Vapor–liquid equilibria for the system 1-propanol+n-hexane near the critical region

Vapor–liquid equilibria and critical point data for the system 1-propanol+n-hexane at 483.15, 493.15, 503.15 and 513.15 K are reported. The critical pressures determined from the critical opalescence of the mixture were compared with published data for the system 2-propanol+n-hexane. Phase behavior measurements were made in a modified circulating type apparatus with a view cell. These mixtures are highly nonideal because of the hydrogen bonding of 1-propanol. Modeling of the experimental data has been performed using the multi-fluid nonrandom lattice fluid with hydrogen-bonding (MF-NLF-HB) equation of state and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with Wong–Sandler mixing rule. The critical points and the critical locus were also calculated.     

High-pressure phase equilibrium for the binary systems of {carbon dioxide (1) + dimethyl carbonate (2)} and {carbon dioxide (1) + diethyl carbonate (2)} at temperatures of 273 K, 283 K,and 293 K

Phase equilibrium data for the binary systems {carbon dioxide (CO₂) + dimethyl carbonate (DMC)} and {carbon dioxide (CO₂) + diethyl carbonate (DEC)} were measured at temperatures of 273 K, 283 K and 293 K in the pressure range of 0.5 MPa to 4.0 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated with the Peng–Robison (PR) equation of state (EOS) and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with van der Waals-1 or Panagiotopoulos–Reid mixing rules. The correlations produced reasonable values for the interaction parameters. The comparisons between calculation results and experimental data indicate that the PRSV equation of state coupled with the Panagiotopoulos–Reid mixing rule produced the better correlated results.     

Volumetric and refractive properties of binary mixtures containing 1,4-dioxane and chloroalkanes

Refractive index deviations, excess volumes, and molar refractions of binary mixtures containing 1,4-dioxane and 1-chloropropane or isomeric chlorobutanes have been calculated from experimental data of refractive indices and densities at temperatures of 298.15 K and 313.15 K. Results obtained have been discussed in terms of intermolecular interactions and a comprehensive discussion has been provided. Excess volumes have been also correlated using Peng–Robinson–Stryjek–Vera cubic equation of state and the relation between parameter b (covolume) from the equation of state and molar refraction has been verified. Refractive indices were compared with those predicted using the equation of state and several mixing rules.     

Applicability of cubic equation of state mixing rules on correlation of excess molar volume of Non-Electrolyte binary mixtures

The excess molar volume V ^E data of the binary liquid systems were correlated by the Peng–Robinson–Stryjek–Vera equation of state coupled with two different types of mixing rules: composition dependent van der Waals mixing rule (vdW) and the mixing rule based on the Gupta–Rasmussen–Fredenslund method (GRF), with the NRTL equation as G ^E model. The results obtained by these models show that type of applied mixing rule, a number and position of interaction parameters are of great importance for a satisfactory correlation of V ^E data. The GRF mixing rules coupled with the NRTL model gave mostly satisfactory results for V ^E correlation of the nonideal binary systems of diverse complexity.     

Vapor–liquid equilibria predictions of hydrogen–hydrocarbon mixtures with the Huron–Vidal mixing rule

An excess Gibbs-equation of state (G^E-EoS) framework based on the Huron–Vidal mixing rule, has been applied to study vapor–liquid equilibria (VLE) of hydrogen–hydrocarbon mixtures. The mixing rule couples the Peng–Robinson–Stryjek–Vera (PRSV) EoS with a local composition solution model. The solution model is based on one-fluid theory treatment and assigns a single energy parameter to each binary pair. This energy parameter relates to the preference of the molecules for like to unlike interactions. The allocation of a system's number of interactions to the individual species in a binary mixture, incorporates the use of size parameters which gain significance only in the liquid phase. In a two parameter form, the framework has been used for the simultaneous data reduction of a large number of binary and several ternary hydrogen–hydrocarbon mixtures. These systems were taken over an extended range of pressures and temperatures. Results from the data reduction are reported in both tabular and graphical forms. Correlations for the model parameters have been identified with the acentric factor of the hydrocarbon in hydrogen–hydrocarbon binary mixtures. In a fully predictive mode, the model has shown to describe well VLE of binary hydrogen–linear alkane systems. Comparisons of these results with calculations from the Peng–Robinson (PR) EoS and the classical mixing rule (vdW) are included.     

