固体溶质在超临界三元系统中的溶解度

溶质在超临界流体中的溶解度数据是研究超临界流体技术的基础.本文对纯组分固体溶质有夹带剂存在的超临界流体三元系统中,夹带剂增大溶质溶解度的作用进行了总结,述评了夹带剂增大溶质溶解度的机理和常用的计算模型.此外,针对两种固体混合溶质共存于超临界流体中的三元系统,讨论了混合溶质共存对彼此溶解度的影响及其相关的理论假说和计算模型.     

Diffusion coefficients of solids in supercritical carbon dioxide: Modelling of near critical behaviour

Most of the models proposed in literature for binary diffusion coefficients of solids in supercritical fluids are restricted to infinite dilution; this can be explained by the fact that most of experimental data are performed in the dilute range. However some industrial processes, such as supercritical fluid separation, operate at finite concentration for complex mixtures. In this case, the concentration dependence of diffusion coefficients must be considered, especially near the upper critical endpoint (UCEP) where a strong decrease of diffusion coefficients was experimentally observed. In order to represent this slowing down, a modified version of the Darken equation was proposed in literature for naphthalene in supercritical carbon dioxide. In this paper, the conditions of application of such a modelling are investigated. In particular, we focus on the order of magnitude of the solubility of the solid and on the vicinity of the critical endpoint. Various equations proposed in literature for the modelling of the infinite dilution diffusion coefficients of the solutes are also compared. Ten binary mixtures of solids with supercritical carbon dioxide were considered for this purpose.     

High-pressure fluid phase equilibria: Experimental methods and systems investigated (1994–1999)

As a continuation of an earlier review, a compilation of systems for which high-pressure phase equilibrium data have been published between 1994 and 1999 is given. Vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE), solid–liquid equilibria, solid–vapor equilibria, solid–vapor–liquid equilibria, critical points, the solubility of high-boiling substances in supercritical fluids and the solubility of gases in liquids (GLE) are included. For the systems investigated, the reference, the temperature and pressure range of the data, and the experimental method used for the measurements is given in 39 tables. Most of experimental data in the literature has been given for binary systems. Of the 824 binary systems, 350 have carbon dioxide as one of the components. Information on 135 pure components, 337 ternary systems and 120 multicomponent systems is given. Experimental methods for the investigation of high-pressure phase equilibria are classified and described.     

On the use of semiempirical models of (solid + supercritical fluid) systems to determine solid sublimation properties

Experimental solubility data of solid–supercritical fluids have significantly increased in the last few years, and semiempirical models are emerging as one of the best choices to fit this type of data. This work establishes a methodology to calculate sublimation pressures using this type of equations. It requires the use of Bartle’s equation to model equilibria data solid–supercritical fluids with the aim of determining the vaporization enthalpy of the compound. Using this method, low deviations were obtained by calculating sublimation pressures and sublimation enthalpies. The values of the sublimation pressures were subsequently used to successfully model different multiphasic equilibria, as solid–supercritical fluids and solid–solvent–supercritical fluids with the Peng–Robinson equation of state (without considering the sublimation pressure as an adjustable parameter). On the other hand, the sublimation pressures were also used to calculate solid sublimation properties and acetaminophen solvation properties in some solvents. Also, solubility data solid–supercritical fluids from 62 pharmaceuticals were fitted with different semiempirical equations (Chrastil, Kumar-Johnston and Bartle models) in order to present the values of solvation enthalpies in sc-CO₂ and vaporization enthalpies for these compounds. All of these results highlight that semiempirical models can be used for any other purpose as well as modeling (solid + supercritical fluids) equilibria.     

Determination of the activity of a molecular solute in saturated solution

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value.     

Why do co-solvents enhance the solubility of solutes in supercritical fluids? New evidence and opinion

The effects of two polar co-solvents, chlorodifluoromethane and acetone, on the solubility and enthalpy of a solution of 1,4-naphthoquinone in supercritical (SC) CO2 were studied. We found that the dissolution process becomes less exothermic in the presence of the co-solvents relative to that in pure CO2, although the solubility is enhanced significantly by the co-solvents. This indicates that the increase in the solubility by adding co-solvents results from the increase of the entropy of solution. On the basis of the unexpected results we propose a new mechanism for the solubility enhancement of the solute by the co-solvents in supercritical fluids (SCF); this should be applicable to cases in which the local density of the SC solvent around the solute and the co-solvent is larger, and the co-solvent associates preferentially with the solute. The results are also very important for the understanding of other fundamental questions of SCF science, such as the effect of co-solvents on the thermodynamic and kinetic properties of the reactions in SCFs.     

