Destabilization of deep-water risers by a heaving platform

Offshore gas and oil fields are being discovered and exploited nowadays in water depths of more than 2000 m. In order to convey the hydrocarbon to the sea level, a steel slender pipe is installed between wellhead at the sea bed and floating platform. If used in deep waters, these pipes are commonly referred to as deep-water risers. The heave (vertical motion) of a floating platform induces a fluctuation in time of the axial tension of the riser. A possible and undesirable phenomenon is the excitation of a transverse riser vibration caused by this fluctuation. Owing to this fluctuation, the governing equation of transverse motion of the riser is a nonlinear partial differential equation containing a time-dependent coefficient. As a first step, this equation is linearized around the straight equilibrium, and stability of this equilibrium is investigated using the Galerkin method and the Floquet theory. Then, the dynamic equilibrium is studied that the riser reaches if its straight equilibrium is unstable. This is done using a numerical time-domain technique. Two qualitatively different mechanisms of stability loss are distinguished, discussed and exemplified. The first is classical parametric resonance that occurs solely due to periodic time variation of the axial tension. The second mechanism occurs if the amplitude of vibration of the platform is large enough to change tension into compression in a segment of the riser for a part of the vibration cycle. It is shown that the second mechanism can cause dangerously large dynamic stresses in the riser.