Modified Soave-Redlich-Kwong equations of state applied to mixtures containing supercritical carbon dioxide

The well-known equation of state Soave-Redlich-Kwong and two of its modifications are applied to describe vapor-liquid equilibrium in binary asymmetric mixtures, which contain supercritical carbon dioxide and a heavy component. Several mixing rules including the classical van der Waals mixing rules with one and two interaction parameters, non-quadratic mixing rules, and the used of a Gibbs free energy model, are used with these equations. Seven mixtures containing supercritical carbon dioxide are considered in the study. The experimental data were obtained from literature sources and the adjustable parameters were found by minimizing the errors between predicted and experimental data of the concentration of the solute in the liquid phase. The work allows concluding on the advantages, disadvantages and expected accuracy of these equations of state and mixing rules for correlating vaporliquid equilibrium data in asymmetric systems as those studied.     

Fluid phase equilibria of the reacting mixture in the dimethyl carbonate synthesis from supercritical CO2

In order to investigate the dimethyl carbonate synthesis from methanol and supercritical CO₂, the thermodynamic behaviour of the reacting mixture, i.e. the quaternary methanol–CO₂–DMC–water mixture, has to be known. The SRK equation of state with MHV2 mixing rules has been chosen to predict fluid phase equilibria in the reactor. The first part of this work is dedicated to the determination of binary interaction parameters, needed in the use of this model. These parameters are deduced from the fitting of experimental data concerning binary or ternary sub-systems existing in the quaternary mixture. Literature data was used for most of the binary sub-systems, but for the DMC–CO₂ and DMC–water mixtures, specific experiments were carried out. The agreement between experimental and predicted fluid phase equilibria was found to be satisfactory. With a view to studying of the operating conditions for the reaction, the thermodynamic model was used to predict fluid phase equilibria in the reactor, by considering several hypothetical feed ratios and conversions. This work shows that CO₂ has to be used in large excess in order to be sure of running the reaction in a homogeneous fluid medium.     

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.     

Phase equilibria of mixtures containing CO2 and organic acids using the UMR-PRU model

The UMR-PRU model, which has been successfully tested in the past to the predictions of different type of phase equilibrium and thermodynamic properties in binary and multicomponent systems, is applied in this work to phase equilibria in mixtures containing CO₂ and organic acids. New interaction parameters are determined by fitting only binary vapor–liquid equilibrium data and then they are used to predict the vapor–liquid, solid–gas and solid–liquid–gas equilibria in CO₂/organic acid systems. Furthermore, the UMR-PRU model with the newly derived interaction parameters is applied to the prediction of the phase equilibrium in ternary mixtures consisting of CO₂, organic acids and water. Satisfactory results are obtained in all cases.     

ON THE COMPOSITION-DEPENDENT INTERACTION PARAMETERS IN EQUATIONS OF STATE

Composition-dependent interaction parameters have been applied to the calculation of vapor-liquid equilibria (VLE) in mixtures containing components of different chemical nature. Binary VLE have been correlated and ternary VLE have been predicted from binary data using five different mixing rules. Binary data can be accurately correlated for systems with moderate deviations from ideality using mixing rules with two binary parameters. For very strongly nonideal mixtures three binary parameters are needed. For the prediction of ternary VLE from binary information only the mixing rules of Panagiotopoulos and Reid (1986) and Schwartzentruber et al. (1987) are reliable. For most systems the quality of predicting ternary data is comparable to the quality of correlating binary data. Significant deviations are noted only for strongly nonideal systems close to phase separation. In these cases it is recommended to use models incorporating association in an explicit form. KEYWORDS Equations of state Mixing rules Multicomponent Vapor-liquid equilibria.     

Calculation of the solid solubilities in supercritical carbon dioxide using a new G mixing rule

The aim of this study is to develop a new EOS/G^ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO₂, by using six mixing rules, namely, the Wong-Sandler (WS) rule, the Orbey-Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide.The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO₂.     

