Hydrate phase equilibrium and structure for (methane + ethane + tetrahydrofuran + water) system

The separation of methane and ethane through forming hydrate is a possible choice in natural gas, oil processing, or ethylene producing. The hydrate formation conditions of five groups of (methane + ethane) binary gas mixtures in the presence of 0.06 mole fraction tetrahydrofuran (THF) in water were obtained at temperatures ranging from (277.7 to 288.2) K. In most cases, the presence of THF in water can lower the hydrate formation pressure of (methane + ethane) remarkably. However, when the composition of ethane is as high as 0.832, it is more difficult to form hydrate than without THF system. Phase equilibrium model for hydrates containing THF was developed based on a two-step hydrate formation mechanism. The structure of hydrates formed from (methane + ethane + THF + water) system was also determined by Raman spectroscopy. When THF concentration in initial aqueous solution was only 0.06 mole fraction, the coexistence of structure I hydrate dominated by ethane and structure II hydrate dominated by THF in the hydrate sample was clearly demonstrated by Raman spectroscopic data. On the contrary, only structure II hydrate existed in the hydrate sample formed from (methane + ethane + THF + water) system when THF concentration in initial aqueous solution was increased to 0.10 mole fraction. It indicated that higher THF concentration inhibited the formation of structure I hydrate dominated by ethane and therefore lowered the trapping of ethane in hydrate. It implies a very promising method to increase the separation efficiency of methane and ethane.     

The partition coefficients of ethylene between vapor and hydrate phase for methane + ethylene + THF + water systems

The vapor-hydrate equilibria were studied experimentally in detail for CH₄ + C₂H₄ + tetrahydrofuran (THF) + water systems in the temperature range of 273.15–282.15 K, pressure range of 2.0–4.5 MPa, the initial gas–liquid volume ratio range of 45–170 standard volumes of gas per volume of liquid and THF concentration range of 4–12 mol%. The results demonstrated that, because of the presence of THF, ethylene was remarkably enriched in vapor phase instead of being enriched in hydrate phase for CH₄ + C₂H₄ + water system. This conclusion is of industrial significance; it implies that it is feasible to enrich ethylene from gas mixture, e.g., various kinds of refinery gases or cracking gases in ethylene plant, by forming hydrate.     

Phase equilibrium measurements of (methane + benzene) and (methane + methylbenzene) at temperatures from (188 to 348) K and pressures to 13 MPa

New isothermal pTxy data are reported for (methane + benzene) and (methane + methylbenzene (toluene)) at pressures up to 13 MPa over the temperature range (188 to 313) K using a custom-built (vapor + liquid) equilibrium (VLE) apparatus. The aim of this work was to investigate literature data inconsistencies and to extend the measurements to lower temperatures. For (methane (1) + benzene (2)), measurements were made along six isotherms from (233 to 348) K at pressures to 9.6 MPa. At temperatures below 279 K there was evidence of a solid phase, and thus only vapor phase samples were analyzed at these temperatures. For the (methane (1) + methylbenzene (3)) system, measurements were made along seven isotherms from T = (188 to 313) K at pressures up to 13 MPa. Along the 198 K isotherm, a significant change in the data’s p,x slope was observed indicating (liquid + liquid) equilibria at higher pressures. The data were compared with literature data and with calculations made using the Peng–Robinson (PR) equation of state (EOS). For both binary systems our data agree with much of the literature data that also deviate from the EOS in a similar manner. However, the data of Elbishlawi and Spencer (1951) for both binary systems, which appear to have received an equal weighting to other data in the EOS development, are inconsistent with the results of our measurements and data from other literature sources.     

