An initial value insensitive method for phase equilibrium calculation: Constrained backtracking search optimization algorithm

Abstract

Phase equilibrium calculations are frequently encountered in various industrial processes and many methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles sprang out. They all can calculate the satisfactory solutions of phase equilibria problem under given volume, temperature, and moles (NVT-flash), but there still exist problems of initial value sensitivity and solving complex derivatives. Thus, a constrained backtracking search optimization algorithm (CBSA), which added constraints handling of the NVT-flash problem to the original operation of BSA, is presented in this paper. The proposed algorithm takes the total Helmholtz free energy as the objective function, and the moles vector and volume of a certain phase as the decision variables. The direct search method and exterior point method were used to handle the constraints of NVT-flash problem. The numerical test results are 100% consistent with the published data, which verify the effectiveness and energy decay property of the proposed algorithm. The proposed scheme is the first successful attempt to apply meta-heuristic algorithm to the field of phase equilibrium calculation. This hints the wide application prospect of meta-heuristic algorithms in this field as well as broadens the application range of meta-heuristic optimization algorithms.