Instability of catenary-type flexible risers conveying fluid in subsea environments

As water depths for oil and gas exploration and extraction increase, structures such as flexible risers, mooring lines, and umbilical cables are increasingly being used for subsea environments. Compared to conventional fixed-type structures and vertical risers, the dynamics of flexible risers is significantly more complex. In particular, the flexible structures may be prone to dynamic instabilities. The goal of the present paper is to provide a comprehensive study of the dynamics, stability, and vibration of flexible risers. We use Kirchhoff's theory of an extensible, flexible rod that resists torsion to develop a set of nonlinear equations for the dynamics of risers. The resulting model incorporates drag and the effects of the fluid being transported internally. Using a nonlinear stability criterion, our analyses show the nonlinear stability of a simple catenary-type riser modeled either as an inextensible or extensible string. For the more advanced rod models, we use a linear stability analysis to show how the internal fluid being conveyed can destabilize certain static configurations