Measurement and modeling of high-pressure (vapour + liquid) equilibria of (CO2 + alcohol) binary systems

An apparatus based on a static-analytic method assembled in this work was utilized to perform high pressure (vapour + liquid) equilibria measurements with uncertainties estimated at <5%. Complementary isothermal (vapour + liquid) equilibria results are reported for the (CO₂ + 1-propanol), (CO₂ + 2-methyl-1-propanol), (CO₂ + 3-methyl-1-butanol), and (CO₂ + 1-pentanol) binary systems at temperatures of (313, 323, and 333) K, and at pressure range of (2 to 12) MPa. For all the (CO₂ + alcohol) systems, it was visually monitored to insure that there was no liquid immiscibility at the temperatures and pressures studied. The experimental results were correlated with the Peng–Robinson equation of state using the quadratic mixing rules of van der Waals with two adjustable parameters. The calculated (vapour + liquid) equilibria compositions were found to be in good agreement with the experimental values with deviations for the mol fractions <0.12 and <0.05 for the liquid and vapour phase, respectively.     

Measurement and modeling of high-pressure (vapor + liquid) equilibria of (CO2 + alkanol) binary systems

Complementary isothermal (vapor + liquid) equilibria data are reported for the (CO₂ + 3-methyl-2-butanol), (CO₂ + 2-pentanol), and (CO₂ + 3-pentanol) binary systems at temperatures of (313, 323, and 333) K, and at pressure range of (2 to 11) MPa. For all (CO₂ + alcohol) systems, it was visually monitored that there was no liquid immiscibility at the temperatures and pressures studied. The experimental data were correlated with the Peng–Robinson equation of state using the quadratic mixing rules of van der Waals with two adjustable parameters. The calculated (vapor + liquid) equilibria compositions were found to be in good agreement with the experimental data with deviations for the mole fractions <8% and <2% for the liquid and vapor phase, respectively.     

High-pressure phase equilibria of {carbon dioxide (CO2) + n-alkyl-imidazolium bis(trifluoromethylsulfonyl)amide} ionic liquids

Ionic liquids (ILs) and carbon dioxide (CO₂) systems have unique phase behavior that has been applied to applications in reactions, extractions, materials, etc. Detailed phase equilibria and modeling are highly desired for their further development. In this work, the (vapor + liquid) equilibrium, (vapor + liquid + liquid) equilibrium, and (liquid + liquid) equilibrium of n-alkyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ionic liquids with CO₂ were measured at temperatures of (298.15, 323.15, 343.15) K and pressure up to 25 MPa. With a constant anion of bis(trifluoromethylsulfonyl)amide, the n-alkyl chain length on the cation was varied from 1-ethyl-3-methyl-imidazolium ([EMIm][Tf₂N]), 1-hexyl-3-methyl-imidazolium ([HMIm][Tf₂N]), to 1-decyl-3-methyl-imidazolium ([DMIm][Tf₂N]). The effects of the cation on the phase behavior and CO₂ solubility were investigated. The longer alkyl chain lengths increase the CO₂ solubility. The Peng–Robinson equation of state with van der Waals 2-parameter mixing rule with estimated IL critical properties were used to model and correlate the experimental data. The models correlate the (vapor + liquid) equilibrium and (liquid + liquid) equilibrium very well. However, extrapolation of the model to much higher pressures (>30 MPa) can results in the prediction of a mixture critical point which, as of yet, has not been found in the literature.     

(Vapour + liquid) equilibria (VLE) of CO2 in aqueous solutions of 2-amino-2-methyl-1-propanol: New data and modelling using eNRTL-equation

This work presents new experimental results for carbon dioxide (CO₂) solubility in aqueous 2-amino-2-methyl-1-propanol (AMP) over the temperature range of (298 to 328) K and CO₂ partial pressure of about (0.4 to 1500) kPa. The concentrations of the aqueous AMP lie within the range of (2.2 to 4.9) mol · dm^?3. A thermodynamic model based on electrolyte non-random two-liquid (eNRTL) theory has been developed to correlate and predict the (vapour + liquid) equilibrium (VLE) of CO₂ in aqueous AMP. The model predictions have been in good agreement with the experimental data of CO₂ solubility in aqueous blends of this work as well as those reported in the literature. The current model can also predict speciation, heat of absorption, enthalpy of CO₂ loaded aqueous AMP, pH of the loaded solution, and AMP volatility.     

