Solid–liquid equilibria for binary and ternary systems with the Cubic-Plus-Association (CPA) equation of state

A systematic investigation of the CPA model’s performance within solid–liquid equilibria (SLE) in binary mixtures (methane + ethane, methane + heptane, methane + benzene, methane + CO₂, ethane + heptane, ethane + CO₂, 1-propanol + 1,4-dioxane, ethanol + water, 2-propanol + water) is presented. The results from the binary mixtures are used to predict SLE behaviour in ternary mixtures (methane + ethane + heptane, methane + ethane + CO₂). Our results are compared with experimental data found in the literature.     

High pressure phase equilibria in methane + waxy systems. 2. Methane + waxy ternary mixture

Liquid–vapour and fluid–solid phase transitions were experimentally determined under pressure on the system methane + a ternary waxy mixture using a full visibility cell. The wax was an approximately equimolar mixture of n-C₁₆, n-C₁₇ and n-C₁₈, the composition being chosen to obtain a mixture with an average molecular weight similar to heptadecane. Measurements were performed according to the synthetic method on different mixtures ranging from 0 to 99.5 mol% of methane. The liquid–solid phase transitions were investigated up to 100 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. Measurements performed on this pseudo-binary system were compared to the phase diagram of the binary system methane + heptadecane.     

Clathrate hydrate formation in (methane + water + methylcyclohexanone) systems: the first phase equilibrium data

The present study experimentally demonstrated clathrate hydrate formation in the systems of (methane + water + each of the three methylcyclohexanone isomers, i.e., 2-methylcyclohexanone, 3-methylcyclohexanone, and 4-methylcyclohexanone) and measured the first data of the quadruple (water rich liquid + hydrate + methylcyclohexanone rich liquid + methane rich vapor) equilibrium pressure and temperature conditions in these systems over the temperatures from T=273 K to T=281 K. In the three systems with methylcyclohexanone, the measured equilibrium pressure at each given temperature is ∼1.3 MPa lower than that in a structure-I hydrate forming (methane + water) system without any methylcyclohexanone, which suggests the formation of structure-H hydrates with methylcyclohexanones as large-molecule guest substances. Among the three systems, 3-methylcyclohexanone provides the highest equilibrium pressure, and 2-methylcyclohexanone, the lowest.     

Raman spectroscopic studies on methane + tetrafluoromethane mixed-gas hydrate system

Raman spectra of intramolecular vibration mode for each guest species in the methane + tetrafluoromethane (CF₄) mixed-gas hydrate crystal have been measured at 291.1 K. Both of pure guest species generate the structure-I hydrate in the present pressure ranges. Isothermal phase-equilibrium curve exhibits two discontinuous points around the equilibrium methane compositions (water-free) in the gas phase of 0.3 and 0.8. At the above points, the Raman spectra of both guest molecules have been drastically changed. One of the most important findings is that the crystal of methane + tetrafluoromethane mixed-gas hydrate shows the structural phase-transition (from the structure-I to the structure-II and back to the structure-I) caused by composition changes.     

Gas-Liquid Fluorination of 1,1,1,2-Tetrafluoroethane and Methane with Elemental Fluorine in a Perfluorinated Liquid

The reaction of 1,1,1,2-tetrafluoroethane with fluorine in a gas-liquid reactor with a high-speed stirrer and with perfluorodecalin or perfluoro-1,3-dimethylcyclohexane as a liquid phase occurs as hydrogen substitution without noticeable cleavage of C-C bonds, yielding penta- and hexafluoroethane. The fluorination of methane in perfluorodecalin under the same conditions yields, depending on the methane and fluorine concentrations in their mixtures with an inert gas, products of successive hydrogen substitution by fluorine when the reaction occurs in approximately isothermal mode and products corresponding to the thermodynamic equilibrium when the reaction occurs in the mode of gas-phase diffusion combustion on the gas bubble scale.

     

High pressure phase equilibria in methane + waxy systems: 1. Methane + heptadecane

Fluid–fluid and fluid–solid phase equilibrium were experimentally determined under pressure on the system methane + heptadecane using a full visibility cell. Measurements were performed using the synthetic method on mixtures ranging from pure heptadecane to 99% of methane. The liquid–solid phase transitions were investigated up to 90 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. The appearance of a minimum in the three phase (V–L–S) equilibrium curve is discussed and it is shown that the difference in the solid phase structure and the presence of a solid–solid phase transition do not affect significantly the phase diagram determined.     

