Algorithm for fluid phase equilibria calculations by means of a multiconstant equation of state

Some methods for correlating multicomponent vapor-liquid equilibria by using an equation of state are examined. A simplified Morbidelli-Carrà algorit is proposed as the best tool for an eight parameter equation previously reported in Chem. Engng Sci. The possibility of reducing the empirical para of this equation from eight to five and the binary interaction parameters from three to two is also discussed. Both these models have been applied to s binary and ternary mixtures of polar and apolar compounds in a wide range of pressure and temperature. The proposed method also correlates systems exhi miscibility gaps or containing quantal gases.     

AN EQUATION OF STATE FOR AQUEOUS ELECTROLYTE SYSTEMS——Prediction of The Solubility of Natural Gas in Formation Water

A new equation of state(PHSMSA EOS)based on perturbation theory is developed for calculating high-pressure phase equilibria of aqueous electrolyte systems containing supercritical gases,light hydrocarbons andpolar components.The binary interaction parameters are determined:for ion-ion pairs by regression of ionicactivity coefficient data;for molecule-molecule pairs by fitting the VLE data of binary nonelectrolyte mixtures;and for ion-molecule pairs by fitting the gas solubility data of ternary gas-water-salt systems.The new EOShas been tested on the prediction of solubilities of methane,nitrogen and natural gas mixtures in brine.Sat-isfactory agreement with the experimental data measured by authors and other investigators is observed.     

Thermodynamics of gas solubilities in molten polymers

Perturbed-hard-chain theory is extended to mixtures of polymers and volatile fluids, including supercritical gases. This extension is used to derive an expression for Henry's constant for a solute in a molten polymer. Theoretical calculations and data reduction are reported for a variety of solutes in polyethylene, polyisobutylene, and poly(dimethyl siloxane) in the temperature region 25–300°C. Calculated Henry's constants and their temperature dependence are generally in good agreement with the limited experimental data now available.     

Adsorption prediction for three binary supercritical gas mixtures on activated carbon based on a NDFT/PSD approach

A non-local density functional theory (NDFT) in combination with the pore size distribution (PSD) analysis has been applied to make a comprehensively theoretical study for correlating and predicting the adsorption equilibria of pure supercritical gases and the corresponding binary supercritical gas mixtures on activated carbon. In this approach, the required PSDs were determined from an input of experimental adsorption data of pure components. By comparing with the experimental data of three different binary systems, CH₄/N₂, CH₄/CO₂, and CO₂/N₂, at high pressure up to 13.6 MPa and temperature 318.2 K with various concentration ranges, the predictive performance of the theoretical approach was evaluated. The adsorption of the mixtures has also been predicted by applying the ideal adsorbed solution (IAS) theory. It was shown that the NDFT/PSD method could be used to predict the mixture adsorption behaviors under high pressure. The developed method has greater superiority over the IAS theory in the prediction of the mixture adsorption.     

Phase behavior of mixtures of ionic liquids and organic solvents

A corresponding-states form of the generalized van der Waals equation, previously developed for mixtures of an ionic liquid and a supercritical solute, is here extended to mixtures including an ionic liquid and a solvent (water or organic). Group contributions to characteristic parameters are implemented, leading to an entirely predictive method for densities of mixed compressed ionic liquids. Quantitative agreement with experimental data is obtained over wide ranges of conditions. Previously, the method has been applied to solubilities of sparingly soluble gases in ionic liquids and in organic solvents. Here we show results for heavier and more-than-sparingly solutes such as carbon dioxide and propane in ionic liquids.     

On the modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species

A technique of modeling of phase and chemical equilibria by equations of state for systems containing supercritical components and ionic species is considered. Attention is focused on the structure of equation of states with inclusion of non-electrolyte and electrostatic contributions. A hole quasichemical model was applied to illustrate the technique and to show how an EOS can be modified for systems with chemical reactions and electrostatic interactions in the liquid phase. The concentration dependency of the density and dielectric permittivity was taken into account in describing the electrostatic contribution that is required for thermodynamic consistency of the results of modeling. A method of assessing the appropriate relationships for mixtures containing supercritical components is suggested, alongside with the way to estimate the “true” composition of mixtures where ionic species are formed due to chemical reactions. The raised questions are discussed with respect to the following systems: solutions of acid gases in water-alkanolamine mixtures and water-ammonia-carbon dioxide system in a broad interval of temperatures and pressures.     

Mixture properties and vapour—liquid equilibria by modified Redlich-Kwong equation of state

The modified Redlich—Kwong equation of state already derived from the analysis of pure substance properties in a previous article[7] is extended here to mixtures by using a new set of combining and mixing rules. The rules were selected by analysing a large set of molar volume data of mixtures. They provide a good representation of the variation of fugacities in both vapour and liquid phases. Vapour—liquid equilibria of multicomponent mixtures are represented with activity coefficients defined in the symmetric convention at infinite pressure reference state using the NRTL model. The method is applied to polar and non polar substances, including supercritical gases.     

Vapor-liquid equilibria calculations by means of an equation of state

An eight parameter equation of state has been applied to correlate vapor liquid equilibria of binary and ternary mixtures, both polar and apolar, representative of various classes of compounds including high molecular weight compounds and quantal gases. The experimental field investigated ranges from subatmospheric to high pressure (up to 400 ata) and from cryogenic to high temperatures. It is shown that three binary interaction parameters are sufficient to correlate each binary system. Rules are given for calculating the eight pure component parameters when volumetric data for some compounds are lacking or inaccurate.     

Theory of gas solubility in mixed solvent systems

A simplified form of perturbation theory for mixtures is applied to the prediction of gas solubility in mixed solvent systems. A method for the determination of Henry's Law constants for gases as a function of solvent composition for any general multicomponent solvent mixture is presented. The theory requires molecular parameters and solvent density to predict the gas solubility. For the accurate prediction of solubility of complex molecules if is necessary to use gas solubility data for the pure solvent; however, solvent mixture activity coefficient data are not required. Comparisons with experimental results indicate that the theory works well for both polar and nonpolar solvent mixtures, provided that the dissolved gas does not chemically combine or associate with the solvents.     

Stofftrennung mit überkritischen Gasen (Gasextraktion)

Mass separation with supercritical gases (gas extraction) . The solvent power of dense gases is considered with ongoing interest for use in technical processes. A great number of gaseous solvents are available, especially if solvent mixtures are included. These solvents can be used in one-stage or multiple-stage processes, running batchwise or continuously in countercurrent process. Design the equipment and simulation of the process requires correlation of the underlying phase equilibria. Remarkable progress has been achieved in this field. In some cases data on mass transfer have also been published. Several companies supply turnkey plants or specialized equipment from laboratory to pilot scale. Commercial plants are used extracting natural products and mineral oil residue processing.     

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.     

Simulation study on biodiesel production by reactive distillation with methanol at high pressure and temperature: Impact on costs and pollutant emissions

Recently, a two-step biodiesel production process which uses short-chain alcohols at supercritical conditions has been proposed. In addition, literature reports suggest that the COSMO-SAC thermodynamic model is a suitable alternative for the prediction of VLE for supercritical methanol/methyl esters mixtures. Thus, in this work a simulation study of the two-step supercritical method for the production of biodiesel is performed by using the COSMO-SAC model. Further, alternative system configurations for biodiesel production based on reactive distillation are proposed and their total emissions are compared to those corresponding to the conventional catalytic method. The study demonstrates the benefits of using reactive distillation for the esterification step and discusses the environmental impact of the supercritical production process. It has been found that the intensified alternatives reduce the emissions considerably and, through the reuse of the excess methanol, the emissions level of the supercritical process can be compared to those of the catalytic method.     

Simple three parameter equations for correlating liquid phase compositions in subcritical and supercritical systems

Two Chrastil type expressions have been developed to model the solubility of supercritical fluids/gases in liquids. The three parameter expressions proposed correlates the solubility as a function of temperature, pressure and density. The equation can also be used to check the self-consistency of the experimental data of liquid phase compositions for supercritical fluid–liquid equilibria. Fifty three different binary systems (carbon-dioxide + liquid) with around 2700 data points encompassing a wide range of compounds like esters, alcohols, carboxylic acids and ionic liquids were successfully modeled for a wide range of temperatures and pressures. Besides the test for self-consistency, based on the data at one temperature, the model can be used to predict the solubility of supercritical fluids in liquids at different temperatures.     

The enthalpy of simple,dense fluid mixtures

Upon using relations suggested by the statistical theory of dense fluids, a method is developed for calculating the enthalpies of simple fluid mixtures at conditions in the neighborhood of the critical. The method is suitable for calculations using an electronic computer and appears to give good results for mixtures of simple nonpolar gases and liquids at low temperatures.     

A group-contribution,continuous-thermodynamics framework for calculation of vapor-liquid equilibria

Continuous thermodynamics is extended to the calculation of vapor-liquid equilibria with UNIFAC. For many mixtures of discrete compounds, the UNIFAC model is an efficient method for calculating vapor-liquid equilibria of systems when experimental data are scarce or non-existent. Such constraints are especially important in continuous mixtures. The continuous distribution is characterized by model compounds chosen to reproduce the TBP analysis. The UNIFAC model is extended to systems including several gases, and the new parameters for several light gases are given. The new algorithm is described in detail. Sample calculations are shown for several semi-continuous systems.     

Phoresis of spherical particles in multicomponent gas mixtures

A theory is developed for the drag, thermophoresis, diffusiophoresis and thermodiffusiophoresis of spherical aerosol particles in multicomponent gas mixtures. The theory is based on a kinetic-theory model in which the particles are treated as giant molecules, and covers the full range of particle Knudsen numbers. It is shown how the theory allows results on multicomponent mixtures to be predicted from results on single gases or binary mixtures.     

Sorption of binary gas mixtures in zeolites: I. Sorption of nitrogen and carbon dioxide mixtures in silicalite

The adsorption of pure CO₂ and N₂ gases, and their mixtures have been determined on a very high silica form of the zeolite ZSM-5 using a newly developed isosteric technique. Unlike more traditional methods, this method allows one to measure mixture isotherms at fixed sorbed phase composition. The shape of the mixture isotherms and the isosteric heats of sorption for the mixture have been identified as functions of the equilibrium gas phase composition, which itself is a temperature dependent function of the sorbed phase composition. None of the isotherms approached saturation at the temperatures and pressures used. The ratio of Henry's constants for the two pure gases gives a reasonable estimate of the separation factor measured experimentally. Selective sorption of CO₂ is marked even at 70°C. Binary mixture sorption isotherms predicted from pure gas data using the ideal adsorbed solution (IAS) theory, are shown to be in close agreement with the experimental data.     

Volumetric properties of pure compounds calculated by means of an equation of state

Some empirical and theoretical modifications of an eight parameter equation of state, previously reported in this journal, are described. The merits of these modifications are discussed by correlating the volumetric behaviour of 13 gases, including 7 apolar and 6 polar compounds, in the whole experimental range. The best results have been obtained by applying an empirical method based on the optimization of all the empirical constants through a most efficient mathematical tool.The experimental data investigated cover pressures ranging from one atmosphere to 10.000 atm and temperatures from 20 to 1070 K. The mean error never exceeds 2%. A method is also described for the correlation of the liquid phase behaviour.