Efficient and robust methods for direct saturation point calculations

Abstract

New algorithms for the calculation of bubble and dew points of binary and multicomponent mixtures are presented. The proposed numerical methods are based on the derivation of the equations that govern phase equilibrium, by starting from the stability criterion of Gibbs and applying a modification, thus resulting in new sets of independent variables and iterative procedures. An additional change of variables is performed to obtain optimal scaling in the minimization problem which is nested in the proposed iterative schemes and thus obtain methods with improved speed and robustness. The algorithms can be applied to calculate at will the lower/upper pressure or low/high temperature bubble or dew point parts of phase diagrams, thus being robust tools when retrograde regions are considered. A simple and widely used initialization method is utilized at low and elevated pressures, while implementation guidelines are given to ensure robust iterative procedures. The proposed methodologies can be applied with or without the use of derivatives of the fugacity coefficients, although their use is strongly advised (if available), since the proposed methods become significantly faster. The new algorithms are tested by calculating saturation points of binary and multicomponent mixtures and prove to be efficient and robust, even in the proximity of critical points in some cases.