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.     

Kinetics of pressure-induced phase separation in polystyrene + acetone solutions at high pressures

The kinetics of pressure-induced phase separation in solutions of polystyrene (M_w = 129,200; PDI = 1.02) in acetone has been studied using time- and angle-resolved light scattering. A series of controlled pressure quench experiments with different quench depths were conducted at different polymer concentrations (4.0%, 5.0%, 8.2% and 11.4% by mass) to determine the binodal and spinodal boundaries and consequently the polymer critical concentration. The results show that the solution with a polymer concentration 11.4 wt% undergoes phase separation by spinodal decomposition mechanism for both the shallow and deep quenches as characterized by a maximum in the angular distribution of the scattered light intensity profiles. Phase separation in solutions at lower polymer concentrations (4.0, 5.0 and 8.2 wt%) proceeds by nucleation and growth mechanism for shallow quenches, but by spinodal decomposition for deeper quenches. These results have been used to map-out the metastable gap and identify the critical polymer concentration where the spinodal and binodal envelops merge.The time scale of new phase formation and growth as (accessed) from the time evolution of scattered light intensities is observed to be relatively short. The late stage of phase separation is entered within seconds after a pressure quench is applied. For the systems undergoing spinodal decomposition, the characteristic wave number qm corresponding to the scattered light intensity maximum Im was analyzed by power-law scaling according to qm∼t−α and Im∼tβ. The results show β≈2α. The domain size is observed to grow from 4 μm to 10 μm within 2 s for critical quench, but about 9 s for off-critical quenches. The domain growth displays elements of self-similarity.     

Thermodynamic modeling of vapor-liquid equilibrium of binary systems ionic liquid + supercritical {CO2 or CHF3} and ionic liquid + hydrocarbons using Peng-Robinson equation of state

Vapor-liquid equilibrium (VLE) data from literature for binary systems involving several ionic liquids were correlated. The Peng-Robinson equation of state, coupled with the van der Waals and Wong-Sandler mixing rules, was used as the thermodynamic model to evaluate the fugacity coefficients. The UNIQUAC and NRTL models were used to calculate the excess Gibbs free energy in the Wong-Sandler mixing rule. A molecular modeling strategy using the software ChemOffice was used to calculate the volume and surface area parameters of ionic liquids for UNIQUAC, while the binary interaction energy parameters for UNIQUAC and NRTL models, as well as the binary interaction parameter of the van der Waals and Wong-Sandler mixing rules were estimated through a method based on the genetic algorithm. The results show that, as expected, the Wong-Sandler mixing rules represented better the data, with both activity coefficient models showing high accuracy. However, in one case, NRTL predicted an erroneous azeotropic condition, while UNIQUAC was able to correlate the data without this error.     

High-pressure phase equilibria for the binary system carbon dioxide + benzyl alcohol

The phase equilibria of the carbon dioxide + benzyl alcohol system were measured at 298.15, 306.35 and 313.15 K, under pressures from 1.03 to 16.15 MPa. An upper critical end point (UCEP) of the binary system was identified at 307.45 K and 7.77 MPa and three-phase equilibria were observed along the liquid-liquid-vapor (LLV) equilibrium line between 279.75 and 307.45 K. The experimental data were correlated well by the Peng-Robinson equation of state with two binary parameters. According to the experimental results, the phase behavior of the carbon dioxide + benzyl alcohol system appears to belong to Type-III according to the classification of van Konynenburg and Scott.     

Estimation of solid vapor pressures from supercritical CO2 + biomolecule systems using a PSO algorithm

A method to estimate the solid vapor pressures of biomolecules using a biologically deriver algorithm is presented. The solid vapor pressure is usually small for most solid compounds and in many cases available experimental techniques cannot be used to obtain accurate values. Therefore, estimation methods must be used to obtain these data. Five binary gas-solid phase systems of supercritical CO₂ + biomolecule containing caffeine, artemisinin, capsaicin, cholesterol, and β-carotene are considered in this study. Particle swarm optimization is used for minimize the difference between calculated and experimental solubility. Then, the solid vapor pressures of biomolecules are calculated from solubility data. The Peng-Robinson equation of state with the Wong-Sandler mixing rules are used to evaluate the fugacity coefficient on the systems. The results show that the method presented is reliable enough and can be used with confidence to estimate the solid vapor pressure of any organic biomolecule.     

