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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

In this work, we present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [1]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Bayesian Model Calibration for Extrapolative Prediction via Gibbs Posteriors

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to quantify uncertainty in physical parameters for extrapolative prediction, then there is no need to perform inference on the discrepancy term. With this in mind, we introduce Gibbs posteriors as an alternative Bayesian method for model calibration, which updates the prior with a loss function connecting the data to the parameter. The target of inference is the physical parameter value which minimizes the expected loss. We propose to tune the loss scale of the Gibbs posterior to maintain nominal frequentist coverage under assumptions of the form of model discrepancy, and present a bootstrap implementation for approximating coverage rates. Our approach is highly modular, allowing an analyst to easily encode a wide variety of such assumptions. Furthermore, we provide a principled method of combining posteriors calculated from data subsets. We apply our methods to data from an experiment measuring the material properties of tantalum.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multiphase Reacting Flow Simulations and Optimization of Commercial-Scale Aerobic Bioreactors

Aerobic bioreactors are widely used in the synthesis of value-added products in pharmaceutical and biotechnology industries, wherein microbial bioreactions aid in the conversion of sugars to macromolecules. These reactors are also being actively investigated as a cost-effective pathway for the production of low-value commodities such as biofuels and animal feed. Reactor scale-up is one of the important challenges when designing these systems. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of commercial-scale (~ 500 m3) aerobic bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for oxygen uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM, to perform these simulations, which has been validated against small-scale reactors in our previous work. This work examines the performance of three different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor oxygen mass-transfer coefficient, gas hold-up, and oxygen distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented.

09 BIOMASS FUELS↗
DOE OSTI2025

DeFault: DEep‐Learning‐Based FAULT Delineation Using the IBDP Passive Seismic Data at the Decatur CO2 Storage Site

Abstract The carbon capture, utilization, and storage (CCUS) framework is an essential component in reducing greenhouse gas emissions, with its success hinging on the comprehensive knowledge of subsurface geology and geomechanics. Passive seismic event relocation and fault detection offer vital insights into subsurface structures and the ability to monitor fluid migration pathways. Accurate identification and localization of seismic events, however, face significant challenges, including the necessity for high‐quality seismic data and advanced computational methods. To address these challenges, we introduce a novel deep learning method, , specifically designed for passive seismic source relocation and fault delineating for passive seismic monitoring projects. By leveraging data domain‐adaptation, allows us to train a neural network with labeled synthetic data and apply it directly to field data. Using , the passive seismic sources are automatically clustered based on their recording time and spatial locations, and subsequently, faults and fractures are delineated accordingly. We demonstrate the efficacy of on a field case study involving injection related microseismic data from Decatur, Illinois area. Our approach accurately and efficiently relocated passive seismic events, identified faults and could aid in potential damage induced by seismicity. Our results highlight the potential of as a valuable tool for passive seismic monitoring, emphasizing its role in ensuring CCUS project safety. This research bolsters the understanding of subsurface characterization in CCUS, illustrating machine learning’s capacity to refine these methods. Ultimately, our work has significant implications for CCUS technology deployment, an essential strategy in combating climate change. Plain Language Summary In our quest to tackle climate change, we use a strategy known as carbon capture, utilization, and storage (CCUS) to keep greenhouse gases out of the atmosphere. This strategy relies heavily on our ability to understand what's happening deep under the earth's surface. To make sure we store super critical safely, we need to accurately map out the geological structure, especially faults, but this is tough without high‐quality data and complex computer programs. We've developed a new tool called “DeFault,” which uses advanced machine learning to improve how we find and map these underground features. “DeFault” is smart enough to learn from numerically simulated data and then apply what it’s learned to real‐world situations. It groups together seismic activity—tiny tremors and shifts in the earth—based on when and where they happen, which helps us spot where there might be cracks or faults. We tested “DeFault” in Illinois, where CO 2 is injected underground, and it successfully pinpointed where these tremors occurred and mapped out the faults, helping to prevent accidents accurately in the future. Our study shows that “DeFault” will be a powerful ally in making CCUS safer and more effective, especially for the Illinois Basin Decatur Project. Key Points Faults and fractures introduced by carbon storage can be monitored by passive seismicity DeFault algorithm enables an automatic process for accurate and efficient passive seismic event locating and clustering

58 GEOSCIENCES↗
DOE OSTI2019

Towards Improved Real-Time Observability of Behind-Meter PhotoVoltaic Systems: A Data-Driven Approach

