Phase equilibria in ternary (carbon dioxide + tetrahydrofuran + water) system in hydrate-forming region: Effects of carbon dioxide concentration and the occurrence of pseudo-retrograde hydrate phenomenon

In the present work, the three- and four-phase hydrate equilibria of (carbon dioxide (CO₂) + tetrahydrofuran (THF) + water) system are measured by using Cailletet equipment in the temperature and pressure range of (272 to 292) K and (1.0 to 7.5) MPa, respectively, at different CO₂ concentration. Throughout the study, the concentration of THF is kept constant at 5 mol% in the aqueous solution. In addition, the fluid phase transitions of L_W–L_V–V → L_W–L_V (bubble point) and L_W–L_V–V → L_W–V (dew point) are determined when they are present in the ternary system. For comparison, the three-phase hydrate equilibria of binary (CO₂ + H₂O) are also measured. Experimental measurements show that the addition of THF as a hydrate promoter extends hydrate stability region by elevating the hydrate equilibrium temperature at a specified pressure. The three-phase equilibrium line H–L_W–V is found to be independent of the overall concentration of CO₂. Contradictory, at higher pressure, the phase equilibria of the systems are significantly influenced by the overall concentration of CO₂ in the systems. A liquid–liquid phase split is observed at overall concentration of CO₂ as low as 3 mol% at elevated pressure. The region is bounded by the bubble-points line (L_W–L_V–V → L_W–L_V), dew points line (L_W–L_V–V → L_W + V) and the four-phase equilibrium line (H + L_W + L_V + V). At higher overall concentration of CO₂ in the ternary system, experimental measurements show that pseudo-retrograde behaviour exists at pressure between (2.5 and 5) MPa at temperature of 290.8 K.     

Phase equilibrium measurements for clathrate hydrates of flue gas (CO2 + N2 + O2) in the presence of tetra-n-butyl ammonium bromide or tri-n-butylphosphine oxide

This paper reports the measured hydrate phase equilibria of simulated flue gas (12.6 vol% CO₂, 80.5 vol% N₂, 6.9 vol% O₂) in the presence of tetra-n-butyl ammonium bromide (TBAB) or tri-n-butylphosphine oxide (TBPO), at (0, 5 and 26) wt%, respectively. The measurements of the phase boundary between (hydrate + liquid + vapor) (H + L + V) phases and (liquid + vapor) (L + V) phases were performed within the temperature range (275.97 to 293.99) K and pressure range (1.56 to 18.78) MPa with using the isochoric step-heating pressure search method. It was found that addition of TBAB or TBPO allowed the incipient equilibrium hydrate formation conditions for the flue gas to become milder. Compared to TBAB, TBPO was largely more effective in reducing the phase equilibrium pressure.     

Isothermal phase equilibria for the (xenon + cyclopropane) mixed-gas hydrate system

Isothermal three-phase equilibria of gas, aqueous, and hydrate phases for the {xenon (Xe) + cyclopropane (c-C₃H₆)} mixed-gas hydrate system were measured at two different temperatures (279.15 and 289.15) K. The structural phase transitions from structure-I to structure-II and back to structure-I, depending on the mole fraction of guest mixtures, occur in the (Xe + c-C₃H₆) mixed-gas hydrate system. The isothermal pressure–composition relations have two local pressure minima. The most important characteristic in the (Xe + c-C₃H₆) mixed-gas hydrate system is that the equilibrium pressure–composition relations exhibit the complex phase behavior involving two structural phase transitions and two homogeneous negative azeotropes. One of two structural phase transitions exhibits the heterogeneous azeotropic-like behavior.     

Experimental measurement and thermodynamic modelling of phase equilibria of semi-clathrate hydrates of (CO2 + tetra-n-butyl-ammonium bromide) aqueous solution

Comprehensive studies on semi-clathrate hydrates phase equilibria are still required to better understand characteristics of this type of clathrates. In this communication, new experimental data on the dissociation conditions of semi-clathrate hydrates of {carbon dioxide + tetra-n-butyl-ammonium bromide (TBAB)} aqueous solution are first reported in a wide range of TBAB concentrations and at different pressures and temperatures. A thermodynamic model is then proposed to predict the dissociation conditions of the semi-clathrate hydrates for the latter system. The (hydrate + TBAB) aqueous solution (H + L_w) phase equilibrium prediction is considered based on Gibbs free energy minimization approach. A modified van der Waals–Platteeuw solid solution theory developed based on the (H + L_w) equilibrium information is employed to predict the dissociation conditions of semi-clathrate hydrates of carbon dioxide + TBAB. The properties of the aqueous solution are estimated using the AMSA-NRTL electrolyte model (considering the association and hydration of ions). The Peng–Robinson equation of state is used for estimating the gas/vapour phase properties. Results show that the proposed model satisfactorily predicts the experimental values with an average absolute relative deviation of approximately 13%.     

Vapor–liquid equilibria in the ternary system isobutyl alcohol + isobutyl acetate + butyl propionate and the binary systems isobutyl alcohol + butyl propionate,isobutyl acetate + butyl propionate at 101.3 kPa

Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system isobutyl alcohol (IBA) + isobutyl acetate (IBAc) + butyl propionate (BUP) and two constituent binary systems: IBA + BUP and IBAc + BUP. The IBA + BUP system show lightly positive deviation from Raoult's law and IBAc + BUP system exhibits no deviation from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is very well predicted from binary interaction parameters. BUP eliminates the IBA–IBAc binary azeotrope. The change of phase equilibria behaviour is significant therefore this solvent seems to be an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.8.The binary VLE data measured in the present study passed the thermodynamic consistency test of Fredenslund et al. [A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, A Group Contribution Method, Elsevier, Amsterdam, 1977], and were correlated by the Wilson, NRTL and UNIQUAC models to relate activity coefficients with mole fractions. The VLE data obtained for the ternary system passed both the Wisniak L–W [J. Wisniak, Ind. Eng. Chem. Res. 32 (1993) 1531–1533] and McDermott–Ellis [C. McDermott, S.R. Ellis, Chem. Eng. Sci. 20 (1965) 293–296] consistency test. The parameters obtained from binary data were utilized directly to predict the phase behaviour of the ternary system. The results showed an excellent agreement with experimental values.     

Isobaric (vapour + liquid) equilibria for sulfolane with toluene,ethylbenzene, and isopropylbenzene at 101.33 kPa

Isobaric (vapour + liquid) equilibrium data have been measured for the (toluene + sulfolane), (ethylbenzene + sulfolane), and (isopropylbenzene + sulfolane) binary systems with a modified Rose-Williams still at 101.33 kPa. The experimental data of binary systems were well correlated by the non-random two-liquid (NRTL) and universal quasi-chemical (UNIQUAC) activity coefficient models for the liquid phase. All the experimental results passed the thermodynamic consistency test by the Herington method. Furthermore, the model UNIFAC (Do) group contribution method was used. Sulfolane is treated as a group (TMS), the new group interaction parameters for CH₂–TMS, ACH–TMS and ACCH₂–TMS were regressed from the VLE data of (toluene + sulfolane) and (ethylbenzene + sulfolane) binary systems. Then these group interaction parameters were used to estimate phase equilibrium data of the (isopropylbenzene + sulfolane) binary system. The results showed that the estimated data were in good agreement with the experimental values. The maximum and average absolute deviations of the temperature were 4.50 K and 2.39 K, respectively. The maximum and average absolute deviations for the vapour phase compositions of isopropylbenzene were 0.0237 and 0.0137, respectively.     

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.     

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.     

Phase equilibria for H2 + CO2 + H2O system containing gas hydrates

Isothermal phase equilibrium (pressure–composition in the gas phase) for the ternary system of H₂ + CO₂ + H₂O has been investigated in the presence of gas hydrate phase. Three-phase equilibrium pressure increases with the H₂ composition of gas phase. The Raman spectra suggest that H₂ is not enclathrated in the hydrate-cages and behaves only like the diluent gas toward the formation of CO₂ hydrate. This fact is also supported by the thermodynamic analysis using Soave–Redlich–Kwong equation of state.     

