Application of the simulated annealing technique to the calculation of critical points of multicomponent mixtures with cubic equations of state

Abstract

In this work we have applied a global optimization method for the calculation of critical points of multicomponent systems. This method, based on the simulated annealing algorithm that does not depend on initial guesses and gives preference to global optima, allows locating multiple critical points of a given mixture without any convergence difficulty. Here, it is showed that using appropriate cooling schedule parameters in the simulated annealing algorithm, the computing time for solution of a critical point is reduced drastically so that it can be used for practical purposes that require extensive critical point calculation in multicomponent mixtures. The criticality conditions, based on the tangent plane distance in terms of the Helmholtz energy, were evaluated using temperature and volume as independent variables. The procedure was tested on binary and multicomponent mixtures using the SRK and PR equations of state. The total computing time for forty multicomponent mixtures containing three to twelve components was 4.11 s ranging from 0.06 s for three components to 0.23 s for twelve components, whereas for a multicomponent mixture containing twenty-five components the average computing time was 0.57 s. The results of the critical points calculated in this work illustrate the capability of the simulated annealing algorithm to locate multiple critical points of binary and multicomponent mixtures.