Modeling high pressure vapor–liquid equilibrium of ternary systems containing supercritical CO2 and mixed organic solvents using Peng–Robinson equation of state

High pressure vapor–liquid equilibrium (VLE) of CO₂-expanded organic solvents was investigated using Peng–Robinson-LCVM-UNIFAC equation of state. Bubble pressure of several ternary mixtures was predicted using this model and correlations were developed based only on binary experimental data. A sensitivity study of the LCVM parameter numerical value was done by considering the coherence between the mathematical features of the mixing rule and the quality of the simulation. The results provided by PR-LCVM-UNIFAC were compared with those ones given by Peng–Robinson equation of state using the classical quadratic mixing rules (PR-CMR). Despite the use of two adjustable parameters for each binary system, PR-CMR is not able to provide good results when applied to ternary systems. The capability of PR-LCVM-UNIFAC model to predict liquid mixture density for ternary systems using parameters regressed only from bubble pressure experimental data was also investigated. Due to the lack of liquid density experimental data, it was possible to perform only a qualitative assessment of the density curves calculated by this equation of state.     

Thermodynamic modeling of liquid-fluid phase equilibrium in supercritical ethylene + copolymer + co-solvent systems using the PC-SAFT equation of state

Copolymers are important in the manufacture of new polymeric materials with specific characteristics. For linear polymers, thermodynamic models based on the thermodynamic perturbation theory are interesting, since this theory regards the association between monomers. In this work, cloud points of mixtures of copolymers (PEH, PEP, PEAA and PEVA) (PEP: poly(ethylene-co-propylene); PEAA: poly(ethylene-co-acrylic acid); PEH: poly(ethylene-co-1-hexene); PEVA: poly(ethylene-co-vinyl acetate)), a supercritical fluid (C₂) and co-solvents (C₁, C₂, C₃, nC₄, 1C₄, 1C₆, AA, VA, He, N₂, CO₂) (C₁: methane; C₂: ethane; C₂: ethylene; C₃: propane; nC₄: n-butane; 1C₄: 1-butene; 1C₆: 1-hexene; AA: acrylic acid; VA: vinyl acetate; He: helium; N₂: nitrogen; CO₂: carbon dioxide) were modeled using the PC-SAFT equation of state (Perturbed Chain-Statistical Associating Fluid Theory) with a one-type van der Waals mixing rule by fitting one single interaction parameter. Pure component parameters for the supercritical fluid and co-solvents were obtained by regression of vapor pressure and density data of saturated liquid, while pure component parameters for polymers that compose the copolymers were obtained by regression of pure liquid PVT data. Binary interaction and pure component parameter estimation was performed by using the modified maximum likelihood method. Relative deviations between the calculated and experimental cloud points show that the PC-SAFT model had an excellent performance.     

Phase equilibrium data and thermodynamic modeling of the system propane + NMP + methanol at high pressures

This work reports phase equilibrium data at high pressures for the binary and ternary systems formed by propane + n-methyl-2-pyrrolidone (NMP) + methanol. Phase equilibrium measurements were performed in a high-pressure variable-volume view cell, following the static synthetic method for obtaining the experimental bubble and dew points transition data in the temperature range of 363-393 K, pressures up to 16 MPa and overall molar fraction of the lighter component varying from 0.1 to 0.998. For the systems investigated, vapor-liquid (VLE), liquid-liquid (LLE) and vapor-liquid-liquid (VLLE) phase transitions were visually recorded. Results show that the systems investigated present UCST (upper critical solution temperature) phase transition curves with an UCEP (upper critical end point) at a temperature higher than the propane critical temperature. The experimental data were modeled using the Peng-Robinson equation of state with the Wong-Sandler and the classical quadratic mixing rules, affording a satisfactory representation of the experimental data.     

