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Cluster Dynamics Modeling Needs for the Advanced Materials and Manufacturing Technologies Program

This milestone report aims to identify and assess the cluster dynamics (CD) modeling requirements within the Department of Energy's Office of Nuclear Energy (DOE-NE) Advanced Materials and Manufacturing Technologies (AMMT) program and to communicate these needs to the DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The goal is to ensure NEAMS is well-informed about the CD modeling requirements to support AMMT's mission of accelerating the development, qualification, demonstration, and deployment of advanced structural materials and manufacturing for nuclear energy applications. CD modeling is an essential tool for predicting the degradation of structural materials under irradiation, which is a key component of AMMT's accelerated qualification process. The AMMT program focuses on both additively manufactured and wrought structural alloys, such as laser powder-bed fusion 316H austenitic stainless steel, alloy 709, Haynes 244, and alloy 617. These materials require a generalized CD modeling framework to facilitate rapid model development and computational simulation. A flexible, generalized CD software, similar to the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework, would enable modeling of various cluster types, including defect clusters, defect-solute clusters, and multicomponent clusters, incorporating thermodynamics and kinetics parameters. Radiation effects, microstructural feature evolution, and multi-dimensional modeling are critical considerations for the CD model. The usability of the CD code should allow for easy modification and coupling with MOOSE-based simulations. Additionally, the software should adhere to Nuclear Quality Assurance-1 standards, include a testing suite for verification and validation, and be version-controlled within a national laboratory-managed Git repository. Benchmark problems are needed to assess code predictions and performance.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Momentum informed muon scattering tomography for monitoring spent nuclear fuels in dry storage cask

Development of an effective monitoring method for spent nuclear fuel (SNF) in a dry storage cask (DSC) is important to meet the increasing demand for dry storage investigations. The DSC investigation should provide information about the quantity of stored SNF, and quality assurance of materials should be possible without opening the cask. However, traditional nondestructive examination (NDE) methods such as x-rays are difficult to deploy for DSC investigation because a typical DSC is intentionally designed to shield against radiation. To address this challenge, cosmic ray muons (CRMs) are used as an alternative NDE radiation probe because they can easily penetrate an entire DSC system; however, a wide application of muons is often hindered due to the naturally low CRM flux (~10 4 muons/m 2 /min). This paper introduces a newly proposed imaging algorithm, momentum-informed muon scattering tomography (MMST) , and presents how a limitation of the current muon scattering tomography technique has been addressed by measuring muon momentum. To demonstrate its functionality, a commercial DSC with 24 pressurized light water reactor fuel assemblies (FAs) and the MMST system were designed in GEANT4. Three noticeable improvements were observed for MMST system as a DSC investigation tool: (1) a signal stabilization, (2) an enhanced capability to differentiate various materials, and (3) statistically increased precision to identify and locate missing FAs. The results show that MMST improves the investigation accuracy from 79 to 98% when one FA is missing and 51% to 88% when one-half FA is missing. The advancement of the NDE technique using CRM for DSC verification is expected to resolve long-standing problems in increasing demand for DSC inspections and nuclear security.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

