Results for “continuous finite element” — Page 8

DOE OSTI2024

A simplified all-frequency stable formulation with an implicit Coulomb gauge

A potential-based finite element formulation has been developed in the past to circumvent the low-frequency breakdown issues commonly encountered in electromagnetic (EM) simulations of low-frequency and multiscale problems. In this formulation, the magnetic vector and electric scalar potentials have been employed to express the electric field and magnetic flux, leading to a set of two equations that represents all four Maxwell’s equations and the current continuity equation. To enforce the Coulomb gauge, an auxiliary potential has been introduced, which results in a total of three equations to be solved simultaneously. To reduce the number of equations and unknowns needed in a simulation, a simplified formulation is proposed in this paper to enforce the Coulomb gauge implicitly without the need for the auxiliary potential. A numerical example is given to demonstrate the accuracy of the proposed formulation.

Mekonnen, Minyechil↗

DOE OSTI2020

Validation of finite-element models using full-field experimental data: Levelling finite-element analysis data through a digital image correlation engine

Full-field data from digital image correlation (DIC) provide rich information for finite-element analysis (FEA) validation. However, there are several inherent inconsistencies between FEA and DIC data that must be rectified before meaningful, quantitative comparisons can be made, including strain formulations, coordinate systems, data locations, strain calculation algorithms, spatial resolutions and data filtering. As such, in this paper, we investigate two full-field validation approaches: (1) the direct interpolation approach, which addresses the first three inconsistencies by interpolating the quantity of interest from one mesh to the other, and (2) the proposed DIC-levelling approach, which addresses all six inconsistencies simultaneously by processing the FEA data through a stereo-DIC simulator to ‘level’ the FEA data to the DIC data in a regularisation sense. Synthetic ‘experimental’ DIC data were generated based on a reference FEA of an exemplar test specimen. The direct interpolation approach was applied, and significant strain errorswere computed, even though therewas no model form error, because the filtering effect of theDIC enginewas neglected. In contrast, the levelling approach provided accurate validation results, with no strain error when no model form error was present. Next, model form error was purposefully introduced via a mismatch of boundary conditions. With the direct interpolation approach, the mismatch in boundary conditions was completely obfuscated, while with the levelling approach, it was clearly observed. Finally, the ‘experimental’ DIC datawere purposefully misaligned slightly fromthe FEA data. Both validation techniques suffered from the misalignment, thus motivating continued efforts to develop a robust alignment process. In conclusion, direct interpolation is insufficient, and the proposed levelling approach is required to ensure that the FEA and the DIC data have the same spatial resolution and data filtering. Only after the FEA data have been ‘levelled’ to the DIC data can meaningful, quantitative error maps be computed.

42 ENGINEERING↗

DOE OSTI2022

Radiative Width of K*(892) from Lattice Quantum Chromodynamics

In this dissertation, we use lattice quantum chromodynamics to explore the radiative transitions of ?K to K, to calculate the radiative-width of the resonant K?(892) which appears in the P-wave ?K ? ?K transition amplitude. The matrix elements are extracted from three-point functions calculated in a finite-volume discretized lattice with a pion mass of 284 MeV. The finite-volume amplitudes, which are constrained over a large number of ?K energy-points and four-momentum transfers, are mapped to the infinite volume transition amplitude by using the Lellouch-Lüscher formalism. The radiative width is determined to be ? = 35 ± 8 keV by analytically continuing the amplitude into the complex energy plane and calculating the residue at the K? pole.

Radhakrishnan, Archana↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗

DOE OSTI2023

Temporally continuous thermofluidic–thermomechanical modeling framework for metal additive manufacturing

