Vapor-Liquid Equilibria for Water+Hydrochloric Acid+Magnesium Chloride and Water+Hydrochloric Acid+Calcium Chloride Systems at Atmospheric Pressure

Vapor-liquid equilibria for water+hydrochloric acid+magnesium chloride and water+hydrochloric acid+calcium chloride systems at atmospheric pressure were measured using a Othmer-type equilibrium still. The experimental data are correlated using a modified Meissner’s method. Satisfactory agreements are obtained between the experimental and the calculated results.

VAPOR-LIQUID EQUILIBRIA FOR PROPYLENE -METHANOL-WATER SYSTEM

In this article VLE data for a ternary system (propylene-methanol-water) under 30～60 C,0. 3～0. 9 MPa with a mass ratio of methanol to water of 9:1, 8: 2, 7: 3 were determined with a static equilibrium still, and were correlated by using Peng-Robinson model. The average relative error ofpropylene concentration in liquid phase is 1. 46 %. The results indicate that the models are very suitablefor the ternary system and the data are reliable.

Measurement and Correlation of Vapor-Liquid Equilibria for Hexamethyl Disiloxane+Vinyl Acetate System at 101.3 kPa

Vapor-liquid equilibrium data of hexamethyl disiloxane+vinyl acetate system at 101.3kPa were measured by using double circulating vapor-liquid equilibrium still.The thermodynamic consistency of the VLE data was examined by Herrington method.Experimental data was correlated by non-random two-liquid(NRTL),Wilson and universal quasichemical(UNIQUAC)parameter models.All the models satisfactorily correlated with the VLE data.The result showed that the NRTL model was the most suitable one to represent experimental data satisfactorily.The system had a minimum temperature azeotrope at 345.71 K and the mole azeotropic composition was 0.0541.

VAPOR-LIQUID EQUILIBRIA FOR MIXTURES OF TOLUENE AND POLYSTYRENE WITH DIFFERENT MOLECULAR WEIGHTS

An experimental system for measuring the VLE of polymer solutions based on the staticvapor-pressure method has been established,VLE data for mixtures of toluene and polystyrene withdifferent molecular weight covering a wide range from 2.98×10~3 to 3.84×10~6 were obtained at 35℃.The reduced pressure p/p°versus weight fraction W plot is found to be independent on the molecularweight of the polymer within the experimental error.Calculated activity coefficients are also independenton the molecular weight.However,for the Flory-Huggins interaction parameter x,not only a strongconcentration dependence is observed,but also the molecular weight of the polymer exerts definiteinfluence.Generally,the parameter x slightly increases as the molecular weight of the polymer decreasesespecially when the molecular weight is low.The dependence of the parameter x on the molecularweight can be neglected when the molecular weight of polymer is greater than 1.00×10~4.

Vapor-Liquid Equilibria for Dimethyl Carbonate-n-Butyl Acetate Binary System at 101.325kPa

The vapor-liquid equilibrium (VLE) data for the dimethyl carbonate-n-butyl acetate binary system were measured by an Ellis equilibrated distillator. The experimental data were checked for their thermodynamic consistency through statistical methods. The VLE data was correlated with Wilson and NRTL activity coefficient models and also with the calculation of the vapor phase fugacity coefficient by the modified Peng-Robinson equation of state.

VAPOR-LIQUID EQUILIBRIA OF N METHYLPYRROLIDONE(1)-WATER(2) BINARY SYSTEM BY AN EBULLIOMETER

1 INTRODUCTIONVapor-liquid equilibrium（VLE）data are useful for the study of solution properties ofnon-ideal mixtures as well as for the design of the separation equipment.Then-methylpyrrolidone（NMP）is a new-type and excellent solvent which can be used in somechemical engineering separation processes.The NMP sucks up moisture so easily that it isnecessary to study the VLE relations of the NMP-H2O binary system,

Experimental results for the vapor-liquid equilibria of 0(formaldehyde+1,3,5-trioxane+methanol+salt+water)systems and comparison with predictions

The salt effect on the vaporliquid phase equilibrium(VLE)of solvent mixtures is of significant interest in the industrial production of 1,3,5trioxane.Experimental data for the VLE of quinary systems(formaldehyde+1,3,5trioxane+methanol+salt+water)and their ternary subsystems(formaldehyde+salt+water),(1,3,5trioxane+salt+water),and(methanol+salt+water)were systematic measured under atmospheric pressure.The salts considered included KBr,NaNO_(3),and CaCl_(2).The extended UNIFAC model was used to describe the VLE of the saltcontaining reactive mixtures.The model parameters were determined from the experimental VLE data of ternary systems or obtained from the literature,and then were used to predict the VLE of systems(1,3,5trioxane+KBr+water),(methanol+KBr+water),(formaldehyde+KBr+water),and(formaldehyde+1,3,5trioxane+methanol+salt+water)with salt=KBr,NaNO_(3),and CaCl_(2).The predicted results showed good agreements with the measured results.Furthermore,the model was used to uncover the salt effect on the VLE of these multisolvent reactive systems.

The Performance of EOS Models in the Prediction of Vapor-Liquid Equilibria in Asymmetric Natural Gas Mixtures

The aim of this work is to apply cubic equations of state(EOS)to vapor-liquid equilibriacalculations of gas-heavy hydrocarbon systems,which are asymmetric in molecular size and areusually found in natural gases.Investigation has been done to test the validity of the original PSRKand the cubic simplified perturbed hard-chain(CSPhC)models for global phase diagrams.Thecalculation results show that both equations overpredict vapor pressure in the near critical region.In the prediction of the solubilities of high molecular weight(MW)hydrocarbons in the naturalgas,the PSRK model gives good agreement for the dew point pressure-vapor composition diagrams.Adjustment of the pure component parameters of the CSPHC EOS for heavy components to fit thevapor-liquid equilibrium(VLE)data has been proved to give significant promoting in predictionaccuracy.However,further improvement of a van der Waals EOS,such as SRK,PT and DG modelsfor the asymmetric systems by adjusting the three pure component properties,T_c, p_c and ?

A G^E/Equation of State Mixing Rule for Vapor-Liquid Equilibria

A new excess Gibbs free energy/equation of state type mixing 0rule was derived byremoving the infinite pressure boundary condition imposed by Wong and Sandler.The mixing rulewas extensively tested in terms of a comprehensive data base,consisting of 52 simple nonpolar-nonpolar,carbon dioxide containing,hydrocarbon-hydrocarbon,CFC,polar-polar,nonpolar-polarbinary and multicomponent systems.Focused on the complete predictive capability,a comparisonbetween the Wong-Sandler and the mixing rule proposed was conducted.The results indicate that thenew mixing rule is in general superior to the Wong-Sandler’s,and the binary interaction parameteras required by the latter is removed,which reduces computing effort and is reliable in predictions ofvapor-liquid equilibria from low pressures to high pressures.

VAPOR-LIQUID EQUILIBRIA BY EXTENDED SOAVE EQUATION OF STATE

The Soave[1]equation of state is extensively accepted because of its accuracy andsimplicity.In 1988,Tan et al.[2]suggested a modification by introducing atemperature-dependent factor to parameter"b"on the basis of statistical meaning,anda good accuracy was obtained for supercritical fluids as well as fluids approaching criti-cal conditions but not for mixtures.In the previous work,an extended Soave equa-tion of state[3]has been proposed to improve the prediction of liquid density.In thispaper,the extended equation is used to calculate vapor-liquid equilibria of mixtures atsubcritical conditions.

