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DOE OSTI2024

Adsorption Thermodynamics for Process Simulation

Adsorption has rapidly evolved in recent decades and is an established separation technology extensively practiced in gas separation industries and others. However, rigorous thermodynamic modeling of multicomponent adsorption equilibrium remains elusive, and industrial practitioners rely heavily on expensive and time-consuming trial-and-error pilot studies to develop adsorption units. Here, this article highlights the need for rigorous adsorption thermodynamic models and the limitations and deficiencies of existing models such as the extended Langmuir isotherm, dual-process Langmuir isotherm, and adsorbed solution theory. It further presents a series of recent advances in the generalization of the classical Langmuir isotherm of single-component adsorption by deriving an activity coefficient model to account for the adsorbed phase adsorbate–adsorbent interactions, substituting adsorbed phase adsorbate and vacant site concentrations with activities, and extending to multicomponent competitive adsorption equilibrium, both monolayer and multilayer. Requiring a minimum set of physically meaningful model parameters, the generalized Langmuir isotherm for monolayer adsorption and the generalized Brunauer–Emmett–Teller isotherm for multilayer adsorption address various thermodynamic modeling challenges including adsorbent surface heterogeneity, isosteric enthalpies of adsorption, BET surface areas, adsorbed phase nonideality, adsorption azeotrope formation, and multilayer adsorption. Also discussed is the importance of quality adsorption data that cover sufficient temperature, pressure, and composition ranges for reliable determination of the model parameters to support adsorption process simulation, design, and optimization.

09 BIOMASS FUELS↗

DOE OSTI2020

Primary solidification of ternary compounds in Al-rich Al–Ce–Mn alloys

Primary solidification of ternary compounds Al 20 Mn 2 Ce and Al 10 Mn 2 Ce were analyzed through the coupling of the thermodynamic modeling and classic nucleation theory. Thermodynamic models of Al 20 Mn 2 Ce and Al 10 Mn 2 Ce were developed using the CALPHAD approach based on first-principles calculated enthalpy of formation and experimental data obtained from this work and the literature. The analysis suggested that despite the larger thermodynamic driving force for nucleation of Al 10 Mn 2 Ce, nucleation is preferred for the Al 20 Mn 2 Ce phase in the highly undercooled liquid due to its smaller interfacial energy. Therefore, manufacturing methods with rapid cooling rates will favor primary solidification of Al 20 Mn 2 Ce for Al-rich Al–Ce–Mn alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives

One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. Furthermore, the relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

An analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure

The objective of this paper is to develop an analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure. This expression for the temperature is obtained for both constant and variable specific heat models and can be used in common models for the material yield strength that include thermal softening due to increase in temperature. Additionally, the material parameters in the model can easily be calibrated to match known experimental data and the model has been used to determine the value of the shock pressure at the onset of melting during shock loading.

42 ENGINEERING↗

DOE OSTI2021

Understanding the microstructural stability in a y’-strengthened Ni-Fe-Cr-Al-Ti alloy

Ni-Fe-Cr-Al-Ti alloys, with Ni levels near 50 wt.%, have the potential to develop a microstructure consisting of a face-centered cubic ? matrix with the homogeneous precipitation of fine ordered ?’ precipitates similar to traditional Ni-based superalloys with significantly greater Ni content. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), atom probe tomography (APT), and CALPHAD -based thermodynamic modeling were employed to understand the phase stabilities and microstructural evolution in an age-hardenable Ni-27Fe-18Cr-1Co-1.6Al-3.75Ti-1.2Mo-0.03C (wt%) alloy. The primary heat-treatment of solution annealing at 1121°C for 4h and age-hardening treatment at 760 °C for 16h resulted in a microstructure consisting of fine ?’ precipitates in an austenitic matrix along with grain boundary carbides, consistent with thermodynamic calculations. Long-term aging at 900 °C for 250h resulted in the coarsening of ?’ along with a change in the morphology of the precipitates from spherical to a more cuboidal shape. In addition, ? phase formation was observed concomitant with the partial dissolution of the ?’ phase. The ability of computational thermodynamic models to predict microstructural characteristics is discussed.

