Vapor-liquid Equilibrium Calculations Research Articles

Comparison of two predictive gE models for vapour—liquid equilibrium calculations

Ash (S.N. Ash, P. Ray and B.V. Detta, AIChE J., 31 (1985) 821; S.N. Ash, Chem. Eng. J., 48 (1992) 183) has proposed a correlation for calculating the binary parameters of the Wilson g E model by using only pure-component parameters: solubility parameters, molar liquid volumes, relative van der Waals volumes and surfaces, critical properties, acentric factors and dipole moments. To evaluate the Ash correlation the vapour—liquid equilibria for 75 binary systems, activity coefficients at ininite dilution and excess enthalpies were predicted and compared with experimental data and with the modified UNIFAC model (J. Gmehling, J. Li and M. Schiller, Ind. Eng. Chem. Res., 32 (1993) 178). It was found that the correlation of Ash and coworkers is significantly inferior to the modified UNIFAC model and cannot be recommended for phase equilibrium predictions for those cases where UNIFAC parameters are available.

Vapor-liquid equilibrium calculation of the system water-nitric acid over the entire concentration range

The vapor-liquid equilibrium of the system water-nitric acid has been described. The activity coefficients in the liquid phase are evaluated according to a new model. This model combines the effect of the long range forces expressed by a Debye-Hückel contribution on a mole fraction basis, with the effect of short range forces expressed by a virial expansion of the NRTL equation. The proposed model can be used to describe the vapor-liquid equilibrium of the system water-nitric acid from 20 to 120 °C over the entire concentration range.

An extended corresponding-states model for predicting thermodynamic properties of N2-Ar-O2 mixtures including vapor-liquid equilibrium

A formulation developed previously for the prediction of the thermodynamic properties of single-phase states of binary and ternary mixtures in the nitrogen-argon-oxygen system has been revised to include the calculation of vapor-liquid equilibrium (VLE) properties. The model is based on the theory of extended corresponding states with van der Waals mixing rules. Binary interaction parameters have been determined with single-phaseP-p-T and vaporliquid equilibrium data to improve the accuracy of thermodynamic property predictions. The model accurately represents single-phase and vapor-liquid equilibrium properties over a wide range of compositions for binary and ternary mixtures. Comparisons of calculated properties to selected mixture data for both single-phase and VLE states are included.

Calculation of vapor-liquid equilibria of polymer solutions using the SAFT equation of state

Abstract Vapor-liquid equilibrium calculations are presented in this study by applying the SAFT equation of state. New pure component parameters of the SAFT equation of some polymer and solvent molecules are reported. Phase equilibrium computations on binary mixtures are investigated by employing the mixing rules of the SAFT equation with optimal binary interaction parameters. The binary parameters of the SAFT equation are correlable in a simple form for some polymer solutions. Calculation results of this work are satisfactory, and are superior to those from other calculation methods.

Equations of state for chainlike polar fluids: a comparison of reference terms

Abstract In order to describe the behaviour of fluids, the generalized van der Waals theory has been utilized as a starting point to combine different repulsive and attractive terms. An example is the work of Tavares and Rajagopal (1992) who proposed an equation of state based on the lattice gas model. Using the attractive term of this equation the performance of several expressions for the repulsive term in the generation of equations of state is compared in this work. Such a comparison is based on the calculation of vapour-liquid equilibria of pure fluids. The following reference terms were considered: the hard-sphere model of Carnahan and Starling (1969); the chain of rotators proposed by Chien et al. (1986); the hard convex body model suggested by Boublik (1975); the Guggenheim-Staverman approach (Staverman, 1950) as used by Tavares and Rajagopal (1992). The selected equation of state which uses the Guggenheim-Staverman approach as reference term, is compared to the SPHCT model, to the Soave cubic equation, and to a modification of this equation proposed by Aznar and Telles (1992) in the correlation of the behaviour of several fluids, ranging from simple apolar molecules to chainlike polar substances; this proved to be the best option for describing the vapour-liquid equilibria.