Computing all the azeotropes in refrigerant mixtures through equations of state

Azeotropic mixtures of fluorocarbon (FC) and hydro fluorocarbon (HFC) with hydrocarbons are gaining popularity as drop-in substitutes for CFCs and HCFCs. A method to compute all the azeotropes in a refrigerant mixture through the equation of state approach is described. The method allows prediction of all the azeotropes in a refrigerant mixture and is in close agreement with the experimental data. Both the vapor and the liquid phase non-idealities are incorporated through fugacity coefficients modeled using Peng–Robinson–Stryjek–Vera equation of state with Wong-Sandler and van der Waals mixing rules. Homotopy continuation based methodology guarantees computation of all the solutions of necessary and sufficient condition of azeotropy in multicomponent refrigerant mixtures. The method establishes the pressure dependency of azeotropic composition allowing prediction of bifurcation pressure where refrigerant azeotropes may appear or disappear and predicts azeotropes at elevated pressures. The approach is independent of equation of state and mixing rules but rely on their ability to represent the phase behavior. The approach is tested with R23–R13, propane–R227ea binary mixtures and a ternary mixture of R32–R125–R143a.     

Phase equilibrium calculations for carbon dioxide + n-alkanes binary mixtures with the Wong–Sandler mixing rules

Phase equilibrium for carbon dioxide + n-alkanes (from methane to n-decane) asymmetric binary systems was calculated using Peng–Robinson Stryjek–Vera equation of state coupled with Wong–Sandler mixing rules. NRTL model was utilized for predicting the excess Helmholtz free energy. The second virial coefficient binary interaction parameter k₁₂ and NRTL model parameters τ₁₂ and τ₂₁ for carbon dioxide + n-alkanes binary systems were optimized trough minimization of two different objective functions: one based on the calculation of the distribution coefficients, and the other one based on the determination of bubble point pressures. Generalized correlations for mixing rule parameters as a function of the n-alkane acentric factor and the equilibrium temperature were obtained from optimal parameters determined by the first objective function. Obtained results using both objective functions were satisfactory, but the estimation of the parameters calculated by the second objective function provided a better accuracy in vapor–liquid equilibrium prediction.     

Calculation of critical lines of hydrocarbon/water systems by extrapolating mixing rules fitted to subcritical equilibrium data

The phase behavior of water/hydrocarbon mixtures in a wide range of pressures is important for various applications ranging from reservoir engineering to environmental engineering. In this work, mutual solubility and critical loci of hydrocarbon/water systems are calculated using the Peng–Robinson–Stryjek–Vera cubic equation of state with four mixing rules: (1) van der Waals mixing rules with one binary interaction parameter (vdW-1), (2) van der Waals mixing rules with asymmetric composition dependent binary interaction parameter (vdW-A), (3) Wong–Sandler mixing rules (WS) and (4) second-order modified Huron–Vidal mixing rules (MHV2). It was found that the parameters obtained from correlating liquid–liquid equilibria using different mixing rules would lead to prediction of completely different forms of critical behavior. Unusual branches of critical loci were found with WS and MHV2 mixing rules. Therefore, equation of states models must be used with extreme caution when applied for predicting phase behavior over wide ranges of temperatures and pressures.     

Applicability of cubic equation of state mixing rules on correlation of excess molar volume of non-electrolyte binary mixtures – Part II

The excess molar volume (V?^E) data of the 24 binary highly non-ideal mixtures containing dicyclic ethers (593 data points) were correlated by the Peng–Robinson–Stryjek–Vera (PRSV) cubic equation of state (CEOS) coupled with two different classes of mixing rules: (i) the composition dependent van der Waals (vdW) mixing rule and (ii) the excess free energy mixing rules (CEOS/G?^E) based on the approach of the Gupta–Rasmunssen–Fredenslund (GRF), as well as the Twu–Coon–Bluck–Tilton (TCBT) mixing rule; both rules with the NRTL equation as the G?^E model. The results obtained by these models show that the type of applied mixing rules, including the number and position of interaction parameters are of great importance for a satisfactory correlation of V?^E data. The GRF mixing rules gave mostly satisfactory results for V?^E correlation of the non-ideal binary systems available at one isotherm of 298.15?K, while for the correlation in temperature range from 288.15 to 308.15?K the TCBT model can be recommended.     

Binary and ternary solubilities of disperse dyes and their blend in supercritical carbon dioxide

Binary and ternary solubilities of C.I. Disperse Blue 134 (1,4-bis(isopropylamino)anthraquinone) C.I. Disperse Yellow 16 (3-methyl-1-phenyl-5-pyrazolone) and their dye mixture in supercritical carbon dioxide (SC-CO₂) were measured by a flow-type apparatus. The solubility measurements were carried out at the pressure ranges from 10.0 to 25.0 MPa for the binary systems at the temperatures from 323.15 to 383.15 K and for the ternary system at 383.15 K. An empirical equation was used to correlate the experimental binary solubilities of the dyes in terms of the density of carbon dioxide. To represent accurately the binary solubility of the dyes in terms of temperature and pressure, we used a modified Peng–Robinson–Stryjek–Vera equation of state (PRSV EOS). The ternary solubilities of the dye blend could be predicted successfully from binary parameters with the modified PRSV EOS.     

