VLE Thermodynamic Consistency: Point Test background

where .
d*_k represents the deviation for individual experimental points, d represents an overall deviation in percent, and e is defined in the Herington Test background. As noted for the Herington test, the value of e cannot be neglected for isobaric data sets. To avoid complexities associated with H^E data sets, the Point Test was not applied to isobaric data sets. The values of g₁, g₂ are first calculated from the experimental values of T-p-x-y data. The calculated values of are fitted by use of a Pade approximation for the activity coefficient, shown here.

In this research, M = 1 and N = 3. This expression reduces to the Redlich-Kister expansion when M = 0. The quantityd*_k is determined with the slope of the fitted Pade approximation and calculated values of . The criteria given by Kojima and coworkers^19,22 are that if d < 5, the VLE data set passes the test, otherwise it fails.

The quality factor for the Point Test can be calculated with the overall percent deviation of the slope:
, with the limits: .