Vapor-liquid Equilibrium Phase Diagrams Research Articles

A clean and short process for the preparation of refined indium and investigation of migration distribution pattern of impurities thallium and tin via vacuum distillation

In this study, a novel two-stage vacuum distillation method was proposed to refine crude indium to prepare refined indium. Low-temperature distillation (1223K, holding time of 3h) and high-temperature distillation (1473K, holding time of 5h) were conducted under a system pressure of 7 × 10−3Pa to successfully purify crude indium (99 wt%) to refined indium (99.995 wt%). This strategy can replace the traditional electrolytic process for the clean production of refined indium and achieve the goals of environmental protection. The vapor-liquid equilibrium (VLE) values of indium-based binary alloys were calculated using the molecular interaction volume model (MIVM), and a VLE phase diagram was drawn. Optimal temperatures of 1173K for low-temperature and 1373K for high-temperature distillation were determined based on the VLE phase diagram, and good purification was achieved. Moreover, this study reveals the migration distribution pattern of typical impurity elements (e.g., Tl and Sn) in crude indium in the low and high-temperature distillation sections, further improving the refining effect. Notably, the combination of MIVM simulations and experiments can obtain optimal experimental parameters for segmental vacuum distillation and further help to avoid the waste of raw materials and energy caused by pre-experiments, realizing the clean and efficient production of refined indium.

Vacuum distillation: A sustainable separation and purification approach for extracting valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys

The vacuum distillation (VD) method was studied for extraction of valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys. The VD studies were carried out between 773 K and 1073 K, at 5 Pa, and for 60 min for the In–Zn alloys. The In content in the residues was greater than 99.999 wt%, and the Zn content in the volatiles was the highest at 99.8962 wt%. For the In-Sn alloys, the VD experiments were carried out from 1323 K to 1573 K at 5 Pa for 540 min for the In–Sn alloys. The Sn content in the residues exceeded 99.9963 wt%, whereas the In content in the volatiles was 99.86 wt%. Further, the In–Sn–Zn VD was carried out between 773 K and 1073 K at 5 Pa for 90 min. The Zn content of the residues decreased from 6.0 wt% to 0.0009 wt%, while the Zn content of the volatiles was 99.79 wt%. Using the M-MIVM and vapor–liquid equilibrium (VLE) theories, the VLE data was predicted and the related phase diagrams for the binary and ternary alloys were displayed. The remarkable similarity between theoretical and experimental VLE phase diagrams demonstrates the reliability of the M-MIVM for In-based alloys.

Clean and efficient recovery of In–Sn and In–Sn–Bi lead-free brazing materials by vacuum volatilization and thermodynamic modeling

In this study, a novel method was proposed for the clean and efficient recovery of high-value-added In–Sn and In–Sn–Bi alloys. Vacuum volatilization of the In–Sn binary alloy was conducted in a temperature range of 1373–1573 K with a system pressure of 5 Pa. The results showed that In and Sn were effectively separated. The Sn content in the residue was 99.9908%, and the In content in the volatile fraction reached 99.66%. Vacuum volatilization of the In–Sn–Bi ternary alloy was conducted out at 1073–1373 K and 5 Pa. The results showed that Bi could be separated from In and Sn, the Bi content in the residue decreased from 32.5% to 3.88%, and the Bi content in the volatile fraction reached 95.67%. The residual In–Sn alloy could be effectively separated by vacuum volatilization. The MIVM, M-MIVM, Wilson equation and NRTL were used to calculate and analyze the activity and activity coefficients of In–Sn, In–Bi, Sn–Bi and In–Sn–Bi alloy elements, respectively, and the results showed that M-MIVM had the highest prediction accuracy. The vapor-liquid equilibrium (VLE) data of the In–Sn, In–Bi, Sn–Bi, and In–Sn–Bi alloys were predicted, and the corresponding VLE phase diagrams were plotted based on the M-MIVM and VLE theory. The predicted VLE values were in good agreement with the corresponding experimental data determined in this study, indicating that the M-MIVM was reliable for indium-based alloys. The results of this work provided reliable experimental data and a thermodynamic model for the VLE study of In-based alloys, opening a new technique for the clean and efficient recycling of binary and multicomponent In-based alloys.