The stochasticity in energy supply introduced by increased PV penetration in grid distribution systems can lead to frequent and sudden supply-demand imbalances, thereby causing voltage and frequency fluctuations. Enhanced observability, in real-time, of grid attributes such as real and reactive power flows, power injections/consumption and voltages is becoming increasingly essential to ensure smooth grid operation under these new large-scale PV integration scenarios. Two significant challenges prevent grid operators from achieving this objective: 1) Computational complexity of quasi-static timeseries simulations, and 2) Partial observability of behind-meter grid assets. In this work, we take a step towards this objective by enhancing the observability of smart inverter equipped PV systems located behind AMI meters. Smart inverters convert the DC output of PV systems into real and reactive power, the ratio of which is governed by a power factor setting. This in turn is governed by the real-time voltage at its terminal, as per a pre-set volt/var curve. While it is possible to infer the power factor setting - thereby, real and reactive power injection of the PV system - at each time interval by quasi-static time series simulations, such methods are not scalable to large grid sizes. We propose to reduce the reliance on simulations by developing a deep neural network based data-driven model which predicts the time dependent power factors of the PV systems in the grid. The model uses a small amount of simulated data to learn the dependence of power factor on 1) load and apparent PV power injection (root mean square of real and reactive power) data, and 2) AMI net-load data (for BTM PV assets). Our results show that our model can predict power factors with mean absolute error of less than 6.2% under full observability scenario and under 8.6% under the partial observability scenario. Thus, our data-driven model can reduce the amount of simulations required to compute real and reactive injections from PV systems in the distribution system with or without complete information.

14 SOLAR ENERGY↗
DOE OSTI2018

ULAMA: A Utilization-Aware Matching Approach for robust on-demand spatial service brokers

This article investigates an on-demand spatial service broker for suggesting service provider propositions and the corresponding time of service to mobile consumers while meeting the consumer’s maximum travel time and wait time constraints. The goal of the broker is to maximize the number of matched requests while also keeping the “eco-system” functioning and robust against variations in the supply–demand ratio by engaging as many service providers as possible and maintaining providers’ participation to ensure that providers do not drop out. This problem is important because of its many related societal applications in the on-demand and sharing economy (e.g., on-demand ride-hailing services, on-demand food delivery, etc.). Challenges of this problem include the need to satisfy many conflicting requirements of the broker, consumers and service providers and the high computational complexity since solving the problem for a number of available consumers at any time instant is NP-hard. Related work in spatial crowdsourcing and ridesharing has mainly focused on maximizing the number of matched requests and minimizing travel cost, but did not consider the importance of maintaining provider engagement and balancing provider utilization, which could become a priority when the available supply exceeds the demand. In this paper, we propose a Utilization-Aware Matching Approach (ULAMA) which employs novel provider-centric heuristics for balancing the utilization of providers, and a consumer-priority-based greedy matching algorithm that prioritizes consumers for maximizing the number of matched requests. Experimental results show that our proposed approach outperforms related work by achieving the lowest variance in provider utilization while matching all available providers even when supply greatly exceeds demand. Our approach also achieved a larger number of matched requests, particularly when supply exceeds demand and also when both supply and demand are balanced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems

Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics given our current understanding. Many plasma problems of interest fall into these categories as there are a wide range of models that exist, however each model is only useful in a certain regime and often limited by computational complexity. To ensure data-driven methods align with theory, they must be consistent and predictable when acting on data whose governing dynamics are known. Weak Sparse Identification of Nonlinear Dynamics (WSINDy) is a recently developed data-driven method that has shown promise in learning governing dynamics from data with high noise levels [1]. This work examines how WSINDy acts on ideal MHD test problems as the initial conditions are varied and specifies limiting requirements for successful equation identification. Furthermore, it is hard to recover the governing dynamics from data that emphasize a single dominant behavior. In these low information cases, Shannon information entropy is able to pick up on the redundancies in the data that affect recoverability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SigTime: Learning and Visually Explaining Time Series Signatures

