Vapor-liquid equilibrium calculations
- Last UpdatedNov 07, 2025
- 5 minute read
At phase equilibrium, the vapor fugacity (fiV) and the liquid fugacity (fiL) are equal for each individual component in a closed system by definition:
For a given temperature (T), pressure (P), and component composition in each phase (yi and xi), we can use the following equations to calculate the vapor and liquid fugacity for a given component (i):
where
fi is the fugacity coefficient of component i in the gas mixture at T and P
yi is the mole fraction of component i in the vapor at equilibrium
xi is the mole fraction of component i in the liquid at equilibrium
gi is the activity coefficient of component i in the liquid mixture at T and P
fi0 is the liquid fugacity for pure component i at T and P
We can use the following equation to calculate fi0 from the fugacity coefficient:
where
fisat is the fugacity coefficient of pure component i at T and Psat
Pisat is the saturation pressure of pure component i at T
is the Poynting correction factor of pure component i at T
If we use this equation to replace fi0 in the original equation for liquid fugacity, we get the following expanded equation for the liquid fugacity:
If we set the two fugacity equations equal to each other, we get the general equation for vapor-liquid equilibrium (VLE):
Typically, is close to 1 except when P is significantly large. If the pressure is low, then we can assume ideal gas behavior
and set the fugacity coefficients (fi and fisat) and to 1, which leads to the following simplified equilibrium expression:
If we further assume ideal liquid behavior, then we can set the activity coefficients (gi) to 1, which leads to Raoult's Law:
Fugacity coefficient calculations
We use one of the equations of state to calculate the fugacity coefficients (fi and fisat).
If you use one of the equations of state as the System method for your Fluid Type, the software calculates the fugacity coefficients according to the selected equation of state.
If you use of one of the liquid activity coefficient (LACT) methods as the System method for your Fluid Type, you can select which equation of state that you want to use to calculate the fugacity coefficients. Use the Vapor Equilibrium list in the Equilibrium Options section of the Fluid Editor to select the equation of state.
If you select Ideal in the Vapor Equilibrium list, we set the fugacity coefficients (fi and fisat) to 1.
Activity coefficient calculations
The activity coefficient relates to the excess Gibbs energy of solution of the liquid:
where
GE is the excess Gibbs energy of the solution compared to an ideal solution
The activity coefficient is a function of T, P, and x. The calculations for the activity coefficient depend on the LACT method that you use as the System method for your Fluid Type. See the following sections for more information:
If you use one of the equations of state as the System method for your Fluid Type, we assume ideal liquid behavior and set the activity coefficients (gi) to 1.
Poynting correction factor
The Poynting correction factor () accounts for the difference between the system pressure and the saturation pressure
of each component. Typically, it is close to 1 except when P is significantly large. You can use the Use Poynting Correction checkbox in the Equilibrium Options section of the Fluid Editor to include or exclude in the equilibrium calculations.
If the Use Poynting Correction checkbox is cleared, we set to 1 to effectively exclude it from the equilibrium calculations.
If you select the Use Poynting Correction checkbox, we use the following equation to calculate its value:
where
is the partial liquid molar volume of component i in the mixture
We can simplify this expression to the following equation:
We can further simplify this expression to the following equation if we use the pure component molar volume instead of the partial molar volume:
This equation always uses the pure component molar volume calculated from the temperature-dependent property correlations for liquid density, as defined in the PURECOMP data bank from the thermodynamic library used by the Fluid Type and the local thermodynamic data overrides specified on the Temp Dep tab in the Component Data section of the Fluid Editor. Changes to the Liquid Density method-override option in the Fluid Editor do not affect these calculations. See Effects of specifying thermodynamic method overrides for more information.