Application of the kirkwoodbuff solution formalism and the hard sphere expansion method with the modified mean density approximation to predict solubility of solutes in supercritical fluids

The Kirkwood-Buff solution theory to give the relations between macroscopic thermodynamic properties and the fluctuation integrals (G_ij) was utilized to predict solubility of solutes in supercritical fluids. The solvent-solute fluctuation integral (G₂₁) in the derivation for solubility of solute is expressed in terms of the solvent-solvent fluctuation integral (G₁₁) using the hard sphere expansion (HSE) conformal solution method with the modified mean density approximation (MMDA) where the scaling factor (R₁₂) represents the ratio of the first peak heights of the radial distribution functions for the mixture and the reference fluid having the mean density determined from the mean density approximation (MDA). The values of R₁₂ were evaluated by considering it as an adjustable parameter and solving the Ornstein-Zernike equation with the hypernetted chain (HNC) closure, and were compared. It is shown that solubility can be evaluated with an equation of state for pure supercritical fluid, three molecular parameters, and the scaling factor (R₁₂) without knowledge of critical properties of solutes, which can not be measured precisely for some organic solids. This model based on the molecular theory leads to better results in solubility calculations than both the Peng-Robinson equation of state with the classical mixing rule and the previous method with the original MDA instead of the MMDA. It might be due to the superiority of the MMDA over the original MDA.     

Expanded ensemble Monte Carlo simulations for the chemical potentials of supercritical carbon dioxide and hydrocarbon solutes

We carry out expanded ensemble Monte Carlo simulations in order to calculate the chemical potentials of carbon dioxide as solvent and those of hydrocarbons as solutes at supercritical conditions. Recently developed adaptive method is employed to find weight factors during the simulation, which is crucial to achieving high accuracy for free energy calculation. The present simulation method enables us to obtain chemical potentials of large solute molecules dissolved in compressed phase from a single run of simulation. Simulation results for the excess chemical potentials of pure carbon dioxide at 300, 325 and 350 K are compared with experimental data and values predicted by the Peng-Robinson equation of state. A good agreement is found for high pressures up to 500 bar. The chemical potentials of hydrocarbon solutes dissolved in carbon dioxide at infinite dilution are predicted by simulation. Less than eight intermediate subensembles are required to gradually insert (or delete) hydrocarbon solute molecules from methane to noctane into dense CO₂ phase of approximately 1.0 g cm⁻³.     

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.     

超临界CO2和植物油脱臭馏出物相平衡研究

研究了植物油脱臭馏出物在超临界CO2中的相平衡问题。基于组分的相似性把含有复杂组分的植物油脱臭馏出物简化为两种虚拟组分,用改进的混合规则和超临界组分的能量参数计算式,结合PR状态方程进行计算：理论计算与实验数据相吻合,为间歇式或连续逆流式超临界CO2萃取分离的设计提供了依据。     

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.     

Distribution of solutes between polymer and supercritical fluid by inverse supercritical fluid chromatography

Two methods of inverse supercritical fluid chromatography (ISFC), frontal analysis supercritical fluid chromatography (SFC) and elution SFC, have been compared for the determination of distribution coefficients of solutes between a polymer and a supercritical CO₂. The logarithm of the distribution coefficient showed monotonic decrease with the density of the supercritical fluid (SF). The abnormal-maximum behavior of solute sorption in the polymer phase was explained by the fluid and solute properties, ϕ₂P/P ₂ ^sat . Interesting open-elliptic shapes of sorption and volume-fraction curves were obtained and explained with the fugacity coefficient. Correction to the capacity factor was employed to eliminate the retention due to the adsorption on the surface of the silica support. A model based on the Flory equation and the Peng-Robinson equation of state (EOS) successfully predicted the phase behavior of the ternary solutesupercritical fluid-polymer systems using only interaction parameters obtained from the binary systems. The solute distribution coefficient at infinite dilution was used to calculate the phase equilibrium at finite concentration using a ternary-phase diagram.     

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO₂ in separation processes. In this work, the Peng-Robinson (PR) and the Esmaeilzadeh-Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong-Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (G^ex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.     

