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At least 55 records · Page 3

Mercury speciation using microcolumns with a direct mercury analyzer (DMA). Development of analytical method for the Savannah River Site liquid system

Mercury in the Savannah River Site (SRS) Liquid Waste System (LWS) exists in various forms, including: a) ionic inorganic mercury, organomercury (e.g., methyl Hg), and other less abundant species dissolved in LWS fluids, b) mercury solids such as oxides, hydroxides, amalgams, sulfides, and sorbed mercury, c) accumulations of dense liquid elemental mercury, and d) vapor phase elemental and organomercury mercury in tank headspace gas and in evaporators. Strategic and proactive management of the estimated 60,000 Kg mercury in the LWS requires deployment of efficient and effective paradigms for sampling and analysis of the total quantity of mercury in the various physical-chemical forms. Scoping tests of selective gas-phase sorbents for mercury speciation were performed to support LWS objectives. This research specifically focused on developing and testing streamlined methods to obtain high-quality analytical results for gaseous mercury species. The proposed methods are straightforward, using small columns (microcolumns) filled with materials that selectively sorb one or more target forms of mercury. Simple differentiation of mercury species and quantification is then achieved using an efficient thermal-desorption-based total mercury analyzer as the final step. Benefits associated with transitioning from multistep procedures such as EPA Methods 245.1, 1630 and 1631to streamlined microcolumn approaches include reduced analysis time, labor, and waste generation. Such transitioning would maximize the value of the current deployment of direct mercury analysis (EPA Method 7473) at SRS. This work has two target end uses: 1) simplifying the analysis steps and reducing costs for liquid samples (e.g., developing a total organic mercury (TOM) method), and 2) providing options for high-quality onsite analysis and rapid turnaround for gas samples in support of SRS LWS industrial hygiene (IH) objectives.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Analysis of Glycolate in Radioactive Waste by Ion Chromatography (IC) and Proton Nuclear Magnetic Resonance (H NMR)

Here, in preparation for implementing the Nitric-Glycolic (NG) acid flowsheet for the Savannah River Site (SRS) Liquid Waste System (LWS), analytical methods for determining glycolate at low concentration, below 20 mg/L in radioactive samples, were developed to support system management and safety. To accommodate the wide range of LWS matrix conditions, two alternative methods were developed, refined, and demonstrated for glycolate analysis in radioactive waste samples: ion chromatography (IC) and a proton nuclear magnetic resonance (H NMR). Investigators validated IC and H NMR methods for glycolate analysis, defined the range of applicability, and demonstrated key supporting analytical protocols. The deployed IC method is applicable in low to moderate ionic strength samples and requires sample pretreatment using a Dionex OnGuard II H + cartridge. The deployed H NMR method is more labor intensive but provides options for a broader range of matrices. Based on the results, high quality glycolate analysis of the Defense Waste Processing Facility (DWPF) condensate in Tank 22 is feasible by IC down to approximately 12 mg/L. Using H NMR, glycolate may be determined to 8 mg/L or lower depending on the run time with the potential for broader applicability of the method to higher ionic strength conditions in other tanks of the SRS LWS.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Dark and bright modes, and their coherent control in dipolar metasurface bilayers

Several plasmonic nanoparticles supporting dipolar resonances can couple to form normal modes. Here, we develop an analytical model to explain the formation of nonradiative “dark” and radiative “bright” modes through radiative coupling in bilayers consisting of dipolar nanoantenna arrays that are separated by a subwavelength distance. We also include near-field contributions in our model and show that the absorption and reflectance spectra obtained from our model agree reasonably well with the respective finite-difference time-domain simulation results for both perfectly aligned and misaligned bilayers. Here, the ability to vary the reflection and absorption spectra of these bilayers by changing the material and geometrical parameters has potential applications in the design of efficient spectral filters. We also show that we can selectively excite these modes by adjusting the phase between two counterpropagating normally incident fields, which has applications in all-optical modulators and switches based on purely linear interferometric effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Lignin Utilization