Additive manufacturing (AM) is known to generate large magnitudes of residual stresses (RS) within builds due to steep and localized thermal gradients. In the current state of commercial AM technology, manufacturers generally perform heat treatments in effort to reduce the generated RS and its detrimental effects on part distortion and in-service failure. Computational models that effectively simulate the deposition process can provide valuable insights to improve RS distributions. Accordingly, it is common to employ Computational fluid dynamics (CFD) models or finite element (FE) models. While CFD can predict geometric and thermal-fluid behavior, it cannot predict the structural response (e.g., stress–strain) behavior. On the other hand, an FE model can predict mechanical behavior, but it lacks the ability to predict geometric and fluid behavior. Thus, an effectively integrated thermofluidic–thermomechanical modeling framework that exploits the benefits of both techniques while avoiding their respective limitations can offer valuable predictive capability for AM processes. In contrast to previously published efforts, the work herein describes a one-way coupled CFD-FEA framework that abandons major simplifying assumptions, such as geometric steady-state conditions, the absence of material plasticity, and the lack of detailed RS evolution/accumulation during deposition, as well as insufficient validation of results. Here, the presented framework is demonstrated for a directed energy deposition (DED) process, and experiments are performed to validate the predicted geometry and RS profile. Both single- and double-layer stainless steel 316L builds are considered. Geometric data is acquired via 3D optical surface scans and X-ray micro-computed tomography, and residual stress is measured using neutron diffraction (ND). Comparisons between the simulations and measurements reveal that the described CFD-FEA framework is effective in capturing the coupled thermomechanical and thermofluidic behaviors of the DED process. The methodology presented is extensible to other metal AM processes, including power bed fusion and wire-feed-based AM.

42 ENGINEERING↗

DOE OSTI2020

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions [including apppendix B]

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation problems is used in which a computational domain is subdivided into non-overlapping subdomains. In the nonlocal setting, this approach is substructuring-based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains Key results include the equivalence between the global, single-domain nonlocal problem and its multi-domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal domain-decomposition methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Meshfree Methods for Modeling Chemo-Mechanical Cathode Cracking in Li-Ion Batteries

Through repeated charging and discharging, the electrodes of a Li-ion battery experience cyclic loading causing swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries. Chemo-mechanical models are simulated mainly by two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a chemo-mechanical crack propagation model that achieves both intermediate accuracy and computational time between a CDM and CZM. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

cathode cracking↗

DOE OSTI2023

Meshfree Multiphysics Damage Modeling of Li-ion Battery Materials

Through repeated charging and discharging cycles, the electrodes of a Li-ion battery experience significant swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries and material interfaces. Chemo-mechanical damage models are generally simulated by one of two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a coupled chemo-mechanical crack propagation model that enhances accuracy while maintaining high computational efficiency. This model features a fully coupled, iterative electrochemistry solution, which informs the meshfree damage model of impending crack formation. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

damage modeling↗

DOE OSTI2020

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗

DOE OSTI2022

Analysis of Conduction Cooling Strategies for Wire Arc Additive Manufacturing

Metal additive manufacturing (AM) processing consists of numerous parameters which take time to optimize for various geometries. One aspect of the metal AM process that continues to be explored is the control of thermal energy accumulation during component manufacturing due to the melting and solidification of the feedstock. Excessive energy accumulation causes thermal failure of the component while minimal energy accumulation causes lack of fusion with the build plate or previous layer. The ability to simulate the thermal response of an AM component can increase research efficiency by reducing the time to optimize thermal energy accumulation. This paper presents an effective implementation of finite element analysis to determine the thermal response of a wire arc additive manufactured component with various build plate sizes and cooling methods including, integral build plate cooling, oversized build plates with passive cooling, and non-integral build plate cooling. The use of integral build plate cooling channels was shown to decrease the interpass temperature at the conclusion of the build process by 55% and build plate temperature by 96% compared to the conventionally deposited sample with 20 second dwell time. The use of a tall build plate with passive cooling was shown to reduce the interpass temperature by 32% as compared to the conventionally deposited sample with 20 second dwell time. Each cooling strategy evaluated decreased the interpass temperature within a range of 20–55% which enables higher deposition rates and decreased dwell times during depositions. The cooling strategies are designed to be implemented in a hybrid or retrofit AM platform to mitigate concerns of the thermal input from the additive process having detrimental effects on the precision of the machining process. This paper shows that accurate simulations of all strategies can be used to accurately predict the thermal response of the various strategies discussed. These cooling strategies will allow for increased deposition rates with comparable interpass temperature and decreased dwell time, increasing deposition efficiency. This model and these simulations are verified by experimental results. It is concluded that passive strategies, such as the over-sized tall build plate, can be used when liquid coolant in the AM environment could negatively affect the deposition process. Active cooling strategies, such as the integral build plate cooling could be used if low thermal conductivity materials are deposited or higher material deposition rates are desired. This paper discusses the use of active and passive cooling used during AM and shows how a simulation model can be used to make design choices for cooling strategies. The model also enables verification of select critical process parameters such as dwell times for a desired interpass temperature.

