基于实验等温线确定超临界气体绝对吸附量的数学方法

A mathematical method was proposed for the determination of absolute adsorption from experimental isotherms. The method is based on the numerical equality of the absolute and the excess adsorption when either the gas phase density or the amount adsorbed is not quite considerable. The initial part of the experimentalisotherms, which represents the absolute adsorption, became linear with some mathematical manipulations. The linear isotherms were reliably formulated. As consequence, either the volume or the density of the supercritical adsorbate could be determined by a non-empirical way. This method was illustrated by the adsorption data of supercritical hydrogen and methane on a superactivated carbon in large ranges of temperature and pressure.     

A STUDY ON SUPERCRITICAL FLUID EXTRACTION OF L-PROLINE

The extraction of L-proline from the fermentation broth filtrate with the supercritical fluid was studied. It has been proved that L-proline and most amino acids are hardly dissolved in the pure supercritical carbon dioxide fluid. When the methyl alcohol was added as an entrainer in L-proline solution or carbon dioxide fluid, the solubility of L-proline in the supercritical fluid would be greatly increased, but ethyl alcohol was unsatisfactory as an entrainer.The influences of extraction pressure, temperature, time, flow rate of fluid, concentrations of L-proline and entrainer on the yield of L-proline have been investigated for searching the optimal extraction conditions.     

垂直上升管内超临界压力下航空煤油传热特性研究(英文)

A research on the heat transfer performance of kerosene flowing in a vertical upward tube at supercritical pres-sure is presented. In the experiments, insights are offered on the effects of the factors such as mass flux, heat flux, and pressure. It is found that increasing mass flux reduces the wall temperature and separates the experimental section into three different parts, while increasing working pressure deteriorates heat transfer. The extended corresponding-state principle can be used for evaluating density and transport properties of kerosene, including its viscosity and thermal conductivity, at different temperatures and pressures under supercritical conditions. For getting the heat capacity, a Soave–Redlich–Kwong (SRK) equation of state is used. The correlation for predicting heat transfer of kerosene at supercritical pressure is established and shows good agreement with the experimen-tal data.     

超临界流体色谱手性分离布洛芬

The separation method using chiral stationary phase （CSP） for the preparation of enantioselective compound was widely used. In this work, supercritical fluid chromatography（SFC） was proposed to resolve the chiral mixtures. To determine the optimum operating conditions for the chiral separation of the racemic ibuprofen, the retention factors and resolutions with the change in pressure, temperature and the content of IPA （%, by volume） in supercritical CO2 were investigated. Experiments showed that the retention factor decreased with the increase of pressure and decrease in temperature. The retention factor was also influenced by the content of IPA in mobile phase, as the content of IPA in the supercritical fluid increased, the retention factor decreased. The resolution of the enantiomers became worse with the increase of IPA in the supercritical fluid. Through optimizing the experimental conditions, a SFC procedure with 13MPa, 311.15K and 4% IPA in CO2 was obtained. The peak shape of the enantiomers was symmetric with supercritical fluid chromatography when compared to the asymmetric peak shape obtained by the conventional liquid chromatography. This work demonstrated that the developed supercritical fluid chromatography procedure was suitable for the chiral separation of ibuprofen enantiomers.     

Solubility of the silver nitrate in supercritical carbon dioxide with ethanol and ethylene glycol as double cosolvents: Experimental determination and correlation

Solubility of the silver nitrate in the supercritical carbon dioxide containing ethanol and ethylene glycol as double cosolvents was measured under certain pressure and temperature range(10–25 MPa, 323.15–333.15 K). The impact of the pressure and temperature on the solubility was also investigated. Based on the experiment data,a correlation model concerning solid's solubility in supercritical fluids was established by combining the solubility parameter with the thermodynamic equation when a binary interaction parameter and a mixed solvent solubility parameter were defined. Experiments show the solubility of AgNO_3 increases with the pressure at a certain temperature. However, the influence of temperature is related to a pressure defined as the turnover pressure(12.3 MPa). When the pressure is higher(or lower) than this turnover pressure, silver nitrate's solubility shows increasing(or decreasing) trend as the temperature rises. Satisfactory accuracy of our presented model was revealed by comparing experimental data with calculated results.     

用活度系数模型和PCOR状态方程预测聚合物溶液中的亨利常数（英文）

In this paper, the polymer chain of rotator (PCOR) equation of state (EOS) was used together with an EOS/GE mixing rule (MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers. The results of the proposed method compared with two equation of state (van der Waals and GC-Flory) and three activity coefficient models (UNIFAC, UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results. The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR, a and b, were fitted with experimental volume data (Tait equation). As a result, the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.     

Measurement and modelization of VLE of binary mixtures of propyl acetate,butyl acetate or isobutyl acetate with methanol at pressure of 0.6 MPa

The vapor–liquid equilibrium of binary mixtures of propyl acetate,butyl acetate and isobutyl acetate with methanol has been determined at a constant pressure of 0.6 MPa.Results have been modeled with the Peng–Robinson equation,a traditional cubic equation of state widely employed in chemical industries,as well as with the perturbed-chain statistical associating fluid PC-SAFT theory of Gross–Sadowski.By correlation of the binary interaction parameters of these equations,the measured vapor–liquid equilibrium data can be accurately predicted.Thus,this work shows that these models are able to represent the experimental data for systems with associating compounds via hydrogen bonding.     

基于矩法和时间域分析法研究稠密CO2中甲苯和对氯苯在硅胶固定床系统中的吸附和传递性质

Based on chromatographic theory, the moment method and the time-domain fitting analysis were applied to measure and evaluate the adsorption equilibrium constant and mass transfer properties (axial dispersion coefficient and effective intra-particle diffusivity) for toluene and p-dichlorobenzene on silica gel adsorbent in the subcritical and supercritical CO2. An apparatus based on supercritical fluid chromatography was established and the experiments were performed at temperatures of 298.15-318.15 K and pressures of 7.5-17.8 MPa. The two methods have been compared. The results show that for the systems studied here the moment method can give reasonable values for both adsorption equilibrium constant and mass transfer properties, but the time-domain analysis only can obtain the adsorption equilibrium constant. The dependence of adsorption equilibrium constant and mass transfer properties on temperature and pressure was investigated.     

基于矩法和时间域分析法研究稠密CO2中甲苯和对氯苯在硅胶固定床系统中的吸附和传递性质

Based on chromatographic theory, the moment method and the time-domain fitting analysis were applied to measure and evaluate the adsorption equilibrium constant and mass transfer properties (axial dispersion coefficient and effective intra-particle diffnsivity) for toluene and p-dichlorobenzene on silica gel adsorbent in the subcritical and supercritical CO2. An apparatus based on supercritical fluid chromatography was established and the experiments were performed at temperatures of 298.15-318.15 K and pressures of 7.5-17.8 MPa. The two methods have been compared. The results show that for the systems studied here the moment method can give reasonable values for both adsorption equilibrium constant and mass transfer properties, but the time-domain analysis only can obtain the adsorption equilibrium constant. The dependence of adsorption equilibrium constant and mass transfer properties on temperature and pressure was investigated.     

多层合采油藏最大有效井径数学模型及精确解

The maximum effective hole-diameter mathematical model describing the flow of slightly compressible fluid through a commingled reservoir was solved rigorously with consideration of wellbore storage and different skin factors. The exact solutions for wellbore pressure and the production rate obtained from layer j for a well production at a constant rate from a radial drainage area with infinite and constant pressure and no flow outer boundary condition were expressed in terms of ordinary Bessel functions. These solutions were computed numerically by the Crump‘‘s numerical inversion method and the behavior of systems was studied as a function of various reservoir parameters. The model was compared with the real wellbore radii model. The new model is numerically stable when the skin factor is positive and negative, but the real wellbore radii model is numerically stable only when the skin factor is positive.     