An equation of state mixing rule for correlating ternary liquid-liquid equilibria

Abstract A new mixing model for cubic equations of states that is theoretically correct in the composition dependence of the second and third virial coefficients is derived. This new mixing rule has been tested in conventional vapor-liquid equilibria calculations. It was found to be as good as activity coefficient models and other equation of state mixing rules for solutions of various kinds of nonideality. It can also be extrapolated over large temperature and pressure ranges. Its salient feature is an extra degree of freedom that accounts for ternary interaction, which enables it to give consistent correlation of vapor-liquid and liquid-liquid equilibria of ternary systems and the corresponding binaries.

Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules

Li, M.-H. and Huang, F.-N., 1994. Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules. Fluid Phase Equilibria, 96: 155-172. Based on generalized van der Waals partition function theory and approximations of radial distribution functions, mixing rules for the attractive part of an equation of state have been presented for extension of an augmented hard-core equation of state to mixtures. Two approximations, the van der Waals one-fluid approximation and the mean density approximation, are applied in this study. Within the framework of the conformal solution theory, the properties of a hypothetical fluid were calculated from the attractive part of an augmented hard-core equation of state. As a preliminary test of the method, an augmented hard-sphere equation of state has been applied. For polar systems in which components do not differ appreciably in size, both the MDA and the VDW models yield satisfactory results for the vapor-liquid equilibrium calculations. However, for strongly non-ideal fluid systems, the MDA is superior to the VDW. Adopting the mixing rules for the repulsive hard-core mixtures to describe structure effects, the proposed method can, in principle, be used to extend any accurate augmented hard-core equation of state to mixtures.

Generalization of a polar-fluid Soave-Redlich-Kwong equation of state

Valderrama, J.O., de la Puente, H. and Ibrahim, A.A., 1994. Generalization of a polar-fluid Soave-Redlich-Kwong equation of state. Fluid Phase Equilibria 93: 377-383. The empirical parameters of a modified Soave expression for α( T R) have been correlated in terms of readily available pure component parameters. Both parameters have been expressed in terms of the group (ω Z C) as correlating parameter. The correlations are recommended for the calculation of pure fluid properties and vapor-liquid equilibrium in mixtures containing polar and non-polar fluids.

Vapor-liquid equilibrium calculations of azeotropic mixtures using the Peng-Robinson equation of state and various mixing rules.

Vapor-Liquid Equilibrium (VLE) calculations have been made on binary and ternary azeotropic mixtures using the Peng-Robinson equation of state (EOS). Various mixing rules of the van der Waals one-fluid model, the local composition model and the group-contribution model for the VLE computations were discussed. In the group-contribution model, we applied the Huron-Vidal method and determined the EOS parameters for mixtures from the UNIFAC activity coefficient model. This study compares the phase equilibrium calculations and investigates the prediction of azeotropic properties. It was shown that the group-contribution mixing model yielded satisfactory results, and provided a superior calculation method to other mixing rules or correlation equations.

Application of LM modification of a cubic equation of state for vapor-liquid equilibrium calculations of binary mixtures

The Lielmezs-Merriman (LM) modification of the Peng-Robinson (PR) equation of state has been expanded to vapor-liquid equilibrium predictions of binary mixtures. The predicted bubble point pressures and vapor mole fractions have been compared with the results calculated by the Redlich-Kwong-Soave (RKS), Peng-Robinson (PR) equations and F-function modifications of RKS (FRKS, F-RKS) and PR (FPR, F-PR) equations.

Vapor-liquid equilibrium calculation of the system water-hydrogen chloride

Brandani, S., Brandani, V. and Di Giacomo, G., 1994. Vapor-liquid equilibrium calculation of the system water-hydrogen chloride. Fluid Phase Equilibria, 92: 67-74. The vapor-liquid equilibrium of the system water-hydrogen chloride has been described. The activity coefficients in the liquid phase are evaluated by an extended Pitzer model, where the reference state for hydrogen chloride is defined according to Henry's law. The results have been compared with those obtained using a modified Engels and Bosen model.

