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Results for “activity coefficient model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Association‐based activity coefficient model for electrolyte solutions

Abstract This work presents an association‐based activity coefficient model that explicitly considers the solution nonideality due to associations among ions and solvent species. Built upon the electrolyte nonrandom two‐liquid (eNRTL) model, the model greatly improves the accuracy of eNRTL model for strongly associating electrolyte solutions due to presence of ionic species with high surface charge density. The model successfully correlates mean ionic activity coefficients of 46 aqueous single‐salt systems from 10 cations and 5 anions at 298.15 K up to their solubility limits. With the ion‐specific association parameters identified, the model accurately predicts activity and osmotic coefficients for aqueous mixed‐salt systems at 298.15 K. The temperature dependence of the model results has also been examined at 273–373 K. With superior accuracy over a wide range of concentration and temperature, the model represents a major advancement over eNRTL model and has a great potential to be a next‐generation model for electrolyte solutions.

Lin, Yu‐Jeng↗
DOE OSTI2022

Thermodynamic modeling of aqueous lithium salt solutions with association electrolyte nonrandom two-liquid activity coefficient model

The high charge density of lithium ion and the resulting strong association phenomena make thermodynamic modeling of aqueous lithium electrolyte solutions extremely challenging. In this study, the association electrolyte nonrandom two-liquid activity coefficient model of Lin et al. (AIChE J. 2022, 68(2), e17422) is utilized to correlate and predict thermodynamic properties and solubility behavior of aqueous single electrolyte solutions of LiCl, LiBr, LiI, and LiNO 3 , and their mixed electrolyte solutions. Capturing self-association of water, cross-association of ion and water for hydration, and cross-association of cation and anion for ion-pairing, the association model accurately represents the literature experimental data up to saturation concentrations and at the temperature ranging from 263 K to 523 K. Here, this study further investigated the effect of anions of the lithium salts, and re-confirmed that the order of solution non-ideality as LiI > LiBr > LiCl > LiNO 3 because the anions with stronger association strengths are more likely to form ion pairs and thus lower the mean ionic activity coefficients.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Nonrandom two‐liquid activity coefficient model with association theory

Abstract Considered one of the most versatile and widely used classical thermodynamic models to correlate phase equilibria behavior of nonideal systems, the nonrandom two‐liquid (NRTL) theory does not explicitly account for specific chemical associations such as hydrogen bonding. This deficiency has been recognized as the cause for unsatisfactory representation of association systems like methanol–alkanes binaries. This work presents a practical approach to integrate Wertheim's perturbation theory for association contribution with the classical NRTL model. Specifically, the association contribution is calculated from pre‐determined molecule‐specific association strengths while the physical interaction contribution is captured with NRTL binary interaction parameters. The resulting association NRTL model correlates fluid phase equilibria of association systems with few adjustable parameters and offers improved predictive capability for higher order systems.

Hao, Yifan↗
DOE OSTI2021

Screening of metal complexes and organic solvents using the COSMOSAC-LANL model to enhance the energy density in a non-aqueous redox flow cell: an insight into the solubility

In this paper, we have proposed a first-principles methodology to screen transition metal complexes against a particular organic solvent and organic solvents against a particular transition metal complex based on their solubility information without the knowledge of heat of fusion and melting temperature. The energy density of a non-aqueous redox flow cell directly depends on the solubility of the redox active species in the non-aqueous medium. Here, we have used the “COSMOSAC-LANL” activity coefficient model which is based on first-principles COSMO calculations where the microscopic information is passed to the macroscopic world via a dielectric continuum solvation model, followed by a post-statistical thermodynamic treatment of the self-consistent properties of the solute particle to calculate the solubility. To model the activity coefficient at infinite dilution for the binary mixtures, a 3-suffix Margules (3sM) function is introduced for the quantitative estimation of the asymmetric interactions and, for the combinatorial term, the Staverman–Guggenheim (SG) form is used. The new activity coefficient model is separately called the “LANL” activity coefficient model. The metal complex and the organic solvent have been treated as a simple binary mixture. The present model has been applied to a set of 14 different organic solvents and 16 different transition metal complexes. Using the new LANL activity coefficient model in combination with the ADF-COSMOSAC-2013 model, we have shown how one can improve the solubility of a transition metal complex in an organic solvent. We applied our model to screen 84 binary mixtures to predict the compatible pair of redox active species and organic solvent to increase the energy density. The solvation mechanism of the transition metal complexes in the organic solvents was obtained using the new model. The results have been compared with the experimental and theoretical results where they are available.

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

Generalization of thermodynamic Langmuir isotherm for mixed‐gas adsorption equilibria

Abstract This work presents a comprehensive thermodynamic model for both pure component isotherms and mixed‐gas adsorption equilibria. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed‐gas adsorption equilibria, and it applies an area‐based adsorption nonrandom two‐liquid activity coefficient model in the activity coefficient calculations for the adsorbate phase. The resulting generalized Langmuir isotherm properly captures both surface loading dependence and adsorbate phase composition dependence for mixed‐gas adsorption equilibria. The model is validated with accurate representations of gas adsorption equilibrium data for varieties of unary, binary, and ternary gas systems. The model results are further compared with those calculated from extended Langmuir isotherm and Ideal Adsorbed Solution Theory.

Hamid, Usman↗
DOE OSTI2022

Thermodynamic modeling of adsorption at the liquid-solid interface

Adsorptive separation techniques are significantly energy efficient in comparison to conventional thermal separation techniques such as distillation. Despite extensive research and development activities undertaken for mixed-gas adsorption, the use of adsorption techniques for the separation of multicomponent liquid mixtures is still limited. A major barrier is the lack of accurate adsorption thermodynamic models, which form the scientific foundation of process simulation of such systems, making the translation to industrial scale challenging. In this work, we have rigorously computed the surface excess of adsorption for six binary liquid mixtures on silica gel at 303 K using the frameworks of the generalized Langmuir isotherm (gL) and the adsorbed solution theory (AST). The six binary liquid mixtures were formed by the pair-wise combinations of four components: benzene, 1,2-dichloroethane, cyclohexane, and n-heptane. We have based our calculations by considering simultaneous equilibria of three phases: saturated vapor phase, bulk liquid phase, and adsorbed phase. Further, the composition of the corresponding saturated vapor phase was estimated by the Nonrandom Two-Liquid activity coefficient model and experimental vapor-liquid equilibria data. The activity coefficients of the adsorbed phase, the central issue of multicomponent adsorption thermodynamics, were calculated using the adsorption Nonrandom Two-Liquid activity coefficient model. Devoid of simplifying assumptions, gL and AST provide rigorous thermodynamic frameworks for adsorption equilibria of multicomponent liquid mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Generalized Brunauer–Emmett–Teller Isotherm for Mixed-Gas Multilayer Adsorption Equilibria

Here, this work presents a rigorous thermodynamic framework to calculate mixed-gas multilayer adsorption equilibria from single-component isotherms and vapor–liquid equilibria. Named the generalized Brunauer–Emmett–Teller (gBET) isotherm, the newly formulated isotherm considers adsorbent surface heterogeneity, competitive adsorption on the monolayer, condensation–evaporation on the subsequent layers, and adsorbed phase nonideality for the monolayer and the subsequent layers. The monolayer adsorbed phase nonideality is tracked by using an area-based adsorption nonrandom two-liquid activity coefficient model. The adsorbed phase composition and corresponding nonideality in the subsequent layers are calculated at the dew point condition of the mixed gas with either an equation of state or an activity coefficient model for the vapor–liquid equilibria. The proposed model is validated with six single and three binary multilayer adsorption equilibrium systems, and the model results are compared against those from the classical BET isotherm for single-component adsorption and ideal adsorbed solution theory for mixed-gas adsorption equilibria.

09 BIOMASS FUELS↗
DOE OSTI2023

Activity coefficient acquisition with thermodynamics–informed active learning for phase diagram construction

This work explores the use of thermodynamics-informed Gaussian processes (GPs) and active learning (AL) to model activity coefficients and construct phase diagrams. Relying on synthetic data generated from an excess Gibbs energy model, GPs were found to accurately describe the activity coefficients of several binary mixtures across large composition and temperature ranges. Moreover, GPs could estimate their own uncertainty and identify composition/temperature regions where activity coefficient data provide the most information to the models. This was leveraged to build AL algorithms targeted at modeling phase equilibria. In many cases, a single active-learning-acquired data point was sufficient to describe the phase diagrams studied. Lastly, the ability of AL to greatly reduce the amount of data needed to obtain accurate models was further verified on experimental case studies, namely individual ion activity coefficients, the solid–liquid and vapor–liquid equilibrium of deep eutectic solvents, and phase equilibria in ternary mixtures.

25 ENERGY STORAGE↗
DOE OSTI2024

Development of a rate-based ENRTL-RK process model for a water-lean solvent

Advanced water-lean solvents (WLS) for post-combustion CO2 capture offer several advantages over the aqueous amine solvents . WLS have lower parasitic energy penalty, lower corrosion, lower temperature and high-pressure CO2 regeneration leading to lower cost of CO2 capture. RTI International, with funding from the US Department of Energy, has been developing its novel water-lean solvent, that has shown specific reboiler duty of 2.3 GJ/t-CO2 at the 60-kWe pilot testing unit (Tiller Plant, SINTEF, Norway) and 2.6 GJ/t-CO2 at the engineering scale testing system (12 MWe) at the Technology Centre Mongstad (TCM) in Norway. All heat duties, including the one from TCM testing, were consistent with Aspen Plus modeling of the specific configuration of each test plant. This work focuses on the development of a detailed process model using in-house laboratory measurements and process data at pilot scale. The eNTRL-RK model used in this work is based on an unsymmetric activity coefficient model with the reference states chosen to be pure liquids for solvents and ideal dilute solution at unit solute molality (resulting in activity coefficient of unity at infinite dilution) for electrolytes. It uses the Redlich-Kwong equation of state for vapor phase properties and Henry’s law for solubility of supercritical gases. The model was validated using process data from the pilot-scale campaign at the Tiller plant, and the engineering scale test campaign at TCM. Data on CO2 capture rate, absorber, and regenerator temperature profiles and specific reboiler duties from two different test campaigns at Tiller and TCM, were used to further refine and validate the model and the model compares favorably to experimental data. The validation results against TCM campaign will be presented in this work.

CO2 capture↗
DOE OSTI2021

Modeling swelling behavior of hydrogels in aqueous organic solvents

Hydrogel, a three-dimensional elastic structure of cross-linked polymer chains, swells or deswells when immersed in aqueous organic solutions. The swelling of hydrogels depends on temperature, solvent composition, and hydrogel structure as the thermodynamic driving forces for hydrogel swelling are due to solvent – hydrogel interactions and expansion of elastic network. Here in this work, polymer Nonrandom Two-Liquid activity coefficient model is used to account for the solvent – hydrogel interactions and a semi-empirical expression for rubber elasticity is used to describe the expansion of elastic network. The model successfully correlates data for both swelling and equilibrium phase compositions for n-isopropyl acrylamide hydrogels in water – ethanol, water – acetone, water – n-butanol, and water – methyl isobutyl ketone mixed solvents.

42 ENGINEERING↗
DOE OSTI2023

Investigation into Na and Cs activity coefficients in high salt solutions to support Cs removal in Hanford tank waste

The treatment of Hanford tank waste is one of the most technically challenging environmental cleanup activities for the U.S. Department of Energy to date. To expedite the processing of liquid waste stored in underground tanks in southeastern Washington state, it is necessary to remove the significant dose contributor, 137 Cs. Toward this effort, ion exchange with crystalline silicotitanate (CST) has been employed as part of the Tank Side Cesium Removal system. The model used to predict Cs exchange onto CST was developed using activity coefficients calculated from the Bromley equation. A series of batch contact tests that varied in [Na] were conducted to look at the impact of Na concentration on Cs distribution. Experimental distribution ratios ( K d ) were compared to the distribution ratios predicted using three different activity coefficient models: (1) commercially available HSC software, (2) the Bromley equation, and (3) a simplified approach adapted from Marcos-Arroyo et al. Ultimately, the Bromley method underpredicted the effect of ionic strength on the Na activity coefficient ( γ Na+ ), HSC overestimated the impact of ionic strength on the expected performance due to the Cs activity coefficient ( γ Cs+ ), but the simplified approach predicted the experimental K d values quite well in a binary matrix. In conclusion, expansion of this approach in complex matrices is necessary for application to Hanford tank waste.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Verification Testing of OLI Systems Mixed Solvent Electrolyte Model for the Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 ) System to High Ionic Strength at 25°C

This technical report summarizes model verification results and summary statistics for 41 evaporite mineral solubility cases evaluated by Savannah River National Laboratory using OLI Systems’ aqueous electrolyte thermodynamic modeling software. The 41 verification cases containing a total of 60 solubility curves comprise mineral solubility data from low to high ionic strength at 25°C for the eight-component system Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 O as reported by Harvie et al. (1984). Thermodynamic calculations were executed using OLI Systems’ Stream Analyzer computation module within the OLI Studio software platform (Ver. 11.0, Rev. 11.0.1.9). The Mixed Solvent Electrolyte (MSE) thermodynamic framework was chosen for this investigation because of its superiority in modeling high ionic-strength inorganic salt solutions and actinide redox chemistry and solubility, both of which are relevant to the geological repository conditions at the Waste Isolation Pilot Plant in Carlsbad, New Mexico. Mineral solubility data in various inorganic salt solutions were digitized and extracted from figures generated by Harvie et al. (1984). For each of the 60 solubility curves, a case-specific chemistry model and input file were generated in OLI Studio using OLI Stream Analyzer and the MSE (H 3 O + ion) public databank provided by OLI Systems. Model simulation results were exported to Microsoft Excel to calculate summary statistics and to generate graphs comparing the OLI model predictions to the solubility data. Summary statistics include residuals (model – data) and concordance (accuracy × precision, where precision is indicated by the Pearson correlation coefficient and accuracy accounts for bias and scale differential). Private databanks were not developed, and activity coefficient model regressions were not performed to improve OLI model fits to the data. Of the 41 model verification plots, 83% have a mean of the percent residuals less than or equal to 25%. Similarly, 75% display a concordance greater than or equal to 0.75. Only seven of the 41 verification plots fail to show good agreement between the model and data. Of these seven, three are relevant to the WIPP repository because they involve the Mg-OH-Cl-SO 4 -CO 3 aqueous system. The remaining four address salt solubilities at the pH extremes (strong acid and strong base). It should be noted that in two of the three Mg-OH-Cl-SO 4 -CO 3 system cases, the regressed Harvie et al. (1984) solubility curve also deviated from the data. Lack of agreement between the OLI model-predicted solubility curves and the data is attributable to one or more of the following: specific solid species are not included in the OLI MSE databank; there is significant variation among the different solubility datasets chosen by Harvie et al. (1984); the OLI MSE model’s thermodynamic parameters were determined using different solubility datasets; and the activity coefficient parameters for certain relevant ion-ion and ion-molecule pairs have not been optimized via data regression. Two recommendations for future work are to (1) evaluate solubility data for the Mg-OH-Cl-SO 4 -CO 3 system at high ionic strength and, if necessary, develop a private OLI MSE database that includes missing species and, where necessary, regressed standard state properties and interaction parameters; (2) perform similar verification testing of the OLI model for actinide solubility data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
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 OSTI2022

Thermodynamic modeling of aqueous polyelectrolyte solutions with mixed-valent counterions

Thermodynamic modeling of aqueous polyelectrolyte solutions with salts is of significant interest for many industrial applications. Here this study applies the polyelectrolyte Nonrandom Two-liquid activity coefficient model to aqueous polyelectrolyte solutions with mixed-valent counterions. A modified Delocalized Binding Theory was proposed to determine the polyion condensation fractions of the mixed counterions. This modified theory accounts for the electrostatic binding of the counterions on the polyion, the dissociation entropy of the counterions, and the electrostatic interactions between the uncondensed ionic species. Given the polyion condensation fractions, the critical value of Manning’s parameter ξ and the amounts of uncondensed polyions and counterions can be calculated along with the activity coefficients of mobile ions. The model successfully correlates experimental data for various aqueous polyelectrolyte systems with mixed-valent counterions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Thermodynamic analysis of hydrogel swelling in aqueous sodium chloride solutions

Here, a comprehensive thermodynamic model is presented for swelling and salt partitioning of poly (n-isopropyl acrylamide) hydrogels in aqueous sodium chloride (NaCl) solutions at 298 K. Together with a Helmholtz energy expression for network elastic energy, a modified electrolyte Nonradom Two-Liquid activity coefficient model is used to represent both the long-range electrostatic interactions and the short-range van der Waals interactions present in the gel phase. The model parameters include one network parameter per hydrogel system plus two binary parameters per interaction pair in the polymer–solvent-salt systems. With semiquantitave agreement with experimental data for both hydrogel swelling and salt partitioning up to salt saturation, the analysis suggests the ion hydration between NaCl and water is the root cause for hydrogel deswelling in aqueous NaCl solution at high NaCl concentrations, i.e., NaCl weight fraction >0.03. On the other hand, the strong repulsive interaction between NaCl and hydrogel polymer is the dominant factor for salt partitioning.

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

Linear relationships for modeling CO 2 absorption in aqueous alkanolamine solutions in a thermodynamically consistent way

A thermodynamically consistent model for the carbon dioxide (CO 2 ) absorption in aqueous alkanolamine system is of great importance in the research and development of a CO 2 capture process. To facilitate the development of thermodynamic models, linear Gibbs free energy, enthalpy, and heat capacity relationships using well-known amines as reference are used to correlate the standard reference state properties of ionic species with those of molecular species in the electrolyte system, which has been approved to provide a reliable and consistent way to estimate required parameters when there is minimal or no appropriate experimental data available. Here, the proposed relationships have been applied to the development of an electrolyte nonrandom two liquid (NRTL) activity coefficient model for CO 2 absorption in aqueous 1-amino-2-propanol (A2P) solution, as an example to demonstration the methodology. With limited vapor–liquid equilibrium data and other thermodynamic properties, the parameters in the electrolyte NRTL model are identified with good accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

This work addresses spreading pressure dependence of Real Adsorbed Solution Theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption Nonrandom Furthermore, two-Liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

42 ENGINEERING↗
DOE OSTI2025

Thermodynamic modeling of aqueous acetic acid, butyric acid, and lactic acid solutions

Based on the activity coefficient – fugacity coefficient approach, a rigorous thermodynamic modeling study is presented for accurate correlation of vapor-liquid equilibrium data of aqueous solutions of acetic acid (293 to 391 K), butyric acid (325 to 436 K), lactic acid (378 to 409 K), and acetic acid + butyric acid binary mixture (358 to 421 K). In addition, the pH data of the three aqueous, single carboxylic acid solutions were measured at 298 to 328 K and successfully correlated. Given that these aqueous carboxylic acid solutions exhibit various degrees of association behavior in both vapor and liquid phases, the thermodynamic models considered for this study include the Redlich-Kwong equation of state (RK-EoS) and the Hayden-O’Connell equation of state (HOC-EoS) for the vapor phase fugacity coefficients and the electrolyte non-random two-liquid model (eNRTL) and the association electrolyte non-random two-liquid model (AeNRTL) for the liquid phase activity coefficients. The combination of the HOC-EoS for the vapor phase and the AeNRTL model for the liquid phase is found to provide the best correlation results, consistent with the fact that the HOC-EoS and the AeNRTL model explicitly account for association behaviors in the vapor phase and the liquid phase, respectively.

09 BIOMASS FUELS↗