A modified clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria

Gow, A.S., 1993. A modified Clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria. Fluid Phase Equilibria, 90: 219-249.

A modified Clausius equation of state with a single temperature dependent energy-volume parameter a(T) in the attractive term was designed to describe the vapor pressure vs. temperature relationship of 39 pure refrigerant fluids including elementary cryogenic materials (e.g. He, Ar, N₂, CO₂, CH₄, etc.), chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), hydrochlorofluorocarbons (HCFCs), fluorocarbons (FCs), and various other simple cryogenic compounds. The equation developed represents the vapor-liquid coexistence dome, and the superheated vapor compressibility factor and enthalpy for pure refrigerants.

The vapor-liquid equilibrium for refrigerant mixtures is calculated using a “phi-phi” method with “one fluid” van der Waals mixing and combining rules for the equation of state parameters a_M(T), b_M and c_M. A single interaction constant k₁₂ is used to describe non-ideal behavior of each binary. The binary interaction constant, which is a strong function of temperature, and the sign of which signifies the type of deviations from Raoult's law, is obtained by correlating experimental bubble point data for isothermal binary refrigerant mixtures. The proposed equation of state generally describes binary P-x,y data more accurately the higher the temperature for a given system. The method presented is extended to predict vapor-liquid equilibria for the R14-R23-R13 ternary system at 198.75 K using binary interaction constants at this temperature for the three binaries involved.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.     

A simple modification of the Flory—Huggins theory for polymers in non-polar or slightly polar solvents

Starting from the concept of free volume dissimilarity, a simple modification of the non-combinatorial part of the Flory—Huggins equation is proposed. According to this modification, a new relation is derived to calculate the activity of a solvent in mixture with a polymer. It contains two empirical parameters, whose values can be determined by regressing binary vapour—liquid experimental data. The proposed equation has been applied to several binary systems which can be grouped in three classes of mixtures: non-polar/non-polar, non-polar/polar and polar/polar. Satisfactory results have been obtained in the case of non-polar or slightly polar mixtures, however, for strongly polar systems, the new equation is inadequate. The proposed modification of the Flory—Huggins theory is particularly suitable for engineering calculations.     

Thermodynamic calculation of supercritical-fluid equilibria: New mixing rules for equations of state

Simple cubic equations of state with conventional mixing rules have played an important role in the calculation of phase equilibria and other thermodynamic properties of non-polar fluid mixtures. In the application of supercritical fluids to separation processes, volumetric as well as phase equilibrium properties are very important for rational process design.

Heyen (1980) proposed a cubic equation of state which shows better accuracy in the calculation of volumetric properties, compared to the Peng-Robinson equation of state. In order to apply his equation to polar mixtures, Heyen recently proposed a density-independent mixing rule, but this does not obey the universally-observed quadratic mixing rule of the second virial coefficient in the low-density limit.

This paper proposes a new density-dependent mixing rule for the Heyen equation of state. The Heyen equation of state with our new mixing rule appears to calculate the phase equilibria and the volumetric properties of CO₂-containing non-polar as well as polar mixtures with good accuracy.     

Comparison of two hard-sphere reference systems for perturbation theories for mixtures

The Carnahan—Starling equation of state for hard spheres can be extended to mixtures using either a one-fluid theory, or the generalization of scaled-particle (or Percus—Yevick theory) proposed by Boublik and by Mansoori and coworkers. The two reference systems are combined with a perturbation term of the van der Waals form; they are then used to correlate the phase behavior of binary mixtures of nonpolar molecules differing significantly in molecular size. In each case, one adjustable binary parameter (a₁₂) is used to correlate vapor—liquid equilibria over the entire composition range. Predicted Henry's constants and liquid densities for the saturated mixture are compared with experiment. The Boublik—Mansoori hard-sphere-mixture equation is superior to the Carnahan—Starling One-Fluid theory, expecially in the dilute region.     

