Example P05.02 Regression of Complete Isobaric VLE-Data Using UNIQUAC

problem:

Regress the binary interaction parameters of the UNIQUAC model to best describe the isobaric VLE data measured by Kojima et al. at 1 atm and listed below. As objective function, use:

a) relative quadratic deviation in the activity coefficients

b) quadratic deviation in boiling temperature

c) relative quadratic deviation in vapor phase composition

d) relative deviation in separation factor

Adjust the vapor pressure curves using a constant factor to exactly match the author's pure component vapor pressures.

Isobarical dataset at P= 1atm

(Kojima K., Tochigi K., Seki H., Watase K., Kagaku Kogaku, 32, p149-153, 1968)

general

constants

and

definitions:

input data

Required pure component data:

Relative VdW volumes and surfaces:

Antoine Constants:

Solution

Antoine-equation:

The Antoine equation is extended by a prefactor to allow adjustment to the authors pure component vapor pressures. First the elements of the vector fac (above) are set to unity. The calculated values from the following expressions are then copied into fac

UNIQUAC-equation:

Regress relative quadratic deviation in the activity coefficients

sum only over the mixture data points:

Definition of the objective Function:

This function transforms two dimensionless parameters into the interaction parameter matrix required for UNIQUAC.

Optimization:

starting values:

Regress quadratic deviation in boiling temperature

As the boiling temperature has to be iterated until the calculated pressure matches the desired value, we start off by defining a function for the total pressure (saturated vapor pressure) of the mixture:

Now we define a function for the boiling temperature using the root function to find the right temperature. The initial value for T is calculated from the mole fraction weighted mean of the pure component boiling temperatures. The pure component boiling temperatures are calculated from the re-arranged Antoine-equation.

Now we can define the objective function:

and perform the regression:

Regress relative quadratic deviation in vapor phase composition

Definition of the Objective Function:

For simplicity we use the experimental boiling temperature instead of iterating to the experimental pressure.

Regress relative deviation in separation factor