Phase behavior of {carbon dioxide + [bmim][Ac]} mixtures

Carbon dioxide solubility {(vapor + liquid) equilibria: VLE} in ionic liquid, 1-butyl-3-methylimidazolium acetate ([bmim][Ac]), has been measured with a gravimetric microbalance at four isotherms about (283, 298, 323, and 348) K up to about 2 MPa. (Vapor + liquid + liquid) equilibria (VLLE: or liquid–liquid separations) have also been investigated with a volumetric method used in our previous works, since the present analysis of the VLE data using our equation-of-state model has predicted the VLLE at CO₂-rich side solutions. The prediction for the VLLE has been confirmed experimentally. CO₂ solubilities at the ionic liquid-rich side show extremely unusual behaviors; CO₂ dissolves in the ionic liquid to a great degree, but there is hardly any vapor pressure above these mixtures up to about 20 mol% of CO₂. It indicates that CO₂ may have formed a non-volatile or very low vapor pressure molecular complex with the ionic liquid. The thermodynamic excess properties (enthalpy, entropy, and Gibbs free energy) of the present system do support such a complex formation. We have conducted several other experiments to investigate the complex formation (or chemical reactions), and conclude that a minor chemical reaction occurs but the complex formation is reversible without much degradation of the ionic liquid.     

High-pressure (vapour + liquid) equilibria for ternary systems composed by {(E)-2-hexenal or hexanal + carbon dioxide + water}: Partition coefficient measurement

A new apparatus based on a static–analytic method assembled in this work was utilised to perform high-pressure (vapour + liquid) equilibria measurements of aqueous ternary systems. This work includes values of isothermal partition coefficients between CO₂ and water of two apple aroma constituents, (E)-2-hexenal and hexanal. Additionally, this work reports new experimental (vapour + liquid) equilibria measurements for the ternary systems (CO₂ + (E)-2-hexenal + water) and (CO₂ + hexanal + water), at fixed liquid phase composition (600 mg · kg⁻¹), at temperatures of (313, 323 and 333) K and at pressures from (8 to 19) MPa. Vapour liquid interphase was checked and monitored visually for all the systems studied in this work. No liquid immiscibility was observed at the composition, temperatures and pressures studied. In order to suggest reasonable operation conditions for fractionation of aromas with dense carbon dioxide, partition coefficients of the aroma compounds between CO₂ and water along with their separation factors from water were calculated. Partition coefficients of (E)-2-hexenal between CO₂ and water were in the range of (6 to 91) and where found to be near six times higher than those of hexanal (9 to 17). Very high separation factors from water were observed (∼10⁴) especially for (E)-2-hexenal. The highest separation factor, for both compounds, was found at a temperature of 313 K and pressures from (12 to 14) MPa.     

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.     

Thermodynamic evaluation and optimization of the (NaCl + Na2SO4 + Na2CO3 + KCl + K2SO4 + K2CO3) system

A complete, critical evaluation of all phase diagrams and thermodynamic data was performed for all condensed phases of the (NaCl + Na₂SO₄ + Na₂CO₃ + KCl + K₂SO₄ + K₂CO₃) system, and optimized parameters for the thermodynamic solution models were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range order, where the cations (Na⁺ and K⁺) were assumed to mix on a cationic sublattice, while anions $({\text{CO}}_3^{2-}\text{,}{\text{SO}}_4^{2-}\text{,}\text{and}{\text{Cl}}^{-})$ were assumed to mix on an anionic sublattice. The thermodynamic properties of the solid solutions of (Na,K)₂(SO₄,CO₃) were modelled using the Compound Energy Formalism, and (Na,K)Cl was modelled using a substitutional model in previous studies. Phase transitions in the common-cation ternary systems (NaCl + Na₂SO₄ + Na₂CO₃) and (KCl + K₂SO₄ + K₂CO₃) were studied experimentally using d.s.c./t.g.a. The experimental results were used as input for evaluating the phase equilibrium in the common-cation ternary systems. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature are reproduced within experimental error limits.     

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.     

The precise measurement of the (vapour + liquid) equilibrium properties for (CO2 + isobutane) binary mixtures

Recently, it has been suggested that natural working fluids, such as CO₂, hydrocarbons, and their mixtures, could provide a long-term alternative to fluorocarbon refrigerants. (Vapour + liquid) equilibrium (VLE) data for these fluids are essential for the development of equations of state, and for industrial process such as separation and refinement. However, there are large inconsistencies among the available literature data for (CO₂ + isobutane) binary mixtures, and therefore provision of reliable and new measurements with expanded uncertainties is required. In this study, we determined precise VLE data using a new re-circulating type apparatus, which was mainly designed by Akico Co., Japan. An equilibrium cell with an inner volume of about 380 cm³ and two optical windows was used to observe the phase behaviour. The cell had re-circulating loops and expansion loops that were immersed in a thermostatted liquid bath and air bath, respectively. After establishment of a steady state in these loops, the compositions of the samples were measured by a gas chromatograph (GL Science, GC-3200). The VLE data were measured for CO₂/propane and CO₂/isobutane binary mixtures within the temperature range from 300 K to 330 K and at pressures up to 7 MPa. These data were compared with the available literature data and with values predicted by thermodynamic property models.     