High-pressure gas-liquid equilibrium measurements by means of a double-chamber recirculation apparatus. Data on the system carbon dioxide-limonene at 50 and 70 °C

Measurements of the phase equilibria for the system carbon dioxide-limonene were performed at 50 and 70 °C in the pressure range 8.54-13.34 MPa. Both the liquid and the gas phase composition were measured. The experiments were carried out by means of a two-chamber recirculation apparatus. According to the procedure, in one of the chambers the gas-liquid equilibrium is established, whereas the second one contains only the gas phase which is continuously recirculated through the chambers to reduce time for equilibration. Before sampling, the chambers are separated to avoid disturbances of the equilibrium when reducing pressure during the withdrawal of the gas phase. Experimental data at 50 °C were used for the validation of the experimental method, through comparison with literature data, whereas those at 70 °C are mostly original. The experimental data were successfully correlated by means of a thermodynamic model based on the Peng-Robinson equation of state.     

High-pressure gas-liquid equilibrium of the system carbon dioxide-citral at 50 and 70 °C

Measurements of high-pressure gas-liquid equilibria of the binary system carbon dioxide-citral were carried out in the present work. The knowledge of the phase equilibrium behaviour of this system is relevant with regard to the design and optimization of the supercritical deterpenation process. The measurements were carried out at 50 and 70 °C, in the pressure range 7.8-15.6 MPa, by means of a two-chamber gas-phase recirculation apparatus of 340 cm³. Both the liquid and the gas phase composition were measured. The data at 50 °C measured in this work were compared with literature data, whereas no comparison was possible at 70 °C because of their lack. The experimental data measured in this work were successfully correlated by means of a thermodynamic model based on the Peng-Robinson equation of state.     

Experimental measurement and thermodynamic modeling of binary and ternary solid-liquid phase equilibrium for the systems formed by L-arabinose,D-xylose and water

Solid-liquid phase equilibrium data for binary (L-arabinose-water) and (D-xylose-water) systems at temperatures from (269.85-298.05) K and ternary (L-arabinose-D-xylose-water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were confirmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.     

High-pressure phase equilibrium for the hydroformylation of 1-octene to nonanal in compressed CO2

The hydroformylation reaction in supercritical carbon dioxide or CO₂-expanded liquids (CXLs) has many advantageous properties. However, accurate phase behavior and equilibrium must be known to properly understand and engineer these systems. In this investigation, the vapor-liquid equilibrium and mixture critical points of CO₂ systems with 1-octene, nonanal, 1-octene and nonanal mixtures, and mixtures of 1-octene, nonanal and syngas (CO/H₂) were measured at 60 °C up to 120 bar of pressure. The Peng-Robinson equation of state with van der Waals two-parameter mixing rule was employed successfully to correlate the binary mixture data and predict the ternary mixture data. The presence of CO/H₂ pressure increased the mixture critical points and decreased the volume expansion at any given pressure. In an actual reaction, the mixture critical point would increase throughout the reaction, while the volume of the liquid phase would decrease. These data will aid the understanding and reaction engineering for the hydroformylation reaction in CO₂-expanded liquids and supercritical fluids.     

Analysis of equilibrium CO2 solubility and thermodynamic models for aqueous 1-(2-hydoxyethyl)-piperidine solution

1-(2-Hydoxyethyl)-piperidine (1-(2HE)-PP) is a new tertiary amine with desirable properties and can be potentially used to formulate superior absorbents for CO₂ capture. The equilibrium CO₂ solubility of 1-(2HE)-PP solution is measured over temperatures from 298 to 333 K, CO₂ partial pressures from 8.1 to 101.3 kPa and initial amine concentrations from 1 to 5 M. Two thermodynamic models, namely semiempirical model and activity coefficient model are developed for the system. The activity coefficient model shows better estimation solubility with an absolute average relative deviation (AARD) of 7.6%. In the comparison between the two models, a comprehensive analysis is presented. Some suggestions are provided for the similar model development. In addition, the speciation plot of CO₂ loaded 1-(2HE)-PP solution is predicted based on the activity coefficient model. The predictive pH values agree well with experimental data with AARD of 1.0%. Finally, the potential of 1-(2-HE)PP to be an alternative amine in CO₂ capture is evaluated.     

