Non-unique holdup and pressure drop in two-phase stratified inclined pipe flow

Abstract

The simplified model of stratified two-phase pipe flow proposed by Taitel & Dukler [ Int. J. Multiphase Flow 2, 591–595 (1976)] has previously been reported to predict non-unique values of liquid holdup in some upward inclined pipes. This paper shows that the multivaluedness is not an artifact of the approximations made in the model, as it is also predicted by the exactly solvable case of laminar flow in an inclined square duct. A physical explanation for multiple liquid holdups is given, and their occurrence is parameterized in terms of simple flow variables. The stability of the three possible equilibria is discussed. A separated flow model predicts that, in general, the flow with the lowest holdup is the most stable, the highest equilibrium is unstable and the intermediate equilibrium can be stable or unstable, potentially leading to hysteresis phenomenon in slightly inclined flows.