North Dakota Integrated Carbon Storage Complex Feasibility Study. Final report

In spring 2017, the Energy & Environmental Research Center (EERC) initiated an effort to determine the feasibility of developing a commercial-scale CO 2 geologic storage complex able to store 50+ million tonnes (Mt) of CO 2 in central North Dakota safely, permanently, and economically. The objective was to fulfill the goals of the U.S. Department of Energy (DOE) Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative and address technical and nontechnical challenges specific to commercial-scale deployment of a CO2 storage project. The findings clearly show that the concept of capturing CO 2 from a lignite-fired electrical generation facility in central North Dakota and safely and permanently storing the CO 2 in the deep subsurface is indeed technically, economically, and socially feasible. This project evaluated two study areas and their respective geologic storage complexes located adjacent to separate coal-fired facilities in North Dakota: the Basin Electric Power Cooperative (BEPC)-owned Great Plains Synfuels Plant (GPSP) and the Minnkota Power Cooperative (Minnkota)-owned Milton R. Young Station (MRYS). These locations, one with CO 2 capture in place and an existing CO 2 pipeline, are bolstered by progressive North Dakota pore space ownership and long-term liability laws. These elements and a motivated team created an ideal synergistic scenario for ensuring success of the CarbonSAFE Initiative and promoting North Dakota’s statewide vision for carbon management. The project included drilling two new geologic characterization wells, integrating an existing 3-D seismic survey, creating a geologic model subsequently used for injection simulation, a risk assessment, public outreach, and generating a site development plan based on results. In addition, the performance of select National Risk Assessment Partnership tools was evaluated. The geologic characterization wells were drilled ~5600 feet deep to the Broom Creek Formation; ~350 feet of core was retrieved from each well. The core included the Broom Creek (targeted injection zone) and a portion of the overlying Opeche Shale (seal). The Flemmer-1 well, west of Beulah, North Dakota, yielded 169 feet of sandstone. The BNI-1 well located south of Center, North Dakota, yielded 124 feet of sandstone. In each case, laboratory analysis of the sandstone showed permeability in the 300–1000-mD range, with porosity of 20%–30%. The Flemmer-1 well was sited within the boundaries of an existing 3-D seismic survey. Colocating the well with the seismic survey maximized the relationship between new and legacy data and developed a first-of-its-kind interpretation of the geologic fabric of the Broom Creek. Geologic characterization data were integrated into a 5544-mi 2 geocellular model that encompassed both new wells and stratigraphy from the surface to the Amsden Formation (underlying the Broom Creek). The model was later expanded vertically to include the deeper Black Island–Deadwood interval to examine its potential viability as a storage target. The geocellular model provided the foundation for dynamic simulation of CO 2 into the Broom Creek. Results of the simulation suggest that the Broom Creek could accept the DOE target rate of 2 Mt/yr of CO 2 into as few as two wells. To bracket the expected capture from MRYS, simulations were also investigated for a 4-Mt/yr rate near MRYS. Although more wells are needed (two additional), the Broom Creek still has the storage resource to accept the CO 2 at the increased rate. A risk assessment exercise was conducted to identify and assess technical and nontechnical risks that could prevent potential candidate storage complexes within the study area from serving as commercial storage sites. The assessment identified and evaluated six technical risk categories: 1) CO 2 injectivity, 2) storage capacity, 3) lateral migration of CO 2 , 4) lateral pressure propagation, 5) vertical migration of CO 2 or formation brine, and 6) induced seismicity. Following two rounds of analysis and scoring, no risks were determined to preclude continued efforts to develop carbon capture, utilization, and storage (CCUS) in central North Dakota. The risk assessment results will be used to guide future site characterization, modeling and simulation, and monitoring activities. A specific nontechnical strategic risk based on challenges that may be realized in amalgamation of pore space resulted in vertically expanding the geologic model to incorporate the potential for stacked storage in multiple saline reservoirs. By including the Black Island–Deadwood interval (the basal sedimentary reservoir in this region), the amalgamated areal extent could be reduced by as much as 45%. Working with a smaller geographic area reduces risks and costs associated with monitoring and pore space leasing. An economic evaluation incorporating capture; transport (<5 mi); Class VI wells; permitting; and monitoring, verification, and accounting suggests implementing commercial-scale CCUS is economically attractive if the federal tax benefits of 45Q are included. This is validated by Minnkota’s continued pursuit of CO 2 capture and geologic storage at MRYS through its Project Tundra initiative, indicating that there is a business case for CCUS in central North Dakota. Currently, North Dakota is the only state with underground injection control (UIC) Class VI primacy. Built into the North Dakota Century Code is a series of regulatory requirements that guide the process to obtain a Class VI CO 2 storage facility permit. As part of this project, a site development plan was compiled to assure compliance with North Dakota’s requirements to permit a commercial-scale CO 2 storage operation and includes a prospective time line encompassing a general breakdown of activities. In total, an estimated 30 months would be needed to execute the necessary steps to attain a North Dakota CO 2 storage facility permit. Outreach was an integral part of the project and encompassed any project-related activity that had contact or exposure beyond the project team. The goals of outreach were to foster an environment from which stakeholders could make informed decisions about the project and gauge community receptiveness to a CCUS project. A consistent set of messages and outreach products were developed in conjunction with an outreach advisory board that integrated project partners and team members. To gauge public acceptability of geologically storing CO 2 , 5611 households in the project area were invited to participate in an online survey. The survey results indicate that the public attitude regarding CCUS is neutral to positive, with strong sentiment that CO 2 capture and storage may be an approach to maintain the economic vitality of the region. To achieve project objectives, critical support in the form of financial backing, engineering evaluations, site access, outreach collaboration, operations data, risk assessment/evaluation, and software access was provided by BEPC, the North Dakota Industrial Commission Lignite Research Council, ALLETE Clean Energy, BNI Energy, North American Coal Corporation, Minnkota, Prairie Public Broadcasting, Computer Modelling Group Ltd., and Schlumberger.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Shorter function summaries for finite state machine-based high consequence systems using logic synthesis and tautologies (Final Report LDRD 24-1302)

