Constrained and unconstrained Gibbs free energy minimization in reactive systems using genetic algorithm and differential evolution with tabu list

Abstract

Phase equilibrium modeling plays an important role in design, optimization and control of separation processes. The global optimization problem involved in phase equilibrium calculations is very challenging due to the high non-linearity of thermodynamic models especially for multi-component systems subject to chemical reactions. To date, a few attempts have been made in the application of stochastic methods for reactive phase equilibrium calculations compared to those reported for non-reactive systems. In particular, the population-based stochastic methods are known for their good exploration abilities and, when optimal balance between the exploration and exploitation is found, they can be reliable and efficient global optimizers. Genetic algorithms (GAs) and differential evolution with tabu list (DETL) have been very successful for performing phase equilibrium calculations in non-reactive systems. However, there are no previous studies on the performance of both these strategies to solve the Gibbs free energy minimization problem for systems subject to chemical equilibrium. In this study, the constrained and unconstrained Gibbs free energy minimization in reactive systems have been analyzed and used to assess the performance of GA and DETL. Specifically, the numerical performance of these stochastic methods have been tested using both conventional and transformed composition variables as the decision vector for free energy minimization in reactive systems, and their relative strengths are discussed. The results of these strategies are compared with those obtained using SA, which has shown competitive performance in reactive phase equilibrium calculations. To the best of our knowledge, there are no studies in the literature on the comparison of reactive phase equilibrium using both the formulations with stochastic global optimization methods. Our results show that the effectiveness of the stochastic methods tested depends on the stopping criterion, the type of decision variables, and the use of local optimization for intensification stage. Overall, unconstrained Gibbs free energy minimization involving transformed composition variables requires more computational time compared to constrained minimization, and DETL has better performance for both constrained and unconstrained Gibbs free energy minimization in reactive systems.