(Liquid + liquid) equilibria of (sulfolane + benzene + n-hexane), (N-formylmorpholine + benzene + n-hexane), and (sulfolane + N-formylmorpholine + benzene + n-hexane) at temperatures ranging from (298.15 to 318.15) K: Experimental results and correlation

The experimental (liquid + liquid) equilibrium (LLE) properties for two ternary systems containing (N-formylmorpholine + benzene + n-hexane), (sulfolane + benzene + n-hexane) and a quaternary mixed solvent system (sulfolane + N-formylmorpholine + benzene + n-hexane) were measured at temperature ranging from (298.15 to 318.15) K and at an atmospheric pressure. The experimental distribution coefficients and selectivity factors are presented to evaluate the efficiency of the solvents for extraction of benzene from n-hexane. The LLE results obtained indicate that increasing temperature decreases selectivity for all solvents. The LLE results for the systems studied were used to obtain binary interaction parameters in the UNIQUAC model by minimizing the root mean square deviations (RMSD) between the experimental and calculated results. Using the interaction parameters obtained, the phase equilibria in the systems were calculated and plotted. The calculated compositions based on the UNIQUAC model were found to be in good agreement with the experimental values. The result of the RMSD obtained by comparing the calculated and experimental two-phase compositions is 0.0163 for (N-formylmorpholine + benzene + n-hexane) system and is 0.0120 for (sulfolane + benzene + n-hexane) system.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl₃ and the (Na,K)₂(Mg,Mn,Fe,Co,Ni)Cl₄ solid solutions were modeled using the Compound Energy Formalism.     

(Liquid + liquid) equilibrium of (NaNO3 + PEG 4000 + H2O) ternary system at different temperatures

Phase diagram and (liquid + liquid) equilibrium (LLE) data for the (NaNO₃ + polyethylene glycol 4000 (PEG 4000) + H₂O) system have been determined experimentally at T = (288.15 and 308.15) K. The effects of temperature on the binodal curves and tie-lines have been studied and it was found that an increasing in temperature caused the expansion of two-phase region. The Chen-NRTL, modified Wilson and UNIQUAC models were used to correlate the experimental tie-line data. The results show that the quality of fitting is better with the UNIQUAC model.     

Thermodynamic evaluation and optimization of the (LiF + NaF + KF + MgF2 + CaF2 + SrF2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiF + NaF + KF + MgF₂ + CaF₂ + SrF₂) system, and optimized model parameters have been found. The (LiF + NaF + KF + MgF₂ + CaF₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase, and the low-temperature and high-temperature (CaF₂ + SrF₂) solid solutions were modelled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Li, Na, K)(Mg, Ca, Sr)F₃ perovskite phase was modelled using the Compound Energy Formalism.     

Thermodynamic evaluation and optimization of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system, and optimized model parameters have been found. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. This is the first of two articles on the optimization of the (NaCl + KCl + MgCl₂ + CaCl₂ + MnCl₂ + FeCl₂ + CoCl₂ + NiCl₂) system.     

Vapor–liquid equilibrium of methane and methane + nitrogen and an equimolar hexane + decane mixture under isothermal conditions

Experimental vapor–liquid equilibrium data of the ternary system composed of methane and an equimolar hexane + decane mixture are reported. The experimental measurements were carried out under isothermal conditions at 258, 273, and 298 K in the pressure range 1–19 MPa. Also, experimental vapor–liquid measurements were carried out for the quaternary system methane + nitrogen and an equimolar hexane + decane mixture, at 258 K in the range 3.5–12 MPa. The results for the ternary system show that the solubility of methane in the equimolar mixture of alkanes increases when the pressure is increased at constant temperature and it increases as the temperature decreases in the whole pressure range studied. For the quaternary system with a constant amount of nitrogen, the solubility of methane in the liquid phase increases as the pressure increases at the studied temperature. The experimental results for the ternary system were satisfactorily correlated with the Peng–Robinson equation of state in the ranges of pressure and temperature studied. The equation of state was used to predict the behavior of the quaternary system using binary interaction parameters. The applicability of the principle of congruence was corroborated by comparing the vapor–liquid behavior of methane in the equimolar hexane + decane mixture with that in pure octane, at the three temperatures studied in this work.     

