Generalized Correlations for the Fugacity Coefficient

Generalized Correlations for the Fugacity Coefficient
The generalized correlation approach which has been presented earlier for calculation compressibility factor Z (section 2.3), and the residual enthalpy and entropy of gases (section 5.7), can also be applied for computing fugacity coefficients for pure gases and gaseous mixtures. Equation (6.90) can be rewritten in a generalized form as follows:

Hence, an alternately,        (at const. Tr)  (6.109)
Substitution for 
The last equation may be written in alternative form:
Where,   (6.113)
For obtaining the values of the integrals in the last two equations, the tabulated data for  for various values of Tr and Pr may be used for numerical or graphical computations. Yet another approach is due to Lee-Kesler which employs a variant of the BWR-EOS (eqn. 2.17) to evaluate the expressions for  for a wide range of values of Tr and Pr and are available in the form of extended tables. In either case the fugacity coefficient is finally computed using eqn. 6.112. (See figs 6.6 and 6.7).
The above set of equations may well be used for estimating the overall fugacity coefficient of a gaseous mixture. As in earlier instance (sections, 2.3 and 5.7) one makes use of pseudo-critical properties that are estimated from the following set of linear relations: 
The subscript ‘i’ runs over all the species present in the mixture ‘m’. The above relations allow the mixture to be treated as single substance; the methodology outlined above for pure species may then be used to compute the fugacity coefficient of the mixture.