The parametrization problem in the modeling of the thermodynamic behavior of solutions. An approach based on information theory fundamentals

Abstract

This work shows a new approach to the parameter-fitting problem useful in the solutions thermodynamic field, providing a more objective framework to obtain better empirical/semiempirical models for chemical engineering applications. A model based on the excess Gibbs energy function gE is used to represent the behavior of real solutions, together with its first derivative hE, using a combined modeling under the paradigm of multiobjective optimization. The problem is formulated as an MINLP methodology to simultaneously consider two aspects: the model complexity and the best parametrization to prevent the overfitting, controlling the trade-off between them by applying the Akaike Information Criterion to gE residuals. Two different solvers, one deterministic (SBB/CONOPT) and another evolutionary (GA), are used, and their ability to solve the problem is analyzed. The designed methodology is applied to three highlighted VLE cases in chemical engineering, and the results obtained show the ability of the method to get the best model in each case. The proposed methodology proved useful for modulating the number of parameters considering the imposed requirements, which decrease as the accuracy requirements for hE are relaxed. The efficient-fronts obtained show a small trade-off region, noting that the proposed framework provides the simplest models with the minimum completeness uncertainty.