Use of the binary interaction parameter Lij( T,P,xi) function for van der Waals-type equations of state in vapor-liquid equilibrium calculations

The predictive accuracy of the newly developed binary interaction parameter function L ij = L ij ( T,P,x i ) of Lielmezs and co-workers has been studied further by means of the Redlich-Kwong-Soave (RKS) and Peng-Robinson (PR) equations of state in the vapor-liquid equilibria calculations over a wide range of P-T-x-y values. Sets of coefficients for use in the binary interaction parameter function L ij = L ij ( T,P,x i ) have been established for 29 selected binary systems. The results calculated of the vapor-liquid equilibria (bubble point) for the binary systems considered (L-RKS, L-PR) are in excellent agreement with the experimental data and the values obtained using the F-function of two-parameter cubic equations of state (F-RKS, F-PR). The predictions made in this work (L-RKS, L-PR) have a slight edge over the results calculated via the original Redlich-Kwong-Soave (RKS) and Peng-Robinson (PR) methods.

A simple generalization of the binary temperature-dependent interaction parameters in the Soave-Redlich-Kwong and Peng-Robinson equations of state for helium-mixtures

Binary temperature-dependent interaction parameters of the Soave-Redlich-Kwong and Peng-Robinson equations of state are determined for mixtures containing helium. The interaction parameters in all helium-mixtures can be calculated by a simple generalized correlation, which is only a function of temperature, critical volume and molecular weight. Vapor-liquid equilibrium calculations using the new correlation are in excellent agreement with experimental data of binary, ternary and multicomponent systems.

An equation of state for hydrogen fluoride

Twu, C.H., Coon, J.E. and Cunningham, J.R., 1993. An equation of state for hydrogen fluoride. Fluid Phase Equilibria 86: 47-62 Twu et al. (1992) [Twu, C.H., Coon, J.E. and Cunningham, J.R., 1992. An equation of state for carboxylic acids. Sixth International Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, July 19–24, 1992 in Italy. Fluid Phase Equilibria, 82: 379-388] applied a generic cubic equation of state to carboxylic acids by taking association into account. The incorporation of chemical theory for carboxylic acids into the cubic equation of state was based on a monomer-dimer chemical equilibrium model. Hydrogen fluoride strongly associates by hydrogen bonding and strong evidence indicates that the vapor exists primarily as monomer and hexamer (Long et al., 1943 [Long, R.W., Hilderbrand, J.H. and Morrell, W.E., 1943. The polymerization of gaseous hydrogen and deuterium fluorides. J. Am. Chem. Soc., 65:182-187.]). Using the same approach as Twu et al. (1992), a monomer-hexamer chemical equilibrium model is built into a cubic equation of state to account for association of hydrogen fluoride. A closed-form equation of state is derived, which is written in terms of monomer parameters and the monomer-hexamer chemical equilibrium constant. This paper provides a new method for calculating the properties of HF. The calculated fugacity coefficient, vapor compressibility factor, heat of vaporization, and enthalpy departure of hydrogen fluoride exhibit significant deviations from ideal behavior. Failure to take this chemical association into account can lead to serious errors in vapor-liquid and liquid-liquid phase equilibrium and energy balance calculations.

Vapor-liquid equilibria from an improved hard convex body expansion method

Abstract Chen, Y.-C. and Chen, Y.-P., 1993. Vapor-liquid equilibria from an improved hard convex body expansion method. Part II. Non-polar mixtures. Fluid Phase Equilibria , 86: 87-109 This study presents an improved vapor-liquid equilibrium calculation method for non-polar mixtures by employing the hard convex body expansion (HCBE) theory. The repulsive contribution to thermodynamic properties is determined at a given density, where the pseudo-volume parameter is calculated by a modified one-fluid theory. A generalized corresponding states equation with two reference fluids is used to calculate the attractive contribution. A combined model applying the van der Waals one-fluid (VDW-1) and the mean density approximation (MDA) theories has been used to determine the pseudo-energy parameter for the attractive property calculations. This work is an extension of our previous studies on non-polar pure fluids in which we have correlated the geometrical acentric factors. The calculation results are very satisfactory and are better than those obtained by applying only the VDW-1 or MDA method for the attractive property computations. Henry's constants of light hydrocarbons in heavy alkanes can also be predicted successfully by the method of this work.