Understanding and distinguishing temporal patterns in time series data is essential for scientific discovery and decision-making. For example, in biomedical research, uncovering meaningful patterns in physiological signals can improve diagnosis, risk assessment, and patient outcomes. However, existing methods for time series pattern discovery face major challenges, including high computational complexity, limited interpretability, and difficulty in capturing meaningful temporal structures. Here, to address these gaps, we introduce a novel learning framework that jointly trains two Transformer models using complementary time series representations: shapelet-based representations to capture localized temporal structures and traditional feature engineering to encode statistical properties. The learned shapelets serve as interpretable signatures that differentiate time series across classification labels. Additionally, we develop a visual analytics system—SigTime—with coordinated views to facilitate exploration of time series signatures from multiple perspectives, aiding in useful insights generation. We quantitatively evaluate our learning framework on eight publicly available datasets and one proprietary clinical dataset. Additionally, we demonstrate the effectiveness of our system through two usage scenarios along with the domain experts: one involving public ECG data and the other focused on preterm labor analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Full Multigrid Method for the Self-Adjoint Angular Flux Equation Based on Cellwise Block Jacobi Iteration

Previous work by Densmore et al. has demonstrated that multigrid methods for the self-adjoint angular flux (SAAF) equation with cellwise block Jacobi smoothing can be extremely effective at solving for the angular flux in one dimension. The extension of that work to two dimensions demonstrated that while the smoother works well, the use of a direct coarse-grid approximation can severely limit the rate of convergence for optically thin cells. In that paper, this convergence limit was evaded through the use of a partially Galerkin coarse-grid approximation. However, relying on a Galerkin coarse-grid approximation is not ideal as constructing the coarse-grid discretization in this approach is complicated. The motivation for this summary is to find a method that can work without the need for a Galerkin coarse-grid approximation. The Full Multigrid (FMG) method is well known as a method that can theoretically solve a problem to its discretization accuracy with optimal linear computational complexity, that is in just O(N) operations for N unknowns. Indeed, we develop an FMG method for the 2-D SAAF equation that yields discretization accuracy and does not require the use of a Galerkin coarse-grid approximation. Until recently, aside from proofs about the order of the error for FMG, little work had been done in quantifying when and how FMG can obtain discretization accuracy. However, recent work by Rodrigo et al. has introduced a Fourier analysis technique called worst-case right-hand side analysis used to calculate the FMG accuracy measure. The FMG accuracy measure is the upper bound on the constant of proportionality between the error of the FMG solution and the discretization error. In this summary, we develop and implement an FMG method for the 2-D Cartesian SAAF equations. We then perform worst-case right-hand side analysis and give numerical examples that demonstrate under what circumstances the method can solve the 2-D SAAF equations to discretization accuracy, for optically thin cells, without the need for a Galerkin coarse-grid approximation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

SU-E-T-500: Initial Implementation of GPU-Based Particle Swarm Optimization for 4D IMRT Planning in Lung SBRT

Purpose 4D-IMRT planning, combined with dynamic MLC tracking delivery, utilizes the temporal dimension as an additional degree of freedom to achieve improved OAR-sparing. The computational complexity for such optimization increases exponentially with increase in dimensionality. In order to accomplish this task in a clinically-feasible time frame, we present an initial implementation of GPU-based 4D-IMRT planning based on particle swarm optimization (PSO). Methods The target and normal structures were manually contoured on ten phases of a 4DCT scan of a NSCLC patient with a 54cm3 right-lower-lobe tumor (1.5cm motion). Corresponding ten 3D-IMRT plans were created in the Eclipse treatment planning system (Ver-13.6). A vendor-provided scripting interface was used to export 3D-dose matrices corresponding to each control point (10 phases × 9 beams × 166 control points = 14,940), which served as input to PSO. The optimization task was to iteratively adjust the weights of each control point and scale the corresponding dose matrices. In order to handle the large amount of data in GPU memory, dose matrices were sparsified and placed in contiguous memory blocks with the 14,940 weight-variables. PSO was implemented on CPU (dual-Xeon, 3.1GHz) and GPU (dual-K20 Tesla, 2496 cores, 3.52Tflops, each) platforms. NiftyReg, an open-source deformable image registration package, was used to calculate the summed dose. Results The 4D-PSO plan yielded PTV coverage comparable to the clinical ITV-based plan and significantly higher OAR-sparing, as follows: lung Dmean=33%; lung V20=27%; spinal cord Dmax=26%; esophagus Dmax=42%; heart Dmax=0%; heart Dmean=47%. The GPU-PSO processing time for 14940 variables and 7 PSO-particles was 41% that of CPU-PSO (199 vs. 488 minutes). Conclusion Truly 4D-IMRT planning can yield significant OAR dose-sparing while preserving PTV coverage. The corresponding optimization problem is large-scale, non-convex and computationally rigorous. Our initial results indicate that GPU-based PSO with further software optimization can make such planning clinically feasible. This work was supported through funding from the National Institutes of Health and Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not required, such as in certain optimization algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Recent developments in the PySCF program package

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. Here, we explain the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Oxidation Behavior and Property Degradation of Nuclear Graphites

During its multidecade operation in the core of nuclear reactors, graphite components are subjected to aggressive and continuous exposure to a high field of ionizing and neutron irradiation, high temperature, and various types of present and postulated chemical attacks. High density, high crystallinity polygranular synthetic graphite is unique among other materials for its extraordinary capacity of resisting and adapting to the aggression inflicted by high temperature, high energy neutron bombardment and ionizing gamma radiation. But, as a carbonaceous material, even though of very high purity, graphite is reactive towards common oxidizing agents: oxygen, carbon dioxide, water. Safe operation of HTGRs relies, among other aspects, on engineered safeguard systems for efficient and continuous protection of graphite components against oxidation. Graphite oxidation behavior was, and continues to be, an important direction of theoretical and experimental research, engineering analyses, models and simulations, and design and safety regulations. The avalanche of publications, reports, experimental data, computer codes, and regulatory documents related to oxidation behavior of nuclear graphite is now accelerating to new levels, prompted by the increased interest for nuclear energy as a clean, carbon-free energy source. Even though public’s perception of nuclear energy advantages may still be influenced by the memories of past accidents of nuclear reactors from generations II and III, the community of informed scientists and engineers, regulators and statemen knows that generation IV of nuclear reactors is designed at very high safety standards, doubled by great advances of scientific knowledge and technological progress. One of routes of these recent advances is directed at better understanding of graphite oxidation behavior, its relationship with graphite manufacturing and microstructural properties, along with the effects of various environmental factors and process variables. Together, the recent progress in manufacturing, properties characterization, and modeling of intricated physical and chemical processes that concur to the oxidation behavior led to development of powerful simulation codes able to analyze various scenarios of normal operation and hypothetical off-normal events, and thus to clearly specify the allowable parameters envelopes for the designers, constructors, and operators of current and future modular HTGRs. This review begins with an introduction on manufacturing methods, structure, and properties of nuclear graphite, including basic requirements that this specialty graphite type must satisfy for nuclear use. It continues with a chapter on environmental effects on nuclear graphite, where emphasis is placed less on irradiation and much more on oxidation phenomena, their safety implications, and the basic traits of chronic and acute oxidation by air (oxygen) and water (humidity, steam). Particular attention is placed on the three graphite grades of interest for this document (IG-110, NBG-18, PCEA). A chapter on properties degradation induced by oxidation follows, with focus on density, dimensional, and mechanical properties changes. The next chapter is intended as a brief review of various approaches used for modeling of graphite oxidation behavior. It summarizes the progress of oxidation models, from the early attempts to complex computational approaches interfaced with specialized computer codes designed for nuclear reactor simulations. Last, a list is presented of knowledge gaps where more research is needed. A short summary concludes the review.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Correlations of the Elemental Compositions of Primary Coal Tar and Char

We report that simulations of large-scale coal combustors rely on accurate submodels to describe the chemical and physical changes in coal during reaction. Typically, researchers use simplified empirical submodels tuned to experimental data to reduce the computational complexity. When data are not readily available, researchers use simplifying assumptions, which can create inaccuracies and biases in a large simulation. One such simplifying assumption in coal research is how to describe the elemental composition of primary pyrolysis products. This paper explores several different empirical model forms to predict the dry, ash-free fractions of C, H, O, N, and S in both the char and the tar, using variables such as parent coal composition, reaction conditions (temperatures and particle residence times), and key coal structural parameters derived from NMR measurements. These model forms were correlated to existing data using a wide range of experimental data using a cross-validation procedure. Since coal structural values can be expensive to measure, several correlations from the literature were used to estimate these values based on information from the proximate and ultimate analyses of the parent coal, including a new correlation for the coal aromaticity. These model forms were tested against a set of measured elemental compositions of tar and char to find the best fit to use in the cross-validation process. Lastly, the best empirical models are presented that predict elemental composition of the coal char and tar after devolatilization.

01 COAL, LIGNITE, AND PEAT↗