Computer programs are often viewed as collections of functions – each function has parameters (inputs) and computes a return value, and each has potential side effects that modify program state (outputs). In this research, a Sandia symbolic execution tool designed to support “human-in-the-loop” analysis was modified to automatically create “function summaries,” and a new tool, “diaboolical,” was created to support enhancing readability of the summary using a novel approach to bit-vector simplification that leverages logic synthesis and tautologies. For this effort, students at Auburn University created several finite state machines (FSMs) to serve as exemplars for high-consequence systems. Function summaries for each of the machines were obtained, and then portions of the summaries were simplified using both diaboolical and the simplification procedure of a popular SMT solver. A comparison of the results shows that diaboolical can often produce smaller function summaries, with expression length improvements over the unsimplified function summaries ranging from 0% to 90% for diaboolical and 0% to 65% for the SMT solver, though diaboolical had a significantly greater cost in time. Diaboolical was evaluated against a collection of “arbitrary” C-code as well as FSM exemplars, and for both datasets it achieved an approximately 10% improvement in expression length compared to simplifications that could be obtained using existing techniques. Function summaries can assist assurance efforts that evaluate existing systems and their executable code. A smaller function summary is likely easier for humans to understand and could thus increase the ability and efficacy of assurance practices centered around the analysis of executable artifacts.

97 MATHEMATICS AND COMPUTING↗

Signal Decomposition for Intrusion Detection in Reliability Assessment in Cyber Resilience (Summary Report)

The complexity of assuring cyber resilience for physical process interactions in connected systems such as energy grids increases dramatically as the coupling between processes becomes more direct and responsive. An example of this growing complexity is provided by Integrated Energy Systems (IES), in which various processes such as nuclear heat generation and commodity production are being directly coupled for increased responsiveness to highly variable signals such as market pricing or electricity demand. As such, the potential attack surface of the coupled processes is larger than the two processes independently. Securing these complex systems requires two-fold monitoring: cybersecure monitoring for potential malicious incursion, and physics monitoring for system tampering. Physics monitoring includes analyzing the behavior of the signals within the system for anomalous behavior. This analysis has been shown to be insufficient if approached by only data-driven machine learning and artificial intelligence (MLAI) techniques or only low-level model comparison. Previous efforts at Purdue University suggested combining high-fidelity models with MLAI algorithms as a basis for a software tool for detecting anomalies in physical processes. This work built on that suggestion, developing an advanced library for signal decomposition and analysis using both MLAI and high-fidelity physics algorithms for greatly improved anomaly detection, especially false data injection. This software can be used as part of a secure imbedded intelligence (SEI) system designed under Consequence-driven Cyber-informed Engineering (CCE) for complex coupled systems. This library established a foundation for online and posteriori analysis of digital signals for the purpose of detecting potential malicious tampering in digital signals representing physical processes. Demonstrations carried out throughout the development highlight the effective use of characterization algorithms to detect signal perturbations, particularly triangle attack-style perturbations, in three wide-ranging applications: seismic monitoring, nuclear thermal hydraulics system simulation, and custom manufacturing.

97 MATHEMATICS AND COMPUTING↗

Climate Influences on Capacity Expansion Planning with Application to the Western U.S

Electric power system planners utilize a variety of planning tools to inform decisions concerning generation and transmission additions to the electric grid, the need for operational changes, and to evaluate potential stressors on the system. Numerous factors contribute to the planning process including projected fuel and technology costs, policy and load profiles. There is also a growing recognition of the interdependency of the electric grid with other natural and engineered systems. Here we explore how future climate change and hydropower operability might influence decisions related to electricity capacity expansion planning and operations. To do so we assemble a multi-model framework. Specifically, water resource modeling is used to simulate climate impacts on future water supply for thermoelectric and hydropower generation. Separately, temperature impacts on electricity load are evaluated. Together, these climate factors spatially constrain a capacity expansion model that projects generation and transmission additions to the grid. The projected new capacity-builds are then evaluated on their operations, reliability, and cost under average and extreme climate conditions using production cost modeling. This coupled framework is demonstrated on the electric grid in the Western U.S., supporting capacity expansion planning by WECC, the North American Electric Reliability Corporation (NERC) regional entity responsible for reliability assurance of the Western Interconnection. This region was selected in part because the West is unique in that it has high potential for renewable penetrations and is experiencing large retirements/displacements of baseload resources, primarily coal, leading to possible operational challenges in terms of changing resource mix and the need for resource flexibility. Toward this challenge, planning scenarios encompass a range of alternative energy, climate and drought futures. In this context we explore answers to two strategic questions: 1) How does changing climate influence electricity expansion planning (generation and transmission) and future operations, including type and capacity of new builds, system reliability, cost and environmental impacts? 2) How does the representation of hydropower in the modeling framework influence the evaluation of bulk power system operations? Results indicate that climate has a measurable influence on recommendations concerning the capacity, type and location of new generation and transmission additions, with up to 17 GW additional capacity needed by 2038 to meet peak loads (~6.6% increase over capacity-builds based on historical climate). The extent of additional infrastructure needs is strongly influenced by future water availability for hydropower and the potential deployment of demand response technologies. Systems designed for future climate conditions were found to maintain high system reliability under a range of electricity and water availability scenarios (including significant drought), with minimal system curtailments. Additional capacity needs due to higher load tend to increase cumulative 20-year investment and operating costs by $\$$5-$\$$17 billion and generation costs increase by 9 to 19%. Finally, changing the representation of hydropower flexibility has a relatively small influence on capacity expansion in the Western Interconnection through 2038, but hydropower flexibility impacts generation costs to a similar extent as climate.

13 HYDRO ENERGY↗

FAST-1.0 Software Acceptance Testing Report

The purpose of this document is to detail the software testing of FAST-1.0 through unit, integration, and assessment tests. More than 400 tests were designed to provide coverage of the requirements for FAST-1.0. These requirements were developed in the NRC Statement of Work (SOW) for NRC Agreement Number NRC-HQ-25-14-D-001 and are transcribed to this document as part of the Software Quality Assurance Plan for the FAST Code System, PNNL-28767. FAST 1.0 represents the merger of the FRAPCON and FRAPTRAN codes and as such FAST-1.0 performs steady state and transient fuel performance calculations described below. FAST-1.0 calculates the steady state response of light-water reactor fuel rods during long-term burnup. The code calculates temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: 1) heat conduction through fuel and cladding to the coolant; 2) cladding elastic and plastic deformation; 3) fuel-cladding mechanical interaction; 4) fission gas release from the fuel and rod internal pressure; and 5) cladding oxidation. FAST is used to perform independent calculations for regulatory evaluations of fuel performance under normal operation and anticipated operational occurrences (AOOs). FAST calculates the temperature and deformation history of a fuel rod as a function of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by FAST include: 1) heat conduction; 2) heat transfer from cladding to coolant; 3) elastic-plastic fuel and cladding deformation; 4) cladding oxidation; 5) fission gas release; and 6) fuel rod gas pressure. FAST code assessment, development and maintenance drive a significant portion of the NRC fuel research activities and the tools are used in a substantial number of regulatory products. Given the centrality of the FAST code to the effectiveness of fuel research, it is critical to assess, develop and maintain this tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Application of Manufacturing Quality Management Principles to PV System Installations

To help SETO/DOE achieve its goals, the IBTS team proposed a project addressing system reliability by improving installation standards and quality management. The proposed approach was designed to help achieve measurable reductions in installation defect density and improvements in the performance of PV systems by optimizing design and installation of residential and commercial PV systems. This approach addressed the soft costs associated with installations and quality management. The project demonstrated improved system reliability and reduced PV system installation costs. The software developed improved operations, decreased risk, and increased the overall value of PV systems across their lifecycle. The project used several data collection methods, including extensive industry surveys, face-to-face high-level interviews at industry conferences, stakeholder teleconferences, and in-depth interviews conducted by IBTS staff. Results from the research found the industry needs a uniform assessment method for national providers to be more efficient; the software should support both code officials and installers; most industry stakeholders would find value in a centralized software system that allows them to collect, report, and review information on in-process and completed solar installations; and mobile solutions that bridge existing knowledge gaps with inspectors and integrate with existing methodologies (such as permitting software) are of great value. The software solution developed is web-based, allowing for national access, and is built on a Google Firebase platform that can handle significant users and data. It can be used onsite or remotely, allowing for code compliance to continue despite ongoing pandemic related delays or shutdowns for local economies. The information provided by the software tool allows users to uniformly assess a system for compliance and use that aggregated data to identify training topics or create internal process designed to improving issues and reducing occurrence. This solution has multiple benefits in managing quality at time of use and promoting an increase in future safety and quality through education. Perhaps most importantly, this software increases public safety by ensuring compliance of installed systems and allows for local AHJs to remotely engage specialized and qualified solar specific expertise for oversite of the installation in their jurisdictions. Data analysis provides the quality feedback loop identifying the root cause of failure and drives installation practices to improve through training and education, resulting in systems with higher performance, greater reliability, and reduced operations and maintenance costs. With the successful completion of this project, the industry can expect reduced soft costs and increased performance and safety and will ultimately benefit from longer performing systems that cost less to operate.

14 SOLAR ENERGY↗

Rapid Evaluation Framework for the CMIP7 Assessment Fast Track

As Earth system models (ESMs) grow in complexity and in volume of output data, there is an increasing need for rapid, comprehensive evaluation of their scientific performance. The upcoming Assessment Fast Track for the Seventh Phase of the Coupled Model Intercomparison Project (CMIP7) will require expeditious response for model analyses designed to inform and drive integrated Earth system assessments. To meet this challenge, the Rapid Evaluation Framework (REF), a community-driven platform for benchmarking and performance assessment of ESMs, was designed and developed. The initial implementation of the REF, constructed to meet the near-term needs of the CMIP7 Assessment Fast Track, builds upon four disparate community evaluation and benchmarking tools that are coupled together using the Coordinated Model Evaluation Capabilities (CMEC) framework. The REF runs within a containerized workflow for portability and reproducibility and is aimed at generating and organizing diagnostics covering a variety of model variables. The REF leverages well documented observational datasets to provide assessments of model fidelity across a collection of diagnostics. All diagnostics were identified and selected with community involvement and consultation. Operational integration with the Earth System Grid Federation (ESGF) will permit automated execution of the REF for selected diagnostics as soon as model output data are published on ESGF by the originating modeling centers. The REF is designed to be portable across a range of current computational platforms to facilitate use by modeling centers for assessing the evolution of model versions or gauging the relative performance of CMIP simulations before being published on ESGF. When integrated into production simulation workflows, results from the REF provide immediate quantitative feedback that allows model developers and scientists to quickly identify model biases and performance issues. After the REF is released to the community, its subsequent development and support will be prioritized by an international consortium of scientists and engineers, enabling a broader impact across Earth science disciplines. For instance, the REF will facilitate improvements to models and will enhance confidence in model projections through process-based selection of models based on their performance with respect to observations. Production of reproducible diagnostics and community-based assessments are key features of the REF. Furthermore, providing interoperability with existing evaluation packages assures that contributions from previous community efforts will be available for use in future model intercomparison projects.