Inhibition effect of 1-ethyl-3-methylimidazolium chloride on methane hydrate equilibrium

The dissociation conditions of methane hydrate in the presence of 0.1, 0.2, 0.3 and 0.4 mass fraction of 1-ethyl-3-methylimidazolium chloride (abbreviated by EMIM-Cl hereafter) were experimentally determined. A high pressure micro-differential scanning calorimeter equipped with a motorized pump was applied to measure the dissociation temperature of the (hydrate + liquid water + vapor) three-phase equilibrium under a constant pressure process with a pressure ranging from (5.0 to 35.0) MPa. The addition of EMIM-Cl would inhibit the methane hydrate formation. The most significant inhibition effect was observed at 0.4 mass fraction of EMIM-Cl in aqueous solution to lower the dissociation temperature by 12.82 K at 20.00 MPa in comparison to that of the (methane + water) system. The Peng–Robinson–Stryjek–Vera equation of state incorporated with COSMO-SAC activity coefficient model and the first order modified Huron–Vidal mixing rule were applied to evaluate the fugacity of vapor and liquid phase. A modified van der Waals and Platteeuw model with an explicit pressure dependence of the Langmuir adsorption constant was applied to determine the fugacity of hydrate phase. The predictive thermodynamic model successfully describes the tendency of phase behavior of methane hydrate in the presence of EMIM-Cl in the range from 0.1 to 0.4 mass fraction with absolute average relative deviation in predicted temperature of 0.70%.     

Application of the perturbed Lennard–Jones chain equation of state to solute solubility in supercritical carbon dioxide

The perturbed Lennard–Jones chain (PLJC) equation of state is a thermodynamic model based on the perturbation theory of liquid state. This equation has been shown in the past to be a successful model for phase equilibria calculations of binary and ternary fluid mixtures and polymer solutions. In this work, we employed for the first time the PLJC equation to model the solubility of 39 solids in supercritical carbon dioxide. It was shown that the model achieves good correlation with three temperature independent parameters. A comparison of the PLJC with the commonly used Peng–Robinson equation reveals the PLJC equation gives better correlation to the solubility data than the Peng–Robinson model that utilizes temperature dependent parameters.     

Multiparameter equations of state for selected siloxanes

This article presents the development of technical equations of state for four siloxanes using the 12-parameter Span–Wagner functional form. Siloxanes are used as heat transfer fluids and working media in energy conversion applications. The investigated fluids are two linear dimethylsiloxanes, namely MM (hexamethyldisiloxane, C₆H₁₈OSi₂) and MD₄M (tetradecamethylhexasiloxane, C₁₄H₄₂O₅Si₆), and two cyclic dimethylsiloxanes, namely D₄ (octamethylcyclotetrasiloxane, C₈H₂₄O₄Si₄) and D₅ (decamethylcyclopentasiloxane, C₁₀H₃₀O₅Si₅). Available measured properties are critically evaluated and selected for the optimization of the equation of state (EoS) parameters. Due to the insufficient number of experimental values, several other properties are estimated with the most accurate ad hoc methods. These estimates are included in the optimization of the equation of state parameters. Moreover, experimental saturated liquid density and vapor pressure data are correlated with the equations proposed by Daubert and Wagner–Ambrose, respectively, to provide short, simple, and accurate equations for the computation of these properties. The performance of the obtained equations of state is assessed by comparison with experimental data and also with estimates obtained with the Peng–Robinson cubic EoS with the modification proposed by Stryjek and Vera. This equation was adopted in previous technical studies. The improvements obtained with the newly developed EoS's are significant. Exemplary state diagrams are also reported as a demonstration of the consistency of the obtained thermodynamic models. Sound speed measurements in the vapor phase are planned for the near future and results will be incorporated in future improvements of the newly developed thermodynamic models.     

