John E. Coon

A cubic equation of state with a new alpha function and a new mixing rule

Twu C.H., Bluck D., Cunningham J.R. and Coon J.E., 1991. A cubic equation of state with a new alpha function and a new mixing rule. Fluid Phase Equilibria, 69: 33-50. A new temperature-dependent function (α) for a cubic equation of state is proposed. The new α function used in the cubic equation of state not only correlates the vapor pressures of pure components, but extrapolates correctly to the supercritical region. The new cubic equation of state has been used to accurately describe the vapor pressure and liquid heat capacity for over 1000 chemical components. The accuracy of reproducing the vapor pressure from the triple point to the critical point is generally within the experimental error. A new mixing rule has also been developed for correlating phase equilibrium data. The mixing rule can reproduce the activity coefficients in the infinite dilution region as well as model phase behavior throughout the finite range of concentration. This mixing rule allows the accurate representation of polar/non-polar systems and can be extended to multicomponent systems. The cubic equation of state with the proposed new α function and the new mixing rule is applicable to important systems encountered in industrial practice.

A new generalized alpha function for a cubic equation of state Part 1. Peng-Robinson equation

Abstract A generalized temperature and acentric factor dependent function of the attractive term, called the alpha function, of the Peng-Robinson cubic equation of state (PR CEOS) is developed. The approach in this work allows the alpha function to become a linear function of the acentric factor at a constant reduced temperature, not a fourth or sixth order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the PR CEOS, allows the accurate reproduction of the vapor pressure data from the triple point to the critical point for hydrocarbons. The new CEOS provides much more reliable and accurate vapor pressure predictions for light as well as heavy hydrocarbons than the original PR equation.

A new generalized alpha function for a cubic equation of state Part 2. Redlich-Kwong equation

Abstract The approach described in the previous paper (Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994a. A new generalized alpha function for a cubic equation of state. Part 1. Peng-Robinson equation. Fluid Phase Equilibria, 105: 49–59) is applied to the Redlich-Kwong cubic equation of state (RK CEOS) to develop a new generalized alpha function for this equation. The new generalized alpha function for the RK CEOS reproduces the vapor pressure for hydrocarbons from the triple point to the critical point with almost identical accuracy to the generalized alpha function used for the Peng-Robinson CEOS in the previous paper. This indicates that the approach developed should be a general one, applicable to any cubic equation of state. The alpha function has been generalized in terms of the reduced temperature and acentric factor, so it can be used for any hydrocarbons and petroleum fractions, with no additional characterization to the standard methods required (Twu, 1984). The new alpha function is more appropriate for the RK CEOS than Soaves alpha function, which has been widely used in phase behavior calculations in the petroleum production and refinery industries over the last twenty years.

Solubilities of families of heterocyclic polynuclear aromatics in organic solvents and their mixtures

The solubilities of anthracene, acridine, xanthene, thioxanthene, carbazole, dibenzofuran, and dibenzothiophene have been experimentally determined in benzene, cyclohexane, thiophene, and pyridine from ambient temperature to approximately 440 K. The results have been correlated using the classical equation for solid-liquid solubility to obtain the experimental activity coefficient of the solute in the solvent. These experimental activity coefficients have been regressed, using three common solution models, to find the binary interaction parameters needed in those models. The solubilities of biphenyl, dibenzofuran, and dibenzothiophene have been experimentally determined in five binary mixtures of the solvents. The experimental activity coefficients have been found and compared to the values predicted by the four solution models, using the binary interaction parameters obtained from the solubilities in the pure solvents and solventsolvent binary interaction parameters obtained from literature vaporliquid equilibria data. The effect of substituting various heteroatoms into the ring structure has been discussed.