Hoffman, Forrest [ORNL] (ORCID:0000000158024134)↗

Heat pulse testing at monitoring wells to estimate subsurface fluid velocities in geological CO 2 storage

Monitoring the injected CO 2 during geological CO 2 storage (GCS) is essential to assure containment and identify CO 2 leakage. Here in this work, a new approach is introduced to estimate the evolution of the downhole fluid velocity at a monitoring well and identify CO 2 arrival time using in-well heat pulse/tracer test. The proposed technique involves using a downhole heater to generate a series of heat pulses and measuring their corresponding temperature response. The surface temperature of the downhole heater is controlled by the supplied electrical power and the heat loss by convection to the surroundings. Convective heat transfer is well described using Newton's law of cooling in which the temperature difference between the heater and the surrounding fluids drives the heat transfer, for which the convection heat transfer coefficient (h) controls the magnitude of heat loss. Among various factors that control h, it depends on the type of the flowing fluid and its velocity. Through analyzing the measured temperature at different heat pulses, the changes in h - due to mobilization of the in-situ brine or CO 2 arrival - can be estimated. Consequently, the velocity of the flowing fluid across the heater can be obtained. Since heat transfer by convection is sensitive to the type of the surrounding fluid, intrusion of CO 2 can be detected from the relatively higher surface temperature obtained at CO 2 arrival. Churchill and Bernstein (1977)'s correlation is adopted to estimate the change of fluid velocity in terms of the change in h. To demonstrate the validity of the proposed technique, the results are applied and validated against those of COMSOL Multiphysics simulation tool for single-phase brine (before CO 2 arrival) and single-phase CO 2 (after CO 2 arrival). The observed temperature heating is sensitive to the flowing fluid velocity and fluid type. The temperature signal observed at CO 2 arrival is large and easily detectable using temperature monitoring tool which provides reliable indication for tracking CO 2 arrival at monitoring wells compared with passive temperature monitoring. The results obtained using the proposed technique agree very well with the numerical results obtained from the simulation tool with a maximum estimation error of 7 percent.

02 PETROLEUM↗

Function-based Taxonomy Implementation

Function-based taxonomies are relational mapping tools used to clearly illustrate how an organization delivers Critical Functions by using various people, processes, technologies, information, and infrastructure (PPTII). Critical Functions are the actions or activities that make up the organization’s primary purpose. Enabling Functions are the combination of PPTII used by the organization to deliver their Critical Functions. A function-based taxonomy provides a framework to categorize information and related artifacts that document an organization’s unique implementation of PPTII for Critical Function delivery. The ideal state of a function-based taxonomy is to organize the existing knowledge the organization already has throughout their numerous systems, policies, people, procedures, and configurations. A well-organized taxonomy helps organizations to effectively leverage their knowledge by clearly identifying dependencies and connections. This document is the result of combined engineering and analytical experience and describes a repeatable method for producing function-based taxonomies.

