A correlation for the prediction of interaction energy parameters for mixtures of small molecules

Abstract

Low temperature, phase-equilibria data for binary systems containing hydrogen, helium, and neon were used to develop a correlation relating deviations from the geometric mean combining rule for the characteristic energy parameter to the ionization potentials of the component species. With the exception of oxygen systems, this relatively simple relationship correctly predicts published deviations, determined by different methods, for a number of systems within expected uncertainties. It is shown that consideration of attractive forces only, os done by Hudson and McCoubrey, is inadequate for such predictions.The development of a satisfactory method of relating parameters for unlike molecule interactions to those for like molecule interactions has been hampered in the past by the lack of appropriate data of sufficient accuracy to provide tests for fundamental relationships.Recent measurements provide data of this type for a complete set of nine binary systems containing hydrogen, helium, and neon, with three different light hydrocarbons as the second component. These data are particularly valuable below the normal boiling point temperature of the condensable component, where assumptions made to simplify models representing the gas-phase compositions are most nearly satisfied. It was found that for the neon and helium systems, predictions of gas-phase compositions by means of an expression based on the virial equation and commonly used combining rules are in error by as much as an order of magnitude, even though excellent pure component parameters are used. Based on these results and others critically selected from the literature, a correlation has been developed relating the deviation from the geometric mean combining rule klz to the ionization potentials of the pure components in the binary mixture. E X P E R I M E N T A L VALUES OF k l zA convenient way to represent the gas phase for systems such as these is in the form of enhancement factors, that is, the ratio of partial pressures to the vapor pressure of the condensable component. Enhancement factors (for the case of an incompressible, pure, condensed phase of component 1 and an essentially pure gas phase of component 2 ) can be represented isothermally with the following expression based on the virial equation of state:Owing to assumptions made in the derivation of this expression, it is rigorous only in the solid-vapor region. However, it is also applicable between the triple point and normal boiling point temperatures (where isothermal, liquid-phase compressibility is insignificant) for systems in which the solubility of gas in the liquid is no more than a few percent.Values of the interaction second virial coefficient B I Z were obtained for the binary systems of hydrogen, helium, and neon with ethylene, ethane, and methane by a leastsquares fit of the data, below the boiling point of the condensable components, to Equation (1). For most of the data, terms containing virial coefficients higher than the third were not needed to obtain a fit within experiment...

Thermodynamic properties of supercritical fluids and their mixtures at very high pressures

“…Figure 12 shows compressibility factors (2 = PV/ R T ) for a mixture of nitrogen and methane, with k12 = 0.046 (Him and Duncan, 1970); calculated results compare well with experimental data of Blake et al (1965). Figure 13 shows a similar comparison with data of Bennett and Dodge (1952) for mixtures of nitrogen and hydrogen with k12 = 0.0 (Hiza and Duncan, 1970) and Figure 14 with data of Canfield et al (1965;see also Pfenning et al, 1965) for mixtures of nitrogen and helium. Finally, Figure 15 presents caIcuIated and ex.…”

“…Estimates of k12 have been given by Chueh and Prausnitz, 1967 (see also Prausnitz, 1969, p. 157), and by Hiza and Duncan (1970) for a variety of binary mixtures. For our calculations at high pressures these k12 factors had at times to be determined from the experimental results on the mixtures which were being studied.…”

“…Therefore, following Guggenheim, we added to Equation (9) a (negative) correction for nonrandomness based on the quasichemical approximation as described elsewhere (Hildebrand and Scott, 1950). To illustrate, Figure 16 shows hGM/RT for the system xenon-helium at 3257°K and 1000 atm, calculated first without, and then with, the nonrandomness correction; k12 = 0.422 (Hiza and Duncan, 1970). The uncorrected results indicate phase-splitting since a common tangent can be drawn to the dashed line.…”

An improved generalized equation of state

“…Values for kij have been tabulated by Chueb and Prausnitz ( 1968) for many systems of practical interest. The method of Hiza and Duncan (1970) or of Chueh and F'rausnitz (1967) found to be the best among those tested although several other methods were found by Starling et al (1971) Finally it is emphasized that the constants in Table 2 are determined from compounds with acentric factors no larger than 0.35 because vapor phase high density data are nearly nonexistent for substances with a larger O. The constants in Table 2 are quadratic in the acentric factor, and extrapolation of second-order functions is usually unreliable except over narrow ranges.…”

Binary interaction parameter kij for calculating the second cross-virial coefficients of mixtures

“…The optimum k ij values are also listed in Table 1. Hiza and Duncan [9] developed a correlation using the ionization potential (IP) parameter I. However, since the Hiza-Duncan correlation was developed using rather different, limited k ij data sets, their correlation cannot be compared with the k ij values of this work using values of I taken from the CRC handbook [10].…”