Valorization of lignin has massive potential economic and sustainability benefits for the lignocellulosic biorefinery. However, challenges remain to realize lignin conversion to coproducts, especially related to selective, high yield depolymerization to monomers and quantitative analytics on lignin, the latter of which is critical for accurate process modeling. Towards these goals, the Lignin Utilization project focuses on catalytic lignin deconstruction chemistries for C-O and C-C bond cleavage, development of analytical chemistry techniques to quantitatively characterize lignin, and syntheses of requisite model compounds for understanding lignin transformations. This work is done with and supports multiple BETO projects, including the Biological Lignin Valorization (BLV) project, the Separations Consortium, and others. Outcomes of Lignin Utilization for analytics and synthesis include 1) development of new mass spectrometry (MS) methods to characterize lignin dimers/oligomers in process streams, 2) deployment of a computational-experimental tool (with Biochemical Process Modeling and Simulation) to identify lignin-derived compounds with high fidelity from MS, and 3) delivery of >40 unique compounds. From a catalysis perspective, we have developed new oxidative approaches to cleave C-O and C-C bonds and produce >50% bio-available aromatic monomers for biological funneling for the BLV project and have developed recoverable bases for base-catalyzed deconstruction of lignin.

BIOMASS FUELS↗

Online Analytics for Remedy Support at DOE Environmental Management Sites

Environmental data is important for managing environmental restoration/waste site remediation, planning of monitoring efforts, addressing climate resilience, and engaging with stakeholders and regulators. A major challenge is how to manage the many different types and the large volume of environmental data in a way that allows practitioners and site managers to understand data implications and support decisions. The Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites (SOCRATES, https://www.pnnl.gov/projects/socrates) is a web application that provides data access, visualization, and rapid analytics to help make sense of environmental data, support remedy decisions, and communicate information. Development of SOCRATES has been funded through the DOE Richland Operations Office (RL) to support communication and decision making for the Hanford Site, thus is only tied into Hanford environmental data. However, the capabilities of SOCRATES are more broadly applicable to DOE-EM sites engaged in environmental remediation and management. This report describes the work to develop mechanisms for bringing non-Hanford data into SOCRATES so that other DOE-EM sites could make use of the visualization and analysis capabilities to support communication and decision making related to managing environmental restoration/waste site remediation, optimization/exit strategies for pump-and-treat systems, planning monitoring efforts, addressing climate resilience, and/or engaging with stakeholders and regulators. The background, approach, data transfer formats, examples, and next steps for this new SOCRATES-EM software are described in this report.

54 ENVIRONMENTAL SCIENCES↗

Persistent Acoustic Sensing for Monitoring A Reactor Facility - Oral Presentation

Measurements over the past few years, taking place within the Multi-Informatics for Nuclear Operations Scenarios (MINOS) project, show that infrasound and low-frequency acoustic monitoring can detect, and often quantify, activities that occur on-site at a large research reactor. Observable activities include: crane translation, lifting, and lowering; differentiation between loaded and unloaded crane operations; access door opening and closing; vehicle operations; and cooling tower fan operation. Advanced data analytic and spectral feature extraction methods can be used to interpret selected signatures to reach a deeper understanding of different reactor activities. These measurements are being conducted using a network of smartphones that continuously operate in conjunction with cloud-based architectures. A recent addition to the system is the development and deployment of a real-time, cloud-based analytic framework that supports near-real-time alarming which can facilitate tip-and-cue protocols. This paper will present recent research advances in this area including studies to explore the transferability of learned parameters from one smartphone to another, the detectability of events from multiple sensors at different locations simultaneously, and the feasibility of porting analytical tools directly to the smartphones to allow edge computing with optimized configurations.

42 ENGINEERING↗

Persistent Acoustic Sensing for Monitoring A Reactor Facility

Measurements over the past few years, taking place within the Multi-Informatics for Nuclear Operations Scenarios project, show that infrasound and low-frequency acoustic monitoring can detect, and often quantify, activities that occur on-site at the High Flux Isotope Reactor. Observable activities include: crane translation, lifting, and lowering; differentiation between loaded and unloaded crane operations; access door opening and closing; vehicle operations; and cooling tower fan operations. Advanced data analytic and spectral feature extraction methods can be used to interpret selected signatures to reach a deeper understanding of different reactor activities. These measurements are being conducted using a network of smartphones that continuously operate in conjunction with cloud-based architectures. A recent addition to the system is the development and deployment of a real-time, cloud-based analytic framework that supports near-real-time alarming which can facilitate tip-and-cue protocols. This paper presents recent research in this area including the use of low-frequency acoustics to tip-off transfer operations and cue a more comprehensive analysis by other sensor networks.