Heinrich, Lauren↗

DOE OSTI2024

Strength-ductility synergy through microstructural and compositional heterogeneity in directed energy deposition additive manufacturing of face-centered cubic materials

Directed energy deposition (DED) is an additive manufacturing (AM) process based on welding technology and offers the advantages of large build volume, high deposition rate, and ability to fabricate multi-material parts. Epitaxial continuous columnar grain growth is a characteristic microstructural feature of DED processed alloys. In this study, a bamboo-like microstructure (periodic alternation of equiaxed and columnar structure) was produced by adopting an intermittent deposition strategy in 316L stainless steel and Inconel 625. The formation of a bamboo-like alternating microstructure was confirmed through electron backscattered diffraction (EBSD) analysis. Hardness mapping showed that the columnar to equiaxed transition (CET) occurred at the region right below the fusion line. A finite element (FE) model was used to investigate the relationship between the temperature gradient (G) and the solidification rate (R). The FE model showed a low G/R ratio at the region right below the interface promoting the CET. The grain size and material-dependent deformation behaviors are analyzed using digital image correlation (DIC). The lower deformation on the fine-grain regions observed in DIC analysis is attributed to a higher strain hardening rate, which is confirmed through dislocation density analysis on a tensile-interrupted specimen. The periodically alternating grain size coupled with the microstructural changes caused by intermittent deposition strategy result in a better strength-ductility synergy in both single-material and bimetallic specimens.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Role of Intersections in Fracture Connectivity

Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X-ray imaging of the simplest element of fracture network, that is, two orthogonal fractures, we perform a percolation and finite-size scaling analysis to study the connectivity provided by fracture intersections. The conditions when an intersection enhances connectivity across a sample depend on spatial correlations in the fracture aperture distributions, on the stress state, and on the direction of flow. Here we consider three flow directions: (a) across intersections, (b) parallel to intersections and (c) around corners. For (a), intersections provide minimal enhancement of connectivity because they contribute little additional void area. For (b), intersections increase the probability of a connected path near threshold by enabling 3D connected pathways that are not possible in parallel fractures. Flow around corners, (c), is fundamentally the result of the intersection connecting two fractures in series and spatial correlations are broken around corners, suppressing the connectivity relative to (a). When the connected fractures are stressed equally, a joint percolation threshold emerges that continues to have scale invariance. However, when the fractures are stressed unequally, the system has mixed percolation without clearly defined percolation thresholds. In all cases, percolation probabilities are found to be scale dependent which has important consequences for the connectivity of larger fracture networks composed of the fundamental element studied here.

02 PETROLEUM↗

DOE OSTI2021

Two-Phase Turbulence Statistics from High Fidelity Dispersed Droplet Flow Simulations in a Pressurized Water Reactor (PWR) Sub-Channel with Mixing Vanes

In the dispersed flow film boiling regime (DFFB), which exists under post-LOCA (loss-of-coolant accident) conditions in pressurized water reactors (PWRs), there is a complex interplay between droplet dynamics and turbulence in the surrounding steam. Experiments have accredited particular significance to droplet collision with the spacer-grids and mixing vane structures and their consequent positive feedback to the heat transfer recorded in the immediate downstream vicinity. Enabled by high-performance computing (HPC) systems and a massively parallel finite element-based flow solver—PHASTA (Parallel Hierarchic Adaptive Stabilized Transient Analysis)—this work presents high fidelity interface capturing, two-phase, adiabatic simulations in a PWR sub-channel with spacer grids and mixing vanes. Selected flow conditions for the simulations are informed by the experimental data found in the literature, including the steam Reynolds number and collision Weber number (Wec={40,80}), and are characteristic of the DFFB regime. Data were collected from the simulations at an unprecedented resolution, which provides detailed insights into the continuous phase turbulence statistics, highlighting the effects of the presence of droplets and the comparative effect of different Weber numbers on turbulence in the surrounding steam. Further, axial evolution of droplet dynamics was analyzed through cross-sectionally averaged quantities, including droplet volume, surface area and Sauter mean diameter (SMD). The downstream SMD values agree well with the existing empirical correlations for the selected range of Wec. The high-resolution data repository from the simulations herein is expected to be of significance to guide model development for system-level thermal hydraulic codes.