Phase behavior measurement for the ethylene glycol dimethacrylate in supercritical carbon dioxide at temperatures between (313.2 and 393.2) K and pressures from (5.8 to 22) MPa

High pressure experimental data are presented on the phase equilibrium of ethylene glycol dimethacrylate in supercritical carbon dioxide. Pressure-composition (P-x) isotherms were measured in static method at five temperatures of (313.2, 333.2, 353.2, 373.2 and 393.2) K and at pressures up to 22.0MPa. This (carbon dioxide+ethylene glycol dimethacrylate) system has continuous critical mixture curves that exhibit maximums in pressure at temperatures between the critical temperatures of carbon dioxide and ethylene glycol dimethacrylate. At a fixed pressure, the solubility of ethylene glycol dimethacrylate for the (carbon dioxide+ethylene glycol dimethacrylate) system increases with increasing temperature. The (carbon dioxide+ethylene glycol dimethacrylate) system exhibits type-I phase behavior. The experimental result for the (carbon dioxide+ethylene glycol dimethacrylate) system is correlated with Peng-Robinson equation of state using mixing rule including two adjustable parameters. The critical property of ethylene glycol dimethacrylate is predicted with Joback and Lee-Kesler method.     

超临界二氧化碳和醇类体系的相平衡计算

应用Peng-Robinson(P-R)状态方程对超临界CO2系统进行了相平衡模拟。对超临界CO2和醇类二元系统进行了汽液相平衡计算,结果表明,P-R状态方程模拟高压下CO2系统的相平衡具有较高的精度。     

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.     

High pressure isothermal vapor-liquid equilibria for the binary system of carbon dioxide (CO<Subscript>2</Subscript>)+1,1,1-trifluoroethane (R-143a)

Isothermal vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO₂)+1,1,1-trifluoroethane (HFC-143a) were measured within the temperature range of 273.15–333.15 K. The data in the two-phase region were measured by using a circulation-type equilibrium apparatus in which both vapor and liquid phases are continuously recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EOS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model. The values calculated by the PR EOS with the W-S mixing rules show good agreement with our experimental data.     

A comparison among three equations of state in predicting the solubility of some solids in supercritical carbon dioxide

Equations of state play an important role in chemical engineering designs, and they have assumed an expanding role in the study of the phase equilibria of fluids and fluid mixtures. In this report, a modified Peng-Robinson equation of state by Danesh et al., a modified Peng-Robinson equation of state by Gasem et al., and the Mansoori-Mohsen Nia-Modarress equation of state are used to predict the solubility of some solids in supercritical carbon dioxide. The systems studied were binary mixtures containing supercritical carbon dioxide with Ascorbic acid, Ascorbyl palmitate, Butyl hydroxyl anisole, Dodecyl gallate and Propyl gallate. Interaction parameters for the studied systems are obtained and the percentage of average absolute relative deviation (%AARD) in each calculation is displayed.     

Measurement and correlation of vapor-liquid equilibria of the binary carbon dioxide-chloroform mixture system

Binary vapor liquid equilibrium data of the carbon dioxide+chloroform system were measured at five isotherms from 310.13 K to 333.32 K. A circulating type apparatus with on-line gas chromatography was used in this study. The experimental data were correlated by classical Peng-Robinson equation of state using van der Waals one fluid mixing rules and the multi-fluid nonrandom lattice fluid (MF-NLF) equation of state.     

Separation of Alkanes and Aromatics with Supercritical Carbon Dioxide

Abstract

The separation of alkanes and aromatics with supercritical carbon dioxide has been studied by measuring vapour-liquid equilibria and selectivities in the model systems 2-methylnaphthalene/hexadecane/ carbon dioxide and 2-methylnaphthalene/dodecane/carbon dioxide. The results have been modelled with the Peng-Robinson equation of state. In both model systems supercritical carbon dioxide appeared selective for the component with the highest vapour pressure, 2-methylnaphthalene respectively dodecane. Consequently alkanes and aromatics will be separated by supercritical carbon dioxide on basis of their difference in vapour pressure instead of their difference in chemical structure.     

Solubility of some phenolic acids contained in citrus seeds in supercritical carbon dioxide: Comparison of mixing rules, influence of multicomponent mixture and model validation

The solubility prediction of any compound in supercritical carbon dioxide is obtained using the dense gas formulation to calculate the phase equilibria. To achieve this, the Peng-Robinson equation of state with the Stryjek-Vera modification is used. Then, this is coupled with the Wong-Sandler and Van der Waals mixing rules. The latter was included in order to evaluate the influence of the mixing rules in the calculation of the solubility. Therefore, the obtained results from the model are compared with experimental data reported in literature for ferulic acid, p-coumaric acid and caffeic acid contained in citrus seeds. Good agreement was obtained between the model and the experimental data for the phenolic acids, when the Wong-Sandler mixing rules are used. Also the influence of the multicomponent mixture is considered for the prediction of the solubility of phenolic acids in supercritical carbon dioxide.     

