Thermodynamic Model Parameters Research Articles

Phase Equilibria and Minor Element Distributions in Complex Copper/Slag/Matte Systems

To address the increasing complexity of feed materials to pyrometallurgical processes, an integrated experimental and thermodynamic modeling research program is in progress to accurately characterize the multi-phase gas-slag-matte-speiss-metal-solids 17-component Cu/Pb-(Cu2O-PbO-ZnO-CaO-FeO-Fe2O3-SiO2)-(Al2O3-MgO)-S-(As-Bi-Sb-Sn-Ag-Au-Ni) system. New experimental data are used to continuously improve the thermodynamic database using FactSage. An example is provided on the slag-matte distributions of Bi, Pb, and Zn in equilibrium with tridymite in the Cu-Fe-O-S-Si system under copper smelting conditions. A closed system equilibration experimental technique with rapid quenching was used. Major element concentrations in phases were measured with electron probe x-ray microanalysis. A laser ablation inductively coupled plasma mass spectrum technique was used for determination of Bi, Pb, and Zn concentrations in slag. New experimental data contributed to the optimization of thermodynamic model parameters. Improved thermodynamic databases can be used to accurately predict the elemental distributions in multi-component systems; an example is given for the minor element distributions between slag and matte for industrial conditions.

Modeling the acentric factor of binary and ternary mixtures of ionic liquids using advanced intelligent systems

Ionic liquids (ILs) have found application in wide range of areas including petroleum industry, extractive distillation, raw material processing, additives for lubricants, functional materials, and catalyst for organic processes. Despite their applications in various fields of science, the use of ILs has been of questionable existence due to their induced toxic effects. To study the phase behavior of these ILs, various methods of obtaining data have been proposed. Notably, the main source of data comes from the laboratory experiments. Despite the existence of experimental methods to quantify the vapor-liquid equilibrium behavior of a fluid – IL system, it is necessary to build a model that can predict the behavior of the system at various states such as, changing temperature, pressure, and volume. Notwithstanding the huge cost and time required during experiments, thermodynamic model has found increasing use for modeling complex mixtures and/or compounds. One of the key parameters of the various thermodynamic models is the acentric factor, which dictates the level of sphericity of a molecule. In this study, the authors explored two different intelligent systems to estimate this key property for binary and ternary mixtures. The algorithm considered in this study include the least square support vector machine and artificial neural network. The input parameters considered include the critical temperature and volume, mole fraction of the solvent(s) and ionic liquid, molecular weight, density of the mixture, and temperature of the fluid. The comparison between the best model and experimental data point indicates very low root mean square error of 0.0164 and 0.0005 for the binary and ternary mixtures respectively. Similarly, the best model produced a very high correlation coefficient of 0.9826 and 1.0000 for the binary and ternary mixtures respectively.

Thermodynamic modeling of G-phase and assessment of phase stabilities in reactor pressure vessel steels and cast duplex stainless steels

Thermodynamic modeling of G-phase in iron-based multicomponent systems was revised and updated by means of a careful literature survey. The thermodynamic parameters were optimized based on DFT data. Additionally intermetallic phases with possible competition to G-phase in multicomponent systems were also optimized. The thermodynamic model parameters were added to multicomponent thermodynamic database and used for calculation of technological steels and possible competition between phases are tested and shown.

Prediction of the solid-liquid interface energy of a multicomponent metallic alloy via a solid-liquid interface sublattice model

Despite central roles in solidification and crystal growth, the solid-liquid interface energy σsl of the multicomponent metallic alloys is scarce and scattered because of the experimental complexity in measurements. Moreover, the theoretical prediction of σsl of the metallic alloy has been long suffered from the incomplete understanding of the solid-liquid interface structures. In this paper, the solid-liquid interface of the metallic alloy is reduced to a two-dimensional layer composed of the solid sublattice and liquid sublattice that is further sandwiched by the bulk solid and liquid phases. This enables the well-defined enthalpy and entropy hence the Gibbs energy model of the metallic solid-liquid interface layer. Via a constraint minimization of the solid-liquid interface layer Gibbs energy, the composition- and temperature-dependent σsl of the Al-based and Ag-based alloys are calculated by coupling with the available thermodynamic model parameters of the alloys. The calculation results are validated by the experimental data. It demonstrates that the built interface sublattice model offers a self-consistent framework for the automatic prediction of σsl of the metallic alloys ranging from the binary to a multicomponent system. It thus provides a more compelling solution to the long-standing issue associated with the modeling of the solid-liquid interface thermodynamics of the metallic alloys under both undercooling and equilibrium states.

Experimental Liquidus Study of the Ternary CaO-ZnO-SiO2 System

Phase equilibria of the ternary CaO-ZnO-SiO2 system have been investigated at 1170 °C to 1691 °C for oxide liquid in equilibrium with air and solid oxide phases: tridymite or cristobalite SiO2 (up to two immiscible liquids), pseudowollastonite (CS) CaSiO3, rankinite (C3S2) Ca3Si2O7, dicalcium silicate (C2S) (Ca, Zn)2SiO4, tricalcium silicate (C3S) (Ca, Zn)3SiO5, lime (Ca, Zn)O, zincite (Zn, Ca)O, willemite Zn2SiO4 and hardystonite (melilite) Ca2ZnSi2O7, covering the ranges of concentrations not studied before. High-temperature equilibration on primary phase (silica) or inert metal (platinum) substrates followed by quenching and direct measurement of the Ca, Zn and Si concentrations in the phases with the electron probe X-ray microanalysis (EPMA) has been used to accurately characterize the system. Liquidus phase equilibrium data of the present authors for the CaO-ZnO-SiO2 system are essential to obtain a self-consistent set of parameters of thermodynamic models for all phases.

A combination of low‐temperature reactive and extractive distillation for methoxy‐2‐propyl acetate synthesis and separation process: simulations and experiments

AbstractBACKGROUNDEsterification of methoxy propanol (MP) and acetic acid (HAC) to methoxy‐2‐propyl acetate (MPA) is a typical reversible reaction. The yield of MPA is low owing to the limitation of chemical equilibrium. In the present study, with the goal of increasing the reaction conversion and preventing the NKC‐9 cation exchange resin catalyst from deactivation at high temperature, a process combining low‐temperature reactive and extractive distillation with cyclohexane (C6H12) as entrainer was investigated by process simulations and experiment methods.RESULTSThe intrinsic kinetic parameters were obtained by catalyst activity evaluation in a batch reactor. Binary interaction parameters of thermodynamic models were determined by the measurement and fitting of vapor–liquid equilibrium data. The effects of different operating parameters on the reaction conversion and column performance were examined in detail, and a production process of MPA with an annual output of 56 000 tons was suggested. The results showed that the purity of MPA reached nearly 100% after further purification following reactive distillation, and the reaction temperature was controlled in the range 75–80 °C, which allowed long‐term operation thermal stability of the catalyst.CONCLUSIONThe developed low‐temperature reactive distillation method ensured a long life of the ion exchange resin catalyst, which should provide insights into further advances of MPA industrial production. © 2019 Society of Chemical Industry

Separation of azeotropic mixture (2, 2, 3, 3-Tetrafluoro-1-propanol + water) by extractive distillation: Entrainers selection and vapour-liquid equilibrium measurements

For separating the azeotrope of 2, 2, 3, 3-tetrafluoro-1-propanol (TFP) and water by extractive distillation, N-methyl pyrrolidone (NMP), N-methyl formamide (NMF) and N, N-dimethyl formamide (DMF) were selected as entrainers using the COSMO-SAC model based on solvent capacity. And the charge density surface of entrainers and each component in the azeotrope system were calculated. The vapour-liquid equilibrium (VLE) data for the mixtures (TFP + NMP), (TFP + NMF) and (TFP + DMF) were measured by a modified Rose-type recirculating still at the pressure 101.3 kPa. The thermodynamic consistency for the VLE data was validated using the Herington and van Ness methods. The VLE data were correlated with NRTL, Wilson and UNIQUAC models, and the interaction parameters of thermodynamic models were fitted. Meanwhile, the effect of the entrainers on the VLE for TFP and water was explored. Compared with NMF and DMF, NMP was adopted as the suitable entrainer for separation of the azeotropic mixture TFP and water by extractive distillation.

ESPEI for efficient thermodynamic database development, modification, and uncertainty quantification: application to Cu–Mg

Abstract

Quantified uncertainty in thermodynamic modeling for materials design

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In most previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition or temperature) and was unable to represent the uncertainty in invariant reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition, activity and Gibbs energy on X-T-P location - irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design.

Simultaneous Parameter Optimization of an Arctic Sea Ice–Ocean Model by a Genetic Algorithm

AbstractImprovement and optimization of numerical sea ice models are of great relevance for understanding the role of sea ice in the climate system. They are also a prerequisite for meaningful prediction. To improve the simulated sea ice properties, we develop an objective parameter optimization system for a coupled sea ice–ocean model based on a genetic algorithm. To take the interrelation of dynamic and thermodynamic model parameters into account, the system is set up to optimize 15 model parameters simultaneously. The optimization is minimizing a cost function composed of the model–observation misfit of three sea ice quantities (concentration, drift, and thickness). The system is applied for a domain covering the entire Arctic and northern North Atlantic Ocean with an optimization window of about two decades (1990–2012). It successfully improves the simulated sea ice properties not only during the period of optimization but also in a validation period (2013–16). The similarity of the final values of the cost function and the resulting sea ice fields from a set of 11 independent optimizations suggest that the obtained sea ice fields are close to the best possible achievable by the current model setup, which allows us to identify limitations of the model formulation. The optimized parameters are applied for a simulation with a higher-resolution model to examine a portability of the parameters. The result shows good portability, while at the same time, it shows the importance of the oceanic conditions for the portability.

Separation of the mixture (isopropyl alcohol + diisopropyl ether + n-propanol): Entrainer selection, interaction exploration and vapour-liquid equilibrium measurements

For separation of the mixture {isopropyl alcohol (IPA) + diisopropyl ether (DIPE) + n-propanol (NPA)} by extractive distillation, propylene glycol ethyl ether (PGEE) was used as an entrainer based on selectivity since isopropyl alcohol + diisopropyl ether can an azeotrope. To explore the interaction mechanism between the entrainer PGEE and the components in the mixture, the charge density surface (σ-profiles) and the interaction energies were calculated based on the COSMO-SAC model and Dmol3, which could provide theoretical insight into interactions at the molecular level. Then, the data of isobaric vapour-liquid equilibrium (VLE) for (IPA + PGEE), (DIPE + PGEE) and (NPA + PGEE) systems were measured at 101.3 kPa. The NRTL, UNIQUAC and Wilson equations were applied to correlate the measured VLE data, and the thermodynamic model parameters for the binary systems were obtained by fitting the VLE data, which is helpful for the simulation and optimization of the separation process.

Experimental Investigation and Thermodynamic Modeling of the Distributions of Ag and Au Between Slag, Matte, and Metal in the Cu–Fe–O–S–Si System

To assist in improving the recoveries of gold and silver in both primary production and metals’ recycling, the distributions of Ag and Au between slag, matte, and metal in the Cu–Fe–O–S–Si system have been investigated using an integrated experimental and thermodynamic modeling approach. The experimental technique involved high-temperature equilibration at selected temperatures and gas atmospheres, and rapid quenching followed up by measurement of phase compositions using microanalysis techniques. Electron probe X-ray microanalysis was used to measure the major element concentrations in the condensed phases. The laser ablation inductively coupled plasma mass spectrum technique was used to measure the concentrations of Ag and Au in slag. The experimentally determined distribution coefficient of Ag between matte and slag decreases with the increasing matte grade below approximately 70% Cu, but then increases with the increasing matte grade between 70 and 80% Cu. The experimentally determined distribution coefficient of Au between matte and slag decrease from log L = − 2.8 for approximately 63% Cu to approximately log L = − 3.8 at 76% Cu. Thermodynamic model parameters describing Ag and Au distributions have been derived following consideration of available data on slag/matte, slag/metal, and slag/matte/metal systems.

Integrated experimental study and thermodynamic modelling of the distribution of arsenic between phases in the Cu-Fe-O-S-Si system

An integrated experimental study and thermodynamic modelling approach has been used in the investigation of the distribution of As between slag and matte in equilibrium with tridymite in the Cu-Fe-O-S-Si system. The experimental technique involves high-temperature equilibration in sealed quartz ampoule, rapid quenching, and direct measurements of phase compositions using microanalysis techniques. Electron Probe X-ray Microanalysis (EPMA) was used to measure major and minor element concentrations in the matte, slag, and solid phases. The experimentally-determined distribution coefficient of As between slag and matte was found to decrease with decreasing P(SO2) from log L = 0.5 at P(SO2) = 25 kPa to approximately log L = −4.0 at lowest P(SO2), corresponding to metal saturation. Thermodynamic model parameters describing As distribution have been derived based on the present and previous data on the slag/matte, slag/metal, and slag/matte/metal equilibria. The thermodynamic model can be used for the evaluation of distribution of As between phases in the high-temperature pyrometallurgical production and refining of copper.

Experimental and thermodynamic study of Li‐O and Li2O‐P2O5 systems

AbstractLiFePO4 (LFP) as a promising cathode material has been extensively studied. However, the high cost of current batch production technology limits its application, especially in automotive industries. To develop the new melting synthesis of LFP, the process conditions have to be strictly controlled, such as temperature, composition, and the partial pressure of oxygen. Reliable and accurate thermodynamic information about Li‐Fe‐P‐O systems could serve as a useful guide for designing operating conditions. As part of ongoing efforts, the Li‐O and Li2O‐P2O5 binary systems have been first studied following the CALPHAD method using FactSage thermodynamic software. The data on thermodynamic properties (Cp, enthalpy of formation, and vapor pressure) and phase diagrams (liquidus/solidus temperature, phase transition, and solid solubility) available in the literature were carefully reviewed and evaluated for the above‐mentioned systems. The modified quasichemical model (MQM) with quadruplet approximation was used for the liquid phase in the present studies. This model simultaneously takes into account the short‐range ordering of first‐nearest‐neighbours (FNN) and second‐nearest‐neighbours (SNN), which improves the thermodynamic description of the Gibbs energy of the liquid. The thermodynamic model parameters of the Gibbs energy have been obtained for all of the phases considered in the Li‐O and Li2O‐P2O5 binary systems. DSC‐TGA experiments on the selected four compositions were carried out to validate the liquidus and phase transition temperature reported in the literature. Overall, the self‐consistent thermodynamic description using the model parameters obtained in this work can successfully reproduce the evaluated experimental data.

Isobaric vapor–liquid equilibrium of three binary systems containing dimethyl succinate, dimethyl glutarate and dimethyl adipate at 2, 5.2 and 8.3 kPa

The isobaric vapor–liquid equilibrium (VLE) data for three binary systems of dimethyl succinate (DMS) + dimethyl glutarate (DMG), dimethyl succinate + dimethyl adipate (DMA) and dimethyl glutarate + dimethyl adipate were determined at 2, 5.2 and 8.3 kPa with a dynamic recirculating apparatus and the temperature ranged from 363.39 to 422.4 K. All the experimental data were verified to be thermodynamically consistent according to the Herington method and point to point method of Van Ness test. Afterwards, the VLE data were correlated with Nonrandom two-liquid (NRTL), Wilson and UNIQUAC activity coefficient models, and the interaction parameters of thermodynamic models of these three binary systems were obtained. The results indicated that the calculated values of these three models agreed well with the experimental data, while the NRTL model and UNIQUAC model provided a slightly better result than Wilson model. The calculated root mean square deviations of NRTL model for the temperature and vapor-phase mole fraction were less than 0.13 K, and 0.0023, respectively.

Experimental Liquidus Study of the Binary PbO-CaO and Ternary PbO-CaO-SiO2 Systems

Phase equilibria of the binary PbO-CaO and ternary PbO-CaO-SiO2 systems have been investigated at 870-1655 °C for oxide liquid in equilibrium with air and solid oxide phases: tridymite or cristobalite SiO2, pseudowollastonite CaSiO3, dicalcium silicate (Ca,Pb)2SiO4, tricalcium silicate (Ca1−xPbx)3SiO5 (x < 0.03), new phase tricalcium-lead silicate (Ca0.8Pb0.2)3SiO5 (Ca12Pb3Si5O25), lime CaO, and calcium plumbate Ca2PbO4, covering the ranges of concentrations not studied before. High-temperature equilibration on primary phase or inert metal (platinum, gold) substrates, followed by quenching and direct measurement of the Pb, Ca and Si concentrations in the phases with the electron probe x-ray microanalysis (EPMA) has been used to accurately characterize the system. Liquidus phase equilibrium data of the present authors for the PbO-CaO-SiO2 system are essential to obtain a self-consistent set of parameters of thermodynamic models for all phases.

