5. Conclusions

The aim of this work is to present the practice carried out on a set of operations constituting a procedure involving the following sequences: experimentation \$ verification \$ modeling \$ simulation. A description of the last three operations is proposed since the necessary experimental information (iso-p and iso-T VLE data and h<sup>E</sup> ) was extracted from the available publications. The proposed methodology is applied to two significant binary systems in the dissolution thermodynamic field, such as acetone-ethanol and benzene-hexane. The data checking is carried out with different classical methods, which is recommended in the recent literature [6]. In addition, a rigorous method recently designed by the authors [7] was also used in order to guarantee the quality of the experimental data used. This method has the advantage of offering some information about the origin of deficiencies in the experimental data.

A polynomial expression was used in the modeling step (see Eqs. (1) and (3)), used in the correlation of thermodynamic properties, from which four sub-models (M1–M4) are established in Section 2.1, depending on the availability of data for each system to avoid overfitting. Modeling in all cases was performed on the Gibbs dimensionless function, g E /RT (VLE), and on h<sup>E</sup> data, two-objective optimization approach addressed as a sequence of mono-objective subproblems according to the ε-constraint algorithm. A set of models are selected from the attained efficient fronts to provide a rationale on the trade-off decision task that is supposed to yield the final model for later uses, such as design/simulation. For the two studied cases, these fronts reveal a quasi-linear trend (with a negative slope) when the number of parameters used in the model is small. Efficient fronts'slope decreases as the number of parameters increases, until the error of VLE delinks to that of the h<sup>E</sup> for highly flexible models.

The rectification of the selected systems was simulated using the RadFrac block of AspenPlus© with the selected thermodynamic parametrizations. For the binary acetone + ethanol, some models showed an immiscible region, not reflected by the experimental information, giving rise to incoherent simulations. Two models gave rise to inexistent azeotropes in the benzene + hexane dissolution, with incorrect results in the simulation. On the other hand, errors in the excess enthalpy estimates did not influence on the procedure simulation, but it should be noted that it has an important role in the modeling of binary systems. In summary, the influence of a certain set of parameters on the simulation varies depending on each particular system. Besides, it is observed that, as the number of parameters grows in a model, the optimization problem mutes toward a mono-objective one since the considered criteria are invariant in one another. In these cases, taking the set of parameters that present the lowest error on h<sup>E</sup> is the best option. However, increasing the number of parameters might lead to overfitting if not enough attention is paid to the model extrapolation capabilities.

A Practical Fitting Method Involving a Trade-Off Decision in the Parametrization Procedure… DOI: http://dx.doi.org/10.5772/intechopen.85743
