physical densities and CSDA ranges. Output was measured in water at 2.1 mm reference-depth in the plateau upstream from the Bragg peak. Following the TRS-398 reference dosimetry protocol for proton beams, the output was calibrated in water. Three radiochromic film models (EBT, EBT3 and HD-V2) were calibrated within Lexan phantom positioned at the same water-equivalent depth. Thicknesses of films sensitive layers were 34 µm, 30 µm and 8 µm, respectively. Small film pieces (1 x 2 cm{sup 2}) were positioned within polyethylene phantom along the beam central axis with an angulation of 5° for PDD measurements. Results: While the output of the proton beam was found to be around 7 Gy/sec, the actual value of the output per monitor chamber reading (2.32 Gy/nC) was used for reference-dose irradiations during film calibration. Dose ratios at the Bragg peak relative to the reference-depth were 3.88, 2.52, 2.19, and 2.02 for the Markus chamber, HD-V2, EBT3, and EBT film models, respectively. Conclusion: Results at hand suggest that quenching effect is reduced when a radiochromic film model with smaller sensitive layer thickness is used for PDD measurements in proton beams. David Lewis is the owner of RCF Consulting, LLC.

07 ISOTOPE AND RADIATION SOURCES↗

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗

Techno-economic assessment of emerging CO 2 electrolysis technologies

Recycling of waste CO 2 to bulk chemicals has a tremendous potential for the decarbonization of the chemical industry. Quantitative analysis of the prospects of this technology is hindered by the lack of flexible techno-economic assessment (TEA) models that enable evaluation of the processing costs under different deployment scenarios. In this protocol, we explain how to convert literature data into metrics useful for evaluation of the emerging electrolysis technologies, derive TEA models, and illustrate their use with a CO 2 -to-ethylene example. For complete details on the use and execution of this protocol, please refer to Barecka et al. (2021a).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Model MC&A for Pebble Bed Reactors (Technical Direction No. 5 Task 2.6 Letter Report)

In preparation for non-light water reactor (non-LWR) activities, US Nuclear Regulatory Commission (NRC) staff are advancing risk-informed and performance-based licensing approaches and addressing key policy issues. One non-LWR reactor concept is a pebble bed reactor (PBR). This reactor design uses spherical fuel elements (pebbles) that are continually added to and removed from the reactor core. The free movement of the fuel in this design presents new challenges for material control and accounting (MC&A) programs. Therefore, an assessment of MC&A program features and measures for a PBR was performed to help NRC staff develop associated MC&A regulations or regulatory guides. The current regulatory framework for non-LWR fuel cycles excludes support for licensing reviews for MC&A programs for PBRs. Licensing reviews of an MC&A program for PBRs can be facilitated by (1) a model MC&A program for a PBR based on identification and assessment of MC&A program features and recommended measures for a reference PBR and (2) a methodology for assessing MC&A performance that can help assess different MC&A program features and measures. This report supports the NRC’s non-LWR Vision and Strategy Near-Term Implementation Action Plans.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FOCAL Campaign I: Advanced Wind Turbine Control Strategies

Campaign I of the Floating Offshore-wind Controls Advanced Laboratory Experimental Program (FOCAL) aims to generate a dataset enabling the validation of aerodynamic performance of a scaled turbine mounted on a rigid tower in a fixed condition. The turbine considered in the FOCAL testing campaigns is the IEA-Wind 15MW Reference Wind Turbine. This scaled model is capable of simulating advanced blade-pitch control strategies in a high-quality wind field. The turbine is fully instrumented to record a variety of parameters in real time such as structural loads and dynamics. The test data considered was generated at the University of Maine's Harold Alfond Wind and Wave (W2) testing facility. The Load Cases (LC) considered in this testing campaign are as follows: LC 1.X - Constant wind and blade-pitch with varying rotor speeds LC 2.X - Constant wind and rotor speed with varying blade-pitch LC 3.X - Varying wind with active closed-loop control Detailed properties on the modeled system are found in the following reference: Lenfest E., Floating Offshore-wind Controls Advanced Laboratory (FOCAL) Experimental Program - Campaign I: 1:70 Model-scale Testing of the IEA-Wind 15MW Reference Turbine. UMaine ASCC Report Number 23-40-1183. Details on the results of the verification and validation are found in the following reference: Mendoza, Nicole et al., "Verification and Validation of Model-Scale Turbine Performance and Control for the IEA Wind 15 MW Reference Wind Turbine," Energies, vol. 15, no. 20, 2022, https://doi.org/10.3390/en15207649.

17 WIND ENERGY↗

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Advanced SAPHIRE 8 Modeling Methods for Probabilistic Risk Assessment via the Systems Analysis Program for Hands-On Integrated Reliability Evaluations (SAPHIRE) Software P-202

1.1. Overview of the Advanced SAPHIRE Material The Advanced SAPHIRE course material is intended to both (1) provide guidance for learning advanced SAPHIRE features during the class and (2) become a stand-alone reference document after finishing the class. Thus, the format for the class material is a combination of the traditional “overhead-type” of presentation information with a structured, reference-type document. Major topics that are covered in the Advanced SAPHIRE class include: Advanced data base concepts such as Model Type (e.g., random, seismic, fire, flood). Definition of house events and how they are used on a sequence-by-sequence basis to manipulate individual fault tree logic using sequence flag sets or fault tree flag sets. ? Basic event templates, compound basic event equation editors, and human error worksheets. A rule-based event tree top event substitution feature (called the Link Event Tree Rule Editor) which allows for top event substitutions. A rule-based cut set post-processing feature (called the Recovery Rules) which allows cut set manipulation. Cut set analysis based upon rule-based end state categories (called End State Analysis). Cut set generation options for both fault trees and event tree sequences. The large event tree methodology and how SAPHIRE can be used to generate sequence cut sets for this method. The transfer of data between SAPHIRE data bases and between other PRA codes (MAR-D).

97 MATHEMATICS AND COMPUTING↗