Prediction of near and supercritical fatty acid ester + alcohol systems with the CPA EoS

The use of supercritical alcohols has been proposed as a non-catalytical method to produce biodiesel, overcoming some of the shortcomings related to conventional catalytic methods.In this work, the Cubic-Plus-Association equation of state is used to predict the vapor-liquid equilibria of several alcohol + fatty acid ester and alcohol + glycerol systems, in the temperature range 493-573 K and pressure range 2-12 MPa. The resulting predictions reproduce accurately the experimental data, within their experimental uncertainty.The ability to predict these phase equilibria is of primary importance for designing, operating and optimizing biodiesel production at near or supercritical conditions. The CPA EoS is shown to be a powerful prediction tool for an adequate design of the operations involved in the biodiesel production with near or supercritical alcohols.     

Phase behavior of the poly(neopentyl methacrylate) + supercritical fluid solvents + neopentyl methacrylate system and CO2 + neopentyl methacrylate mixtures at high pressure

High-pressure phase behaviors are measured for the CO₂ + neopentyl methacrylate (NPMA) system at 40, 60, 80, 100, and 120 °C and pressure up to 160 bar. This system exhibits type-I phase behavior with a continuous mixture-critical curve. The experimental results for the CO₂ + NPMA system are modeled using the Peng-Robinson equation of state. Experimental cloud-point data up to the temperature of 180 °C and the pressure of 2000 bar are presented for ternary mixtures of poly(neopentyl methacrylate) [poly(NPMA)] + supercritical solvents + NPMA systems. Cloud-point pressures of poly(NPMA) + CO₂ + NPMA system are measured in the temperature range of 60-180 °C and to pressures as high as 2000 bar with NPMA concentration of 0.0, 5.2, 19.0, 28.1 and 40.2 wt%. It appears that adding 51.2 wt% NPMA to the poly(NPMA) + CO₂ mixture does significantly change the phase behavior. Cloud-point curves are obtained for the binary mixtures of poly(NPMA) in supercritical propane, propylene, butane, 1-butene, and dimethyl ether (DME). The impact of dimethyl ether concentration on the phase behavior of the poly(NPMA) + CO₂ + x wt% DME system is also measured at temperature of 180 °C and pressure range of 36-2000 bar. This system changes the pressure-temperature (P-T) slope of the phase behavior curves from upper critical solution temperature (UCST) region to lower critical solution temperature (LCST) region as the NPMA concentration increases.     

Vapor-liquid equilibrium of polymer + solvent systems: Experimental data and thermodynamic modeling

In this work, experimental vapor-liquid equilibrium (VLE) data for binary systems polymer + solvent were obtained using a gravimetric sorption apparatus. The studied systems were benzene + polystyrene, hexane + polystyrene, benzene + poly(methyl methacrylate), benzene + poly(ethyl methacrylate), hexane + poly(vinyl chlorate) and water + poly(vinyl chlorate), in the range of 30-40 °C.The experimental data were modeled with two group contribution models for the activity coefficient, Elbro-FV and UNIFAC-Zhong; the latter method considers the free-volume of molecules of high molecular weight, such as polymers. UNIFAC groups in the literature as well as new groups that were proposed for the monomers were used. The necessary energy interaction parameters between these groups were estimated. There were observed mean deviations between experimental and calculated mass fractions of about 8.5% with Elbro-FV, and about 17% with UNIFAC-Zhong when original groups were used, while there were observed mean deviations of about 7% with Elbro-FV and about 16% with UNIFAC-Zhong when new groups were used. The Elbro-FV model represents the experimental data with better precision in both cases; on the other hand, the data were better correlated with both models when new groups were used.     

High-pressure phase equilibrium measurements and thermodynamic modeling for the systems involving CO2, ethyl esters (oleate,stearate, palmitate) and acetone

The aim of this work was to study the phase behavior of systems involving carbon dioxide (CO₂), fatty acid ethyl esters (ethyl oleate, ethyl stearate and ethyl palmitate) and acetone at high pressures. The phase behavior involving these components is an important step regarding the design and optimization of industrial processes based on supercritical conditions, such as biodiesel production and fatty esters fractionation involving supercritical and/or pressurized solvents. In addition, supercritical CO₂ can offer an interesting alternative for glycerol separation in water-free biodiesel purification processes. The binary systems investigated in this work were CO₂ + ethyl oleate, and CO₂ + ethyl stearate and these were compared with the CO₂ + ethyl palmitate system. The ternary CO₂ + ethyl palmitate + acetone was also investigated at two different ethyl palmitate to acetone molar ratios of (1:1) and (1:3). The static synthetic method using a variable-volume view cell was employed to obtain the experimental data in the temperature range of 303.15–353.15 K. Vapor–liquid (VL), liquid–liquid (LL) and vapor–liquid–liquid (VLL) phase transitions were observed in these systems. In the binary systems, the solubility increased with the presence of unsaturation and decreased with the number of carbon atoms in the fatty ester chain. Addition of acetone as well as ethanol eliminated the liquid–liquid immiscibility and reduced the pressure transitions, therefore increasing the solubility of the ester in supercritical CO₂. The experimental data sets for the binary and ternary systems were successfully modeled using the Peng–Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and Wong-Sandler (PR-WS) mixing rule. Both models showed good performance in the phase equilibrium correlations and in predictions for the binary and ternary systems.     