(Liquid + liquid) equilibria for mixtures of (ethylene glycol + benzene + cyclohexane) at temperatures (298.15, 308.15, and 318.15) K

Experimental (liquid + liquid) equilibrium (LLE) data for a ternary system containing (ethylene glycol + benzene + cyclohexane) were determined at temperatures (298.15, 308.15, and 318.15) K and at atmospheric pressure. The experimental distribution coefficients and selectivity factors are presented to evaluate the efficiency of the solvent for extraction of benzene from cyclohexane. The effect of temperature in extraction of benzene from the (benzene + cyclohexane) mixture indicated that at lower temperatures the selectivity (S) is higher, but the distribution coefficient (K) is rather lower. The LLE results for the system studied were used to obtain binary interaction parameters in the UNIQUAC and NRTL models by minimizing the root mean square deviations (RMSD) between the experimental results and calculated results. Using the interaction parameters obtained, the phase equilibria in the systems were calculated and plotted. The NRTL model fits the (liquid + liquid) equilibrium data of the mixture studied slightly better. The root mean square deviations (RMSDs) obtained comparing calculated and experimental two-phase compositions are 0.92% for the NRTL model and 0.95% for the UNIQUAC model.     

Quaternary isobaric (vapor + liquid + liquid) equilibrium and (vapor + liquid) equilibrium for the system (water + ethanol + cyclohexane + heptane) at 101.3 kPa

Experimental isobaric (vapor + liquid + liquid) and (vapor + liquid) equilibrium data for the ternary system {water (1) + cyclohexane (2) + heptane (3)} and the quaternary system {water (1) + ethanol (2) + cyclohexane (3) + heptane (4)} were measured at 101.3 kPa. An all-glass, dynamic recirculating still equipped with an ultrasonic homogenizer was used to determine the VLLE. The results obtained show that the system does not present quaternary azeotropes. The point-by-point method by Wisniak for testing the thermodynamic consistency of isobaric measurements was used to test the equilibrium data.     

Isobaric (vapour + liquid + liquid) equilibrium data for (di-n-propyl ether + n-propyl alcohol + water) and (diisopropyl ether + isopropyl alcohol + water) systems at 100 kPa

Isobaric (vapour + liquid + liquid) equilibria were measured for the (di-n-propyl ether + n-propyl alcohol + water) and (diisopropyl ether + isopropyl alcohol + water) system at 100 kPa.The apparatus used for the determination of (vapour + liquid + liquid) equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer couple to the boiling flask.The experimental data demonstrated the existence of a heterogeneous ternary azeotrope for both ternary systems. The (vapour + liquid + liquid) equilibria data were found to be thermodynamically consistent for both systems.The experimental data were compared with the estimation using UNIQUAC and NRTL models and the prediction of UNIFAC model.     

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + ZnCl2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaCl + KCl + MgCl₂ + CaCl₂ + ZnCl₂) system, and optimized model parameters have been found. The (NaCl + KCl + MgCl₂ + CaCl₂) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase.     

Thermodynamic evaluation and optimization of the (NaF + AlF3 + CaF2 + BeF2 + Al2O3 + BeO) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases and relevant gaseous species of the (NaF + AlF₃ + CaF₂ + BeF₂ + Al₂O₃ + BeO) system, and optimized model parameters have been found. The (NaF + AlF₃ + CaF₂ + Al₂O₃) subsystem, which is the base electrolyte used for the electro-reduction of alumina in Hall–Héroult cells, has been critically evaluated in a previous article. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase. The thermodynamic database developed is a first step towards a quantitative study of the beryllium mass balance in an electrolysis cell. In particular, the predominant Be-containing species in the gas phase evolved at the anode were identified; and, for a given beryllium content of the alumina, the beryllium content of the electrolytic bath at steady state was assessed under several approximations.     

Liquid–liquid equilibrium in ternary systems N,N-dimethylformamide + 2-methylpentane + methanol and N,N-dimethylformamide + methylcyclohexane + methanol

In the present paper, a study of temperature behaviour of the liquid–liquid equilibrium in ternary systems N,N-dimethylformamide + 2-methylpentane + methanol and N,N-dimethylformamide + methylcyclohexane + methanol. The analysis of critical curves of the liquid–liquid equilibrium by means of the regular solution model was carried out. The acquired predictions were subsequently verified experimentally.     

Thermodynamic investigation of the (LiF + NaF + CaF2 + LaF3) system

In this work a thermodynamic assessment of the (LiF + NaF + CaF₂ + LaF₃) system is reported. For the thermodynamic modeling of the liquid phase, the classical polynomial model, and the modified quasi-chemical model were used in parallel and compared. The extrapolation to higher order systems was done according to the Toop mathematical formalism. Furthermore, differential-scanning calorimetry data of the ternary (LiF + CaF₂ + LaF₃), (NaF + CaF₂ + LaF₃), and the quaternary (LiF + NaF + CaF₂ + LaF₃) mixtures are presented. Good agreement between the experimental data and the thermodynamic assessment was obtained.     