Theoretical research on vacuum separation of Au−Ag alloy

To provide an accurate prediction of the product component dependence of temperature and pressure in vacuum distillation and give convenient and efficient guidance for the designing of the process parameters of industrial production, according to the molecular interaction volume model (MIVM), the separation coefficient (β) and vapor−liquid equilibrium composition of Au−Ag alloy at different temperatures are calculated. Combined with the vapor−liquid equilibrium (VLE) theory, the VLE phase diagrams, including the temperature−composition (T−x) and pressure−composition (p−x) diagrams of Au−Ag alloy in vacuum distillation are plotted. The triple points and condensation temperatures of gold and silver vapors are calculated as well. The results show that the β decreases and the contents of gold in vapor phase increase with the distillation temperature increasing. Low pressures have positive effect on the separation of Ag and Au. The difference between the condensation temperatures of gold and silver is about 450 K in the pressure range of 1−10 Pa.

Calculation of vapor-liquid equilibrium of binary precious metal alloys using modified molecular interaction volume model

In this work, the activities and activity coefficients of binary precious metal alloys (Ag-Pb, Ag-Sb, Ag-Bi, Au-Pb, Pd-Pb, Pt-Pb and Cu-Pb) were predicted using molecular interaction volume model (MIVM), modified MIVM (M-MIVM), Wilson equation and nonrandom two-liquid (NRTL) model. The average standard deviation and average relative deviations of these models were also calculated. The results show that the prediction deviations of the M-MIVM were smallest among the four thermodynamic models, indicating that the M-MIVM is reliable. On this premise, the separation coefficient and vapor-liquid equilibrium (VLE) data of Ag-Pb, Au-Pb, Pd-Pb and Pt-Pb were calculated based on the M-MIVM. The results show that the separation coefficients were much larger than one, indicating that these alloys can be easily separated by vacuum distillation. There is good agreement between the predicted and experiment VLE data, indicating that M-MIVM is reliable for the VLE calculation in vacuum distillation. The VLE phase diagrams procured in this work can afford theoretical guidance for experimental design and industrial production in vacuum distillation.

Experimental investigation and modeling of vapor-liquid equilibria for Bi–Zn and Bi–Sn–Zn systems at 10 Pa

For the Bi–Zn and Bi–Sn–Zn systems, vacuum distillation experiments were carried out at 10 Pa. The results show that the content of Zn for the Bi–Zn system in the vapor phase could reach more than 0.999 mol fraction in vacuum distillation. The VLE (vapor-liquid equilibrium) data were correlated using the Tsuboka-Katayama's modification of the Wilson equation (T-K-Wilson). The correlation showed good agreement with experimental data. Thermodynamic consistency tests of experimental data for the binary and ternary systems were presented by the Van Ness method. The results demonstrate that VLE phase diagram is reliable for predicting the process of vacuum distillation for the systems. It provides an efficient way to guide the separation and purification of crude Zn in vacuum metallurgy

Vacuum separation of zinc-silver alloy: Measurement and modeling of vapor-liquid equilibrium