Measurement of phase equilibria of the systems CO2 + styrene and CO2 + vinyl acetate using different experimental methods

The experimental determination of high-pressure phase equilibria is often the only suitable method to obtain reliable data because high-pressure phase behavior is complex and difficult to predict. This contribution gives a brief classification of applied experimental methods. A new high-pressure apparatus is described, which can be used for phase-equilibrium measurements with different experimental methods, namely the analytical-isothermal method, the synthetic-isothermal method as well as the non-visual- and the visual-synthetic method. The different techniques have been tested for the measurement of the phase behavior of systems containing CO₂ + styrene and CO₂ + vinyl acetate. The measured data were compared with data from literature and discussed in terms of accuracy, advantages and drawbacks of the applied methods.     

Phase equilibria of carbon dioxide + 1-nonanol system at high pressures

Vapor-liquid-equilibria (VLE) and vapor-liquid-liquid equilibria (VLLE) data for the carbon dioxide + 1-nonanol system were measured at 303.15, 308.15, 313.15, 333.15, and 353.15 K. Phase behavior measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between 1.15 and 103.3 bar. The Soave-Redlich-Kwong (SRK) equation of state (EOS) coupled with both classical van der Waals and a Gibbs excess energy (G^E) mixing rules was used in semi-predictive approaches, in order to represent the complex phase behavior (critical curve, liquid-liquid-vapor (LLV) line, isothermal VLE, LLE, and VLLE) of the system. The topology of phase behavior is correctly predicted.     

Thermodynamic analysis of absorption refrigeration cycles using ionic liquid + supercritical CO2 pairs

Absorption refrigerators are alternative systems to conventional compression cycles in which the energy necessary for the refrigeration is provided by heating instead of mechanical power. Commercial absorption refrigerators use two absorbent/refrigerant pairs: NH₃-H₂O and H₂O-LiBr. These systems have some limitations due to the difficulty of separating absorbent and refrigerant, the narrow refrigeration temperature range, or the possibility of corrosion and salt deposition. The application of ionic liquids as absorbents with supercritical carbon dioxide as refrigerant can solve some of these problems because separation of ionic liquid from CO₂ is easy due to the negligible vapor pressure of ionic liquids. In this work, suitable ionic liquids-CO₂ pairs have been selected considering their phase equilibrium properties, calculated with the Group-Contribution equation of state developed by Skjold-Jørgensen. The energetic efficiency of the process with ionic liquids has been estimated by calculation of the Coefficient of Performance (COP) of the process. It has been found that the process with ionic liquids has a lower COP than conventional NH₃-H₂O systems due to the necessity of operating with a higher solution flowrate. Nevertheless, near-optimum performance is obtained in a wide range of process conditions.     

Extension of a compressible lattice model to CO2 + cosolvent + polymer systems

We have recently proposed a compressible lattice model for CO₂ + polymer systems in which CO₂ forms complexes with one or more functional groups in the polymer. Furthermore, we have shown that this model is able to simultaneously correlate phase equilibria, sorption behavior, and glass transition temperatures in such systems. In the present work, we extend the model to ternary CO₂ + cosolvent + polymer systems and demonstrate that cloud point behavior in CO₂ + dimethyl ether + poly (?-caprolactone), CO₂ + dimethyl ether + poly (isopropyl acrylate), and CO₂ + dimethyl ether + poly (isodecyl acrylate) systems can be predicted using parameters obtained from binary data. Our results also suggest that dimethyl ether may form weak complexes with poly (?-caprolactone), poly (isopropyl acrylate), and poly (isodecyl acrylate).     

High pressure phase behavior of carbon dioxide + nitrobenzene binary system at 298.15, 310.45 and 322.75 K

The phase behavior of the carbon dioxide + nitrobenzene binary system has been studied in a high-pressure variable-volume view cell using an analytical method. The phase boundaries were measured at temperatures of 298.15, 310.45 and 322.75 K under pressures between 2.76 and 12.83 MPa, and it was found that three-phase equilibria existed over a temperature range from 303.60 to 313.65 K. The experimental data could be correlated with the Peng-Robinson equation of state (PR EoS) and two binary parameters. The phase behavior of the carbon dioxide + nitrobenzene system appears to belong to Type-V according to the classification of van Konynenburg and Scott.     

