Application of the Firefly and Luus–Jaakola algorithms in the calculation of a double reactive azeotrope

Abstract

The calculation of reactive azeotropes is an important task in the preliminary design and simulation of reactive distillation columns. Classically, homogeneous nonreactive azeotropes are vapor–liquid coexistence conditions where phase compositions are equal. For homogeneous reactive azeotropes, simultaneous phase and chemical equilibria occur concomitantly with equality of compositions (in the Ung–Doherty transformed space). The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. In a previous paper (Platt et al 2013 J. Phys.: Conf. Ser. 410 012020), we investigated some numerical aspects of the calculation of reactive azeotropes in the isobutene + methanol + methyl-tert-butyl-ether (with two reactive azeotropes) system using two metaheuristics: the Luus–Jaakola adaptive random search and the Firefly algorithm. Here, we use a hybrid structure (stochastic + deterministic) in order to produce accurate results for both azeotropes. After identifying the neighborhood of the reactive azeotrope, the nonlinear algebraic system is solved using Newton's method. The results indicate that using metaheuristics and some techniques devoted to the calculation of multiple minima allows both azeotropic coordinates in this reactive system to be obtains. In this sense, we provide a comprehensive analysis of a useful framework devoted to solving nonlinear systems, particularly in phase equilibrium problems.