A differential-algebraic system is presented to model unstable two-phase flows in pipe-riser systems. Equations derive from the space integration of an isothermal drift-flux model assuming quasi-equilibrium momentum balance. A linear analysis of this system gives a new stability criterion for gas-liquid flows in pipe-riser systems. This criterion is validated by laboratory experiments. Then, a nonlinear analysis shows that the severe slugging phenomenon is a hydrodynamic instability coming from a supercritical Hopf bifurcation.

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