Calculation of phase equilibrium for water+carbon dioxide system using nonrandom lattice fluid equation of state

For the geological sequestration of carbon dioxide to prevent global warming, the phase equilibrium data for water and carbon dioxide mixture play an important role in process design and operation. In this work, the nonrandom lattice fluid equation of state with hydrogen bonding (NLF-HB EOS) was applied for the prediction of phase equilibrium of mixtures containing water and carbon dioxide. A new set of pure component parameters for carbon dioxide above critical condition was found and optimum binary interaction parameters were reported to correlate mutual solubility of mixtures. The calculated results were compared with the Peng-Robinson Equation of State with the conventional mixing rule (PR-EOS) and the Wong-Sandler mixing rule (PR-WS-EOS). The calculation results show that NLF-HB EOS can correlate mutual solubility of water+carbon dioxide mixtures with reasonable accuracy within a single theoretical framework.     

Density correlation of solubility of C. I. disperse orange 30 dye in supercritical carbon dioxide

The solubility of C. I. Disperse Orange 30 (O30) dye in CO₂ has been measured by using a closed-loop (batch) solid-fluid equilibrium apparatus at temperatures between 313 and 393 K and at pressures between 11 and 33 MPa. Kumar and Johnston’s equation based on Chrastil’s concept has been used to describe the experimental solubility data. The solubility versus density plot appears much simpler than the solubility versus pressure plot. The isotherms are nearly straight and parallel to each other, as seen in the previous studies. Peng-Robinson equation of state (PR EOS) has also been used successfully in modeling the dye solubility in supercritical carbon dioxide as a function of pressure or density of the fluid phase. The validity of this method has been verified by the vapor pressure calculation. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Measurements and correlation of effect of cosolvents on the solubilities of complex molecules in supercritical carbon dioxide

A new transparent microscale circulation-type high pressure equilibrium cell with on-line sampling was devised. With this apparatus, experimental solubility of molecularly complex species such as steroids (cholesterol, stigmasterol and ergosterol) and fatty acids (palmitic acid and stearic acid) in supercritical carbon dioxide(sc-C0₂) were measured. Also, to find an appropriate substance for enhancing both the polarity and the solubility power of the SC-CO₂ solvent, we arbitrarily selected three polar substances such as acetone, methanol and water and the effect of these cosolvents on the solubility of solutes in SC-CO₂ are examined. The supercritical phase equilibrium data of solute-cosolvent-sc-CO₂ systems were quantitatively correlated using a new equation of state based on the lattice fluid theory incorporated with the concept of multibody interaction. We found that the addition of tracer amount of acetone or methanol to SC-CO₂ enhances the solubility of all solutes about thirty to sixty times when compared with the case of pure sc-CO₂ However, for the case of cosolvent water, no further enhancement of the solubility of solutes was realized. Also, the versatile fittability of the equation of state proposed in this work was demonstrated with the newly measured ternary supercritical equilibrium data.     

Development of artificial neural network models for supercritical fluid solvency in presence of co-solvents

This paper presents the application of artificial neural networks (ANN) to develop new models of liquid solvent dissolution of supercritical fluids with solutes in the presence of cosolvents. The neural network model of the liquid solvent dissolution of CO₂ was built as a function of pressure, temperature, and concentrations of the solutes and cosolvents. Different experimental measurements of liquid solvent dissolution of supercritical fluids (CO₂) with solutes in the presence of cosolvents were collected. The collected data are divided into two parts. The first part was used in building the models, and the second part was used to test and validate the developed models against the Peng-Robinson equation of state. The developed ANN models showed high accuracy, within the studied variables range, in predicting the solubility of the 2-naphthol, anthracene, and aspirin in the supercritical fluid in the presence and absence of co-solvents compared to (EoS). Therefore, the developed ANN models could be considered as a good tool in predicting the solubility of tested solutes in supercritical fluid.     

High pressure isothermal vapor-liquid equilibria of carbon dioxide+1,1-difluoroethane

Vapor-liquid equilibrium data for the binary mixture of carbon dioxide (CO₂)+1,1-difluoroethane (HFC-152a) were measured at five evenly spaced temperatures of (273.15, 283.15, 293.15, 303.15 and 313.15) K by using a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated. The experimental data were correlated with the Peng-Robinson equation of state (PR-EoS) using the Wong-Sandler mixing rules combined with the NRTL excess Gibbs free energy model and the Carnahan-Starling-DeSantis equation of state (CSD EoS). Almost all the calculated values with these two models showed good agreement with the experimental data.