Modeling and analysis of the isothermal flash problem and its calculation with the simulated annealing algorithm

This paper describes a new formulation of the vapor-liquid equilibrium problem. The proposed model reveals a great mathematical similarity between the stability test problem and the isothermal flash problem, particularly in regions of interest in reservoir engineering near phase boundaries and in the vicinity of critical points. This similarity is mathematically studied and then explored to find a means of minimizing the Gibbs free energy in a more efficient way. The Peng-Robinson cubic equation of state was used to represent the phase behavior of multicomponent mixtures. The simulated annealing (SA) algorithm was used to carry out isothermal flash calculations and phase stability tests. The SA algorithm is essentially an iterative random search procedure whose moves are adapted by some suitable mechanism. It is robust and easy to implement. The algorithm was tested for several hydrocarbon mixtures. The few experimental data available in the literature were compared with theoretical predictions. The proposed methodology produced high-quality solutions.