Example P05.01b VLE Behavior of Ethanol - Water Using the Wilson Model

problem:

Calculate the pressure and the vapor phase mole fraction for the system ethanol (1) - water (2) at 70°C with the help of the different g^E-models (Wilson, NRTL, UNIQUAC) for an ethanol mole fraction of 0.252 using the interaction parameters, auxiliary parameters and Antoine constants given in Fig, 5.30 and assuming ideal vapor phase behavior. Besides total and partial pressures and vapor phase composition, calculate also K-factors and separation factors. Repeat the calculation using the real gas factors F₁=0.9955 and F₂=1.0068.

general

constants

and

definitions:

input data

Liquid mole fractions, pure component vapor pressures and temperature:

Real gas factors:

Wilson parameters:

liquid molar volume at 25°C

Solution

Calculation of the activity coefficients:

First assume ideal vapor phase behavior and neglect the Pointing correction:

Calculation of the total pressure:

Calculation of the vapor phase composition:

Using the calculated total pressure and the calculated vapor phase composition, the real gas factor can be calculated. Repeating the calculation will result in new values for total pressure and vapor phase composition and therefore new real gas factors. Iteration leads to:

Using these values the total pressure is:

Calculation of the vapor phase composition:

The K-factors and separation factors can be calculated in two different ways: