Example 05.20 Liquid-Liquid Equilibrium for the System Water – Ethanol – Benzene
K-Factor Method UNIQUAC

problem:

Calculate the liquid-liquid equilibrium composition for the system water (1) - ethanol (2) - benzene (3) for the following feed stream: n₁ = 1 mol, n₂ = 0.3 mol, and n₃ = 1 mol at 25 °C with the help of the UNIQUAC model.

general

constants

and

definitions:

input data

Components: 1 - water

2 - ethanol

3 - benzene

UNIQUAC parameters:

Solution

In the first step a convenient function to convert the mole flow vector into a mol fraction vector is defined:

The interaction parameter matrix Du is converted to the t matrix only once as temperature is constant in the calculation:

The following functions yield the logarithmic activity coefficient and activity coefficient vector using the UNIQUAC equation (Table 5.6):

As an example, activity coefficients for the components in the feed stream are calculated:

For the K-factor method, an initial estimation of the mole flows in the first liquid outlet stream is required:

The iterative K-factor method can be programmed into a simple function:

Now the K-factor function is used to calculate the mole flows in the first liquid outlet stream. The second liquid stream is found by solving the mass balance:

In the last step, the result is verified by applying the isoactivity criterion. The sum of squared deviations in activity between the outlet streams over all components should result in a very small number: