An equation for predicting third virial coefficients of nonpolar gases

Abstract

An empirical correlation for calculating third virial coefficients of nonpolar gases is developed in agreement with the corresponding states theorem. This equation requires the use of a third parameter which can be estimated from molecular parameters. The method is reliable, even for systems where no experimental data are available. The extension to mixtures involves one interaction constant for all possible binary sets. SCOPEVolumetric and thermodynamic properties of gases and vapors can be conveniently estimated by the virial equation of state. The virial equation is normally used up to moderate pressures, since only data of second virial coefficients are plentiful in the literature. Indeed, several analytical methods have been developed for calculating second virial coefficients (Tsonopoulos, 1974; Hayden and OConnell, 1975;Tarakad and Danner, 1977). However, the advantages of the virial equation could be increased if quantitative information were available on the third virial coefficient.Calculations of the third virial coefficients with intermolecular potential functions cannot be carried out with sufficient accuracy because of the present uncertainties on the real potential functions and on their nonpairwise additivity corrections. Empirical correlations are more useful. The only one available is that of Chueh and Prausnitz (1967) which, however, does not allow calculations in the absence of data.This work provides a predictive method based on the available data and on recent advances in the theoretical estimates of the third virial coefficient. CONCLUSIONS AND SIGNIFICANCEA successful correlation for predicting the third virial coefficients of pure and mixed nonpolar gases in temperature ranges of practical interest has been developed. The equation is in agreement with the corresponding states theorem and requires a knowledge of the critical volume and temperature, acentric factor, dipole polarizability, and molecular volume of the compounds involved. A binary interaction constant is also required to extend the method to mixtures. The correlation is a reliable predictive method of the third virial coefficients as shown by comparisons with experimental data.The main significance of this work concerns the possibility of extending the virial equation up to about threefourths of the critical density to calculate fugacity coefficients. These are required to interpret multicomponent vapor-liquid and gas-liquid equilibria at high pressures. where B, the second virial coefficient, is related to the potential energy between two molecules; C, the third virial coefficient, is related to the interaction energy among three molecules, etc. The theoretical calculations of C for various gases are hindered by the uncertainties about the real form of binary intermolecular potentials and about the nonpairwise additivity contributions. Simple POtential functions with two or three parameters do not allow accurate calculations, even if several three-body contributions are taken into account (De Santis and Grande, 1979).

Correlation for the third virial coefficient usingTc,Pcand ω as parameters

“…The pressure explicit virial equation of state, truncated after the second virial coefficient, is a useful expression for the calculation of thermodynamic properties of gases a t conditions such that the reduced volume is greater than 2. According to recent studies (De Santis and Grande, 1979), the addition of the third virial coefficient extends the applicability of the virial equation to conditions of temperature and pressure for which the reduced volume is greater than 1.3.…”

“…Correlations for the third virial coefficient presented in the literature (Chueh and Prausnitz, 1967a;Pope et al, 1973;De Santis and Grande, 1979), have used the critical volume as a parameter. This fact makes the use of the truncated virial equation awkward.…”

Precision Methods for the Determination of the Solubility of Gases in Liquids

“…Extended CST correlations for C have been presented by Chueh and Prausnitz, 147 Pope et al' 48 (this method is limited, however, to substances with small isi), De Santis and Grande, 149 and most recently by Orbey and Vera. 150 For pure substances the empirical equation suggested by De Santis and Grande is of the form:…”

Improvement of hydrogen solubility and entrainment in hydrocracker feedstocks. Final technical report

“…where Chuech and F'rausnitz [20] In the following description of the themodynanlic background for hydrogen solubility calculations, we focus on expression for the liquid phase fugacity. The detailed procedures will be discussed in following section.…”