Examining the effect of binary interaction parameters on VLE modelling using cubic equations of state

Vapor-liquid equilibrium (VLE) data are important in the optimization of thermodynamic cycles. As energy concerns continue to grow, improving the efficiencies of power and refrigeration cycles is increasingly important. Numerical simulations using empirical equations of state provide an excellent alternative to time consuming experimental measurement of VLE data. However, it is important to understand the limitations of using correlative equations for data prediction. In this study, a water-ethanol mixture is simulated with various VLE models. Non-optimal binary interaction parameters are considered and model accuracy is evaluated in terms of average absolute percent deviation (%AAD) between simulated and experimental bubble and dew point pressures. For this system, it is found that as the correlative accuracy of a model increases, the predictive ability decreases. Specifically, the temperature dependence of the binary interaction parameters is shown to be an important consideration for the water-ethanol system when more complex combining rules are implemented.     

Generalized parameters of the Stryjek–Vera and Gibbons–Laughton cohesion functions for use with cubic EOS of the van der Waals type

In this work, the parameters of the Stryjek–Vera and Gibbons–Laughton cohesion functions were determined for over 800 fluids by fitting vapor pressure data generated from the DIPPR database from the triple to the critical point. Parameter sets were obtained for use with the van der Waals, Redlich–Kwong and Peng–Robinson equations of state. The average vapor pressure deviations did not exceed 2.6%, with the Gibbons–Laughton function performing slightly better. Contrary to assertions in the literature, we showed that a generalized correlation of these parameters is possible. We developed this in the framework of a four-parameter corresponding states principle for non-polar and polar compounds, which allows the estimation of Stryjek–Vera and Gibbons–Laughton parameters from the acentric and critical compressibility factors of any given fluid.     

Boyle temperature and cubic equations of state

The sensitivity of Boyle temperature to changes in parameters appearing in cubic equations of state and to volume shift is analyzed. Analytical expressions for the Boyle temperature and for the dependency to the shift of the equation of state are given for the most common cases of the alpha function.     

Volumetric properties of the ternary system ethanol + chloroform + benzene at temperature range (288.15–313.15) K: Experimental data,correlation and prediction by cubic EOS

Densities ρ of the ternary system (ethanol + chloroform + benzene) and binaries (ethanol + chloroform) and (chloroform + benzene), have been measured at six temperatures (288.15, 293.15, 298.15, 303.15, 308.15, 313.15) K and pressure 101.33 kPa with an Anton Paar DMA 5000 digital vibrating tube densimeter. Excess molar volumes V^E were calculated from these densities data and fitted by the polynomial Redlich–Kister (for binary data) and Nagata and Tamura (for ternary data) equations. Radojkovi? et al. equation was used for the prediction of the V^E of ternary data. The obtained results have been explained in terms of different effects between molecules of present species, taking into consideration influence of temperature on them.     

Prediction of vapor-liquid equilibrium data of the system MTBE + methanol + ethanol by PRSV2 EOS

The Stryjek and Vera (1986) [9] modification of Peng-Robinson (PRSV2) equation of state has been applied for modeling vapor-liquid equilibrium of the systems MTBE + methanol, MTBE + ethanol and methanol + ethanol. Binary interaction parameters for mixing rules have been estimated by using experimental data at the atmospheric pressure. The calculated binary interaction parameters were used for predicting azeotropic behavior at high pressure and also for isobaric equilibrium points which showed an excellent agreement with experimental data. In addition, estimated binary interaction parameters for binary systems were used for ternary system (MTBE + methanol + ethanol). The predictions deviated only slightly from the experimental data. The results show PRSV2 can be used for VLE prediction of polar systems.     

