A Generalized Algorithm for Tracking Multiphase Envelopes and Its Application to Three-Phase and Four-Phase Envelope Tracking

Summary In this work, we develop a new general formulation to solve for any envelope point (EP) along multiphase envelopes involving more than two phases. On the basis of such a new formulation, we develop a generalized trust-region-based algorithm that can be applied to track multiphase envelopes. A significant advantage of the generalized algorithm is that if we want to track EPs involving a different number of phases, we only need to change the number of phases without making any additional treatments. We also develop another general formulation that can be solved to locate muster points (where two incipient phases appear) along multiphase envelopes involving at least four phases. We apply the newly developed algorithms to construct three-phase and four-phase envelopes. A total of eight fluid mixtures are used to examine the performance of the generalized algorithm, including six hydrocarbon/CO2/water mixtures and one heavy-oil/water mixture that may exhibit four-phase vapor-liquid-liquid-aqueous equilibria, and another heavy-oil/water mixture that may exhibit four-phase vapor-liquid-asphaltene-aqueous equilibria. The testing results demonstrate the robustness and efficiency of the generalized algorithm in constructing three-phase and four-phase envelopes.