Solubility of supercritical gases in organic liquids

Chrastil (1982) [6] demonstrated that the solubility of a substance in a supercritical fluid (SCF) can be correlated with the density of the pure supercritical gas. Therefore, Chrastil's equation permits calculation of the supercritical phase composition of binary SCF + substance mixture based on the knowledge of the supercritical gas density and avoiding the use of equation of state based models.In this work, it is demonstrated that the supercritical fluid density also defines the liquid phase composition of binary systems; a density-dependent relationship is presented to calculate the solubility of supercritical gases in organic liquids. The isothermal solubility of several gases commonly employed in supercritical processing, such as carbon dioxide, methane, and ethane, in different organic liquids, including alkanes, alkenes, alcohols, acids, ketones, esters, terpenes and aromatic compounds, was successfully correlated as a function solely of the pure supercritical fluid density. As an application, pressure vs. composition phase diagrams of binary SCF + substance mixtures were obtained circumventing the use of equation of state models.     

基于超临界流体密度的烷基化内扩散影响动力学

利用烷基化反应实验数据和超临界流体密度计算数据,开展了考虑内扩散影响的烷基化反应动力学研究,采用优化计算方法进行模型参数估值,确定了烷基化反应速率常数、有效扩散系数、催化剂失活速率常数.研究结果表明,基于PengRobinsn(PR)方程计算流体密度的动力学模型在显著性水平α=0.01下有较高的实验数据拟合精度和模型可信度,说明该方法是计算超临界流体密度的较好方法.从有效因子大小可以看出,烷基化反应总体上处于中孔扩散阻力区.     

ADJUSTMENT OF THE SELECTIVITY OF A DIELS-ALDER REACTION NETWORK USING SUPERCRITICAL FLUIDS

The thermodynamic pressure effect on rate constants is reported in supercritical fluid carbon dioxide for a homogeneous reaction network over a wide density range. The selectivity, or ratio of rate constants, has been controlled over a continuum for the parallel Diels-Alder additions of methyl acrylate and cyclopentadiene by adjusting the pressure at constant temperature. This reaction network is well-suited to provide fundamental insight into the nature of supercritical solvent effects since three simplifications arise: the pressure effect on the selectivity is independent of the partial molar volumes of the reactants, the temperature effect on the selectivity is independent of the partial molar enthalpies of the reactants, and the ratio of the endo- to exo-rate constants based on mole fraction units is the same as that based on concentration units. The selectivity for the more polar product, the endo-adduct, increases as the pressure or density increases, which indicates that it has a more negative partial molar volume in the transition state due in part to stronger induction forces. The slope of the logarithm of the selectivity is shown theoretically to increase as a function of the isothermal compressibility at constant temperature. At constant pressure, the selectivity decreases with temperature which indicates that the magnitude of the partial molar enthalpy is greater for the more polar endo-transition state than the exo-state. Solvatochromic polarity scales may be used to correlate quantitatively the solvent on this reaction network at supercritical fluid conditions.     

Natural convection on a vertical plate with variable heat flux in supercritical fluids

The present article investigates laminar free convection with uniform or non-uniform prescribed surface heat flux over a vertical flat plate in supercritical fluid, numerically. A new equation for thermal expansion coefficient in a supercritical fluid is derived based on Redlich–Kwong equation of state as a function of pressure, temperature and the compressibility factor. Calculated values of thermal expansion coefficient have been compared with the experimental results which show better accuracy in comparison with van der Waals ones. The governing systems of partial differential equations were solved numerically using the finite difference method. The local Nusselt number was calculated and plotted as a function of the local Rayleigh number. Using supercritical fluids in constant heat flux free convection, decrease wall temperature in comparison with under critical fluids. It was observed that positive and negative slopes of surface heat flux distribution increases and decreases the heat transfer coefficient, respectively.     

