Global Gibbs Free Energy Minimization in Reactive Systems via Harmony Search

Abstract

Phase equilibrium calculations in systems subject to chemical reactions play a major role in the design of reactive separation schemes including chemical reaction engineering. Basically, these calculations involve the global minimization of Gibbs free energy constrained by the material balances and chemical equilibrium restrictions. However, Gibbs free energy function is non-convex, highly non-linear with many decision variables, and may have several local minimums including trivial and nonphysical solutions. In these conditions, conventional numerical methods are not suitable for solving reactive phase equilibrium problems. Recently, there has been a significant and increasing interest in the development of global strategies for reliably solving reactive phase equilibrium problems subject. Harmony search (HS) is a global stochastic optimization method, which has been conceptualized using the musical process of searching for a perfect state of harmony. Until now, HS has been successfully applied to solve various engineering and optimization problems. However, there are few studies concerning the application of this optimization method for chemical engineering calculations. To the best of our knowledge, the performance of HS for solving reactive phase equilibrium problems has not yet been reported. Therefore, this paper introduces the application of HS-based algorithms to the constrained global minimization of Gibbs free energy in reactive systems. Specifically, we have studied the performance of three variants of HS in reactive phase equilibrium calculations. Our results are useful to identify the capabilities and relative strengths of HS with respect to other stochastic optimization methods for the simultaneous calculation of physical and chemical equilibrium.