Prediction of Vapor-Liquid Equilibria of Alcohol-Hydrocarbon Systems by ^1H NMR and Azeotropic Point

With the energy parameters obtained from1H nuclear magnetic resonance(NMR)chemical shifts data by local composition model and coupled with azeotropic point,the low-pressure vapor-liquid equilibrium is satisfactorily predicted for alcohol+hexane,alcohol+cyclohexane,and alcohol+benzene binary systems at different temperatures.The relationship between the spectroscopic information and thermodynamic property is presented.

Experimental Measurements and Correlations Isobaric Vapor-Liquid Equilibria for Water ＋ Acetic Acid ＋ Sec-butyl Acetate at 101.3 kPa

Isobaric vapor-liquid equilibrium(VLE) data for acetic acid + sec-butyl acetate and water+acetic acid + sec-butyl acetate systems were determined at 101.3 kPa using a modified Rose type.The nonideality of the vapor phase caused by the association of the acetic acid was corrected by the chemical theory and Hayden-O'Connell method.Thermodynamic consistency was tested for the binary VLE data.The experimental data were correlated successfully with the Non-Random Two Liquids(NRTL) model.The Root Mean Square Deviation(RMSD) of the ternary system was 0.0038.The saturation vapor pressure of sec-butyl acetate at 329 to 385 K was measured by means of two connected equilibrium cells.The vapor pressures of water and sec-butyl acetate were correlated with the Antoine equation.The binary interaction parameters and the ternary VLE data were obtained from this work.

A Modified Mixing Rule for PSRK Model and Application for the Prediction of Vapor-Liquid Equilibria of Polymer Solutions

To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied[bij1/2= 1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters ofpure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.

CALCULATIONS OF VAPOR-LIQUID EQUILIBRIA FOR HYDROGEN-CONTAINING SYSTEMS WITH MODIFIED PENG-ROBINSON EQUATION OF STATE

Peng-Robinson equation of state was modified to represent vapor-liquid equilibria for hydrogen-containing systems. A new expression of the temperature dependent parameter for the supercritical gas hydrogen, and the binary interaction parameters were introduced to improve the description of VLE for 19 binary systems. Results show that this work is superior to the previous work. Moreover, estimations of PVT behavior, the second virial coefficients for hydrogen, and predictions of the volumetric properties of liquid mixtures and VLE for the ternary systems are in good agreement with the experimental data.

Extension of LCVM-type mixing rule to three-parameter equations of state for vapor-liquid equilibria of mixtures

In this paper, the LCVM mixing rule is extended to the multi-parameter equations of state by combining infi- nite-pressure and zero-pressure mixing rule models. The new LCVM-type mixing rule, coupled with Patel-Teja equation of state (EOS) is applied for vapor-liquid equilibria of different polar and non-polar systems in which the NRTL activity coefficient model is used to calculate the excess Gibbs free energy. The tested results agree well with existing experimental data within a wide range of temperatures and pressures. In comparison with the Van der Waals mixing rule, the new mixing rule gives much better corre- lations for the vapor-liquid equilibria of non-polar and polar systems.

Sensitivity Analysis of Computations of the Vapor-Liquid Equilibria of Methane + Methanol or Glycols at Gas Hydrate Formation Conditions

The Soave-Redlich-Kwong (SRK-EOS) and Peng-Robinson (PR-EOS) equations of state are used often to describe the behavior of pure substances and mixtures despite difficulties in handling substances, like water, with high polarity and hydrogen bonding. They were employed in studying the binary vapor-liquid equilibria (VLE) of methane + methanol, monoethylene glycol (MEG), and triethylene glycol (TEG). These liquids are used to inhibit the formation of gas hydrates. The investigation focused on the conditions at which methane-water clathrates can form 283.89?K to 323.56?K and 5.01?MPa to 18.48?MPa. The pressure of methane in methanol is overestimated by a factor of two by either the SRK-EOS or the PR-EOS. In the methane + MEG system, the predicted pressures for both equations of state are generally less than experimental pressure except for the highest concentration of methane in MEG calculated by the SRK-EOS. In the methane + TEG system, the predictions of both models are close and trend similarly. Because of the comparative lack of extensive experimental methane + TEG data, the similarity of the methane + TEG computed results can be used as a basis for further study of this system experimentally.