Experimental investigation of incipient equilibrium conditions for the formation of semi-clathrate hydrates from quaternary mixtures of (CO2 + N2 + TBAB + H2O)

The three-phase (vapour + liquid + solid) equilibrium conditions for semi-clathrates formed from three mixtures of (CO₂ + N₂), in aqueous solutions of tetra-butyl ammonium bromide (TBAB), were measured in an isochoric reactor. The experiments were conducted at temperatures between (281 and 290) K, at pressures between (1.9 and 5.9) MPa and in aqueous TBAB solutions of w_TBAB = (0.05, 0.10, and 0.20). The experimental results obtained in this study were compared with previously obtained results for gas hydrates, formed from the same three mixtures of (CO₂ + N₂) and it was observed that semi-clathrates formed at a substantially lower pressure than did gas hydrates.     

(Vapor + liquid) equilibrium properties of (ethane + ethanol) system at (295, 303, and 313) K

The (vapor + liquid) equilibrium data for binary system of (ethane + ethanol) at three temperatures (295, 303, and 313) K were measured using a designed pressure–volume–temperature (PVT) apparatus. A wide range of pressures, (1 to 5) MPa, were considered for the measurements. The phase composition, saturated density, and viscosity of liquid phase were measured for each pressure and temperature. The experimental (vapor + liquid) equilibrium data were compared with the modeling results obtained using the Peng–Robinson and Soave–Redlich–Kwong equations of state.     

Phase equilibrium data and thermodynamic modeling of the system (CO2 + biodiesel + methanol) at high pressures

The main objective of this work was to investigate the high pressure phase behavior of the binary systems {CO₂(1) + methanol(2)} and {CO₂(1) + soybean methyl esters (biodiesel)(2)} and the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} were determined. Biodiesel was produced from soybean oil, purified, characterized and used in this work. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (303.15 to 343.15) K and pressures up to 21 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.2383 to 0.8666) for the binary system {CO₂(1) + methanol(2)}; (0.4201 to 0.9931) for the binary system {CO₂(1) + biodiesel(2)}; (0.4864 to 0.9767) for the ternary system {CO₂(1) + biodiesel(2) + methanol(3)} with a biodiesel to methanol molar ratio of (1:3); and (0.3732 to 0.9630) for the system {CO₂ + biodiesel + methanol} with a biodiesel to methanol molar ratio of (8:1). For these systems, (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals (PR-vdW2) and Wong-Sandler (PR–WS) mixing rules. Both thermodynamic models were able to satisfactorily correlate the phase behavior of the systems investigated and the PR–WS presented the best performance.     

Phase behavior of (CO2 + methanol + lauric acid) system

In this study the phase equilibrium behaviors of the binary system (CO₂ + lauric acid) and the ternary system (CO₂ + methanol + lauric acid) were determined. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (293 to 343) K and pressures up to 24 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.7524 to 0.9955) for the binary system (CO₂ + lauric acid); (0.4616 to 0.9895) for the ternary system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (2:1); and (0.3414 to 0.9182) for the system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (6:1). For these systems (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid), and (solid + fluid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals mixing rule with a satisfactory correlation between experimental and calculated values.     

Phase equilibrium measurements for semi-clathrate hydrates of the (CO2 + N2 + tetra-n-butylammonium bromide) aqueous solution system

The application of semi-clathrate hydrate formation technology for gas separation purposes has gained much attention in recent years. Consequently, there is a demand for experimental data for relevant semi-clathrate hydrate phase equilibria. In this work, semi-clathrate hydrate dissociation conditions for the system comprising mixtures of {CO₂ (0.151/0.399 mole fraction) + N₂ (0.849/0.601 mole fraction) + 0.05, 0.15, and 0.30 mass fraction tetra-n-butylammonium bromide (TBAB)} aqueous solutions have been measured and are reported. An experimental apparatus which was designed and built in-house was used for the measurements using the isochoric pressure-search method. The range of conditions for the measurements was from 277.1 K to 293.2 K for temperature and pressures up to 16.21 MPa. The phase equilibrium data measured demonstrate the high hydrate promotion effects of TBAB aqueous solutions.     