Extension of the electrolyte Trebble–Bishnoi EOS to mixed-salt systems,and application to vapour liquid and solid (hydrate) vapour liquid equilibrium calculations

This work examines the use of the electrolyte Trebble–Bishnoi equation of state (eTBEOS) in predicting high-pressure phase equilibria in the presence of aqueous mixed-salt solutions. The eTBEOS combines the Trebble–Bishnoi equation of state with a Born energy term, a mean spherical approximation term, and a cation solvation term. Shortcomings in the originally regressed set of eTBEOS parameters are identified and discussed, and a new set of equation of state parameters is subsequently regressed for 58 salts. In order to extend the eTBEOS to mixed-salt systems, two approaches for computing the EOS parameters of the ionic species are investigated. The first approach uses the originally regressed parameter set plus parameter mixing rules, where appropriate, whereas the second approach uses the newly regressed parameters and no mixing rules. In the prediction of osmotic coefficients in mixed-salt solutions, the maximum relative difference between the experimental and computed values was 5.70%. For the gas solubility predictions, data were available for the solubility of CO₂, CH₄, and N₂ in a small number of mixed electrolyte solutions; the maximum relative difference was 5.79%. Finally, CH₄, C₂H₆, C₃H₈, and CO₂ gas hydrate formation conditions were predicted in a number of mixed-salt solutions, with a maximum relative difference of 10.76%. Overall, it was seen that both approaches allowed for comparable accuracy in phase equilibrium calculations. However, in the case of solutions made from salt mixtures with common cations, the second approach consistently resulted in improved accuracy.     

Near-infrared spectroscopic solubility measurement for thermodynamic analysis of melting point depressions of biphenyl and naphthalene under high-pressure CO2

Melting temperatures of organic solids are often depressed by high-pressure CO₂ due to a dissolution of CO₂ in the molten organic compounds. For thermodynamic analysis of the melting point depression, solubilities of CO₂ in molten biphenyl and naphthalene were measured by near-infrared spectroscopy at various temperatures and pressures up to 20 MPa. Molarity of the organic component was determined from the 3ν_CH absorption band, and that of CO₂ from the 2ν₁ + ν₃ band. Mole fraction of CO₂ in the liquid phase was found to be an increasing function of the pressure up to 0.6 at 20 MPa and a weakly decreasing function of the temperature. The solubility data were used for modeling of the mixtures by the Peng–Robinson equation of state with a binary interaction parameter k₁₂. Calculation of the solid–liquid–gas phase equilibrium for the model fluid qualitatively described a large decrease in the melting temperature with increasing pressure up to 10 MPa followed by a small change at higher pressures. The melting point change was interpreted by the two competing effects: hydrostatic pressure effect increases the melting point by ca. 8 °C at 20 MPa, whereas CO₂ solubility effect reduces it by ca. 30 °C. Decomposition of the solubility effect into ideal and non-ideal mixing parts revealed that the non-ideality increases the melting point by more than 10 °C.     

Measurement of VLE data of carbon dioxide (CO2) + methyl iodide (CH3I) system for the direct synthesis of dimethyl carbonate using supercritical CO2 and methanol

Isothermal vapor⿿liquid equilibrium data for the binary system carbon dioxide + methyl iodide were measured at temperatures from 283.15 to 323.15 K at 10 K intervals. Data in the two-phase region were measured by using a circulation-type equilibrium apparatus and gas chromatography. This binary mixture system showed positive deviation from the Raoult's law and no azotrope observance. The experimental data were correlated with the Peng⿿Robinson equation of state (PR-EoS) using the Wong⿿Sandler (W⿿S) mixing rule, which was combined with the nonrandom two-liquid (NRTL) excess Gibbs free energy model and Peng⿿Robinson equation of state (PR-EoS) using the Universal mixing rule (UMR) as well as with the UNIQUAC model. The calculated results with this combination of equations show positive agreement with experimental data taken within this study.     