Phase equilibria relations in the V_(2)O_(5)-rich part of the Fe_(2)O_(3-)TiO_(2)-V_(2)O_(5) system at 1200℃ related to converter vanadium-bearing slag

The efficient recycling of vanadium from converter vanadium-bearing slag is highly significant for sustainable development and circular economy.The key to developing novel processes and improving traditional routes lies in the thermodynamic data.In this study,the equilibrium phase relations for the Fe_(2)O_(3)-TiO_(2)-V_(2)O_(5)system at 1200℃in air were investigated using a high-temperature equilibrium-quenching technique,followed by analysis using scanning electron microscopy-energy dispersive X-ray spectrometer and X-ray photoelectron spectroscopy.One liquid-phase region,two two-phase regions(liquid-rutile and liquid-ferropseudobrookite),and one three-phase region(liquid-rutile-ferropseudobrookite)were determined.The variation in the TiO_(2)and V_(2)O_(5)contents with the Fe_(2)O_(3)content was examined for rutile and ferropseudobrookite solid solutions.However,on further comparison with the predictions of FactSage 8.1,significant discrepancies were identified,highlighting that greater attention must be paid to updating the current thermodynamic database related to vanadium-bearing slag systems.

Vapor-liquid equilibria of CH_4, CO_2 and their binary system CH_4 + CO_2: A comparison between the molecular simulation and equation of state

An accurate knowledge about phase behaviors of CH4, CO2 and their binary mixture is crucial in fields of natural gas liquefaction and refrigeration applications. In this work, two all-atom force fields of TraPPE-EH and EMP2 were used for the components CH4 and CO〉 respectively. Then the vapor-liquid equilibria （VLE） of CH4, CO2 and their binary system were calculated via the NVT- and NpT Gibbs Ensemble Monte Carlo Simulations. Meanwhile the traditional method using Equation of State （EoS） to correlate the VLE properties was also investigated. The EoSs considered in this work were three classic cubic RK, SRK, PR and another advanced molecular-based PC-SAFT equations. For pure components, both molecular simulations and the PC-SAFT EoS could obtain satisfactory predictions for all the saturated properties. However, the saturated liquid densities calculated by the cubic EoSs were not so good. It was also observed that the TraPPE-EH force field had a good representation for CH4 molecule, while the EMP2 force field was not enough accurate to represent CO2 molecules. For the mixture CH4 ＋ CO2, SRK and PR showed the best predictions for the saturated pressure-component property, while good results were also obtained via molecular simulations and PC-SAFT EoS. It was suggested that special combining rules or binary interaction parameters were important to obtain enough accurate prediction of the mixed phase behavior. Compared with the cubic EoS, the PC-SAFT and molecular simulation method showed better adaptabilities for both the pure and mixture systems. Besides, the accurate molecular parameters used in the PC-SAFT and molecular simulations could bring about direct and deep understanding about the molecular characteristics.

STUDIES ON VAPOR-LIQUID AND LIQUID-LIQUIDVAPOR EQUILIBRIA FOR THE TERNARY SYSTEM METHANOL-METHYL METHACRYLATEWATER (Ⅱ) TERNARY SYSTEM

Isothermal P-x data for homogeneous, and P-x’-x" data for partially miscible mixtures for the ternary system methanol-methyl methacrylate-water have been determined at 25, 35, 45, 55 and 60℃. By using a modified UNIQUAC model and binary parameters only, the predicted ternary phase equilibrium data were found to be in good agreement with the experimental results, indicating the adequacy of using binary model parameters in computing vapor-liquid and liquid-liquid-vapor equilibria covering pressures ranging from reduced to atmospheric.

Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows

In this paper, the problem of finding exact solutions to the magnetohydrodynamic(MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation(PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.