Vacuum distillation of a zinc-silver (Zn–Ag) alloy under a system pressure of 5–10 Pa was conducted in the temperature range of 1173–1373 K. The Zn content in the Zn–Ag alloy was reduced from 70.80 wt% to 0.0026 wt% via a single-stage distillation process at a temperature >1373 K. The molecular interaction volume model (MIVM) was reasonably simplified. The activities of the Zn–Ag alloy components were calculated using the simplified molecular interaction volume model (SMIVM). The calculated average standard deviation for Zn and Ag were ±0.0078 and ±0.0082, and the average relative deviations were ±4.6758% and ±4.7564%, respectively. Simplicity and reliability are significant advantages of the SMIVM. The vapor-liquid equilibrium (VLE) phase diagram (T-x diagram) of the Zn–Ag alloy during vacuum distillation was calculated using the SMIVM and VLE theory. The results agree with the VLE data determined from experiments, which indicate that the resulting VLE phase diagram is reliable. The VLE phase diagram of alloys provides an intuitive and effective method for process optimization, development, and prediction of the dependence of product composition on system pressure and temperature during vacuum distillation.

Molecular Mechanism for Azeotrope Formation in Ethanol/Benzene Binary Mixtures through Gibbs Ensemble Monte Carlo Simulation.

Azeotropes have been studied for decades due to the challenges they impose on separation processes but fundamental understanding at the molecular level remains limited. Although molecular simulation has demonstrated its capability of predicting mixture vapor-liquid equilibrium (VLE) behaviors, including azeotropes, its potential for mechanistic investigation has not been fully exploited. In this study, we use the united atom transferable potentials for phase equilibria (TraPPE-UA) force field to model the ethanol/benzene mixture, which displays a positive azeotrope. Gibbs ensemble Monte Carlo (GEMC) simulation is performed to predict the VLE phase diagram, including an azeotrope point. The results accurately agree with experimental measurements. We argue that the molecular mechanism of azeotrope formation cannot be fully understood by studying the mixture liquid-state stability at the azeotrope point alone. Rather, azeotrope occurrence is only a reflection of the changing relative volatility between the two components over a much wider composition range. A thermodynamic criterion is thus proposed on the basis of the comparison of partial excess Gibbs energy between the components. In the ethanol/benzene system, molecular energetics shows that with increasing ethanol mole fraction, its volatility initially decreases but later plateaus, while benzene volatility is initially nearly constant and only starts to decrease when its mole fraction is low. Analysis of the mixture liquid structure, including a detailed investigation of ethanol hydrogen-bonding configurations at different composition levels, reveals the underlying molecular mechanism for the changing volatilities responsible for the azeotrope.

The Equilibrium of the System “Gas–Liquid” for Alloy Sn-Sb in Vacuum Distillation

In the processing of lead bullion necessary to separate the metal from impurities – copper, tin, antimony, arsenic, silver, bismuth, and with the possible use of environmentally friendly, technologically effi cient and cost-eff ective high performance vacuum distillation. To analyze the behavior of multicomponent alloy processing, pre-selection of temperature and pressure of the system, evaluate the eff ectiveness of component separation in a vacuum distillation using phase diagrams temperature–composition “of T–h,” pressure–composition “R–x”. The aim of this work was to calculate the equilibrium “gas–liquid” VLE (vapor liquid equilibrium), including the dependence of phase composition on temperature (T-x) and pressure (P-x) for Sn-Sb alloy during vacuum distillation on the basis of the three-dimensional model of molecular interaction MIVM (мolecular interaction volume model), as well as determination of thermodynamic parameters of the process. In the temperature range 823-1073 to the calculated saturated vapor pressure (Pa) Sn (3.32.10–9–8.12.10–5) and Sb (3.954–273.66). High values of the ratio р*Sb / р*Sn = (1190–3.37).106 and separation factor logβSb = 6.25–9.44 create a theoretical background for the selective separation of these metals by vacuum distillation, when the antimony is enriched in the gas phase (βSb > 1), and tin – liquid. The mole fraction of tin in the gas phase уSn = (1–5000).10–9 increases with increasing temperature 823-1073 K and the molar fraction of the metal in the alloy хSn = 0.1–0.9. Using the MIVM model calculated activity coeffi cients of antimony γSb = 0.439–0.992 and tin γSn = 0.433–0.992 for Sn-Sb alloy with diff erent composition in the investigated temperature range. For phase diagrams VLE can be used by the lever rule (rule lines) to help predict quantities of substances, residues and sublimates at a predetermined temperature. For the phase boundary “liquid–gas” Sn-Sb alloy the values of the excess Gibbs energy, enthalpy and entropy: 􀈂 􀜩􀯠 􀮾 = 0.744–2.096 kJ/mol; – = 0.763–2.166 kJ/mol; = 0.0181–0.0891 J/mol.K. VLE phase diagrams alloys provide the necessary information for the design of technological parameters in industrial production, vacuum metallurgy, as well as to predict temperature and pressure process for obtaining Sn – and Sbcontaining products of a given composition