Excess molar volume,viscosity, and refractive index study for the ternary mixture {2-methyl-2-butanol (1) + tetrahydrofuran (2) + propylamine (3)} at different temperatures. Application of the ERAS-model and Peng–Robinson–Stryjek–Vera equation of state

Densities, viscosities, and refractive indices of the ternary mixture consist of {2-methyl-2-butanol (1) + tetrahydrofuran (THF) (2) + propylamine (3)} at a temperature of 298.15 K and related binary mixtures were measured at temperatures of (288.15, 298.15, and 308.15) K at ambient pressure. Data were used to calculate the excess molar volumes and the deviations of the viscosity and refractive index. The Redlich–Kister and the Cibulka equations were used for correlating binary and ternary properties, respectively. The ERAS-model has been applied for describing the binary and ternary excess molar volumes and also Peng–Robinson–Stryjek–Vera (PRSV) equation of state (EOS) has been used to predict the binary and ternary excess molar volumes and viscosities.     

Modification of the predictive capability of the PRSV-2 equation of state for critical volumes of binary mixtures

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for critical properties of binary mixtures showing continuous critical lines has been investigated. The procedure adopted by Heidemann and Khalil and discussed by Abu-Eishah et al., in a previous paper, has been followed. The effect of using the pure-component parameters of the PRSV-2 equation of state (κ₁, κ₂ and κ₃), new values of κ₁, revised values of κ₁, or giving zero values for these parameters have been investigated. The effect of using zero values or optimized values for the binary interaction parameter on the PRSV-2 predictive capability of critical properties have also been investigated. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for the 20 nonpolar and 18 polar systems studied here agree well with experimental data, and are always better than those predicted by the group-contribution method. A correction has been introduced here to the critical volume predicted by PRSV-2 equation of state that makes the average deviations between the predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Bubble pressures and saturated liquid molar volumes of trichlorofluoromethane—chlorodifluoromethane mixtures. Representation of refrigerant-mixtures vapor—liquid equilibrium data by a modified form of the Peng—Robinson equation of state

Experimental vapor—liquid equilibrium data and saturated liquid molar volumes of chlorodifluoromethane—trichlorofluoromethane binary mixtures have been obtained at four temperatures (298.15, 323.15, 348.15 and 373.15 K) using apparatus described previously.The experimental vapor—liquid equilibria are represented well by a modified form of the Peng—Robinson equation of state with one interaction parameter, but the mean deviation between the calculated and experimental densities is 5%.Vapor—liquid data for binary refrigerant mixtures from the literature are treated using the modified form of the Peng—Robinson equation of state with one adjusted interaction parameter in the mixing rule for a. The representation is fair and is not improved by introducing an additional parameter in the mixing rule for b.     

Simultaneous prediction of interfacial tension and phase equilibria in binary mixtures: An approach based on cubic equations of state with improved mixing rules

Vapor–liquid interfacial tensions of miscible mixtures have been predicted by applying the gradient theory to an improved Peng–Robinson equation of state. The modified Huron–Vidal mixing rule model has been considered for fitting vapor–liquid equilibrium data of miscible polar and non-polar mixtures and, then, for predicting the interfacial tension of these mixtures. According to results, an accurate and globally stable fitting of the vapor–liquid equilibrium data results on a physically coherent prediction of interfacial tensions in the full concentration range. In addition, we present a criteria based on the geometry of the grand potential function along the interface for assessing the predictive value of the GT. Calculations for subcritical binary mixtures are presented and compared to experimental data and the Parachor method for demonstrating the potential of the unified approach suggested in this work.     

Phase equilibrium measurements and modelling of ternary system (carbon dioxide + ethanol + palmitic acid)

This work reports phase equilibrium measurements for the ternary system (palmitic acid + ethanol + CO₂). The motivation of this research relies on the fact that palmitic acid is the major compound of several vegetable oils. Besides, equilibrium data for palmitic acid in carbon dioxide using ethanol as co-solvent are scarce in the literature. Phase equilibrium experiments were performed using a high-pressure variable-volume view cell over the temperature range of (303 to 343) K and pressures up to 20 MPa and mole fraction of palmitic acid from 0.0199 to 0.2930. Vapour–liquid and solid–fluid transitions were visually observed for the system studied. The Peng–Robinson equation of state, with the classical van der Waals quadratic mixing rule was employed for thermodynamic modelling of the system investigated with a satisfactory agreement between experimental and calculated values.     

Vapor–liquid equilibrium measurements and correlations for an azeotropic system of ethane + hexafluoroethane

The research on the isothermal vapor–liquid phase behavior for the ethane (R170) + hexafluoroethane (R116) system is presented in this paper. The vapor–liquid equilibrium (VLE) data were measured at four temperatures 189.31, 192.63, 247.63 and 252.80 K with an apparatus based on recirculation method. The experimental results were correlated with the Peng–Robinson equation of state using two types of mixing rules, the Panagiotopoulos–Reid mixing rule and the Huron–Vidal mixing rule involving the NRTL model. The calculated data using the regressed parameters were compared with the previous measured results, and good agreements can be observed.