Inicialização global topográfica aplicada a problemas da termodinâmica do equilíbrio de fases

Abstract

The optimization methods that derive from differential calculus are generally very efficient. However, due to the local nature of the mathematical analysis, these methods may present difficult to calculate the global minimums because they depend on good initial estimates. In this context, the topographical global initialization was proposed with the purpose of generating adequate initial estimates for the local search methods. In the present work, different optimization methods equipped with the topographical global initialization were used to solve thermodynamic problems that arise in the simulation of tertiary oil recovery processes, in the projects of chemical reactors and in the processes of chemical and of the oil industry. We studied the problems the phase stability analysis, calculation of critical points and parameter estimation in thermodynamic models. These problems are challenging because they present difficulties of numerical and geometric nature. To evaluate the efficiency of optimization methods equipped with topographical initialization, were performed numerical tests using problems described in the literature, where some of them present more than one solution. In all tests, including those with multiple solutions, the topographical global initialization was efficient in selecting suitable initial estimates for the local search methods, showing that this is an effective and promising methodology for solving optimization problems. An important scientific contribution of the present work is the application of the theory of complementarity to the problems of phase stability analysis and calculation of critical points. This approach allowed the use of a Newton type method that uses information only from the first derivatives.