Solution nonuniqueness for separated gas-liquid flow in pipes and wells. I. Occurrence

The Occurrence Of Multiple Solutions has been investigated and discussed in this paper. Multiple Solution regions are displayed by either a U-SL-U-SG map or a X-Y map. It is found that many parameters impose influence on the multiple solution regions, including fluid properties, pipe ID, pipe inclination angle, wall inflow Or Outflow, empirical correlations for wall friction and interfacial friction factors, and so on. For example, the multiple Solution region could change significantly if different interfacial friction factor correlations are applied. Multiple solutions are only possible for upward flow for separated flow in a pipe without wall mass transfer. However, for wellbore flow case, depending on wall inflow or outflow of fluids and their flow rates, multiple solutions may also exist for horizontal and downward flow. More specifically, for wall inflow case (production well), multiple solutions only exist for upward flow for the gas inflow-dominant case, whereas they may exist for upward, horizontal and downward flow for liquid inflow-dominant situations. The opposite is expected for wall Outflow (injection well) case.