Isobaric (vapour + liquid) equilibria of binary Pb-Sn and Sb-Sn system AT2Pa

A new experimental method for determining vapor-liquid equilibrium (VLE) of binary alloys was designed in this study. The VLE data of Pb-Sn and Sb-Sn alloys were determined by using this new method. The experimental data passed the thermodynamic consistency test (Van Ness test), and the y(MAD) was 0.4066 and 0.6667, respectively, indicating that the experimental method is correct and reliable. The activity coefficient of Pb-Sn and Sb-Sn alloys was calculated by using the molecular interaction volume model (MIVM). The maximum average relative deviation Si and maximum average standard deviation Si* are ?1.34% and ?0.009, respectively, which indicates that the calculation of the activity coefficient of the Pb- Sn and Sb-Sn alloys by MIVM is reliable. The VLE data of Pb-Sn and Sb-Sn alloys were calculated based on the VLE theory and MIVM, and the calculated results agreed well with the experimental VLE data. The VLE phase diagrams of Pb-Sn and Sb-Sn alloys were also established in this study. The VLE phase diagrams offer a valid and intuitive way to analyze the product compositions? dependence of temperature and pressure during the process of vacuum distillation. This will have immense significance in guiding the actual production of vacuum metallurgy.

Fractionation Effect and Method Improvement in the Experiment of Vapor-Liquid Equilibrium Phase Diagram of Cyclohexane-Ethanol System

Fractionation Effect and Method Improvement in the Experiment of Vapor-Liquid Equilibrium Phase Diagram of Cyclohexane-Ethanol System

Prediction of Vapor–Liquid Equilibria for Pb–Pd and Pb–Pt Alloys Using Ab Initio Methods in Vacuum Distillation

The vapor–liquid equilibrium (VLE) phase diagrams of Pb–Pd and Pb–Pt alloy systems in vacuum distillation were obtained based only on pure-component properties and the structures of the atoms. The interaction energies between pairs of atoms were calculated from ab initio methods and were used as the input energy parameters for the Wilson equation. The calculated activity data of the components, using energy parameters which were obtained by ab initio methods, are in good agreement with the experimental data. It is revealed that a cluster size of eight atoms, optimized using the NVT ensemble at 300 K, a time step of 1 femtosecond, and the simulation time 10 ps gives a good representation of the liquid phase systems. This approach can be used to obtain accurate VLE predictions for alloy systems in vacuum distillation. The VLE phase diagram has a significant advantage in guiding experiment and industrial production in vacuum metallurgy.

Free Energy-Based Coarse-Grained Force Field for Binary Mixtures of Hydrocarbons, Nitrogen, Oxygen, and Carbon Dioxide.

The free energy based Lennard-Jones 12-6 (FE-12-6) coarse-grained (CG) force field developed for alkanes1 has been extended to model small molecules of light hydrocarbons (methane, ethane, propane, butane, and isobutane), nitrogen, oxygen, and carbon dioxide. The adjustable parameters of the FE-12-6 potential are determined by fitting against experimental vapor-liquid equilibrium (VLE) curves and heat of vaporization (HOV) data for pure substance liquids. Simulations using the optimized FE-12-6 parameters correctly reproduced experimental measures of the VLE, HOV, density, vapor pressure, compressibility, critical point, and surface tension for pure substances over a wide range of thermodynamic states. The force field parameters optimized for pure substances were tested on methane/butane, nitrogen/decane, and carbon dioxide/decane binary mixtures to predict their vapor-liquid equilibrium phase diagrams. It is found that for nonpolar molecules represented by different sized beads, a common scaling factor (0.08) that reduces the strength of the interaction potential between unlike beads, generated using Lorentz-Berthelot (LB) combination rules, is required to predict vapor-liquid phase equilibria accurately.