Phase behavior of the system hyperbranched polyglycerol + methanol + carbon dioxide

Phase equilibrium data have been measured for the ternary system hyperbranched polyglycerol + methanol + carbon dioxide at temperatures of 313–450 K and pressures up to 13.5 MPa. Phase changes were determined according to a synthetic method using the Cailletet setup. At elevated temperatures the system shows a liquid–liquid–vapor region with lower solution temperatures. Besides the vapor–liquid and liquid–liquid equilibria, the vapor–liquid to vapor–liquid–liquid and vapor–liquid–liquid to liquid–liquid phase boundaries are reported at different polymer molar masses and can serve as test sets for thermodynamic models. A distinct influence of the polymer molar mass on the vapor–liquid equilibrium can be noticed and indicates the existence of structural effects due to the polymer branching. Modeling the systems with the PCP-SAFT equation of state confirms these findings.     

Volumetric properties of the water + ethylenediamine mixture at atmospheric pressure from 288.15 to 353.15 K

Densities of the water + ethylenediamine binary system were measured at atmospheric pressure over the whole range of compositions at temperatures from 288.15 to 353.15 K using an Anton Paar digital vibrating glass tube densimeter. Density increases with water content. The experimental excess molar volume data have been correlated with the Redlich-Kister equation, and partial molar volumes calculated at infinite dilution for each component.     

Temperature influence on mixing properties of {ethyl tert-butyl ether (ETBE) + gasoline additives}

The densities and ultrasonic velocity of {ethyl tert-butyl ether (ETBE) + (benzene, toluene, ethylbenzene, isooctane, tert-butyl alcohol, and ethanol)} over the temperature range (288.15 to 323.15) K and atmospheric pressure, have been measured over the whole concentration range. The experimental excess volumes and deviation of isentropic compressibilities data have been analysed in terms of different theoretical models. The gathered data improve open literature related to gasoline additives, and help to understand the ETBE volumetric and acoustic trend into different chemical environment.     

Densities and derived thermodynamic properties of ternary mixtures 1-butyl-3-methyl-imidazolium tetrafluoroborate + ethanol + water at seven pressures and two temperatures

This work is a continuation of our studies on experimental measurements of physical properties on binary mixtures of the ionic liquid (IL) family 1-alkyl-3-methyl imidazolium tetrafluoroborate (CnMIM-BF₄) with water and ethanol. Here, we present density for the ternary system Butyl-MIM-BF₄ + ethanol + water at two temperatures (298.15 K and 323.15 K) and seven pressures (from 0.1 to 30 MPa). It should be noted that BMIM-BF₄ is the only IL of the family CnMIM-BF₄ that can be mixed with water and ethanol in all range of concentrations at room conditions. From the density data measured in function of pressure and temperature other important derived thermodynamic properties can be calculated, such us excess molar volumes, isothermal compressibility, isobaric expansion and the thermal pressure coefficients. These properties for selected ternary mixtures will be discussed and compared with data from the scarce number of published results for similar ternary mixtures with this same IL.     

Modeling of thermodynamic behavior of PVT properties and cloud point temperatures of polymer blends and polymer blend + carbon dioxide systems using non-cubic equations of state

In recent years, many factors influencing phase behavior of polymer blends have been studied because of their widely technological importance, as a simple method of formulating new materials with tailored properties which make them suitable for a variety of applications. This work has three main goals which were reached by using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS), which in previous works have shown their ability to handle long chain and associating interactions. First, both equations of state were tested with the correlation of the specific volumes of pure blends (PBD/PS, PPO/PS, PVME/PS, PEO/PES) and the prediction of the specific volumes for blends; second, the modeling of blend miscibilities in the liquid–liquid equilibria (LLE) of PBD/PS, PPG/PEGE, PVME/PS, PEO/PES, and PnPMA/PS blends; third, the modeling of the phase behavior of PS/PVME blends at various compositions in the presence of CO₂. PC-SAFT and SL pure-component parameters were regressed by fitting pure-component data of real substances (liquid pressure–volume–temperature, PVT, data for polymers and vapor pressure and saturated liquid molar volume for CO₂) and the fluid phase behavior of blend systems were simulated fitting one binary interaction parameter (k_ij) by regression of experimental data using the modified likelihood maximum method. Results were compared with experimental data obtained from literature and an excellent agreement was obtained with both EoS, which were also capable of predicting the fluid phase behavior corresponding to the critical solution temperatures (LCST: lower critical solution temperature, UCST: upper critical solution temperature) of blends.     