Saini, Nadish↗

DOE OSTI2024

Plasticity-mediated deformation instabilities in thin film-compliant substrate systems: direct three-dimensional simulations

Abstract Surface wrinkles driven by mechanical instability commonly form in thin-film structures attached to a compliant substrate. In this study, a recently developed computational approach is employed to simulate the formation and transformation of wrinkles involving plastic yielding of the thin film. The three-dimensional (3D) finite element models contain an embedded imperfection at the film-substrate interface, serving to trigger the bifurcation modes. Successful application of this technique to allow for film plasticity is demonstrated, including the evolution of 3D surface patterns and their correlation with the overall load–displacement response. The simulations reveal that plastic yielding transforms the surface instability patterns into more localized forms. Under uniaxial loading, the sinusoidal elastic wrinkles undergo the wrinkle-to-fold transition. With equi-biaxial loading, the initial square-checkerboard array turns into continuous tall ridges along the 45° directions. In both loading modes, the plasticity-induced instability patterns are only partially relieved upon unloading, leaving permanent features on the surface.

36 MATERIALS SCIENCE↗

DOE OSTI2021

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

2020 Annual Report of Available Drawdowns for Each Oil Storage Cavern in the Strategic Petroleum Reserve

The Department of Energy maintains an up-to-date documentation of the number of available full drawdowns of each of the caverns owned by the Strategic Petroleum Reserve (SPR). This information is important for assessing the SPR's ability to deliver oil to domestic oil companies expeditiously if national or world events dictate a rapid sale and deployment of the oil reserves. Sandia was directed to develop and implement a process to continuously assess and report the evolution of drawdown capacity, the subject of this report. A cavern has an available drawdown if after that drawdown, the long-term stability of the cavern, the cavern field, or the oil quality are not compromised. Thus, determining the number of available drawdowns requires the consideration of several factors regarding cavern and wellbore integrity and stability, including stress states caused by cavern geometry and operations, salt damage caused by dilatant and tensile stresses, the effect of enhanced creep on wellbore integrity, and the sympathetic stress effect of operations on neighboring caverns. A consensus has now been built regarding the assessment of drawdown capabilities and risks for the SPR caverns. The process involves an initial assessment of the pillar-to-diameter (P/D) ratio for each cavern with respect to neighboring caverns. A large pillar thickness between adjacent caverns should be strong enough to withstand the stresses induced by closure of the caverns due to salt creep. The first evaluation of P/D includes a calculation of the evolution of P/D after a number of full cavern drawdowns. The most common storage industry standard is to keep this value greater than 1.0, which should ensure a pillar thick enough to prevent loss of fluids to the surrounding rock mass. However, many of the SPR caverns currently have a P/D less than 1.0 or will likely have a low P/D after one or two full drawdowns. For these caverns, it is important to examine the structural integrity with more detail using geomechanical models. Finite-element geomechanical models have been used to determine the stress states in the pillars following successive drawdowns. By computing the tensile and dilatant stresses in the salt, areas of potential structural instability can be identified that may represent "red flags" for additional drawdowns. These analyses have found that many caverns will maintain structural integrity even when grown via drawdowns to dimensions resulting in a P/D of less than 1.0. The analyses have also confirmed that certain caverns should only be completely drawn down one time. As the SPR caverns are utilized and partial drawdowns are performed to remove oil from the caverns (e.g., for occasional oil sales authorized by the Congress or the President), the changes to the cavern caused by these procedures must be tracked and accounted for so that an ongoing assessment of the cavern's drawdown capacity may be continued. A proposed methodology for assessing and tracking the available drawdowns for each cavern was presented in Sobolik et al. (2018). This report includes an update to the baseline drawdowns for each cavern, and provides an initial assessment of the evolution of drawdown expenditure for several caverns

02 PETROLEUM↗