Deep-water flexible risers conveying hydrocarbon oil and gas flows may be subject to internal dynamic fluctuations associated with the spatial variations of phase densities, velocities and pressure drops. Many studies have focused on single-phase flows in pipes whereas understanding of multiphase flow effects is lacking. This study aims to investigate the planar free-vibration characteristics of a long flexible catenary riser carrying the steady-state, multiphase slug oil-gas flows in order to understand how the inclination-dependent internal slug flows affect riser natural frequencies and modal shapes. The influence of slug characteristics such as phase velocities on the riser vibration is also studied. The catenary riser planar motions are mathematically described by a two-dimensional continuum model capturing coupled horizontal and vertical responses. Based on the selected two-phase flow rates at the wellhead, riser geometric configurations and specified slug unit lengths, a steady-state slug flow model is considered by taking into account several empirical closure correlations and riser mechanical properties, solving for the multiphase flow aspects including pressure, velocities, liquid holdup and gas fraction.
By assigning an undamped free-vibration shape of an empty catenary riser as initial displacement conditions, the space-time numerical simulations are performed using a finite difference approach. Comparisons of oscillation frequencies, time histories, phase planes, time-space varying responses and dynamic stresses of catenary risers with and without slug flows are presented, identifying the dynamic modifications arising from the internal slug-induced mass momentum change and pressure loss. To understand the influence of slug flow properties, parametric studies are carried out with different gas velocities. Numerical results highlight the reduced riser tensions, decreased oscillation frequencies, multiple oscillation modes, amplified amplitudes and stresses. These key observations will be useful for the forced vibration analysis of catenary risers subject to combined internal (multiphase) and external (vortex-shedding) flow excitations.