Modeling alcohol + water + hydrocarbon mixtures with the group contribution with association equation of state GCA-EoS

The growing interest on first- and second-generation biofuels requires the development of thermodynamic tools with predictive capacity for mixtures containing a wide variety of organo-oxygenated compounds, water and hydrocarbons. Modeling this type of mixtures is challenging due to the presence of association and solvation effects. In this work, we present a revision of the group contribution with association equation of state (GCA-EoS) parameters, with the purpose of extending and improving the predictive capacity of the model for systems containing water, alcohols and hydrocarbons.     

Vapor-liquid and liquid-liquid equilibrium properties of ethane + methanol system at ambient temperature

The liquid-liquid and vapor-liquid equilibrium data for the binary system of ethane + methanol were measured at ambient temperature over a wide range of pressures using a designed PVT apparatus. The experimental liquid-liquid and vapor-liquid equilibrium data were compared with the modeling results obtained using the Peng Robinson and Soave-Redlich-Kwong equations of state.     

Thermodynamic properties for liquid mercury using GMA equation of state

The important known regularities and thermodynamic properties of liquid mercury have been studied based on the average potential energy. Recognised regularities, the linearity of Zeno contour, bulk modulus and secant bulk modulus as functions of temperature, isochors of pressure versus temperature and near linearity of the inverse isobaric expansion coefficient have been investigated, all evaluated using the Goharshadi–Morsali–Abbaspour equation of state. The validity of the equation of state in predicting thermophysical properties is confirmed by a statistical parameter, absolute average deviation, with a maximum value of 0.41, showing excellent agreement with the experiment at temperatures between 293.15 and 323.15?K from low to high pressures.     

Volumetric properties of the water + 3-(dimethylamino) propylamine (DMAPA) mixture at atmospheric pressure from 283.15 to 353.15 K

Densities of the water + 3-(dimethylamino) propylamine (DMAPA) binary system were measured at atmospheric pressure over the whole range of compositions at temperatures from 283.15 to 353.15 K using Anton Paar digital vibrating glass tube densimeter. The density of this system has been found an increasing function of water composition and a decreasing function of temperature. Excess molar volumes have been correlated using Redlich-Kister equations. Sets of parameters have been determined from experimental data to obtain correlations in the measurement range uncertainty. Partial molar volumes on the whole concentration range have been determined using Redlich-Kister parameters.     

Physical properties and their corresponding changes of mixing for the ternary mixture acetone + n-hexane + water at 298.15 K

Experimental density and the refractive index of the ternary mixture acetone + n-hexane + water, and their binary systems were experimentally measured and correlated at 298.15 K and atmospheric pressure. A maximum in refractive indices has been observed for the acetone + water system while the excess molar volume and the molar refraction change are all negative. For the mixture acetone + n-hexane, the excess molar volume is always positive and the molar refraction change of mixing showed a S-shaped dependence on acetone composition. The excess molar volumes and molar refraction changes of mixing were correlated using the Redlich-Kister expression and Cibulka equation. The coefficients and standard deviation between the experimental and fitted values were estimated. Good agreement between both results was obtained.     

Effect of temperature on the volumetric properties of (cyclohexanone + an aromatic hydrocarbon)

The excess molar volume of (cyclohexanone + benzene, or toluene, or ethylbenzene, or styrene) were obtained from the densities measured by means of a vibrating-tube densimeter over the whole composition range at temperatures (293.15, 303.15, 313.15, 323.15, 333.15, 343.15, 353.15) K and atmospheric pressure. The excess molar volume provide the temperature dependence of in the temperature range of (293 to 353) K. The results were correlated using the fourth-order Redlich-Kister equation, with the maximum likelihood principle being applied for the determination of the adjustable parameters. It was found that the in the systems studied increase with rising temperature.     