Improved Density Correlation for Supercritical CO2

An experimental apparatus was designed to measure accurately the density of supercritical CO₂ in wide temperature and pressure ranges. Based on experimental results, the curves for CO₂ density as function of pressure at certain temperatures were divided into linear‐growth, rapid‐growth, and slow‐growth intervals. The relative error between the experimental and calculated density values for a number of frequently used equations of state was evaluated. These equations were corrected after analyzing the accuracy of each equation in the different intervals. A new method for calculating the density of supercritical CO₂ that includes 28 constant parameters is proposed to determine the density at a known temperature and pressure.     

SUPERCRITICAL AND SUB-CRITICAL FLUID SOLVENT EFFECTS ON A DIELS-ALDER REACTION

The effect of pressure on the measured bimolecular rate constant of the Diels-Alder reaction between maleic anhydride and isoprene was investigated in supercritical CO₂ and sub-critical propane. The reaction was carried out at 35°C in CO₂ and 80°C in propane. Measured bimolecular rate constants are also compared to predictions from the thermodynamic pressure effect using transilion state theory and the Peng-Robinson equation of state. The rate constants in supercritical C0₂ agreed closely with the thermodynamic pressure effect predictions over the entire pressure range. Furthermore, the mole fraction based rate constants were found to vary linearly with the density of the solution. The rate constants in the sub-critical propane solvent significantly diverged from the thermodynamic pressure effect predictions and were found to deviate from this linear density dependence at the lower pressures studied. The results are interpreted in the context of local reactant concentrations about the reacting maleic anhydride and solvent-solute and cosolvent-solute interactions.     

Solubility of hinokitiol in supercritical fluids; measurement and correlation

Supercritical fluid technology has been an alternative for purification and separation of biological compounds in cosmetic, food, and pharmaceutical products. Solubility information of biological compounds in supercritical fluids is essential for choosing a supercritical fluid processes. The equilibrium solubility of hinokitiol was measured in supercritical carbon dioxide and ethane with a static method in the pressure range from 8 to 40MPa and at temperatures equal to 313.2, 323.2 and 333.2 K. The experimental data were correlated well by Peng-Robinson equation of state and quasi-chemical nonrandom lattice fluid model.     

Phase equilibrium characteristics of supercritical CO2/poly(ethylene terephthalate) binary system

The solubility of carbon dioxide in poly (ethylene terephthalate) (PET) at high pressure and elevated temperature conditions was investigated for a better understanding of the phase equilibrium characteristics of supercritical CO₂/PET binary system and useful data for the process development of the supercritical fluid dyeing. Based on the principle of pressure decaying, a novel experimental apparatus suitable to high pressure and high temperature measurement was established. The solubilities of CO₂ in PET were measured with the apparatus at temperatures of 110, 120, and 130°C and pressures up to 30.0 MPa. The results show that the solubility of CO₂ in PET increases with the increase of pressure and CO₂ density, respectively, at a constant temperature, whereas it decreases with the increase of temperature at a constant pressure. The Sanchez‐Lacombe equation of state (S‐L EOS) was used to correlate the experimental data. The calculated results are in good agreement with the experimental ones. The average absolute relative derivation (AARD) is less than 3.91%. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

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.     

A comparison between models based on equations of state and density-based models for describing the solubility of solutes in CO2

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability. However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the particle size. At present, supercritical fluid based particle size reduction processes are gaining in importance in pharmaceutical technology. For the design of such particle formation processes and the determination of their best operating conditions the knowledge of phase equilibrium and solute solubility in a supercritical fluid is essential. Today, models based on equations of state, together with different mixing rules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore the accurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molar volume, and sublimation pressure of the solutes is essential. However, the common, non-equation of state based group-contribution methods are mostly empirical and often lead to inconsistent and unreliable results. Thus, due to the lack of information on these data, density-based models are often used for the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO₂ is correlated by different methods: two methods for the pressure-solubility correlation and two methods for the density-solubility correlation. In addition, the influence of solute data predicted by different group-contribution methods is investigated. With the exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubic equation of state while a cubic equation of state gives less accurate results. In addition, it is shown that for the solutes investigated, the equation of state based method is very sensitive to the values of the sublimation pressure.