42 ENGINEERING↗

Description of FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment

The urgency to deliver fusion power is growing now more than ever, with increasing pressure for both public programs and private companies to meet milestones timelines and overcome significant remaining technical challenges to ensure growth of a nascent fusion industry in time to meet rapidly growing clean energy demands. With incredible advancements in computation and years of investment in fusion model development and validation, integrated modeling is poised to fill a key role in accelerating the timeline to a fusion pilot plant (FPP). Future fusion pilot plants will operate in regimes far beyond current experience, and device design will rely on physics-based prediction and extrapolation. Many concepts will also rely on simulation to assess safety (shielding, tritium management, materials activation and lifetimes), economics and scalability before the decision to build. Importantly, integrated simulation can be used to reveal and solve the complexities of system integration that may otherwise not be apparent in physical components or models developed in isolation. New experimental test facilities that produce relevant conditions to validate and resolve key technical challenges for various subsystems (materials, blankets, fuel cycle, etc.) have been repeatedly called for by the fusion community but are not yet realized. Integrated modeling has an important role in identifying realistic load conditions (thermal, electromagnetic, plasma, neutron and photon loads, etc.) and defining the components and experiments for these test facilities in order to ensure meaningful validation that sufficiently reduces modeling uncertainties and technical risk for the full integrated reactor. The Fusion REactor Design and Assessment (FREDA) SciDAC project is building a component-based integrated modeling framework & data structure to enable self-consistent, multi-fidelity, iterative optimization workflows for the fusion reactor design process. FREDA aims to shorten the time to viable designs by providing a set of flexible workflows to support the various stages of the design process using an integrated model hierarchy, ranging from the simple analytic descriptions to the highest fidelity, theory-based plasma and engineering modeling developed by the fusion and fission communities. These tools are expected to be needed for timely support of FPP design in the milestone program and in the FIRE collaboratives. The plasma simulation backbone of FREDA is IPS-FASTRAN with newly developed coupled Core-Edge Pedestal-SOL (CESOL) workflows, which is being extended to the far-SOL region up to the plasma facing components. FREDA incorporates the FERMI engineering modeling suite and will enable self-consistent evaluation of the thermal shields, limiters, blanket, magnets, and other surrounding structures with predictions of temperatures, erosion, dpa, activation, tritium generation and transport, creep, corrosion, material degradation, etc. Parametric generation of 3D CAD enables rapid iteration of component geometry in response to plasma and loading specifications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

FY25 Electric Grid Security Annual Report

Sandia’s Electric Grid Security program advances a national vision of energy dominance and accessibility, while applying our national security -emphasis on ensuring of a secure, resilient, and affordable electric system for all users. Our achievements reflect a strategic approach combining technology development; modeling, simulation, and data analytics; and partnered demonstrations and outreach to further the adoption of advanced grid and storage technologies. Our FY25 efforts leverage the strengths of our partnerships—spanning Sandia’s core science and technology competencies as well as external technology leaders—to develop the solutions today which enable the grid of tomorrow. Key accomplishments in this report that support our strategy span our technical program areas and include: • New open-source analytical tools for systems -level planning and optimization, including significant advances to the QuESt analytical environment; • Further advancement of artificial intelligence and machine learning to enhanced grid operations and planning as we rise to the challenge of new large loads; • Development of solid-state power conversion technologies and a new medium-voltage research lab; • New technologies to assess wildfire vulnerabilities and mitigate potential impacts; • Advanced applications of new cybersecurity technologies with industry partners; • Contributions to understanding the impacts of electromagnetic pulses and geomagnetic disturbances on grid components; and • Digital twin development for hybrid microgrids with multiple generators, storage, and loads. This report indicates key areas of research and engagement and summarizes the impact of Sandia’s contributions through notable accomplishments, journal publications, patents, and technical conferences and presentations. It is provided with the hope that readers discover ways we can further team to create our modern grid and apply the outcomes of our efforts. The bulk of work described herein is funded by several offices within the U.S. Department of Energy (USDOE), including the Office of Electricity (OE); Cybersecurity, Energy Security, and Emergency Response (CESER); former offices such as the Office of Energy Efficiency and Renewable Energy (EERE), the Grid Deployment Office (GDO), the Office of Clean Energy Demonstrations (OCED), and other key programs at USDOE. As we continue to state in these annual reports, the contributors to our successes are too numerous to name here, though our team wishes to express our deep gratitude to the numerous program and project sponsors at the US Department of Energy, who often function equally as technical collaborators; our many partners in industry, academia, utilities, and other national labs; and fellow researchers and business partners at Sandia whose leadership and creativity have enabled the accomplishments described herein.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A multiplexed nanostructure-initiator mass spectrometry (NIMS) assay for simultaneously detecting glycosyl hydrolase and lignin modifying enzyme activities

