Equations for the UNIQUAC method
- Last UpdatedSep 08, 2025
- 6 minute read
The Universal Quasi-Chemical (UNIQUAC) method is a liquid activity coefficient (LACT) method. AVEVA Process Simulation uses a standard set of equilibrium calculations for most LACT methods. See the following sections for more information:
The main difference in the equilibrium calculations between the different LACT methods is the calculation of the activity coefficient.
Activity coefficient calculations
The expression for the activity coefficient is:
The following equations show how the UNIQUAC method calculates the variables in the activity coefficient expression:
where
nc is the number of components
ji is the segment or volume fraction of molecules i
qi is the area fraction of molecules i
ri is the molecular volume (called the van der Waals volume)
qi is the molecular surface area (called the van der Waals area)
= 10, because the average coordination number, that is, the number of molecules around
a central molecule, is usually taken to be 10
The UNIQUAC method estimates ri and qi by using the group contribution values of Bondi6, R and Q:
where
ng is the number of different functional groups in the mixture
nki is the number of functional groups of type k in molecule i
Rk is the volume parameter for each functional group k
Qk is the surface area parameter for each functional group k
In the UNIQUAC method, there are "dimensionless" values of Rk and Qk. These values are based on the van der Waals volume and surface values of Bondi6, but are normalized by using the volume and external area of the CH2 unit in polyethylene:
where
Awk is the van der Waals area of molecule k
Vwk is the van der Waals volume of molecule k
The SimSci component library includes calculated ri and qi values for each component.
The UNIQUAC method uses the following equations to calculate the remaining variables in the activity coefficient expression:
where
Uij is the interaction parameter between components i and j
aij, aji, bij, bji, cij, cji, dij, and dji are values taken from the binary data bank in AVEVA Thermodynamic Data Manager
The UNIQUAC method requires two adjustable parameters, tij and tji(or equivalently Uij and Uji), for each binary pair; you can make these parameters temperature-dependent, as described in the preceding equations. If you do not use temperature dependence for Uij, you can typically obtain better results over a range of temperatures by using aij and setting bij to 0.
Vapor-liquid equilibrium for Henry's solutes
We use the general vapor-liquid equilibrium calculations for all Henry's solvents. See Vapor-liquid equilibrium calculations for more information.
For molecular solutes (Henry's solutes), we use Henry's Law to model the equilibrium between the gaseous solute and the dissolved gas in the liquid phase:
where
Hi is the Henry's constant for component i in the mixed solvent
gi¥ is the infinite dilution (xi → 0) activity coefficient of molecular solute i in the mixed solvent
For Henry's solutes, we assume ideal behavior and set the activity coefficient (gi*) for all Henry's solute to one. This assumption simplifies the equilibrium equation between the gaseous solute and the dissolved gas to the following equation:
We use a simple additive mixing rule to calculate Hi:
where
A is the set of solvent components in the mixed solvent
XA is the mole fraction of solvent component A on a solute-free basis
HiA is the Henry's constant for component i in pure solvent A
You can include a pressure correction in the calculation of HiA. You use the Apply Henry's Law Pressure Correction using Brelvi O'Connell Model checkbox in the Equilibrium Options section of the Fluid Editor to turn on or turn off the pressure correction. When you select this checkbox, we use the following equation to calculate HiA:
where
PAsat is the saturation pressure of solvent A at the current temperature
viA¥ is the partial molar volume of molecular solute i at infinite dilution in pure solvent A
We use the Brelvi-O'Connell method[6] to calculate viA¥ as a function of characteristic volumes:
where
vCi is the characteristic volume from Brelvi-O'Connell[6] of component i
vCA is the characteristic volume from Brelvi-O'Connell[6] of solvent A
v0A is the liquid molar volume of pure solvent A calculated from the temperature-dependent property correlation for liquid density for pure solvent A
The temperature-dependent property correlations for liquid density are defined by the pure component (PURECOMP) data bank that the Fluid Type uses and by the local thermodynamic data overrides specified on the Temperature Dependent tab in the Component Data section of the Fluid Editor. Refer to Override temperature-dependent property data for more information.
You can also provide the characteristic volume data for components as temperature-dependent property data on the Temperature Dependent tab. If data is not available for a component, we fill the characteristic volume for the component (vCi) with the critical volume (Vci) data.
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.