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

Prediction of latent heat of vaporization of multicomponent mixtures

A very simple method has been developed for predicting the differential latent heat of vaporization involved in vapor-liquid equilibria of multicomponent mixtures. The technique uses the UNIFAC method for predicting activity coefficients.In order to establish this method, 88 binary systems and 13 ternary systems, both nonazeotropic and azeotropic, were tested successfully. On the basis of the 101 systems investigated, the mean overall deviation between the observed and predicted values was found to be 4.6%. Despite the fact that the majority of the systems tested were azeotropic, a consequence of the small amount of data available for the differential heats of nonazeotropic systems, the method proposed is equally applicable to nonazeotropic systems.For azeotropic mixtures, it is possible to predict the latent heat (integral or differential) by means of an analytical equation which involves only the parameters of Antoine's equation, with a mean overall deviation of 6.1%.From the differential heats obtained by the proposed method, it is possible to calculate integral heats by applying equations derived here which relate these quantities.     

Association model of fluids. Phase equilibria in sulphur dioxide mixtures

The vapor-liquid and liquid-liquid equilibria of binary mixtures formed by sulphur dioxide with organic components are reproduced well using a new associated-solution model whose association and solvation constants are defined in terms of the modified segment fractions of chemical species. The model shows a good performance in predicting ternary vapor-liquid and liquid-liquid equilibria of sulphur dioxide mixtures from only binary parameters.     

Equations of state for strongly nonideal fluid mixtures: Application of local compositions toward density-dependent mixing rules

A local-composition, two-fluid model has been developed for equation-of-state calculations of fluid-phase equilibria for asymmetric mixtures; it is applicable to any equation of state of the van der Waals form. A modification of the quasichemical theory of Guggenheim is applied to mixtures at all fluid densities. Desirable boundary conditions are met at low densities, at high densities, and at high temperatures.In effect, the local-composition model uses density-dependent mixing rules. It contains no new adjustable binary parameters and can be extended to multicomponent mixtures without ternary (or higher) parameters. It appears that, when compared to conventional one-fluid models, significant improvement may be obtained in predictions for vapor-liquid equilibria of typical asymmetric mixtures.     

Liquid—liquid coexistence curves for binary systems

The liquid—liquid coexistence curves of polar+non-polar binary systems have been determined experimentally. The polar compounds studied were ethanenitrile, methanol and N-methylpyrrolidone, whereas the non-polar compounds were chosen from the n-alkane series. The upper critical solution temperature for each set of mixtures increases with increasing n-alkane chain length, and the critical composition of the polar component also increases in this fashion.     

An effective modification of the Benedict–Webb–Rubin equation of state

A modification of the BWR equation of state is proposed, which is a simplified form of a previously proposed one. It applies to systems formed by hydrocarbons and related compounds, with particular attention to the critical conditions. The range of treatable compounds was extended to a value 0.9 of the acentric factor, corresponding to C₂₀ hydrocarbons. The critical compressibility factor Z_c was made independent of the acentric factor, for a more accurate prediction of pure-component properties (the previous equation did not give the same improvement). Mixing rules require one binary interaction constant for each component pair. Zero binary constants can be used for methane–alkane and alkane–alkane pairs. Examples of applications to pure hydrocarbons and their mixtures are given.     

Binary phase behavior and aggregation of dilute methanol in supercritical carbon dioxide: a Monte Carlo simulation study

Configurational-bias Monte Carlo simulations in the Gibbs and isobaric-isothermal ensembles using the transferable potentials for phase equilibria force field were carried out to investigate the thermophysical properties of mixtures containing supercritical carbon dioxide and methanol. The binary vapor-liquid coexistence curves were calculated at 333.15 and 353.15 K and are in excellent agreement with experimental measurements. The self-association of methanol in supercritical carbon dioxide was investigated over a range of temperatures and pressures near the mixture critical point. The temperature dependence of the equilibrium constants for the formation of hydrogen-bonded aggregates (from dimer to heptamer) allowed for the determination of the enthalpy of hydrogen bonding, DeltaHHB, in supercritical carbon dioxide with values for DeltaHHB of about 15 kJ mol(-1) falling within the range of previously proposed values. No strong pressure dependence was observed for the formation of aggregates. Apparently the decrease of the entropic penalty and of the enthalpic benefit upon increasing pressure or solvent density mostly cancel each other's effect on aggregate formation.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Molecular thermodynamics on the basis of an equation of state for argon. II. Binary mixtures of weakly nonspherical molecules