Lignocellulosic biomass is composed of three major biopolymers: cellulose, hemicellulose and lignin. Analytical tools capable of quickly detecting both glycan and lignin deconstruction are needed to support the development and characterization of efficient enzymes/enzyme cocktails. Previously we have described nanostructure-initiator mass spectrometry-based assays for the analysis of glycosyl hydrolase and most recently an assay for lignin modifying enzymes. Here we integrate these two assays into a single multiplexed assay against both classes of enzymes and use it to characterize crude commercial enzyme mixtures. Application of our multiplexed platform based on nanostructure-initiator mass spectrometry enabled us to characterize crude mixtures of laccase enzymes from fungi Agaricus bisporus (Ab) and Myceliopthora thermophila (Mt) revealing activity on both carbohydrate and aromatic substrates. Using time-series analysis we determined that crude laccase from Ab has the higher GH activity and that laccase from Mt has the higher activity against our lignin model compound. Inhibitor studies showed a significant reduction in Mt GH activity under low oxygen conditions and increased activities in the presence of vanillin (common GH inhibitor). Ultimately, this assay can help to discover mixtures of enzymes that could be incorporated into biomass pretreatments to deconstruct diverse components of lignocellulosic biomass.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterizing PuO 2 Powder at Oak Ridge National Laboratory for the Multi-Lab Plutonium Process Signatures Campaign FY 2022

This report highlights the development of advanced analytical capabilities at Oak Ridge National Laboratory to characterize PuO 2 powder to support the Multi-Lab Plutonium Process Signatures Campaign in FY 2022. Two samples from a batch of 76 statistical precipitation runs were packaged and shipped from Pacific Northwest National Laboratory to Oak Ridge National Laboratory at the beginning of FY 2022. Techniques were used to characterize the sample, including powder X-ray diffraction, Raman spectroscopy, and diffuse reflectance spectroscopy. A brief description of each technique, the results and discussion, and future work are described in this report. Opportunities to expand current capabilities and include additional analytical capabilities for the next campaign will also be discussed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Tunable Few-Layer van der Waals Crystals and Heterostructures as Emerging Energy and Quantum Materials (Final Technical Report)

2D and layered (van der Waals) semiconductors offer extraordinary opportunities for manipulating optically excited charge carriers, many-body excitations, and non-charge based quantum numbers. To date, research has focused on a limited group of materials, mostly transition metal dichalcogenides in the monolayer limit. Other van der Waals semiconductors, and especially few-layer to multilayer crystals and their heterostructures, carry large potential for the discovery of phenomena of interest for future energy and information technologies. But they remain largely unexplored, often due to a lack of access to high-quality materials and approaches for measuring their properties at the relevant scales. The goal of this project was to develop an EPSCoR-State/National Laboratory Partnership that addresses the challenges of preparing high-quality van der Waals semiconductors and of probing their structure, composition, and especially their optoelectronic and photonic properties, near the atomic scale using electron microscopy techniques. A central component of the project was the development of advanced methods for electron microscopy and electron-excited spectroscopy, taking advantage of unique samples as well as leading capabilities and expertise at the partner institutions. Efforts to advance leading-edge techniques was supported by ancillary developments, such as precision sample preparation for electron microscopy/spectroscopy, coordinated chemical imaging, and analytical electron microscopy. Experiments in materials synthesis and technique development were closely linked to theory and computation. The results obtained under this project yielded multifaceted benefits to the involved partners and their institutions, DOE-BES, the wider scientific community, and society at large, particularly in the State of Nebraska through dividends from knowledge and human capital generated under the project.