Solubility of CO2 in Methanol, 1-Octyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide, and Their Mixtures

Solubility data of carbon dioxide (CO₂) (1) in methanol (2), 1-octyl-3-methylimidazolium bis(trifluoro- methylsulfonyl)imide ([omim]⁺[Tf₂N]^-) (3), and their mixtures (w₃ 0.2, 0.5, and 0.8) at temperatures 313.2 and 333.2 K and pressures up to 7.0 MPa were measured by a high-pressure view-cell technique. The solubility of CO₂ in methanol (w₃=0), [omim]⁺[Tf₂N]^- (w₃=1.0) and their mixtures follows the order of (w₃=0)<(w₃=0.2)< (w₃=0.5)<(w₃=0.8)<(w₃=1.0) at the same temperature and pressure, while the magnitude of Henry's constants follows the reverse order at a given temperature, which is consistent with the COSMO-RS (conductor-like screening for real solvents) calculation. The solubility data of CO₂ in methanol and [omim]⁺[Tf₂N]^- are correlated with the Peng-Robinson equation of state, and the solubility of CO₂ in the mixtures of methanol and [omim]⁺[Tf₂N]^- can be well predicted based on the mole fraction average of methanol and [omim]⁺[Tf₂N]^- over the solubility of CO₂ in pure methanol and [omim]⁺[Tf₂N]^-. The mixtures of methanol and [omim]⁺[Tf2N]^- may be used as physical solvents for capturing CO₂ with high partial pressures since they combine the advantages of organic solvents and ionic liquids.     

Influence of the alkyl tail on the solubility of poly(alkyl acrylates) in ethylene and CO2 at high pressures: Experiments and modeling

Cloud point data to 230°C and 2200 bar are presented for poly(acrylate)–ethylene mixtures. When the length of the alkyl tail is increased, the cloud point curve is shifted towards lower pressure, but this trend switches when going from poly(ethyl hexyl) to poly(octadecyl) acrylate. It is apparent that there is an optimum alkyl tail length that balances energetic acrylate–acrylate, ethylene–ethylene, and ethylene–acrylate interactions and free-volume, entropic effects. Both ethylene–poly(acrylate) and CO₂–poly(acrylate) data are modeled by the Statistical Associating Fluid Theory (SAFT) equation of state. A pseudogroup contribution method is developed for the calculation of the following pure polymer characteristic parameters: m, the number of segments, and v⁰⁰, the volume of a segment. This method cannot be applied for u⁰/k, the attractive energy of a segment, which changes in a nonlinear manner with changes in the structure of the acrylate repeat group. The energy parameter is then calculated from monomer data or fitted directly to one cloud point curve. The experimental data are represented well, even if little predictive power is obtained since a temperature-independent interaction parameter k_ij is needed. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1979–1991, 1999     

Phase equilibria for the 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in supercritical CO2 at various temperatures and pressures up to 20 MPa

The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems at 313.2, 333.2, 353.2, 373.2 and 393.2 K as well as pressures up to 20.59 MPa have been investigated using variable-volume high pressure view cell by static-type. The solubility curve of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate in the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems increases as the temperature increases at a constant pressure. The (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems exhibit type-I phase behavior. The experimental results for the (CO₂ + 2-ethoxyethyl acetate) and (CO₂ + 2-(2-ethoxyethoxy)ethyl acetate) systems correlate with the Peng–Robinson equation of state using a van der Waals one-fluid mixing rule including two adjustable parameters. The critical properties of 2-ethoxyethyl acetate and 2-(2-ethoxyethoxy)ethyl acetate are predicted with the Joback–Lyderson group contribution and Lee–Kesler method.     

Integrated experimental and thermodynamic modeling study of phase equilibria in the ‘CuO0.5’-MgO-SiO2 system in equilibrium with liquid Cu metal for characterizing refractory-slag interactions

An integrated experimental and thermodynamic modeling study of the phase equilibria in the ‘CuO_0.5’-MgO-SiO₂ system in equilibrium with liquid Cu metal has been undertaken to better understand the reactions between MgO-based refractories and liquid slag in copper converting and refining processes. New experimental phase equilibria data at 1250–1680 °C were obtained for this system using a high-temperature equilibration of synthetic mixtures with predetermined compositions in silica ampoules or magnesia crucibles, a rapid quenching technique, and electron probe X-ray microanalysis of the equilibrated phase compositions. The system has been shown to contain primary phase fields of cristobalite (SiO₂), tridymite (SiO₂), pyroxene/protoenstatite (MgSiO₃), olivine/forsterite (Mg₂SiO₄), periclase (MgO), and cuprite (Cu₂O). Three regions of 2-liquid immiscibility were found—two in the high-silica range of compositions above the cristobalite primary phase field (close to ‘CuO_0.5’-SiO₂ and MgO–SiO₂ binaries) and one in the low-SiO₂, high-‘CuO_0.5’ compositional region above the periclase and olivine phase fields. The results obtained in this study indicate that silica in high-copper refining slags likely led to olivine and pyroxene phase formation, increased solubility of MgO in liquid slag, and decline in the performance of MgO-based refractories. New experimental data were used in the development of a thermodynamic database describing this pseudo-ternary system.     

