Equations for the Wilson method
- Last UpdatedSep 08, 2025
- 5 minute read
The Wilson 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:
where
ViL is the liquid molar volume of component i
aij, aji, bij, bji, cij, cji, dij, dji eij, eji fij, and fji are values taken from the WILSON binary data bank
Sij corresponds to the volRatio value in the WILSON binary data bank
When you set Sij to 0 (NOVOL) for a binary interaction pair, you should ensure that your aij, bij, and other coefficient values account for the volume term that no longer appears as part of the equations.
These equations apply to WILSON binary data banks configured with the 12-parameter format in AVEVA Thermodynamic Data Manager. AVEVA Process Simulation always uses these equations when it performs calculations for the Wilson method. If your Fluid uses a WILSON binary data bank configured with the older two-parameter format, you must override the values from the data bank so that the values align with the 12-parameter form of the equations. Specifically, you must change the sign for the aij and aji parameters. See the AVEVA Thermodynamic Data Manager User Guide for more details on how the two-parameter form and the 12-parameter form of the equations differ. See Override the binary interaction data for a Wilson-based Fluid Type for more information on how to override the values from the WILSON binary data bank.
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.