36 MATERIALS SCIENCE↗

Bridging Equipment Reliability Data and Robust Decisions in a Plant Operation Context

In order to reduce operation and maintenance (O&M) costs, nuclear power plants (NPPs) are moving from corrective and periodic maintenance to predictive maintenance strategies. Such transition requires changes on the data that needs to be retrieved and on the type of decision processes to be employed. Advanced monitoring and data analysis technologies are essential to support predictive strategies. They can in fact provide precise information about health of a component, track its degradation trends, and provide information of its expected failure time. With such information, maintenance operations for a component can be performed right before its expected failure time. This dynamic context of O&M operations requires new methods to analyze data, propagate component health information from the component to the system level, and optimize plant resources. In this respect, the risk informed asset management (RIAM) project has been tasked to develop and test this new class of methods into a risk analytics toolset. This toolset consists of data analytics tools coupled with reliability methods designed to manage plant assets and performances in a predictive maintenance context. This report shows the latest improvements on such development and the initial testing of our methods on the three main research areas that the RIAM project is focusing on. These areas are the following: equipment reliability data analytics, system reliability modeling, and plant resources optimization methods. We show how the methods developed in these areas can support predictive maintenance strategies by: 1) analyzing equipment reliability data (either in numeric and textual form), 2) assessing component and system health through an innovative margin-based reliability approach, and 3) identifying the most critical components and set optimal maintenance schedule based on plant economic and operational constraints.

97 MATHEMATICS AND COMPUTING↗

Energy Resilient Recovery in Puerto Rico: Hurricane Maria Recovery Support

This report covers microgrids as a special application of distributed energy resources (DERs) in Puerto Rico. This is one of a series of reports describing the U.S. Department of Energy (DOE) multi-laboratory efforts undertaken. To ensure the sustainable, long-term recovery of Puerto Rico's electric power grid from hurricanes Maria and Irma and to build capacity to manage future potential natural disasters in the most secure and resilient way, DOE convened experts from multiple national laboratories to develop a comprehensive set of data, models, analytic tools, and studies, considering inputs from a wide variety of stakeholder groups, to support technically sound recommendations for Puerto Rico's energy investment decisions. In Phase 1 of the multi-laboratory effort to support Puerto Rico's recovery, the National Renewable Energy Laboratory (NREL) provided the utility company Puerto Rico Electric Power Authority (PREPA) recommendations for a new framework of interconnection standards to accelerate the integration of utility-scale, transmission-connected, renewable electrical generation and energy storage that ensure cross-technology compatibility and enable high deployment levels without compromising grid reliability, safety, or security (https://www.nrel.gov/docs/fy19osti/73848.pdf). In Phase 2, NREL published a report focused on the interconnection of distributed energy resources (DERs) to the electric distribution system in Puerto Rico (https://www.nrel.gov/docs/fy21osti/77127.pdf). This report familiarized the reader with Puerto Rico's distribution infrastructure and operational practices and procedures that are relevant to DER interconnection. The report also provided considerations for streamlining the interconnection process given the expected increase in deployments resulting from Puerto Rico's renewable portfolio standard goal of 100% renewables by 2050. Accordingly, the report identifies considerations and concerns associated with the increase in intermittent generation, strategies for DER interconnection best practices, and the potential use of the latest technological solutions identified in the latest revision of the Institute of Electrical and Electronics Engineers 1547-2018 interconnection standard. Additionally, the report identified ways to improve the physical resiliency of installed DERs. This task describes how distributed energy systems may participate in and contribute to improving the resiliency of Puerto Rico's energy infrastructure in the future. This report presents an analysis of the Puerto Rico grid to illustrate the possible different microgrid and minigrid scenarios. The capability to form sustained microgrids and minigrids has the potential to provide a high level of resiliency during disturbances on the grid. DERs, on the other hand, have the capability to aid in the microgrid operation by providing grid support as well as grid-forming functionality. Other tasks in Phase 3 include voltage regulation in distribution networks using DERs and transmission-and-distribution co-simulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Analysis of Ionic Mercury Species in SRR Samples Measured by SRNL and Eurofins FGS