Using a molecular perturbation theory based on an equation of state for pure argon, excess properties and vapor-liquid equilibria are predicted for various binary mixtures composed of weakly nonspherical molecules. The results are rather satisfactory and generally much better than obtained using typical empirical methods. It is further demonstrated that a binary parameter in the dispersion energy results in only modest improvement     

Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method

Vetere, A., 1986. Vapor-liquid equilibria with supercritical gases calculated by the excess Gibbs energy method. Fluid Phase Equilibria, 28: 265–281.A thermodynamic method for vapor-liquid equilibria calculations of mixtures containing supercritical components is described. According to the proposed method the Raoult law is assumed as a reference point also for the supercritical gases, and the non-ideality of the liquid phase is represented by using the NRTL equation in the one parameter form.The vapor phase is described by applying the Redlich-Kwong equation. Literature data of 10 binary systems formed by N₂, CH₄, CO₂, H₂S and CH₃OH are correlated by applying the new procedure. The binary interaction parameters calculated for these systems are used for the prevision of one ternary and two quaternary systems formed by the cited gas in methanol, which is an industrial solvent used for the purification of natural streams from the sour gases.Rules are given to describe the dependence on temperature of the binary interaction parameters.     

Prediction of ternary phase equilibria from binary data

The two-parameter UNIQUAC equation is modified to give better results of vapor—liquid and liquid—liquid equilibria for a variety of binary systems. The proposed equation is easily extended to a multicomponent system without including any ternary (or multicomponent) parameters. The good capability of the equation in data reduction is shown by many illustrative examples for various kinds of strongly nonideal binary and ternary mixtures.     

Gas solubility calculations. II. Application of a new group-contribution equation of state

A new equation of state has been developed for polar as well as nonpolar components. It is based on the generalized van der Waals partition function and uses local-composition mixing rules. The group-contribution version of this equation of state (the GC-EOS) is described and tables containing parameters for 14 solvent groups and 9 gases (H₂, N₂, CO, O₂, CH₄, C₂H₄, CO₂, C₂H₆ and H₂S) are presented.The GC-EOS predicts vapor-liquid equilibria well for all kinds of systems involving the groups considered. The method requires only information concerning readily accessible pure-component properties. Calculations for multicomponent systems show that the method suggested provides very good predictions of multicomponent high-pressure vapor-liquid equilibria and fairly good predictions of Henry's constants in mixed solvents.     

Extension of polar GC-SAFT to systems containing some oxygenated compounds: Application to ethers, aldehydes and ketones

The GC-SAFT equation of state proposed by Tamouza et al. (2004) [51], extended to polar molecular fluids NguyenHuynh et al. (2008) [32], is here applied to model vapor-liquid phase equilibria of various binary mixtures containing at least one oxygenated compound belonging to ethers, ketones or aldehydes chemical families.These systems are modeled using a polar version of the three different versions of SAFT-EOS (original, VR-SAFT and PC-SAFT) in a predictive manner: binary interaction parameters k_ij and l_ij are all set to zero.In the case of alcohol + ether, +ketone, +aldehyde systems, a cross-association interaction between an oxygenated compound (non self-associating compound) and an alcohol is necessary to model/predict accurately the mixture VLE. The corresponding association parameters are assumed to be equal to the self-association parameters of pure 1-alkanols.The above-cited systems have been treated in a comprehensive manner. The general agreement between polar GC-SAFT and experimental data is good (within 4-5% deviation on pressure), similar to the one obtained on previously investigated systems using GC-SAFT.