Gwalani, Bharat↗

DOE OSTI2022

Hybrid Solid Oxide Fuel Cell/Gas Turbine Model Development for Electric Aviation

A thermodynamic model was developed and validated to analyze a high-performance solid oxide fuel cell and gas turbine (SOFC-GT) hybrid power system for electric aviation. This study used a process simulation software package (ProMax) to study the role of SOFC design and operation on the feasibility and performance of the hybrid system. Standard modules, including compressor, turbine, heat exchanger, reforming reactor, and combustor were used from the ProMax tool suite while a custom module was created to simulate the SOFC stack. The model used an SOFC test data set as an input. Additional SOFC stack performance effects, such as pressure, temperature, and utilization of air and fuel, were added from open source data. System performance predictors were SOFC specific power, fuel-to-electricity conversion efficiency, and hybrid system efficiency. Using these input data and predictors, a static thermodynamic performance model was created that can be modified for different system configurations and operating conditions. Prior to creating the final aircraft performance model, initial demonstration models were developed to validate output results. We used the NASA SOFC model as a benchmark, which was created with their Numerical Propulsion System Simulator (NPSS) software framework. Our output results matched within 1% of both the NASA model and open source SOFC performance data. With confidence gained in the accuracy of this model, a 1-MW SOFC-GT hybrid power system was constructed for an aircraft propulsion concept. Overall hybrid system efficiencies of > 75% FTE were observed during standard 36,000 feet cruise flight conditions.

30 DIRECT ENERGY CONVERSION↗

NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

DOE OSTI2026

First-principles thermodynamic assessment of Sr-containing secondary phase formation in strontium-substituted lanthanum manganites for solid oxide cell applications

Sr-secondary phase formation is a potentially significant degradation mode with direct impact upon solid-oxide cell (SOC) commercial viability. A first-principles based thermodynamic study was performed for La 1−x Sr x MnO 3±δ (LSM) perovskites to assess their stability against formation of different Sr-secondary phases, including SrO, SrCrO 4 , SrSO 4 , SrCO 3 , and Sr(OH) 2 , for SOC applications. The Sr-secondary phase formation reaction free energies were determined via a thermodynamic model by combining ab initio lattice dynamics calculations for the solid phases and ab initio thermodynamic data for the gas phases. The current approach expands the previously reported thermodynamic modeling studies by integrating first-principles based point defect equilibria into the thermodynamic analysis. The modeling results obtained using this new approach indicate an increased tendency to form the SrO oxide upon decreasing the oxygen partial pressure. Additionally, the enhancing factors to form the Sr-related secondary phase from the associated SrO activity in LSM are further quantified by considering the equilibrium of SrO reacting with the contaminant gas species as a function of temperature and pressure.

defect thermodynamics modeling↗

DOE OSTI2023

Geochemical Modeling Using OLI Systems Mixed Solvent Electrolyte Model in Support of the Waste Isolation Pilot Plant

Aqueous electrolyte thermodynamic models were developed for synthetic Salado (GWB) and Castile (ERDA-6) brines to inform the experimental design and to facilitate laboratory data interpretation in geochemical studies supporting disposal in the Waste Isolation Pilot Plant (WIPP). The thermodynamic models, which include the relevant vapor-liquid-solid equilibria for the oxidation-reduction conditions of interest, enable computation of system parameters such as activity-based pH, E h [vs. standard hydrogen electrode (SHE)], ionic strength, total dissolved solids, and solution density; the chemical speciation of all phases; saturation tendencies for thermodynamically feasible solids; and changes in brine chemistry because of the addition of H 2 (g), argon, MgO, Fe(0), and other waste form components. The impacts of oxidation-reduction potential (ORP) and pH on aqueous speciation and dominant solid phases were also assessed with the aid of real-solution Pourbaix diagrams for key elements of interest. In addition to the OLI modeling results, limited measurement data for pH and ORP standards are provided, analyzed, and discussed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Formation, cooling history and age of impact events on the IIE iron parent body: Evidence from the Miles meteorite