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 optimization of the (Na2O + SiO2 + NaF + SiF4) reciprocal system using the Modified Quasichemical Model in the Quadruplet Approximation

All available thermodynamic and phase diagram data for the condensed phases of the ternary reciprocal system (NaF + SiF₄ + Na₂O + SiO₂) have been critically assessed. Model parameters for the unary (SiF₄), the binary systems and the ternary reciprocal system have been found, which permit to reproduce the most reliable experimental data. The Modified Quasichemical Model in the Quadruplet Approximation was used for the oxyfluoride liquid solution, which exhibits strong first-nearest-neighbor and second-nearest-neighbor short-range ordering. This thermodynamic model takes into account both types of short-range ordering as well as the coupling between them. Model parameters have been estimated for the hypothetical high-temperature liquid SiF₄.     

High pressure measurement and CPA equation of state for solubility of carbon dioxide and hydrogen sulfide in 1-butyl-3-methylimidazolium acetate

Removal of acid gases such as CO₂ and H₂S from natural gas is essential for commercial, safety and environmental protection that demonstrate the importance of gas sweetening process. Ionic liquids (IL) have been highly demanded as a green solvent to remove acid gases from sour natural gas and capturing of CO₂ from flue gases. In this work, the solubility of CO₂ in 1-butyl-3-methylimidazolium acetate ([bmim][Ac]) is measured at temperatures (303.15, 328.15, 343.15) K and pressure range of (0.1 to 3.9) MPa. Moreover, the experiments are carried out for simultaneous measurements of (CO₂ + H₂S) (70% + 30% on a mole basis) solubility in the same ionic liquid at T = (303.15, 323.15, 343.15) K and a pressure range of (0.1 to 2.2) MPa. To model the solubility of acid gases in IL, both physical and chemical equilibria are applied so that the (vapour + liquid) equilibrium calculation is carried out through Cubic-Plus-Association (CPA) EoS. The reaction equilibrium thermodynamic model is used in liquid phase so that the chemical reaction is taking place between IL and acid gasses. The Henry’s and reaction equilibrium constants are obtained though optimization of the solubility data. Using CPA EOS, the pure parameters of [bmim][acetate] are optimised and consequently using these parameters, gas partial pressure calculation is performed for the (CO₂ + IL) and (CO₂ + H₂S + IL) systems. For the (CO₂ + IL) system, the percent average absolute deviation (AAD%) of 4.83 is resulted and for the (H₂S + CO₂ + IL) system the values of 18.8 and 13.7 are obtained for H₂S and CO₂, respectively.     

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.     

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.     

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 (NaNO3 + KNO3 + Na2SO4 + K2SO4) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaNO₃ + KNO₃ + Na₂SO₄ + K₂SO₄) ternary reciprocal system, and optimised model parameters have been found. The model parameters obtained for the four binary common-ion subsystems (i.e. (NaNO₃ + Na₂SO₄), (KNO₃ + K₂SO₄), (NaNO₃ + KNO₃) and (Na₂SO₄ + K₂SO₄)) are used to predict thermodynamic properties and phase equilibria for the entire system. The Modified Quasichemical Model in the Quadruplet Approximation for short-range ordering was used for the molten salt phase, and the Compound Energy Formalism was used for the various solid solutions.     

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%.     

(Liquid + liquid) equilibrium of aqueous biphasic systems composed of 1-benzyl or 1-hexyl-3-methylimidazolium chloride ionic liquids and inorganic salts

(Liquid + liquid) equilibria for {1-benzyl-3-methylimidazolium chloride ([BzMIM]Cl) or 1-hexyl-3-methylimidazolium chloride ([HMIM]Cl) + inorganic salts (potassium phosphate K₃PO₄, potassium carbonate K₂CO₃, or dipotassium hydrogen phosphate K₂HPO₄) + H₂O} aqueous biphasic systems (ABSs) are presented at T = 298.15 K. An empirical equation was used to correlate the binodal data. The experimental tie lines were appropriately correlated by the Othmer–Tobias and Brancroft empirical equations. The influence of the selected inorganic salts in the phase segregation was investigated by means the calculated effective excluded volume (EEV) and Setschenow-type equation. The salting-out ability of salts was also evaluated in terms of the Gibbs energy of hydration of salt (ΔG_hyd) and assessed with EEV values.