CO2混合工质的气液相平衡的混合规则对比与预测研究

CO₂混合工质兼顾高效和环境友好的特点,在新一代热功转化循环中受到广泛关注。混合工质气液相平衡性质是循环分析与计算的基础。为了提高CO₂混合工质气液相平衡数据的计算精度,采用PR状态方程结合三种混合规则（vdW、MHV1、WS）,对7种CO₂+HFCs/HFOs及4种CO₂+HCs混合工质的气液相平衡性质进行了计算。结果表明,对CO₂+HCs混合工质,vdW混合规则可达较好的结果;对CO₂+HFCs/HFOs混合工质,在亚临界区三者计算精度相近,但在超临界区,WS混合规则对计算精度提升明显。最后,提出了一种差值模型预测CO₂混合工质气液相平衡性质,预测的AARD(p)值为2.03%,AAD(y)值为0.0120,预测精度较高。     

A modified Peng–Robinson equation of state for phase equilibrium calculation of liquefied,synthetic natural gas,and gas condensate mixtures

A modified Peng–Robinson equation of state, MPR2 EOS, is introduced by incorporating a new alpha function and a temperature dependent function for covolume, b. The modified cubic EOS has three input per each substance: critical temperature, critical pressure, and acentric factor. The coefficients of temperature dependence of the alpha and beta functions, relating to the parameters a and b of the new cubic EOS, are obtained by simultaneous fitting of saturated experimental vapour pressure and liquid density data for several pure components. The percent absolute average deviation (AAD%) of 1.38, 4.80 and 2.89 are obtained to correlation of the saturation vapour pressure, liquid density and vapour volume, respectively. Also the ADD% of 2.575 is computed for prediction of saturation enthalpy of vapourisation of the pure compounds. For calculation of phase equilibrium of mixture, the modified PR EOS is used for prediction of liquid density of the LNG mixtures. Also the new EOS is applied for construction of the phase envelop of synthetic natural gas, SNG, mixtures and calculation vapour–liquid equilibria of gas condensates. The results demonstrate that the new MPR2 EOS can be used for calculation of vapour–liquid equilibrium of pure components and mixtures with good accuracy.     

Experimental phase equilibria study and thermodynamic modelling of the PbO-“FeO”-SiO2-ZnO,PbO-“FeO”-SiO2-Al2O3 and PbO-“FeO”-SiO2-MgO systems in equilibrium with metallic Pb and Fe

Phase equilibria of the PbO-“FeO”-SiO₂-ZnO, PbO-“FeO”-SiO₂-Al₂O₃ and PbO-“FeO”-SiO₂-MgO slags with liquid Pb metal, solid or liquid Fe metal and solid oxides (cristobalite and tridymite SiO₂, willemite (Zn,Fe)₂SiO₄, wustite (Fe,Al)O_1+x, spinel (Fe,Al)₃O₄, olivine Fe₂SiO₄, corundum (Al,Fe)₂O₃, mullite Al₆Si₂O₁₃ and pyroxene (Mg,Fe)SiO₃) were investigated at 1125–1670 °C. These conditions correspond to the minimum solubility of PbO in slag in presence of Pb and Fe metals at reducing conditions and represent the limit of lead smelting and slag cleaning process. High-temperature equilibration on silica, corundum or iron foil substrates, followed by quenching and direct measurement of Pb, Fe, Si, Zn, Al and Mg concentrations in the liquid and solid phases with the electron probe X-ray microanalysis (EPMA) was used. Present data can be used to improve the thermodynamic models for all phases in this system.