Application of Chebyshev polynomials to predict phase behavior of fluids containing asphaltene and associating components using SAFT equation of state

In this work, a thermodynamic model based on statistical association fluid theory (SAFT) is developed to predict the phase behavior of mixtures containing asphaltene contents. The SAFT equation of state is a good candidate for closing that gap between statistical mechanic models and the classical models dominated by cubic equation of state. A robust, fast and accurate computational algorithm based on Chebyshev polynomial approximation is developed to calculate the density and hence fugacity using SAFT equation of state in order to perform phase equilibrium calculations. Application of Chebyshev polynomials to approximate pressure-density function leads to an interpolation error of degree 10⁻¹³. Application of the proposed algorithm to calculate density of binary systems composed of ethanol and toluene shows an average relative deviation of 0.143% in the temperature range 283.15-353.15 K and for pressures up to 45 MPa. The proposed model is developed to predict the precipitation behavior of petroleum fluids containing asphaltene. The effect of pressure, temperature and solvent concentration on the amount of asphaltene precipitation is investigated. A good agreement with an AAD of 2.593% is observed between experimental and predicted amount of asphaltene precipitate. The model is also tested to investigate the effect of temperature and solvent concentration on asphaltene onset pressures (upper and lower). Again, an excellent agreement is observed between experimental and predicted values of the asphaltene onset pressure at different temperatures and solvent concentrations with an average 0.705% relative error. The accuracy of the proposed model is compared with WinProp software using Peng-Robinson equation of state with average 53.132% and 8.657% relative errors for the amount of asphaltene precipitate and onset pressure, respectively.     

碳酸铈在NaCl-H2O体系中的相平衡热力学模型

碳酸铈是生产CeO2的重要前驱体,对其性质具有决定性影响。碳酸铈的结晶特征取决于反应结晶过程中过饱和度的控制,其在NaCl-H2O体系中的相平衡数据是关键基础数据。本工作首先在298.15~363.15 K温度范围内合成了碳酸铈,XRD分析结果显示,323.15 K及以下得到的产品为八水碳酸铈[Ce2(CO3)3?8H2O],343.15 K及以上得到的产品为碱式碳酸铈[CeCO3OH]。本工作采用经典等温法测定了这两种碳酸铈化合物在NaCl-H2O体系中的相平衡数据,并利用Aspen Plus平台的ELEC-NRTL方程建立了可准确预测Ce2(CO3)3?8H2O和CeCO3OH在NaCl-H2O体系中相平衡数据的热力学模型。在无限稀释假设的基础上,通过回归Ce2(CO3)3?8H2O和CeCO3OH在水中的溶解度数据,确定了这两种化合物的溶度积。采用赋存形态分析方法,将CeCO3+, CeOH2+, CeHCO32+等组分引入热力学模型。利用实验数据获得了新的离子对(Ce3+-HCO3-和Ce3+-Cl-)参数,提高了新模型的预测能力,所建立的热力学模型预测值与实验数据吻合较好。     

Phase stability analysis using the PC-SAFT equation of state and the tunneling global optimization method

Phase stability calculation is a very important topic in phase equilibrium modeling. Usually the phase stability problem is solved by minimization of the tangent plane distance (TPD) function, the sign of the objective function at its global minimum indicating the state of the mixture at given conditions. The TPD function is non-convex and may be highly non-linear, many phase stability problems being really challenging. The tunneling global optimization method had been successfully used for solving a variety of phase equilibrium problems, including stability, with cubic equations of state (EoS). In this work, we test the ability of the tunneling method to solve the phase stability problem for more complex EoS like PC-SAFT. Calculations are performed for several benchmark problems, for mixtures of non-associating molecules, from binaries to multicomponent. In one example, the mixture contains hydrogen sulphide, for which the three parameters required by the PC-SAFT EoS were unavailable in the literature. These parameters, as well as the binary interaction parameter (BIP) between hydrogen sulphide and methane, were calculated based on experimental data.     

Solubility prediction of disperse dyes in supercritical carbon dioxide and ethanol as co-solvent using neural network

Nowadays artificial neural networks(ANNs) with strong ability have been applied widely for prediction of nonlinear phenomenon. In this work an optimized ANN with 7 inputs that consist of temperature, pressure, critical temperature, critical pressure, density, molecular weight and acentric factor has been used for solubility prediction of three disperse dyes in supercritical carbon dioxide(SC-CO2) and ethanol as co-solvent. It was shown how a multi-layer perceptron network can be trained to represent the solubility of disperse dyes in SC-CO2. Numeric Sensitivity Analysis and Garson equation were utilized to find out the degree of effectiveness of different input variables on the efficiency of the proposed model. Results showed that our proposed ANN model has correlation coefficient, Nash–Sutcliffe model efficiency coefficient and discrepancy ratio about 0.998, 0.992, and 1.053 respectively.