Density,viscosity, vapour–liquid equilibrium,excess molar enthalpy,and their correlations of the binary system [1-pentanol + R-(+)-limonene] over the complete concentration range,at different temperatures

Density and viscosity measurements in the T = (293.15–373.15) K range of pure 1-pentanol, R-(+)-limonene, as well as of the binary system {x₁ 1-pentanol + (1 − x₁) limonene} over the whole concentration range were made. The experimental results were fitted to empirical equations, which permit the calculation of these properties in the studied temperature range. Calculated values are in agreement with the experimental ones. Data of the binary mixtures were further used to calculate the excess molar volume and viscosity deviations. Excess enthalpy at 303 K and vapour–liquid equilibrium measurements in the T = (328.15–343.15) K range were also obtained for the binary system. These last experimental results were used to calculate activity coefficients and the excess molar Gibbs energy. This binary system exhibits a maximum pressure azeotrope. Excess or deviation properties were fitted to the Redlich–Kister polynomial relation to obtain their coefficients and standard deviations. Vapour pressure of 1-pentanol over the P = (2.3–95.1) kPa range were also measured. Furthermore, functional relationships between the total pressure and the mole fraction of 1-pentanol with the temperature of the azeotropic point were also deduced. These equations are useful to calculate the azeotropic point coordinates in the temperature and pressure ranges studied in this work.     

Solid–liquid equilibria of acenaphthene with o-, m-, or p-dichlorobenzene

A differential scanning calorimetry (DSC) was used to determine binary solid–liquid equilibria (SLE) for acenaphthene  + o-dichlorobenzene, +m-dichlorobenzene, and +p-dichlorobenzene over the whole concentration range. It was found that all systems are simple eutectic systems. The eutectic point of the (acenaphthene + o-dichlorobenzene) system is at 254.95 K and 0.0334 mole fraction of acenaphthene, that of the (acenaphthene + m-dichlorobenzene) system at 246.15 K and 0.0460 mole fraction of acenaphthene and that of the (acenaphthene + p-dichlorobenzene) system at 307.75 K and 0.2940 mole fraction of acenaphthene. Furthermore, the activity coefficients of the components in the binary mixtures have been correlated by the Scatchard–Hildebrand expression with one adjustable parameter. This approach offers a useful procedure for estimating with good accuracy.     

Measurement and modeling of mean activity coefficients of NaBr and amino acid in (sodium bromide + potassium phosphate + glycine + water) system at T (298.15 and 308.15) K

Electrochemical measurements are done on (water + NaBr + K₃PO₄ + glycine) mixtures at T (298.15 and 308.15) K by using (Na⁺ glass) and (Br⁻ solid-state) ion selective electrodes. The mean ionic activity coefficients of NaBr are determined at five NaBr molalities (0.1, 0.3, 0.5, 0.7, and 1) in the above mixtures. The activity coefficients of glycine are evaluated from mean ionic activity coefficients of sodium bromide. The ratio of mean ionic activity coefficient of NaBr in the (water + NaBr + K₃PO₄ + glycine) mixtures to the mean ionic activity coefficients of NaBr at the same molalities in the (H₂O + NaBr) mixtures are correlated by using a new expression.     

Thermophysical properties of dimethyl sulfoxide + cyclic and linear ethers at 308.15 K: Application of an extended cell model

Excess molar enthalpies and heat capacities of dimethyl sulfoxide + 1,4-dioxane, dimethyl sulfoxide + 1,3-dioxolane, dimethyl sulfoxide + tetrahydropyran, dimethyl sulfoxide + tetrahydrofuran, dimethyl sulfoxide + 1,2-dimethoxyethane, and dimethyl sulfoxide + 1,2-diethoxyethane have been measured at 308.15 K and at atmospheric pressure using an LKB micro-calorimeter and a Perkin-Elmer differential scanning calorimeter. Heat capacities of pure components were determined in the range (293.15 < T/K < 423.15). The results of excess molar enthalpies were fitted to the Redlich-Kister polynomial equation to derive the adjustable parameters and standard deviations, and were used to study the nature of the molecular interactions in the mixtures. Results of excess molar enthalpy were interpreted by an extended modified cell model.     

Liquid-liquid equilibria for mixtures of (ethylene carbonate + aromatic hydrocarbon + cyclohexane)

Liquid-liquid equilibrium data for mixtures of (ethylene carbonate + benzene + cyclohexane) at temperatures 303.15 and 313.15 K and (ethylene carbonate + BTX + cyclohexane) at temperature 313.15 K are reported, where the BTX is benzene, toluene and m-xylene. The compositions of liquid phases at equilibrium were determined by gas liquid chromatography. The selectivity factors and partition coefficients of ethylene carbonate for the extraction of benzene, toluene and m-xylene from (ethylene carbonate + BTX + cyclohexane) are calculated and presented. The obtained results are compared with the selectivity factors and partition coefficients of ethylene carbonate for the extraction of benzene from (ethylene carbonate + benzene + cyclohexane). The liquid-liquid equilibrium data were correlated with the UNIQUAC and NRTL activity coefficient models. The phase diagrams for the studied mixtures are presented and the correlated tie line results have been compared with the experimental data. The comparisons indicate the applicability of the UNIQUAC and NRTL activity coefficients model for liquid-liquid equilibrium calculations of the studied mixtures. The tie line data of the studied mixtures also were correlated using the Hand method.     

CO2 and CH4 mole fraction measurements during hydrate growth in a semi-batch stirred tank reactor and its significance to kinetic modeling

A new experimental technique has been developed to measure the mole fraction of the gas hydrate former in the bulk liquid phase, at the onset of hydrate growth and thereafter, in a semi-batch stirred tank reactor. The mole fraction of carbon dioxide and methane in the bulk liquid phase was obtained for the first 11 and 13 min of the growth stage, for the carbon dioxide–water and methane–water systems respectively. Experiments were conducted at temperatures ranging from 275.3 K to 281.4 K and at pressures ranging from 2017 kPa to 4000 kPa for the carbon dioxide–water system, while temperatures ranging from 275.1 K to 279.1 K and pressures ranging from 3858 kPa to 6992 kPa were investigated for the methane–water system. The mole fraction of carbon dioxide in the bulk liquid phase was found to be constant during the growth period, varying on average by 0.6% and 0.3% at 275.4 K and 279.5 K. Similarly, the mole fraction of methane in the bulk liquid phase was found to remain constant during the growth stage, varying on average by 2.0%, 0.8% and 0.2% at 275.1 K, 277.1 K and 279.1 K respectively. The mole fraction of the gas hydrate former in the bulk liquid phase was also found to increase with pressure and decrease with temperature, while remaining greater than its hydrate-liquid water equilibrium value. As a result, an alternate formulation of a hydrate growth model is proposed.     

Theoretical study on the reaction mechanism of CH4 with CaO

The reaction pathways and energetics for the reaction of methane with CaO are discussed on the singlet spin state potential energy surface at the B3LYP/6-311+G(2df,2p) and QCISD/6-311++G(3df,3pd)//B3LYP/6-311+G(2df,2p) levels of theory. The reaction of methane with CaO is proposed to proceed in the following reaction pathways: CaO + CH₄ → CaOCH₄ → [TS] → CaOH + CH₃, CaO + CH₄ → OCaCH₄ → [TS] → HOCaCH₃ → CaOH + CH₃ or [TS] → CaCH₃OH → Ca + CH₃OH, and OCaCH₄ → [TS] → HCaOCH₃ → CaOCH₃ + H or [TS] → CaCH₃OH → Ca + CH₃OH. The gas-phase methane–methanol conversion by CaO is suggested to proceed via two kinds of important reaction intermediates, HOCaCH₃ and HCaOCH₃, and the reaction pathway via the hydroxy intermediate (HOCaCH₃) is energetically more favorable than the other one via the methoxy intermediate (HCaOCH₃). The hydroxy intermediate HOCaCH₃ is predicted to be the energetically most preferred configuration in the reaction of CaO + CH₄. Meanwhile, these three product channels (CaOH + CH₃, CaOCH₃ + H and Ca + CH₃OH) are expected to compete with each other, and the formation of methyl radical is the most preferable pathway energetically. On the other hand, the intermediates HCaOCH₃ and HOCaCH₃ are predicted to be the energetically preferred configuration in the reaction of Ca + CH₃OH, which is precisely the reverse reaction of methane hydroxylation.     

VLE of CO2 + glycerol + (ethanol or 1-propanol or 1-butanol)

Vapour-liquid equilibrium of CO₂ + [0.00871 glycerol + 0.99129 (ethanol or 1-propanol or 1-butanol)] mixtures was measured at the temperatures of 313.15 K and 333.15 K, and close to the critical line, at pressures up to 12 MPa. On the liquid side, the bubble points measured for these ternary mixtures follow closely the behaviour of VLE reported by several authors for the corresponding binary mixtures without glycerol. On the vapour side, however, dew points for the ternary mixtures deviate significantly from VLE results for the binaries. A correlation of the results obtained for the CO₂ + glycerol + ethanol mixture with the Peng-Robinson equation of state, admitting quasi-binary behaviour, equally yields good agreement on the liquid side, and significant deviations on the vapour side.     

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.     

Multiphase equilibria for mixtures containing water, isopropanol, propionic acid, and isopropyl propionate

Vapor pressures of isopropyl propionate and isobaric vapor-liquid equilibrium (VLE) properties of isopropyl propionate + isopropanol and propionic acid + isopropyl propionate were measured. Isothermal vapor-liquid-liquid equilibrium (VLLE) data were also determined experimentally for water + isopropyl propionate and water + isopropyl propionate + isopropanol at temperatures from 323.24 K to 373.15 K. The binary VLE and VLLE data can be correlated well with the NRTL-HOC and the UNIQUAC-HOC models. The ternary VLLE data were used to test the validity of two versions of the UNIFAC model and the NRTL-HOC and the UNIQUAC-HOC models with the parameters determined from the phase equilibrium data of the constituent binaries. The ternary VLLE data were also correlated with the NRTL-HOC and the UNIQUAC-HOC models and the Soave-Redlich-Kwong equation of state with the Wong-Sandler mixing rule.     

Solubilities of cholesterol and desmosterol in binary solvent mixtures of n-hexane + ethanol

The solubilities of cholesterol and desmosterol in binary solvent mixtures of n-hexane + ethanol at temperatures of 293.2–323.2 K were determined by a static equilibrium method. The solubilities increase with temperature and go through a maximum at a specific solvent composition. The fusion enthalpy Δ_fusH and the melting point T_m, determined by differential scanning calorimeter (DSC), are 28.5 kJ/mol, 421.7 K for cholesterol and 15.9 kJ/mol, 388.2 K for desmosterol, respectively. The solubilities of cholesterol and desmosterol in pure n-hexane or ethanol follow a linear Van’t Hoff relation with temperature. Activity models, such as Wilson, NRTL and UNIQUAC models were used to correlate and predict the solubilities of cholesterol and desmosterol in n-hexane + ethanol mixed solvents. The interaction parameters were expressed as a function of temperature.     

(Vapour + liquid) equilibrium in (N,N-dimethylacetamide + methanol + water) at the temperature 313.15 K

Total vapour pressures, measured at the temperature 313.15 K, are reported for the ternary mixture (N,N-dimethylacetamide + methanol + water), and for binary constituents (N,N-dimethylacetamide + methanol) and (N,N-dimethylacetamide + water). The present results are compared with previously obtained data for binary mixtures (amide + water) and (amide + methanol), where amide=N-methylformamide, N,N-dimethylformamide, N-methyl-acetamide, 2-pyrrolidinone and N-methylpyrrolidinone. Moreover, it was found that excess Gibbs free energy of mixing for binary mixtures varies roughly linearly with the molar volume of amide.     

Vapor–liquid equilibria and density measurement for binary mixtures of toluene,benzene, o-xylene,m-xylene,sulfolane and nonane at 333.15 K and 353.15 K

Isothermal vapor–liquid equilibria at 333.15 K and 353.15 K for four binary mixtures of benzene + nonane, toluene + o-xylene, m-xylene + sulfolane and o-xylene + sulfolane have been obtained at pressures ranged from 0 to 101.3 kPa over the whole composition range. The Wilson, NRTL and UNIQUAC activity coefficient models have been employed to correlate experimental pressures and liquid mole fractions. The non-ideal behavior of the vapor phase has been considered by using the Peng–Robinson equation of state in calculating the vapor mole fraction. Liquid and vapor densities of these solutions were measured by using two vibrating tube densitometers. The excess molar volumes of the liquid phase were also determined. The P–x–y phase behavior indicates that mixtures of m-xylene + sulfolane, o-xylene + sulfolane and benzene + nonane present large positive deviations from the ideal solution and belong to endothermic mixings because their excess Gibbs energies are positive.