Most iron meteorites formed in planetary cores during differentiation, but the IIE iron meteorites have chemical and physical features that are inconsistent with this origin. By combining mineral chemistry, mineral modes and three-dimensional petrography, we reconstruct the bulk chemistry of the felsic silicate-bearing Miles IIE iron meteorite and demonstrate that the silicate inclusion compositions are similar to partial melts produced experimentally from an H chondrite composition. We use the reconstructed bulk composition, mineralogy and thermodynamic modelling to show that melting above ~ 1200°C under reducing conditions formed metal (Fe-Ni alloy) and felsic silicate partial melts. Upon cooling, the melts crystallized Mg-rich pyroxenes, Na- and K-rich feldspars, and tridymite. Importantly, this mechanism enriches cosmochemically volatile elements (i.e., those with a 50% condensation temperature of ~430–830°C, like Na and K) to the level found in the felsic silicate inclusions. The presence of crystallographically disordered srilankite (only stable above 1160°C) and an absence of Widmanstätten texture require both high peak temperatures and rapid cooling, which cannot be explained by core formation. Instead, they point to small melt volumes, a transient heat pulse, and small thermal mass, and imply efficient physical segregation of silicate and metallic melts through buoyancy separation followed by rapid cooling that arrested the separation of metal and silicate liquid phases. In situ 207 Pb/ 206 Pb age of 4542.3 ± 4.0 Ma in Zr-oxide and phosphate minerals dates the melting event that formed the silicate inclusions. This age aligns with the earliest ages found in other IIE iron meteorite silicates and requires a heating event ~25 million years after the solar system formed. We found 39 Ar/ 40 Ar ages of 3495 ± 52 Ma (low-T) and 4303 ± 7 Ma (high-T) in a K-feldspar grain, with the 3495 Ma age aligning with later thermal events recorded in other IIE iron meteorites. Dating reveals the complex petrogenetic and thermal history of Miles and the IIE iron meteorites. This is the first IIE iron meteorite found to record evidence of heating at 4.5 and 3.5 Ga likely from impact events. We propose that high-velocity impact(s) into an iron-rich, porous chondritic parent body at ~4.54 Ga produced immiscible metal and silicate melts that cooled rapidly and trapped low density silicate inclusions within high density metal. Other IIE irons that formed at lower peak temperatures (900–1000°C) contain chondritic silicate inclusions and relict chondrules, supporting this conceptual model. In conclusion, this petrogenesis is consistent with thermodynamic modelling, experimental data and the wide range of peak temperatures and cooling rates observed in the IIE iron meteorites.

58 GEOSCIENCES↗

DOE OSTI2024

Model associated with: "Thermodynamic control on the decomposition of organic matter across different electron acceptors"

This model data package is associated with the publication “Thermodynamic control on the decomposition of organic matter across different electron acceptors” submitted to Soil Biology and Biochemistry (Zheng et al., 2023; https://doi.org/10.1016/j.soilbio.2024.109364).In this research, a thermodynamic modeling framework is built to flexibly incorporate both organic matter (OM) molecules and electron acceptors for estimating potential free energy release from various redox reactions and to further predict reaction rates based on Microbial Transition State Theory. The model package includes scripts for thermodynamic modeling and postprocessing. Input Fourier-transform ion cyclotron resonance (FTICR) data are from a previous experimental study (Boye et al., 2018), and model outputs are free energy predictions and stoichiometric coefficients associated with all possible redox reactions.This data package is associated with the project GitHub repository found at MM_bioenergetic_modeling.This data package contains four folders (Input_FTICR, Model, Output, and Output_processing), a file-level metadata (FLMD) csv, and a data dictionary (dd) csv. Please see Zheng_bioenergetic_modeling_flmd.csv for a list of all files contained in this data package and descriptions for each. The Zheng_bioenergetic_modeling_dd.csv file describes the csv column headers. The “Model” folder contains scripts to run energy balance calculations for each electron acceptor. The “Output” folder contains csv files with stoichiometric information from model simulations. And the "Output_processing" folder contains scripts for reaction rate calculations and to generate plots.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Recycling of Lead Pastes from Spent Lead–Acid Batteries: Thermodynamic Constraints for Desulphurization