(Vapor + Liquid) Equilibrium (VLE) for Binary Lead-Antimony System in Vacuum Distillation: New Data and Modeling Using Nonrandom Two-Liquid (NRTL) Model

In this work, new experimental vapor–liquid equilibrium (VLE) data of lead-antimony alloy (Pb-Sb alloy) in vacuum distillation are reported. The activity coefficients of components of Pb-Sb alloy were calculated by using the NRTL model. The calculated average relative deviations were ±0.1425 and ±0.2433 pct, and the average standard deviations were ±0.0009 and ±0.0007, respectively, for Pb and Sb. The VLE phase diagrams, such as the temperature composition (T-x) and pressure composition (P-x) diagrams of Pb-Sb alloy in vacuum distillation were predicted based on the NRTL model and VLE theory. The predicted results are consistent with the new experimental data indicating that VLE phase diagrams obtained by this method are reliable. The VLE phase diagrams of alloys will provide an effective and intuitive way for the technical design and realization of recycling and separation processes. The VLE data may be used in separation processes design, and the thermodynamic properties as the key parameters in specific applications.

Vapor–liquid phase equilibria of binary tin–antimony system in vacuum distillation: Experimental investigation and calculation

Vacuum distillation experiments were conducted for tin-antimony alloy (Sn–Sb alloy) under the system pressure of 5 Pa. The content of Sb (mole fraction) in crude Sn, viz., xSb was reduced from 0.5000 to 0.0619 in a single stage distillation process under the condition of residual pressure of 5–10 Pa, distillation temperature of 1373 K and distillation time of 60 min. The activity coefficients of components of Sn–Sb alloy were calculated by using the molecular interaction volume model (MIVM), and the calculated average relative deviation and the average standard deviation were ±0.00039 and ± 0.173%, respectively for both Sn and Sb. The vapor–liquid equilibrium (VLE) phase diagrams, including the temperature-composition (T-x) and pressure-composition (p-x) diagrams of Sn–Sb alloy in vacuum distillation were calculated based on VLE theory and the MIVM. A reasonable agreement between the calculated results and the experimental data indicates that VLE phase diagrams obtained by this method are reliable. The VLE phase diagrams of alloys will provide an effective and convenient way for the designing of the process parameters of industrial production of vacuum metallurgy, and for the prediction of the needed product component dependence of temperature and pressure during the process of vacuum distillation.

Thermodynamics and separation process for quaternary acrylic systems

Vapor‐liquid equilibrium (VLE) and liquid‐liquid equilibrium (LLE) data of binary and ternary acrylic systems were systematically measured. Subsequently, VLLE phase diagrams of binary systems, tridimensional VLE phase diagrams of methyl acrylate (MA)‐methanol (Me)‐H2O ternary system, and quaternary LLE phase diagrams of MA‐Me‐H2O‐methyl acetate (MeOAc) system were constructed. These diagrams clearly demonstrated the effects of temperature on phase equilibrium. The experimental data was fitted by the NRTL and UNIQUAC models, and the best‐fitted parameters were used to predict interaction properties of ternary and quaternary mixture. Therefore, the phase equilibrium data were provided as reference for the design of acrylic systems rectification or extraction process. Residue curve was mapped out for MA‐Me‐H2O system through Aspen plus software. Finally, using thermodynamics and residue curve as theoretical basis, two novel separation processes were proposed and applied to the quaternary acrylic systems. © 2015 American Institute of Chemical Engineers AIChE J, 62: 228–240, 2016