On the suitability of the virial equation for modeling the solubility of solids in supercritical fluids

Five model systems, the van der Waals fluid, the Soave-Redlich-Kwong fluid, the Peng-Robinson fluid, the hard-sphere fluid, and the square-well fluid, are used to examine the performance of the truncated virial expansion in describing the fugacity of a solute at infinite dilution in a solvent. It is demonstrated that the virial fugacity results deteriorate at significantly lower densities as the solute becomes larger. This has consequences for attempts to describe the solubility of solids in supercritical fluids, where the virial expansion, truncated after the third virial coefficient, has been considered as a modeling option. The results of this work suggest that, for the densities and solute-to-solvent size ratios commonly encountered in supercritical extraction, the truncated virial expansion should not be expected to describe correctly the solute fugacity, and therefore any success it has in fitting solubility data should be viewed with caution.     

Prediction and experimental verification of the salt effect on the vapour–liquid equilibrium of water–ethanol–2-propanol mixture

Experimental vapour–liquid equilibria of water–ethanol–2-propanol saturated with NaNO₃, NaCl, KCl and containing 0.05 mol CH₃COOK/mol total solvent compared well with those predicted by Tan–Wilson and Tan–non-random two liquid (NRTL) models for multicomponent solvent–solute mixture using a set of solvent–solvent interaction parameters obtained from the regression of the vapour–liquid equilibrium of the solvent mixture without the dissolved solute and a set of solute–solvent interaction parameters calculated from the bubble points of the individual solvent components saturated or containing the same molar ratio of solute/total solvents as the mixture. The results also showed that a solvent component i is salted-in or out of the liquid phase relatively more than solvent component j would depend on whether A_sj/A_si (Tan–Wilson model) or exp(τ_is−τ_js) (Tan–NRTL model) is less or greater than 1. This is consistent with earlier publications on the effect of dissolved solutes (electrolytes and non-electrolytes) on the binary solvents mixtures. These findings confirmed that Tan–Wilson and Tan–NRTL models for multicomponent solvent–solute system can provide an accurate and rapid screening of electrolytes and non-electrolytes for their suitability in facilitating solvent separation by salt distillation of ternary solvent mixtures simply by determining the relative ratios of the solute–solvent interaction parameters from the respective bubble points of the solvent components containing the dissolved solute. The results also suggest that this may also be extended to other multicomponent solvent mixtures.     

用微扰硬球链理论计算超临界CO-2-溶质二元系的密度

溶质在超临界流体中的溶解度与流体的密度密切相关。本文采用微扰硬球链理论对纯CO2及CO2-正戊烷、CO2-正庚烷、CO2-正癸烷体系在不同条件下的密度进行计算，计算值与文献给出的实验值符合很好。     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

Thermophysical properties of supercritical fluids with special consideration of aqueous systems

Selected thermophysical properties of polar, dense supercritical fluids are discussed. The static dielectric constant of water and the freon R22 (CHClF₂) is shown in some detail. Examples of critical curves for binary systems with water and methanol are given. New experimental data of excess volumes up to 400 °C and 2000 bar are shown for water combined with H₂, CH₄ and benzene. Excess Gibbs energies and activity coefficients for water-benzene are also shown. Results of the solubility of anthracene in ten different high pressure fluids, obtained by UV-spectroscopy, are presented. The PVT-data of concentrated supercritical aqueous NaCl-solutions and the ion product of pure water to 1000 °C are discussed.     

Entrainer effect in supercritical mixtures

The objective of this paper is to propose a predictive method for the estimation of the change in the solubility of a solid in a supercritical solvent when another solute (entrainer) or a cosolvent is added to the system. To achieve this goal, the solubility equations were coupled with the Kirkwood–Buff (KB) theory of dilute ternary solutions. In this manner, the solubility of a solid in a supercritical fluid (SCF) in the presence of an entrainer or a cosolvent could be expressed in terms of only binary data. The obtained predictive method was applied to six ternary SCF–solute–cosolute and two SCF–solute–cosolvent systems. In the former case, the agreement with experiment was very good, whereas in the latter, the agreement was only satisfactory, because the data were not for the very dilute systems for which the present approach is valid.     

Solubilities of poly(ethylene glycol)s in the mixtures of supercritical carbon dioxide and cosolvent

The solubilities of poly(ethylene glycol) (PEG6000) (M.W.=7500) in the mixtures consisting of supercritical carbon dioxide (CO₂) and cosolvent have been measured by observing the cloud points at 313.15 K and 16 MPa. Ethanol and toluene were used as cosolvents. The solubility of PEG6000 is extremely low in either CO₂ or ethanol, but becomes about 20 wt.% in a mixture of the two. The maximum solubility is achieved at about 50 wt.% (polymer-free) ethanol. The solubilities of PEG6000 in the mixtures of supercritical CO₂ and the cosolvent have been correlated by a regular solution model using the local compositions of solvents around a solute molecule, and an expanded liquid equation of state model.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Effect of a supercritical fluid on the characteristics of sorption processes

The effect of an inert supercritical (SC) component of a gas mixture on the equilibrium adsorption conditions was investigated theoretically. The adsorption isotherms were calculated within the framework of the lattice-gas model taking into account lateral interactions of the nearest neighbors in the quasichemical approximation. The physical adsorption and chemisorption isotherms were calculated at specified chemical potentials of the main and supercritical components and at specified mole fractions of the supercritical component. The binary phase diagrams SC component-atoms of the solid characterizing the solubility conditions of SC molecules in the solids are considered.     

Correlation and Calculation of Multicomponent Adsorption Equilibria Data Using a Generalized Adsorption Isotherm

Enhanced by the need for reliable and accurate data of multicomponent gas adsorption equilibria on porous solids like activated carbons or zeolites, a new method to measure and correlate coadsorption equilibria has been developed. This method is a combination of gravimetric or volumetric measurements of the total load of pure or multicomponent adsorbates (Staudt, 1994; Gregg and Sing, 1982) and a correlation and calculation procedure using a new adsorption isotherm (AI) (Keller, 1990). This AI is thermodynamically consistent and describes adsorbates with fractal dimension for single- or multicomponent systems and load dependent adsorption energies. This method allows calculation of partial loads of multicomponent coadsorption equilibria from pure component data and the total loads of the mixture adsorption equilibria. This will be demonstrated for binary and ternary adsorption equilibria of CH₄, C₂H₄ and C₂H₆ on activated carbon (Reich et al., 1980).     

Solubility of light hydrocarbons and their mixtures in pure water under high pressure

New solubility data of methane, ethane, n-butane and their mixtures in pure water are obtained at 344.25 K, from 2.5 to 100 MPa. The results agree well with those of the literature in the case of pure hydrocarbons in water, but differ significantly for hydrocarbon mixtures. In contrast to the conclusion reached by Amirijafari and Campbell [B. Amirijafari, J. Campbell, Solubility of gaseous hydrocarbon mixtures in water, Soc. Pet. Eng. J. (1972) 21–27.], the experimental solubility data of methane–ethane mixtures shows an ideal solution behavior, while the solubility data of methane–n-butane mixtures shows a weaker non-ideality than that observed by McKetta and Katz [J.J. McKetta, D.L. Katz, Methane–n-butane–water system in two-and three-phase regions, Ind. Eng. Chem. 40 (1948) 853–863]. The pure hydrocarbon solubility data are satisfactorily correlated using the Soreide and Whitson modification [I. Soreide, C.H. Whitson, Peng–Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine, Fluid Phase Equilib. 77 (1992) 217–240] of the Peng–Robinson equation of state.     

Molecular-dynamics studies of binary mixtures of Lennard-Jones fluids with differing component sizes

Molecular-dynamics calculations have been carried out for six pure liquids and three binary mixtures of Lennard-Jones fluids with differing component sizes and attractive interactions. Internal energies, radial-distribution functions, velocity autocorrelation functions and self-diffusion coefficients have been calculated and are discussed together with our previous results. The three mixtures obey the Lorentz-Berthelot rules and show endothermic mixing. The excess internal energy ΔU^E of mixtures with equal-sized components is symmetrical with respect to the mole fraction, but those for mixtures of different-sized components become asymmetrical. A comparison is made between the present ΔU^E data and those for real mixtures.     

Solubilities of lactic acid and 2-hydroxyhexanoic acid in supercritical CO2

Solubilities of lactic acid and 2-hydroxyhexanoic acid in supercritical CO₂ have been measured at T=(311 or 313, 318, 328 K) in the pressure range from 50 to 200 bar. The measurements have been performed using a flow-type apparatus. The solute solubility in compressed carbon dioxide increased with pressure at all investigated temperatures. At pressures below 130 bar, a solubility decrease on temperature increase was observed. An accurate correlation method for the solubility of low volatile substances in supercritical CO₂ has been applied for the interpolation of the experimental results.