Lead–acid batteries are important to modern society because of their wide usage and low cost. The primary source for production of new lead–acid batteries is from recycling spent lead–acid batteries. In spent lead–acid batteries, lead is primarily present as lead pastes. In lead pastes, the dominant component is lead sulfate (PbSO 4 , mineral name anglesite) and lead oxide sulfate (PbO•PbSO 4 , mineral name lanarkite), which accounts for more than 60% of lead pastes. In the recycling process for lead–acid batteries, the desulphurization of lead sulfate is the key part to the overall process. In this work, the thermodynamic constraints for desulphurization via the hydrometallurgical route for recycling lead pastes are presented. The thermodynamic constraints are established according to the thermodynamic model that is applicable and important to recycling of lead pastes via hydrometallurgical routes in high ionic strength solutions that are expected to be in industrial processes. The thermodynamic database is based on the Pitzer equations for calculations of activity coefficients of aqueous species. The desulphurization of lead sulfates represented by PbSO 4 can be achieved through the following routes. (1) conversion to lead oxalate in oxalate-bearing solutions; (2) conversion to lead monoxide in alkaline solutions; and (3) conversion to lead carbonate in carbonate solutions. Among the above three routes, the conversion to lead oxalate is environmentally friendly and has a strong thermodynamic driving force. Oxalate-bearing solutions such as oxalic acid and potassium oxalate solutions will provide high activities of oxalate that are many orders of magnitude higher than those required for conversion of anglesite or lanarkite to lead oxalate, in accordance with the thermodynamic model established for the oxalate system. An additional advantage of the oxalate conversion route is that no additional reductant is needed to reduce lead dioxide to lead oxide or lead sulfate, as there is a strong thermodynamic force to convert lead dioxide directly to lead oxalate. As lanarkite is an important sulfate-bearing phase in lead pastes, this study evaluates the solubility constant for lanarkite regarding the following reaction, based on the solubility data, PbO•PbSO 4 + 2H + ⇌ 2Pb 2+ + SO 4 2– + H 2 O(l).

25 ENERGY STORAGE↗

DOE OSTI2022

Unraveling Thermodynamic and Kinetic Contributions to the Stability of Doped Nanocrystalline Alloys using Nanometallic Multilayers

Abstract Targeted doping of grain boundaries is widely pursued as a pathway for combating thermal instabilities in nanocrystalline metals. However, certain dopants predicted to produce grain‐boundary‐segregated nanocrystalline configurations instead form small nanoprecipitates at elevated temperatures that act to kinetically inhibit grain growth. Here, thermodynamic modeling is implemented to select the Mo–Au system for exploring the interplay between thermodynamic and kinetic contributions to nanostructure stability. Using nanoscale multilayers and in situ transmission electron microscopy thermal aging, evolving segregation states and the corresponding phase transitions are mapped with temperature. The microstructure is shown to evolve through a transformation at lower homologous temperatures (<600 °C) where solute atoms cluster and segregate to the grain boundaries, consistent with predictions from thermodynamic models. An increase in temperature to 800 °C is accompanied by coarsening of the grain structure via grain boundary migration but with multiple pinning events uncovered between migrating segments of the grain boundary and local solute clustering. Direct comparison between the thermodynamic predictions and experimental observations of microstructure evolution thus demonstrates a transition from thermodynamically preferred to kinetically inhibited nanocrystalline stability and provides a general framework for decoupling contributions to complex stability transitions while simultaneously targeting a dominant thermal stability regime.