Isobaric Vapor–Liquid Equilibrium Measurements for Separation of Azeotrope (Methanol + Methyl Acetate)

For separation of the azeotrope (methanol + methyl acetate), extractive distillation is applied and isobutyl acetate, isopentyl acetate, and p-xylene are chosen as the entrainers. To obtain the binary interaction parameters of thermodynamic models for design of the extractive distillation process, the isobaric vapor–liquid equilibrium (VLE) data for the three binary systems of (methyl acetate + isobutyl acetate), (methyl acetate + isopentyl acetate), and (methyl acetate + p-xylene) were determined at the pressure of 101.3 kPa. The thermodynamic consistency for the VLE experimental data of the three mixtures were tested by the Herington and van Ness methods. The NRTL, UNIQUAC, and Wilson thermodynamic models were adopted to correlate the VLE experimental data, and the binary interaction parameters of the three models were regressed.

Isothermal Bubble Pressure Data for the Binary System of C2F6 and n-Octane

Bubble pressure data for the system of hexafluoroethane and n-octane were measured at four temperatures in the range of (292.9 to 323.4) K and at pressures of up to 5.6 MPa. These isothermal P–x data were measured using a variable-volume static-synthetic apparatus. The Peng–Robinson Equation of State modified with the Mathias–Copeman alpha function coupled to the Wong–Sandler mixing rule was used to model the experimental data. The nonrandom two-liquid activity coefficient model was used to model the excess Gibbs energy term within the Wong–Sandler mixing rule. The temperature dependency of the thermodynamic model parameters was investigated at the temperatures for which data were measured. The binary system was categorized according to the van Konynenburg and Scott classification system.

Technical note: Comparison and interconversion of pH based on different standard states for aerosol acidity characterization

Abstract. Aerosol pH is often calculated based on different standard states thus making it inappropriate to compare aerosol acidity parameters derived thereby. However, such comparisons are routinely performed in the atmospheric science community. This study attempts to address this issue by comparing PM2.5 aerosol pH based on different scales (molarity, molality and mole fraction) on the basis of theoretical considerations followed with a set of field data from Guangzhou, China as an example. The three most widely used thermodynamic models (E-AIM-IV, ISORROPIA-II, and AIOMFAC) are employed for the comparison. Established theory dictates that the difference between pHx (mole fraction based) and pHm (molality based) is always a constant (1.74, when the solvent is water) within a thermodynamic model regardless of aerosol property. In contrast, pHm and pHc (molarity based) are almost identical with a minor effect from temperature and pressure. However, when the activity coefficient is simplified as unity by thermodynamic models, the difference between pHm and pHc ranges from 0.11 to 0.25 pH units, depending on the chemical composition and the density of hygroscopic aerosol. Therefore, while evaluating aerosol acidity (especially, trend analysis) when the activity coefficient is simplified as 1, considering the pH scale is important. The application of this pH standardization protocol might influence some conclusions on aerosol acidity reported by past studies, and thus a clear definition of pH and a precise statement of thermodynamic model parameters are recommended to avoid bias when pH comparisons are made across studies.

Application of the unscented transform in the uncertainty propagation of thermodynamic model parameters

The choice of an appropriate thermodynamic model is one of the critical concerns in the chemical process simulation problems. After the selection of the most appropriate thermodynamic model, the uncertainties associated with the parameters of the model should be taken into account and the effects of such uncertainties should be addressed in the chemical plant design.In this work, the assumption of normal probability distributions for thermodynamic model parameters is coupled with unscented transform for efficient uncertainty propagation and obtaining probabilistic characteristics of output variables of the simulation model. The proposed methodology can be used easily when the input-output representation of the system such as process simulators are used as the modeling tool of the chemical processes. The law sampling points required in the unscented transform formulation can considerably reduce the computational burden while an acceptable accuracy compared to Monte Carlo techniques can be obtained. The methodology is illustrated by two case studies.