A Comparative Study of Gibbs Free Energy Minimization in a Real System Using Heuristic Methods

The knowledge of phase and chemical equilibrium is clearly important in the analysis and design of a wide variety of chemical processes. These problems are described mathematically by complex systems due to the nonlinear nature of the thermodynamic models. This equilibrium state is characterized by the minimization of the Gibbs free energy. Usually, this problem is calculated by using the method of Lagrange multipliers together with the mass balance conditions as necessary subsidiary conditions. However, the convergence is highly dependent of initial estimates of the Lagrange multipliers. The development of robust and efficient methods for the computation of thermodynamic multi-phase systems has long been a challenge in both chemical engineering and materials science. In this context, both heuristic methods, Genetic Algorithms and Differential Evolution, are able to escape from local minima and saddle points. As main disadvantage the high number of objective function evaluations as compared with classic methods can be mentioned. To overcome this disadvantage, this work proposes the dynamic updating of the population size to reduce the number of objective function evaluations. The methodology is applied to determine phase compositions at the chemical equilibrium of real systems. The results demonstrated that the methodology used represents a promising alternative for the problem studied.