VLE Thermodynamic Consistency: Quality Assessment Procedure and TDE Quality Factor

where M is a molar thermodynamic property, M_i bar is a partial molar property, and T, p, and x are temperature, pressure, and liquid composition, respectively. The summation is over the i components in the chemical system. If the property M is the excess Gibbs energy divided by the product of the gas constant R and T, then

where g is an activity coefficient, V^E is the excess volume and H^E is the excess enthalpy. The above 3 equations are the foundation for the consistency tests in TDE. The four consistency tests considered determine the quality of a VLE data set on a pass-fail basis. Although these tests can be useful for rejection of VLE data sets with inconsistencies, it is difficult to decide whether to accept or reject a data set, when test results conflict. For such cases, quantitative test results can be very helpful. In TDE, quality factors F_test,i for each test are evaluated as values ranging from 0.025 to 0.25, resulting in the sum of the factors having values ranging from 0.1 to 1.
, if all tests are passed.

The quality factors for each test are combined alegebraically to produce the overall TDE Quality Factor Q_VLE. A check of consistency is also made between VLE data-set "endpoints" (i.e., mole fraction composition approaching 0 or 1) and pure-component vapor pressures. This is termed the Pure Component Consistency Test (DETAILS), and a 5^th quality factor F_pure is derived.

The TDE Quality Factor Q_VLE is used as a weighting factor in model-fitting procedures in TDE and is calculated based on the results of all tests as follows:

, with the limits indicated.

The numerical value of the TDE Quality Factor Q_VLE is listed on the VLE Data Sets and Consistency Tests Form following application of the consistency tests.