The effect of temperature and molar mass on the (liquid + liquid) equilibria of (poly ethylene glycol dimethyl ether + di-sodium hydrogen citrate + water) systems: Experimental and correlation

The (liquid + liquid) equilibrium for the {polyethylene glycol dimethyl ether 2000 (PEGDME₂₀₀₀) + di-sodium hydrogen citrate + H₂O} system was studied at T = (298.15, 308.15 and 318.15) K and atmospheric pressure (≈85 kPa). The free energies, enthalpies and entropies of cloud points were calculated in order to investigate the driving force formation of this two-phase system. To investigate the effect of molar mass of the polymer on the binodals and tie-lines, similar measurements were also made at T = 298.15 K on this two-phase system consisting of the PEGDME with molar masses of 500 and 250 g ⋅ mol⁻¹. The effective excluded volume model was used for representation of the phase-forming ability in PEGDME systems. An empirical and the Merchuck equations with the temperature dependency were used to correlate the binodal curves. The Othmer–Tobias and Bancraft and Setschenow equations, the osmotic virial and the extended NRTL models were used to fit the tie-line data.     

Measurement of (liquid + liquid) equilibria for ternary systems of (N-formylmorpholine + benzene + cyclohexane) at temperatures (303.15, 308.15, and 313.15) K

This work demonstrates the ability of N-formylmorpholine (NFM) to act as an extraction solvent for the removal of benzene from its mixture with cyclohexane. The (liquid + liquid) equilibria (LLE) were measured for a ternary system of {N-formylmorpholine (NFM) + benzene + cyclohexane} under atmospheric pressure and at temperatures (303.15, 308.15, and 313.15) K. The experimental distribution coefficients (K) and selectivity factors (S) were obtained to reveal the extractive effectiveness of the solvent for separation of benzene from cyclohexane. The LLE results for the system studied indicate that increasing temperature decreases selectivity of the solvent. The reliability of the experimental results was tested by applying the Othmer–Tobias correlation. In addition, the universal quasichemical activity coefficient (UNIQUAC) and the non-random two liquids equation (NRTL) were used to correlate the LLE data using the interaction parameters determined from the experimental data. The root mean square deviations (RMSDs) obtained comparing calculated and experimental two-phase compositions are 0.0367 for the NRTL model and 0.0539 for the UNIQUAC model.     

Thermodynamic evaluation and optimization of the (Ca + C + O + S) system

A critical evaluation of all available thermodynamic and (solid + liquid) phase equilibrium data for the (Ca + C + O + S) system has been performed. The liquid phase was modelled using the Modified Quasichemical Model in the pair approximation. The present database reproduces the (solid + liquid) equilibria of the experimentally studied subsystems of the (Ca + C + O + S) system within the experimental error limits. Estimations of the phase equilibria of systems lacking experimental data were made. The database of thermodynamic data for all phases can be used, along with other databases and Gibbs free energy minimization software, to calculate the phase equilibria and all thermodynamic properties of (Ca + C + O + S) mixtures, which are of great importance for several industrially relevant processes.     

(Liquid + liquid) equilibria of three ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), (heptane + xylene + N-formylmorpholine) from T = (298.15 to 353.15) K

(Liquid + liquid) equilibrium (LLE) data for ternary systems: (heptane + benzene + N-formylmorpholine), (heptane + toluene + N-formylmorpholine), and (heptane + xylene + N-formylmorpholine) have been determined experimentally at temperatures ranging from 298.15 K to 353.15 K. Complete phase diagrams were obtained by determining solubility and tie-line data. Tie-line compositions were correlated by Othmer–Tobias and Bachman methods. The universal quasichemical activity coefficient (UNIQUAC) and the non-random two liquids equation (NRTL) were used to predict the phase equilibrium in the system using the interaction parameters determined from experimental data. It is found that UNIQUAC and NRTL used for LLE could provide a good correlation. Distribution coefficients, separation factors, and selectivity were evaluated for the immiscibility region.