Example 05.10 Thermodynamic Consistency Using the Area Test

problem:

Check the isothermal VLE data of the system ethanol (1) water (2) measured by Mertl et al. at 70°C for thermodynamic consistency using the area test.

general

constants

and

definitions:

input data

Vapor pressure of the pure components at 70°C:

Experimental data:

(the data are given here without pure component vapor pressures, which were not reported by the author)

Solution

In the first step the activity coefficients are calculated from the experimental data points using the assumption of ideal vapor phase behavior.

To perform the area test, the logarithm of the ratio of the activity coefficients is first regressed using a flexible mathematical expression (polynomial). Please note that expressions for g^{E} like Redlich-Kister or Legendre-polynomials cannot be used in this case as they can only describe thermodynamically consistent behavior. In this case the convenient MathCad functions "regress" and "interp" are used.

Data regression

Sum of squared deviations (SSD):

Calculation of the relative area deviation in the above plot:

In this test, a relative area deviation of -5.5% is found. In case of isothermal data sets, consistency is assumed for relative area deviations below 10%. For isobaric data sets, this percentage is increased by (T_{max}-T_{min})/T_{min} * 150%. The data can thus be considered to be thermodynamically consistent from the point of view of an area test.

Further discussion of these tests can be found in:

Redlich, O., Kister, A.T., Ind. Eng. Chem. 40 (1948) 345

Herington, E.F.G., Nature 160 (1947) 610

Herington, E.F.G., J. Inst. Petrol. 37 (1951) 457