25 ENERGY STORAGE↗

NASA NTRS2013

Development and Integration of an Advanced Stirling Convertor Linear Alternator Model for a Tool Simulating Convertor Performance and Creating Phasor Diagrams

A simple model of the Advanced Stirling Convertors (ASC) linear alternator and an AC bus controller has been developed and combined with a previously developed thermodynamic model of the convertor for a more complete simulation and analysis of the system performance. The model was developed using Sage, a 1-D thermodynamic modeling program that now includes electro-magnetic components. The convertor, consisting of a free-piston Stirling engine combined with a linear alternator, has sufficiently sinusoidal steady-state behavior to allow for phasor analysis of the forces and voltages acting in the system. A MATLAB graphical user interface (GUI) has been developed to interface with the Sage software for simplified use of the ASC model, calculation of forces, and automated creation of phasor diagrams. The GUI allows the user to vary convertor parameters while fixing different input or output parameters and observe the effect on the phasor diagrams or system performance. The new ASC model and GUI help create a better understanding of the relationship between the electrical component voltages and mechanical forces. This allows better insight into the overall convertor dynamics and performance.

Metscher, Jonathan F.↗

NASA NTRS2013

Development and Integration of an Advanced Stirling Convertor Linear Alternator Model for a Tool Simulating Convertor Performance and Creating Phasor Diagrams

Metscher, Jonathan F.↗

DOE OSTI2023

Thermodynamic description of molten salt systems: KCl-LiCl-NaCl and KCl-LiCl-NdCl 3

The mixture of KCl and LiCl has been used as electrolyte in the electrorefining process to recover uranium from used nuclear fuels due to the low melting point. However, lanthanides and sodium in the reactor waste continuously dissolve into it and thus alter its thermodynamic properties. To understand the thermodynamic behavior evolution of the electrolyte with the accumulation of impurities, thermodynamic modeling for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and four constituent binary systems in the entire composition space was performed using the CALPHAD (CALculation of PHAse Diagrams) approach. The ionic liquid was described by the two-sublattice model, where neutral species were introduced to consider short-range ordering (SRO) within the melt, whereas the solid solution was modeled based on the Compound Energy Formalism. Literature data on phase equilibria and thermochemical properties were critically evaluated and used during the optimization of thermodynamic parameters for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and their subsystems. The calculated phase diagrams and mixing enthalpies are in good agreement with the experimental data. The thermodynamic modeling for the KCl-LiCl-NdCl 3 system was carried out for the first time. To fill the gap in experimental measurement, enthalpy of mixing for the KCl-LiCl-NdCl 3 melt was estimated using the surrounded-ion model. These data then served as critical inputs for thermodynamic optimization. Furthermore, the present study can provide insights into thermodynamic property evolution of the electrolyte and solubility limit of various impurities during the electrorefining process.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Thermodynamic control on the decomposition of organic matter across different electron acceptors

The increasing availability of high-resolution characterization of natural organic matter (OM) data has shifted the paradigm of lumped descriptions of OM components and potential microbial activities. Our recent development of a substrate-explicit thermodynamic model uniquely enables incorporating complex OM pools to formulate biogeochemical reaction models based on their elemental compositions. While this previous work facilitates prediction of aerobic respiration of complex OM, it is equally imperative to consider the role of non-oxygenic electron acceptors in regulating OM turnover and the fate of carbon. In this study, we significantly expand our previous model by flexibly incorporating both detailed OM chemistry and electron acceptors other than oxygen. Here, our modeling analysis has revealed substantial variations in the energy status of OM molecules across different soils, which drive the co-occurrence of different electron-accepting processes. We demonstrated the effectiveness of the proposed model using a consistency check with experimental data. Through systematic evaluation of the impact of diverse chemical inputs (both electron donors and acceptors) on OM decomposition, the new model also revealed how key microbial growth parameters such as carbon use efficiency (CUE) and reaction rates vary across different electron-accepting processes. Our model provides a unified framework integrating thermodynamic and kinetic constraints on microbial metabolic activities. It complements traditional kinetic models, which are often designed solely to capture mass fluxes. We conclude that thermodynamic modeling emerges as a powerful tool for describing the mechanisms underlying the interplay between microbial growth and OM chemistry and cycling across different electron acceptors, enhancing our ability to project complex ecosystem behaviors in dynamic environments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Triple_Conducting_Perovskite_Defect_Model

An Octave based script for solving defect thermodynamic model to generate Brouwer diagram of triple conducting perovskite as a function of temperature, P(O2)/P(H2O), or P(H2)/P(H2O) based on nonstoichiometry dependent defect formation energies and entropies.

Brouwer diagram↗