A Calorimetric Method for the Determination of Binary Phase Compositions at High Temperatures and Pressures

Abstract

The design and operation of supercritical separation equipment are dependent upon an accurate knowledge of phase equilibria among the components involved in the processes. Using high-pressure, high-temperature flow calorimeters, we have developed a method for determining phase splitting in binary mixtures from heat-of-mixing data taken in the region of the mixture critical locus. The flow calorimetric procedure for determining heats of mixing, phase equilibria, and the critical locus curve is described. The advantages and simplicity of using flow calorimetry to determine these data are discussed. Phase behavior of several binary CO₂-hydrocarbon systems is presented.     

Peng-Robinson状态方程及保形溶液混合规则用于汽-液平衡计算

Peng-Robinson状态方程式用于推算三组二元系统的汽-液平衡:甲烷、二氧化碳及氢与烃类.对含甲烷及二氧化碳的二元系统.推荐了经过关联的相互作用参数.将保形溶液(Conformal Solu-tion)混合规则及本文提出的对温度有关的系数α的修正式应用于高度非对称的含氢二元系统,较Peng-Robinson的原始工作更为精确地表述了汽-液平衡.     

Simultaneous modeling of VLE,LLE and VLLE of CO2 and 1, 2, 3 and 4 alkanol containing mixtures using GC-PPC-SAFT EOS

A polar version of the group contribution PC-SAFT equation of state (GC-PPC-SAFT; Tamouza et al., 2004; NguyenHuynh et al., 2008) combined with a method for correlation/prediction of binary interaction parameters k_ij (NguyenHuynh et al., 2008) is here applied to model vapor–liquid, liquid–liquid and vapor–liquid–liquid phase equilibria of CO₂ + alkanol mixtures simultaneously.A cross-association interaction between CO₂ and alkanol had to be taken into account to model/predict the mixtures equilibria accurately. The cross-association parameters were evaluated using the so-called CR1 mixing rules supported by ab initio computations.Extensive prediction tests on CO₂ + alkanol mixtures involving linear and branched alkanols are carried out. The results obtained showed that in most cases, the correlation and prediction calculations are qualitatively and quantitatively satisfactory: the overall deviations on liquid phase and vapor phase are respectively ΔX = 3–4% and ΔY = 1–2%.     

Measurement and prediction of high-pressure vapor-liquid equilibria for binary mixtures of carbon dioxide + n-octane, methanol, ethanol, and perfluorohexane

We report the measurement of high-pressure vapor-liquid equilibrium data for binary mixtures of carbon dioxide + n-octane, +methanol, and +ethanol systems at 313.14 K and carbon dioxide + perfluorohexane at 303.15-323.15 K. The experimental data were collected using a new simple apparatus for measuring high-pressure vapor-liquid equilibria and correlated using a modified SRK equation with the three-parameter conventional mixing rule proposed by Adachi and Sugie. The SAFT-VR equation of state has also been used to predict the phase behavior and found to be in good agreement with experimental data. For the carbon dioxide + methanol, carbon dioxide + ethanol and carbon dioxide + perfluorhexane systems simple Lorentz-Berthelot combining rules can be used to determine the cross interactions and predict the phase behavior. For the carbon dioxide + n-octane system cross interaction parameters fitted to experimental data are needed in order to capture the non-ideal phase behavior exhibited by this system.     

Experimental measurement and correlation of phase behavior for the CO2+heptafluorobutyl acrylate and CO2+heptafluorobutyl methacrylate systems at high pressure

Experimental data of high pressure phase behavior from 313.2 to 393.2 K and pressures up to about 14.3 MPa were reported for binary mixture of 2,2,3,3,4,4,4-heptafluorobutyl acrylate (HFBA) and 2,2,3,3,4,4,4-heptafluorobutyl methacrylate (HFBMA) in supercritical carbon dioxide. The high pressure experiment was performed by static method using variable-volume view cell apparatus. The CO₂+HFBA and CO₂+HFBMA systems are correlated with the Peng-Robinson equation of state using a van der Waals one-fluid mixing rule. The CO₂+HFBA and CO₂+HFBMA systems exhibit type-I phase behavior with continuous critical mixture curves.     