Savannah River Remediation (SRR) requested the development of mercury speciation capabilities at the Savannah River National Laboratory (SRNL) to support the Liquid Waste Operations at SRS. As part of that method development, SRR requested that SRNL Analytical Development (AD) compare their results with those obtained from their outside contract laboratory, Eurofins Frontier Global Sciences (FGS). This document reports on this method development work performed at SRNL as well as the comparative analyses conducted between the two laboratories. Development, optimization, and validation were undertaken at SRNL to produce a method for the species-specific analysis of ionic mercury. This method was developed as a secondary step to an existing method, L16.1-ADS-1579 Purgeable Mercury Cold Vapor Atomic Fluorescence Spectrophotometry. As such, much of the development and validation were performed in service of development of L16.1-ADS-1579. Six samples, representing two consecutive quarterly Tank 50 batches, were tested for ionic mercury by SRNL-AD and Eurofins FGS. The mean values reported by each lab for ionic mercury differed by less than one standard deviation, therefore the values reported by both labs were considered to be in agreement. SRNL-AD reported values for the six samples that differed by -5.56 mean percent, relative to Eurofins FGS. Together with comparable quality control data reported by each laboratory, these data represent a high level of agreement among both laboratories. With a viable method for ionic mercury that matches the data quality provided by outside commercial laboratories, SRNL-AD has demonstrated competency in measuring methylmercury, ethylmercury, total mercury, soluble & particulate mercury, purgeable mercury, and ionic mercury species in a variety of radioactive tank samples.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Global Experiences with HPC Operational Data Measurement, Collection and Analysis

As we move into the exascale era, supercomputers grow larger, denser, more heterogeneous, and ever more complex. Operating such machines reliably and efficiently requires deep insight into the operational parameters of the machine itself as well as its supporting infrastructure. To fulfill this need, early adopter sites have started the development and deployment of Operational Data Analytics (ODA) frameworks allowing the continuous monitoring, archiving, and analysis of near realtime performance data from the machine and infrastructure levels, providing immediately actionable information for multiple operational uses. To understand their ODA goals, requirements, and use cases, we have conducted a survey among eight early adopter sites from the US, Europe, and Japan that operate top 50 high-performance computing systems. We have assessed the technologies leveraged to build their ODA frameworks, identified use cases and other push and pull factors that drive the sites' ODA activities, and report on their operational lessons.

Ott, Michael↗

Review of analytical studies on seismic fluid-structure interaction of base-supported cylindrical tanks

Analytical solutions for seismic fluid-structure interaction (FSI) of tanks are used by analysts and engineers for a number of purposes, including preliminary sizing, risk assessment, and verification of numerical models. Analytical solutions for seismic FSI of tanks were first developed in the 1930s and have been extended and/or modified in the following nine decades to accommodate different seismic inputs and boundary conditions. This report reviews published analytical solutions for rigid and flexible, base-supported, cylindrical tanks subjected to unidirectional horizontal motion of a small amplitude. The studies parsed the fluid-structure (FSI) response into an impulsive and a convective component, and addressed frequencies of lateral motions of the tank (i.e., impulsive frequencies), hydrodynamic pressures, frequencies of waves (i.e., convective frequencies), wave heights, and reactions at the base. The solutions were categorized into exact and approximate solutions based on the methodologies used. Herein, FSI responses are calculated and compared for a range of tank dimensions using the analytical solutions from the different studies. The responses presented here are normalized to be unitless, and can be used for tanks with different dimensions and mechanical properties, and subjected to different input motions. A sample steel water tank is analyzed using the normalized solutions for two earthquake ground motions with different frequency contents. Ignoring tank flexibility may significantly underestimate seismic responses of the tank and its contained fluid. The approximate solutions, which have been widely used for decades, may not be sufficiently accurate in the modern era. Calculation errors in the reviewed studies are identified and corrected, and differences are quantified for the sample tank.

42 ENGINEERING↗