Equations for the NRTL method
- Last UpdatedOct 02, 2025
- 7 minute read
The non-random two-liquid (NRTL) 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 coefficients is:
where
(temperature unit is K)
These equations require three parameters, tij, tji, and aij = aji, for each binary. We can make these parameters temperature-dependent, as described in the preceding equations. If you want to represent tij with only one constant, empirical data shows that you obtain better results over a range of temperatures if you use only Bij and Aij = Cij = 0. The a parameter does not vary greatly from binary to binary, and you can fix it at 0.3 for vapor-liquid systems or 0.2 for liquid-liquid systems to obtain satisfactory results.
Vapor-liquid equilibrium for Henry's solutes
We use the standard 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 mixed solvent
We use the following equation to calculate the infinite dilution activity coefficient (gi¥):
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
gis¥ is the infinite dilution (xi → 0) activity coefficient of molecular solute i in pure solvent component A
We can use the following equation to calculate the contribution of a given solvent (A) to the infinite dilution activity coefficient (gi¥):
where
B is the set of solvent components in the mixed solvent
For some Henry's solutes, we can assume ideal behavior and set the activity coefficient (gi*) for that Henry's solute to one. This assumption simplifies the equilibrium equation between the gaseous solute and the dissolved gas to the following equation:
The Include activity coefficient in liquid fugacity for Henry's solutes (select for solutes in Component List) checkbox in the Equilibrium Options section of the Fluid Editor determines whether to include the activity coefficient in the vapor-liquid equilibrium (VLE) calculations for selected Henry's solutes.
When you clear the Include activity coefficient in liquid fugacity for Henry's solutes (select for solutes in Component List) checkbox, we set the activity coefficients for all Henry's solutes to one, and we use the simplified equilibrium equation for all Henry's solutes.
When you select the Include activity coefficient in liquid fugacity for Henry's solutes (select for solutes in Component List) checkbox, the Henry Activity column appears in the table in the Component List section of the Fluid Editor. You use the checkboxes in the Henry Activity column to choose which Henry's solutes use activity coefficients in their equilibrium equations.
If you clear the Henry Activity checkbox for a Henry's solute, we set its activity coefficient to one, and we use the simplified equilibrium equation for that Henry's solute.
If you select the Henry Activity checkbox for a Henry's solute, its equilibrium equation includes the activity coefficient.
You use the Include rigorous mixing with activity coefficient and critical volumes for Henry's Law checkbox in the Equilibrium Options section of the Fluid Editor to determine which mixing rule to use to calculate the Henry's constant in the mixed solvent (Hi). When you clear this checkbox, we use a simple additive mixing rule to calculate Hi:
where
HiA is the Henry's constant for component i in pure solvent A
When you select the Include rigorous mixing with activity coefficient and critical volumes for Henry's Law checkbox, we use the rigorous mixing rule to calculate Hi, which uses the activity coefficient and critical volume to account for the non-ideality of the system:
where
wA is a weighting factor
We calculate the weighting factor for a given solvent (A) from the critical volumes of the pure solvents:
where
VcA and VcB are the critical volumes of solvent A and solvent B, respectively
You can override the critical volume data (Vc) for components on the Constants tab in the Component Data section of the Fluid Editor. Refer to Override constant property data for more information.
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.