42 ENGINEERING↗

Fiscal Year 2023 Software Quality Assurance Activities for the ARC Software

The Argonne Reactor Code (ARC) software suite [1-17] has been developed by Argonne researchers for fast reactor design and analysis since the 1970s. With the ARC software suite, a user can quickly build a model of a proposed or existing fast spectrum reactor and carry out fuel cycle, nominal thermal analysis and flow requirements, and assess, as is appropriate, whether the core design and constraint system yield an acceptable mechanical behavior. For transient reactor analysis with SAS4A [18], the ARC software suite can be used to generate reactivity coefficients and kinetics parameters at any modeled fuel cycle time point which forms part of the input to SAS4A. The ARC suite was consistently being developed until the 1990s and followed a software QA program which was an appropriate standard for the time. In the 1990s, the DOE funding to fast reactor research and development was all but eliminated and the ARC software was put into maintenance mode. In the early 2000s, the software quality assurance (SQA) program for ARC was still in place to define an official version, but by 2005 it all but was abandoned as there were insufficient staff to fill the work roles. Since 2005, there has been a considerable increase in research and design work on fast spectrum reactors. The ARC software as a whole has since been exported to many universities and commercial companies and ANL support has been given to the various projects over the years [19-23]. Further, MC 2 -3, PERSENT, and DASSH were all developed after 2005 without any adherence to a software standard. In recent time, the DOE VTR project [22] paid for verification work to be done on the ARC software as part of the goal of making it NQA-1 complaint. The VTR project was not considered the appropriate pathway to fund and maintain a SQA program for the ARC software and while software developments (DASSH) were made and several manuals were updated and software verification work was carried out, the ARC software is not NQA-1 compliant. More recently the Advanced Reactor Development Program (ARDP [23]) has funded the creation of manuals for some ARC utility programs and funded additional software verification work on DIF3D [6, 7] and MC 2 -3 [2-5] for the purpose of commercial grade dedication. Because of the VTR and ARDP projects, software verification work was completed on MC 2 -3 and DIF3D, and detailed reports were created for each piece of software, which discuss the inputs and outputs from the codes that are covered by the verification work and link various analytic, code-to-code, and hand calculation based verification work presented in the report with verification test problems provided with the software. This is a key part of the commercial grade dedication work and constitutes the bulk of the cost to get the ARC software to commercial grade. The ARC software suite is a valuable asset as a fast reactor design and analysis tool set that has been reasonably well verified and validated with various fast reactor benchmark problems and experiments over decades. Some or all of the ARC software suite has been utilized for designing the IFR [20], PGSFR [21], VTR [22], and Natrium [23] reactors and we can expect it to continue to be used for advanced fast reactor design and/or confirmatory calculation purposes in the future. Due to increased interest by commercial companies and regulatory bodies, it is becoming more important to make the ARC software suite complete and ready-to-use in terms of its SQA pedigree and commercial grade dedication needs. This report discusses the achievements made towards building a new SQA program for the ARC software and dealing with outstanding identified QA gaps.

97 MATHEMATICS AND COMPUTING↗

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗

VADER: A Tool for Criticality Safety Validation

The purpose of criticality safety is to prevent any inadvertent criticality from occurring during the handling or storage of fissile material. Calculations are frequently used to demonstrate that a sufficient subcritical margin exists. Validation is a key aspect of the evaluation process, establishing the suitability, accuracy, and associated uncertainty of the computational method and data to be used for the intended application. The validation process is performed by comparing the results of critical experiments with the calculated results from models of the experiments using the computational method to be validated. Laboratory critical experiments are controlled systems that achieve a k eff of approximately 1 in order to investigate the parameters at which such a critical condition is achieved. The validation parameters that are traditionally applied to safety analysis calculations are the bias and the bias uncertainty . The bias is the deviation of the average k eff of the validation suite from unity. The bias uncertainty accounts for the statistical uncertainty in the bias based on the standard deviation, sample size, and distribution of k eff values of the validation suite. The values of bias and bias uncertainty ensure that the systems predicted to be subcritical by the computational method will indeed be subcritical. The bias and bias uncertainty are often combined to determine an upper subcritical limit (USL) or computational margin that can then be applied to safety analysis calculations. Many methods have been developed by different organizations to calculate the bias and bias uncertainty for various types of criticality analyses. Each of these methods typically requires that the validity of various underpinning statistical assumptions be confirmed to demonstrate that the method is appropriate for the analysis of a given validation suite. An example of the validation decision making flow is shown in Fig.1. As shown in Fig. 1, the analyst performing the validation fits a trend line to the data and performs a test to determine if the trend was a statistically better representation of the data than if it were treated as an uncorrelated sample. If the trend line is a better representation of the data, then the analyst uses any one of a number of trending techniques to determine the bias and bias uncertainty. If a trend is not an appropriate representation of the data, then the analyst proceeds to perform a normality assessment for the data. If the normal assumption can be shown to be acceptable, then the analyst calculates the bias and bias uncertainty with the parametric technique. If the assumption of normality cannot be justified, then the nonparametric technique is used. Once the decision flow has been followed and the appropriate technique has been selected, the bias and bias uncertainty is typically combined with an administrative margin to determine a USL below which calculated values of k eff for safety analysis models can be considered subcritical. The calculations used in each decision are often performed with spreadsheets or with small programs available at various sites performing criticality analyses. Expertise in understanding and interpreting the results must be maintained to perform these calculations. This can often be an error-prone process. Oak Ridge National Laboratory (ORNL) is currently developing the Validation and Data Evaluation Resource (VADER) to simplify and automate the criticality safety validation process and to provide a software quality assurance pedigree to the calculational methods used. This paper discusses the use of the Fulcrum user interface with VADER, the anticipated initial capabilities of VADER to perform validation analyses, and the output from the code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Global Trends of ASME "N-Stamp" Certifications for Nuclear Component Vendors