Experimental investigation and calculation of vapor–liquid equilibria for Cu–Pb binary alloy in vacuum distillation

In this study, vacuum distillation experiments of high-lead crude copper were performed under the vapor pressure 5Pa. The content of lead in crude copper was reduced from 15% to less than 0.01% in a single stage distillation process with residual vapor pressures of below 10Pa, distillation temperatures of 1423K and distillation times of 60min. The vapor–liquid equilibrium (VLE) phase diagrams of Cu–Pb binary alloy in vacuum distillation were calculated using the Wilson equation. Thermodynamic experimental data taken from literature were used for calculating Wilson equation temperature dependent interaction parameters. The calculations give a satisfactory accuracy with the experimental data for separation of Cu–Pb alloy in vacuum distillation. The results indicate that VLE phase diagrams under vacuum obtained by this method are reliable for predicting the process of vacuum distillation for Cu–Pb alloy. The VLE phase diagrams of alloys will have significant benefits for the industrial production of vacuum metallurgy especially for the process of multistage distillation in the vacuum furnace.

Vapor–liquid phase diagrams of Pb–Sn and Pb–Ag alloys in vacuum distillation

A procedure has been proposed to calculate the vapor–liquid equilibrium (VLE) phase diagrams of Pb–Sn and Pb–Ag alloys in vacuum distillation based on VLE calculations and molecular interaction volume model (MIVM). The results show good agreement with experimental data which indicate that VLE phase diagram under vacuum obtained by this method is available and reliable. The VLE phase diagram provides an intuitive and convenient way to analyze the product component dependence of temperature or pressure during the process of vacuum distillation. It has a significant advantage to guide for the experiment and industrial production in vacuum metallurgy.

Vapor–liquid equilibria for the binary systems ethylene + water, ethylene + ethanol, and ethanol + water, and the ternary system ethylene + water + ethanol from Gibbs-ensemble molecular simulation

The conceptual design of a reactive separation process for the hydration of ethylene to ethanol requires reliable vapor–liquid equilibrium (VLE) data for the ternary system ethylene+water+ethanol. Due to the paucity of experimental data points in the VLE phase diagrams that have been reported for that system, molecular simulation looks appealing in order to predict such data. In this work, the Gibbs-ensemble Monte Carlo (GEMC) method was used to calculate the VLE of the pure components (ethylene, water, and ethanol), the binary subsystems (ethylene+water, ethylene+ethanol, and ethanol+water), and the ternary system (ethylene+water+ethanol). A set of previously validated Lennard-Jones plus point-charge potential models were chosen for the pure components, and the validity of these models was corroborated from the good agreement of the GEMC simulation results for the vapor pressure and the VLE phase diagrams of those components with respect to calculations carried out by means of the most accurate (reference) multiparameter equations of state currently available for ethylene, water, and ethanol. These potential models were found to be capable of predicting the available VLE phase diagrams of the binary subsystems: ethylene+water at 200 and 250°C, ethylene+ethanol at 150, 170, 190, 200, and 220°C, and ethanol+water at 200, 250, 275, and 300°C. Molecular simulation predictions for the VLE phase diagrams of the ternary system at 200°C and pressures of 30, 40, 50, 60, 80, and 100atm, were found to be in very good agreement with predictions previously made by use of a thermodynamic model that combines the Peng–Robinson–Stryjek–Vera equation of state, the Wong–Sandler mixing rules, and the UNIQUAC activity coefficient model. The agreement between the predictions of these two independent approaches gives confidence for the subsequent use of molecular simulation to predict the combined phase and chemical equilibrium of the ternary system and check the validity of predictions previously made by means of the thermodynamic model.

Predicting Mixture Phase Equilibria and Critical Behavior Using the SAFT-VRX Approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.