紫杉醇在二氯甲烷-超临界二氧化碳混合溶剂中的溶解度

Phase behavior of paclitaxel in solvent mixtures of dichloromethane and supercritical carbon dioxide was investigated using a supercritical phase monitor. Cloud point pressures were determined as a function of temperature, pressure and paclitaxel content from 313.1 to 343.1 K and pressures up to 33.52 MPa. The ternary mixtures exhibit a typical lower critical solution temperature behavior. When paclitaxel content increases, the single-phase region shrinks in size. Three cubic equations of state (Redlich-Kworng, Soave-Redlich-Kwong and Peng-Robinson equation of state) coupled with the van der Waals one-fluid mixing rules were selected to correlate the experimental data. The results indicate that SRK EOS coupled with two binary interaction parameters kij and lij can pre-dict paclitaxel solubility for the best fit of experimental data.     

A modification of Wong-Sandler mixing rule for the prediction of vapor-liquid equilibria in binary asymmetric systems

Systems consisting of light components and heavy hydrocarbons are highly asymmetric and industrially important. Design and control of facilities for separation and purification of such mixtures require vapor-liquid equilibrium data. Coupling of the cubic equation of state (EOS) with excess Gibbs energy models (EOS/G ^ex models) failed to represent the vapor-liquid equilibria (VLE) of such systems accurately. The main purpose of this work is to present a modification of Wong-Sandler mixing rule with using the composition dependent binary interaction parameter. Vaporliquid equilibria for 30 binary systems are calculated using the SRK equation of state with proposed model and Wong-Sandler mixing rule. Calculated pressures and mole fractions of vapor phase are compared with experimental data. The average absolute percentage deviation indicates that error involved in the application of modified Wong-Sandler model is less than Wong-Sandler model in most cases.     

A new semiempirical equation of state for fluids—III Application to phase equilibria in binary mixtures

The equation of state derived in a previous publication [1] is used to correlate vapour-liquid, liquid-liquid, and gas-gas equilibria in binary mixtures. Special mixing rules for the parameters of the equation of state are derived from a quasichemical lattice model. It is possible to describe phase equilibria at very high pressures (beyond 1000 bar) with reasonable accuracy. The unlike interaction potential parameters, which are used as adjustable data to obtain a good fit, have physically reasonable values.     

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO₂ + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO₂ + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013     

High-pressure phase equilibria of systems carbon dioxide + n-eicosane and propane + n-eicosane

In this work we investigated the phase equilibrium behavior of the binary asymmetric systems propane (C3) + n-eicosane (C20) and carbon dioxide (CO₂) + n-eicosane (C20). We used a variable-volume view cell for obtaining fluid–fluid equilibrium (FFE), solid–fluid equilibrium (SFE) and solid–fluid–fluid equilibrium (SFFE) experimental data. We modeled the phase equilibria of both systems using the Peng–Robinson Equation of State for describing the fluid phases and an expression for the fugacity of pure solid n-eicosane with parameters fit to reproduce the pure n-eicosane melting line. We performed the phase equilibrium calculations by implementing path-following methods for tracking entire solid–fluid (SF) and solid–fluid–fluid (SFF) equilibrium curves for binary asymmetric mixtures. This made it possible to obtain complete isoplethic lines or complete three-phase equilibrium lines in single runs. Although the model is relatively simple, it is able to grasp the complex observed behavior for the systems studied here.     

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.     

High-pressure phase equilibria of systems carbon dioxide + n-eicosane and propane + n-eicosane

In this work we investigated the phase equilibrium behavior of the binary asymmetric systems propane (C3) + n-eicosane (C20) and carbon dioxide (CO₂) + n-eicosane (C20). We used a variable-volume view cell for obtaining fluid–fluid equilibrium (FFE), solid–fluid equilibrium (SFE) and solid–fluid–fluid equilibrium (SFFE) experimental data. We modeled the phase equilibria of both systems using the Peng–Robinson Equation of State for describing the fluid phases and an expression for the fugacity of pure solid n-eicosane with parameters fit to reproduce the pure n-eicosane melting line. We performed the phase equilibrium calculations by implementing path-following methods for tracking entire solid–fluid (SF) and solid–fluid–fluid (SFF) equilibrium curves for binary asymmetric mixtures. This made it possible to obtain complete isoplethic lines or complete three-phase equilibrium lines in single runs. Although the model is relatively simple, it is able to grasp the complex observed behavior for the systems studied here.     

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.