Direct calculation of bubble points by Monte Carlo simulation

Abstract

The calculation of bubble points, i.e, the conditions in which a liquid starts to form a vapour phase, is a problem of industrial interest in petroleum and chemical engineering. Phase equilibrium at specified global composition, temperature and volume—or pressure—can be computed by the Gibbs Ensemble Monte Carlo method (GEMC). However it is not directly applicable to bubble points, which require one to solve the problem where the liquid composition and temperature are specified, and while pressure and vapour composition are sought. In order to provide an efficient algorithm, the present article proposes a pseudo ensemble in which liquid mole numbers, temperature and global volume are imposed, while mole numbers in the vapour phase and phase volumes are allowed to fluctuate. The partition function, probability density and thermodynamic potential are given. This pseudo ensemble satisfies the conditions of mechanical and thermal equilibrium, while chemical equilibrium is satisfied by imposing the chemical potential of the liquid phase to the vapour. A Monte Carlo method is proposed to generate a Markov chain simulating the ensemble, with a specific move for molecule insertion or deletion in the vapour phase. Various solutions are considered to evaluate the chemical potential of the liquid phase using test insertion methods. Finally, we show that an efficient procedure for bubble point calculation is to use the proposed algorithm as an initialization of a GEMC simulation run. The method has been tested on the argon—krypton binary system for which a Lennard-Jones intermolecular potential enables one to reproduce experimental vapour—liquid equilibrium data. It is shown that the method provides a satisfactory prediction of phase diagrams and that it is applicable to near-critical conditions. Its application to determine bubble points of multicomponent molecular systems thus appears promising.