A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines

A novel mechanistic two-fluid model (CB model) similar, in spirit, to the Taitel and Dukler [1, 2] (TD model), for the identification of possible multiple solutions of a multi-phase (gas-liquid) stratified flow in slightly inclined pipelines, is proposed. While Blasius-type closures are used in the TD model to represent the wall friction coefficients, the newly-implemented CB model makes use of Colebrook-White-type closures. Moreover, different closures for the interfacial shear are also employed in the CB models. The predictive capabilities of the CB model have been tested by using several experimental data, finding a better agreement between measured and calculated data than that existing when the TD model is used. The region of multiple solutions is influenced by the closures in use, such a dependence is more evident when different interfacial friction factors are used. Moreover, for the CB model also the fluid mixture in use influences the boundaries of the non-uniqueness region, while by using the TD model the multiple-solution region is unchanged. The choice of closures for the interfacial friction strongly influences the holdups, the Andritsos and Hanratty [10] correlation significantly shifting the non-uniqueness region to small values of the inclination parameter. Such a behaviour is more and more significant with the increase of the superficial gas velocity, even if for values of the inclination parameter within the range of inclinations for stratified flows (i.e. less than about 30° from the horizontal [11]), multiple solutions were not found. Finally, for the fluid mixture and flow conditions analyzed, multivalued solutions are obtained only for upward flows. Moreover, the portion of multiple-solution region interested by co-current flow (that occurs for slightly upward and downward pipes) is rather small, so that the operational point unlikely falls within such a region in the case of the studied hydrocarbon gas-liquid mixture.