CEOS/AE mixing rules from infinite pressure to zero pressure and then to no reference pressure

Abstract A CEOS/AE mixing rule with no reference pressure is presented. An approach is developed that shows that the excess Helmholtz free energy at any pressure relative to its value for a van der Waals fluid is equivalent to the same relative value of the excess Gibbs energy at the same pressure. This approach allows the mixing rule to incorporate a GE model at any pressure and temperature without requiring any additional binary interaction parameters or causing any thermodynamic inconsistency. The methodology of developing the no-reference-pressure mixing rule avoids the common assumption of constant excess Helmholtz free energy with respect to pressure that is often made for the infinite pressure approach and extends the range of solution of the liquid volume to the critical point for the zero-pressure approach. The mixing rule is density (temperature) dependent in an explicit form. Because of this density function, the mixing rule reproduces accurately the incorporated GE model.

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.

A generalized vapor pressure equation for heavy hydrocarbons

Abstract Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994. A generalized vapor pressure equation for heavy hydrocarbons. Fluid Phase Equilibria, 96: 19-31. Pitzers acentric factor is widely used in physical property estimations; one important area is that of generalized vapor pressure correlations. Since Pitzers acentric factor is defined in terms of the vapor pressure at a reduced temperature equal to 0.7, using this approach to generalize a vapor pressure equation gives excellent accuracy at reduced temperatures between 0.7 and 1.0, but predicts vapor pressures less accurately at lower reduced temperatures. To improve the vapor pressure prediction of hydrocarbons at low reduced temperatures, the definition of the acentric factor is re-examined and a modified acentric factor is proposed. Two sets of generalized vapor pressure equations are presented, with Pitzers acentric factor and the modified acentric factor, respectively, as the third corresponding states parameter. These two equations are applied from the triple point to the critical point. Both correlations give more accurate vapor pressure predictions than the Lee-Kesler (1975) 2 correlation, especially at low reduced temperatures, with the correlation using the modified acentric factor as the third parameter being the most accurate. Additionally, an internally consistent approach is proposed for estimating the normal boiling point, critical temperature and critical pressure of petroleum fractions using a single low temperature vapor pressure data point. The procedure proposed uses either correlation from this work and gives an accurate estimation of the normal boiling point and acentric factor for heavy petroleum fractions for use in equations of state.

An equation of state for carboxylic acids

Abstract A cubic equation of state (CEOS) has been extended to treat systems containing carboxylic acids by taking into account association. The incorporation of chemical theory for carboxylic acids into the cubic equation of state is based on the simple and elegant approach for pure components by Heidemann and Prausnitz (1976). Using the approach of Heidemann and Prausnitz, a monomer-dimer chemical equilibrium model is built into the cubic equation of state to take care of association of carboxylic acid molecules. A closed-form equation of state, which is in terms of monomer parameters and the chemical equilibrium constant, is derived. The determination of the pure monomer parameters of an associating component is a crucial step in the application of an equation of state for associated systems. An internally consistent method is proposed to determine the pure monomer parameters for the associated component. The method reproduces the critical point and the saturated vapor pressure of the associated component accurately.

A comparison of solid—liquid equilibrium with vapor—liquid equilibrium for prediction of activity coefficients in systems containing polynuclear aromatics

Abstract This study compares activity coefficients from conventional vapor—liquid equilibria (VLE) experiments with those from solid—liquid solubilities for a number of systems consisting of polynuclear aromatic compounds. The solubility studies involved 12 polynuclear aromatic hydrocarbons which have been studied from ambient temperature to near the melting point of the solutes with tetralin and decalin (an isomeric mixture of cis - and trans -decalin) as solvents. Solubilities of seven of the solutes in a 50%-50% mixture of tetralin and decalin, typical hydrogen donor solvents, have also been measured. The results have been correlated using the classical equation for solid—liquid solubility to obtain the experimental activity coefficients of the solutes in the solvents or solvent mixtures and the binary interaction parameters necessary for three well-known solution models. These parameters have been used to predict the solubilities of the solutes in the three-component systems. The VLE data were measured for four of the binary systems covered in the solubility studies. These data were analyzed to obtain the experimental activity coefficients, which were compared with those obtained from the solubility studies. The results of the two methods are discussed, particularly the uncertainties associated with the binary parameters obtained from each kind of data. Conclusions concerning the two methods are given, together with some ideas for future work.

An equation of state for hydrogen fluoride

Abstract 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.