Historically, nuclear component manufacturing vendors, from small businesses through large conglomerates, have felt compelled to obtain an American Society for Mechanical Engineers (ASME) Nuclear Certification, known colloquially as an "N-stamp", to assure supply chain quality standards that will be acceptable to regulators and safety concerns. Since the N-stamp quality standard is a U.S.-origin code, combined with the apparent decline in the U.S. nuclear industry alongside the growth of the Asian nuclear industry, there is the question of whether the rest of the world, including new entrants to the nuclear industry, also regard N-stamp as a needed certification. This study addresses this question through analysis of the entire N-stamp database of holders, and former holders, of N-stamp certificates of all types and for all regions worldwide from 1989-2020 (the dates available in the database). From this 30 years of data, we find that actually U.S.-based vendors still consistently obtain the largest number of N-stamps worldwide over all time periods, but also find that the countries participating in the N-stamp certification process has broadly expanded beyond just North America, Japan, S. Korea and Western Europe (the primary N-stamp recipients before the mid-2000's). We produced global heats maps and bar charts to illustrate our findings, as well as further investigation into why the data shows changes over time and region. We note that nuclear entities involved with Soviet-type reactors do not participate in the N-stamp process, but instead pursue the Russian version PNAE, which is substantially similar to the ASME code. We conclude that at least from the N-stamp database, the United States nuclear component manufacturing industry is alive and well, although there have been some consolidations, and that the ASME N-stamp appears to still be a valued certificate worldwide, including in China which now ranks second only to the United States in obtaining N-stamp certificates in recent years. We further note that the vendors of new reactor types, in particular High Temperature Gas-Cooled Reactors (HTGRs) and Small Modular Reactors (SMRs), are actively engaged with ASME (and other U.S.-based nuclear standards bodies such as the American Nuclear Society and Nuclear Energy Institute) to coordinate updates to the ASME N-Stamp criteria to ensure applicability of the code for these new designs. Implications of these findings include the following: The global use of the U.S.-origin N-stamp certification supports the view that, despite the decline of the U.S. nuclear industry, the United States remains an esteemed global leader in the area of nuclear safety. As the U.S. Government works to revitalize the U.S. nuclear industry, especially in the area of exports, it may be beneficial to leverage the global standing of the N-stamp certification. The findings indicate that the N-stamp database would be a useful tool for the U.S. Government to use to track the growth of the civil nuclear industry in foreign countries, under certain circumstances. The Excel-format N-stamp database produced as part of this study may be a useful tool for this purpose. N-stamp data may be a useful tool for foreign governments to use to identify nuclear manufacturers within their own country, especially to identify "targets" for outreach on nuclear export control compliance. The U.S. Government could carry this message to foreign partners during bilateral engagements or as part of Nuclear Suppliers Group (NSG) discussions on industry outreach.

42 ENGINEERING↗