A systematic approach for the efficient estimation of interaction parameters in equations of state using binary vle data

AbstractA systematic and computationally efficient approach for the estimation of the interaction parameters in equations of state using binary vapor liquid equilibrium (VLE) data is presented. Initially, the best set of interaction parameters is estimated by implicit least squares. Subsequently, the VLE calculations are performed using these parameters. Based on the quality of the fit it is decided whether these estimates suffice or implicit maximum likelihood estimation should be performed to obtain the statistically best values. Estimation subject to the liquid phase stability constraint is performed when erroneous phase behavior is computed. The approach is illustrated with typical examples.

Vapor—liquid equilibria calculations with a cubic equation of state: group contributions for heavy hydrocarbons containing mixtures

Given the high number of components in the petroleum fluids, the models of thermodynamic properties based on a group contribution method are attractive. Among them, a recent model developed by Abdoul and Peneloux, based on the concept of group contribution and on the definition of the excess Helmholtz energy at constant packing fraction, deviates very slightly from the classical mixing rules, but is predictive. This method is studied here and extended to polycyclic and ramified heavy hydrocarbons by defining new groups and evaluating their interaction parameters with methane.

The use of the F-function of the two-parameter cubic equation of state in vapour—liquid equilibrium calculations of binary mixtures

The recently developed F-function of Shaw and Lielmezs, Mak and Lielmezs, and Liu, Lim and Lielmezs, modified to fit the van der Waals type cubic equations of state, has been used to assess the vapour—liquid equilibria calculations of binary mixtures over a wide range of P– T– x– y values. Sets of coefficients for use in the binary interaction parameter function L ij = L ij ( T, P, x i ) were determined for 23 representative binary mixtures. The prediction (this work) of the vapour—liquid equilibria (bubble point calculations) of the binary systems considered are in excellent agreement with the experimental data, and show slight improvement over the values obtained by means of the original Redlich—Kwong—Soave (RKS) and Peng—Robinson (PR) equations.

Modeling phase equilibria using an equation of state incorporating association

Abstract A previosly proposed equation of state incorporating association in an explicit form (AEOS = Association + Equation of State) is applied to the calculation of vapor-liquid and liquid-liquid equilibria in mixtures containing water or alcohols and hydrocarbons. The AEOS model consists of two terms: a chemical one based on an association model and a physical one which is equivalent to an equation of state for nonassociating fluids. Attention is focused on the evaluation of pure component parameters which are crucial for mixture calculations. It is shown that the parameters should not only accurately reproduce pure component properties but also ensure the correct magnitude of the chemical and physical terms. A new algorithm is proposed to simplify the evaluation of pure component parameters. The AEOS equation, coupled with the new algorithm, is convenient for routine engineering calculations. It is capable of very accurately representing vapor-liquid and liquid-liquid equilibria over large temperature ranges. Only one binary parameter is needed. Moreover, the accuracy of predicting ternary equilibria using only binary parameters is very similar to the accuracy of correlating binary data.

A new cubic equation of state

Abstract Two-parameter cubic equations of state are analyzed and a new three-parameter cubic equation of state is proposed with the critical compressibility factor taken as substance dependent. An apparent critical compressibility factor is determined by optimizing the calculation of saturated liquid densities while the equality of fugacities along the saturation curve is imposed. The new cubic equation of state, combined with a previously proposed α function and mixing rule, proves to be a powerful equation for predicting properties of pure components and mixtures. The new equation not only improves volumetric property calculations relative to earlier efforts, but also achieves high degree of accuracy in the calculation of vapor-liquid equilibria for highly nonideal systems such as polar/nonpolar mixtures. Alcohol/hydrocarbon mixtures are used as an extreme test of the new equation of state.