Phase equilibria in the ternary system isobutyl alcohol + isobutyl acetate + 1-hexanol and the binary systems isobutyl alcohol + 1-hexanol,isobutyl acetate + 1-hexanol at 101.3 kPa

Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system isobutyl alcohol (IBA) + isobutyl acetate (IBAc) + 1-hexanol and two constituent binary systems: IBA + 1-hexanol and IBAc + 1-hexanol. The IBA + 1-hexanol system exhibits no deviation from ideal behaviour and IBAc + 1-hexanol system show lightly positive deviation from Raoult's law. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is well predicted from binary interaction parameters. 1-Hexanol eliminates the IBA–IBAc binary azeotrope. However, the change of phase equilibria behaviour is small therefore this solvent is not an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.28 (close to unity).     

Isobaric (vapor + liquid) equilibrium data for the binary system methanol + 2-butyl alcohol and the quaternary system methyl acetate + methanol + 2-butyl alcohol + 2-butyl acetate at P = 101.33 kPa

In this paper, isobaric (vapor + liquid) equilibrium (VLE) data for the binary system methanol + 2-butyl alcohol and the quaternary system methyl acetate + methanol + 2-butyl alcohol + 2-butyl acetate were determined at P = 101.33 kPa in a modified Rose still. The binary VLE data were found to be thermodynamic consistency by the Herrington method. The VLE data for the binary system were correlated by the Wilson and NRTL equations respectively, which were used to predict the VLE data of the quaternary system. The results showed that the Wilson and NRTL models matched well with the (vapor + liquid) phase equilibrium data. The deviations for the vapor-phase compositions and the equilibrium temperatures are reasonably small and the models are both suitable for these systems.     

Thermodynamic evaluation of the (LiF + NaF + BeF2 + PuF3) system: An actinide burner fuel

In this work the LiF–BeF₂, NaF–BeF₂, and BeF₂–PuF₃ binary phase diagrams have been thermodynamically assessed. The first two systems have been optimized based on the known experimental data, whereas the last one has been treated ideally. To describe the excess Gibbs parameters of the liquid solution the modified quasi chemical model based on the quadruplet approximation has been used. The results obtained together with the data of the (LiF + PuF₃), (NaF + PuF₃), and (LiF + NaF) systems, which have been assessed in previous studies, were used to extrapolate the (LiF + NaF + BeF₂ + PuF₃) quaternary system. The calculated (LiF + NaF + BeF₂) ternary subsystem has been compared with the experimental results published in literature. The nuclear fuel properties such as the melting behaviour, the vapour pressure, or the solubility of PuF₃ in the matrix of LiF–NaF–BeF₂ have been derived based on our assessment and compared with measurements in literature.     

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.     

Hydrate phase equilibrium in the system of (carbon dioxide + 2,2-dimethylbutane + water) at temperatures below freezing point of water

The four-phase equilibrium conditions of (vapor + liquid + hydrate + ice) were measured in the system of (CO₂ + 2,2-dimethylbutane + water). The measurements were performed within the temperature range (254.2 to 270.2) K and pressure range (0.490 to 0.847) MPa using an isochoric method. Phase equilibrium conditions of hydrate formed in this study were measured to be at higher temperatures and lower pressures than those of structure I CO₂ simple hydrate. The largest difference in the equilibrium pressures of structure I CO₂ hydrate and the hydrate formed in the present study was 0.057 MPa at T = 258.3 K. On the basis of the four-phase equilibrium data obtained, the quintuple point for the (ice + structure I hydrate + structure H hydrate + liquid + vapor) was also determined to be T = 266.4 K and 0.864 MPa. The results indicate that structure H hydrate formed with CO₂ and 2,2-dimethylbutane is stable exclusively at the temperatures below the quintuple temperature.     

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.