Article published by International Journal of Multiphase Flow “Nonlinear stability analysis for severe slugging in an air–water two-phase flow”

An oil production system is designed to produce in a regime with a steady state flow; however, this steady state condition may not exist. The stability of this system depends on the set of parameters that defines the operational state. A stability solver was developed by the research group at NDF, with many contributions over the last years.

Within the unstable region a regime exists in which there is a continuous gas inflow at the bottom of the riser; this regime, called SS3 (severe slugging type 3), is not as dangerous for the offshore systems as regimes SS1 or SS2. Also, liquid backflow can be encountered at the top of the riser.

In this pioneer contribution, nonlinear stability analysis was used to determine the unstable regions corresponding to SS3 and liquid backflow.

The Landau equation, considered as an asymptotic solution of a two-phase flow model in a pipeline–riser system, is derived. From the Landau equation, the Landau coefficient 𝜇 is calculated and, consequently, the saturation amplitudes of the state variables (gas and liquid superficial velocities and pressure)  at the limit cycle are determined. Based on the amplitude of the gas superficial velocity at the bottom of the riser, the condition where severe slugging type 3 occurs can be determined. Also, based on the amplitude of the liquid superficial velocity at the top of the riser, the condition of severe slugging with liquid fallback can be determined.

The results are presented in stability maps and are compared with experimental data reported in the literature, with a good agreement.

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