Parametric Instability of Deep-Water Risers

Abstract

During the last decade, some major changes took place in the offshore industry. These changes were associated with new oil and gas fields which were discovered in severe environments, at depths of 1500 meter and more. Nowadays, offshore companies face challenges in the design of risers which could reliably facilitate such deep-water exploration. The heave motion of a floating platform induces a fluctuation in time of the axial tension in the riser. A possible and undesirable phenomenon is the excitation of the lateral response caused by this fluctuation. This phenomenon is called parametric instability. The objective of this study is to gain better insight in this phenomenon. The focus is on the occurrence of instability for deep-water risers induced by the variation of the effective tension in time. Due to this tension variation the governing equation of motion for the transverse motion of the riser is a partial differential equation containing a time-dependent coefficient. To analyse the stability of the system described by this differential equation three main steps are taken. The normal modes of a closely related system are determined to make it possible to apply the Galerkins Method. The normal modes are obtained for the system without the time varying component of the tension force. This equation is a linear partial differential equation of the fourth order whose coefficients are independent of time. To integrate this differential equation a standard FORTRAN routine is used. A study is carried out to find out the features of different methods which are commonly used for analysing the dynamic stability of systems. Three methods are investigated to construct the stability charts of a one-degree of freedom system and a two-degree of freedom system: a small-parameter method, the Floquet theory and the Hills method of infinite determinants. A stability chart shows the combinations of magnitude and period of the time varying force for which the system is unstable. The Floquet theory is applied to different riser configurations. Not only stability charts are obtained to gain insight in the riser behaviour but also numerically integrations in time are performed for the most critical heave motions of the platform. The results of this analysis are used to estimate the maximum riser displacements. Using these results the bending stresses and additional tensile stresses are calculated.