The Truncated Virial equation of state may be used to calculate vapor fugacity coefficients for the Liquid Activity Methods. The original Virial method has a sound theoretical background and is free of simplifying assumptions. The compressibility factor is expressed as a power series in the reciprocal volume:
z = Pv / RT = 1 + B / v + C / v2 + D / v3 + ...
where: v = molar volume
B,C,D,... = second, third, fourth, etc, virial coefficients
The virial coefficients are a function of temperature and composition only. For low or moderate vapor densities, the virial equation may be truncated after the second coefficient and converted to the following form:
z = 1 + BP / RT
The compositional dependence of B for a mixture may be calculated by using a combinatorial rule to combine the individual component virial coefficients. Note also that the truncation of the higher virial coefficients limits this method to systems at low pressures.
See "Truncated Virial Equation of State" under "Vapor Fugacities" in Chapter 2, Volume 1 of the PRO/II Reference Manual.