About Liquid Activity Coefficients

Liquid activity coefficient methods for phase equilibrium calculations are fundamentally different from the equation-of-state (EOS) methods. Whereas the EOS methods are based on liquid and vapor fugacity coefficients referenced to the ideal gas state, the liquid activity methods use the pure liquid at the mixture temperature and pressure as the reference state for each component in the liquid phase.

The fugacity of each component in the liquid phase is written:

 fLi = gi xi foLi

where: foLi = standard state fugacity for component i in liquid phase

xi = mole fraction of component i in the liquid

gi = liquid phase activity coefficient for component i

The standard state liquid fugacity is further defined as:

 foLi = pisat fisat exp [ integral { vLi / RT dP}]

where:  pisat = vapor pressure of component i at the system temperature

fisat = fugacity coefficient of component i at T and pisat

R = gas constant 

vLi = liquid molar volume of component i at T and P

Standard conditions for liquid molar volume are 1.0 atmosphere and 77F (25C). This differs from standard conditions for a vapor or gas (60F or 15.5556C).

P = system pressure 

T = system temperature 

and the integral is evaluated from pisat to P.

The exponential term corrects for compressibility effects on the liquid phase and is known as the Poynting correction.

The fugacity of each component in the vapor phase is written as:

 fVi = fVi yi P

where: yi = mole fraction of component i in the vapor phase

 P = system pressure 

 fVi = fugacity coefficient of component i in vapor

Combining the above expressions and rearranging;

 Ki = yi / xi = gi foLi / fVi P

When vapor phase imperfections may be ignored and the pressure effect on the liquid phase is small, the expression may be simplified as follows:

 Ki = yi / xi = gi pisat/ P

The liquid activity coefficient method is useful for systems comprised of components of similar volatility with highly non-ideal liquid behavior. However, the method meshes very poorly near the mixture critical point and an equation of state method must be used under these conditions.