The Soave,Twu and Boston–Mathias alpha functions in cubic equations of state. Part II. Modeling of thermodynamic properties of pure compounds

Cubic equations of state (EoS) are commonly used for industrial applications, due to their simplicity in predicting pure compound and mixture thermodynamic properties in vapor and liquid phases. The accuracy of their predictions mainly depends on the choice of the attractive term a(T) and numerous models were developed in literature for this purpose. Among them, the Soave and the Twu models have acquired a wide popularity, as well as the Boston–Mathias model commonly used for supercritical applications. However, most of the works concerned with the comparison of literature attractive terms only focuses on the representation of pure component saturation properties. In particular, the analysis of the respective influence of the EoS and the first and second derivatives of the alpha function on the modeling of enthalpies and heat capacities with respect to temperature and pressure, especially in the supercritical range, was never reported in literature. This is precisely the purpose of the present study.     

Thermodynamic properties of the ternary system {yNH4Cl + (1 − y)MgCl2} (aq) at 298.15 K

The mixture {yNH₄Cl + (1 − y)MgCl₂} (aq) has been studied using the hygrometric method at the temperature 298.15 K. The water activities are measured at total molalities from 0.30 mol kg⁻¹ up to saturation for different ionic strength fractions y of NH₄Cl with y = 0.20, 0.50 and 0.80. The obtained data allow the deduction of osmotic coefficients. Experimental results are compared with the calculations using the models of Zdanovskii–Stokes–Robinson, Kusik and Meissner, Robinson and Stokes, Lietzke and Stoughton, Reilly–Wood and Robinson and Pitzer. Thermodynamic properties have been modeled using the Pitzer ion-interaction model with inclusion of an ionic strength dependence of the third virial coefficient for the binary systems. From these measurements and the obtained binary parameters β⁽⁰⁾, β⁽¹⁾, C⁽⁰⁾ and C⁽¹⁾, the mixing ionic parameters θNH₄Mg${\theta }_{\text{N}{\text{H}}_4\text{Mg}}$ and ψNH₄MgCl${\psi }_{\text{N}{\text{H}}_4\text{MgCl}}$ are determined by the standard Pitzer model. The results show that a good accuracy is obtained with the standard Pitzer model using extended binary parameters. The parameters θNH₄Mg${\theta }_{\text{N}{\text{H}}_4\text{Mg}}$ and ψNH₄MgCl${\psi }_{\text{N}{\text{H}}_4\text{MgCl}}$ were used for evaluation of activity coefficients in the mixture. The excess Gibbs energy is also determined.     

A new equation of state for studying the thermodynamic properties of real gases

In this study, based on the compressibility effect of gas molecules, a new three-parameter cubic equation of state (EOS) is derived. To validate this EOS, density predictions of methane, ethane, carbon dioxide and oxygen have been studied using the new EOS at the temperature of 373 K and at the pressures up to 100 MPa. The results show a good agreement with reference data and this suggests that the proposed EOS would help to improve the study of thermodynamic properties for real gases.     

High-pressure phase behavior of CO2 + 1-butyl-3-methylimidazolium chloride system

The phase behavior of carbon dioxide (CO₂) and the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride ([bmim][Cl]) was measured and correlated at high pressures up to ∼40 MPa and at temperatures between 353.15 K and 373.15 K. The solubility data of CO₂ in [bmim][Cl] were obtained by observing the bubble point pressure at specific temperatures. A variable-volume view cell, which is a high-pressure equilibrium apparatus, was used to measure the CO₂ + [bmim][Cl] system solubility under varying pressure and temperature conditions. In addition, liquid–liquid–vapor (LLV) three-phase behavior was investigated using the equilibrium cell to be able to determine the classification of phase-behavior type by Scott and Van Konynenburg. Based on the LLV phase behavior, this system most likely has type III phase-behavior which is common for IL + CO₂ systems. The resulting data showed that CO₂ dissolved well in the IL at low CO₂ concentrations, but that the pressure derivative of CO₂ solubility dramatically decreased as the mole fraction of CO₂ was increased. The experimental data were well fitted by the Peng–Robinson equation of state with a quadratic mixing rule and cubic parameters estimated by the Joback method.