A Marine Riser With Internal Flow-Induced Vibration
Authors: Chen B.C.M. 
Published: October 2008

Abstract
The internal fluid dynamic and other conventional forces are described completely in the governing equation of the lateral vibration of a marine riser. The current scope of work is to determine the natural frequency and the mode shape of an undamped riser. With proper tension expressions, the equation is applicable to the neutrally, negatively or positively buoyant riser system.
From the fluid-elastic vibration point of view, the fluid dynamic force produces the effect which is opposite to that of the riser tension. The force decreases the natural frequency and may create a dynamic instability as the fluid flow velocity approaches the critical, buckling or significant values.

Introduction
A marine riser is a conductor which links the floating vessel on the sea surface and the manifold on the sea bottom. The depth of the sea can be from several hundred to a couple thousand feet. The riser can be a single rigid pipeline for the drilling riser system, or a bundle of flowlines which are assembled as an integral unit for the production riser system. The riser system can be installed for the tension leg platform (TLP), floating production and storage unit (FPSU).
To avoid the collapse and buckle of a riser by its own weight and to reduce the excess load on the manifold in the deep sea, a constant top tension is applied. Buoyant material is strapped around the riser at intervals to provide an additional buoyancy and to reduce the required top tension. The additional buoys make the riser neutrally, negatively or positively buoyant depending on the applications. These are some of the features of the deep sea marine riser. An applied mechanics for marine riser systems has been provided by Morgan (l).
The drilling or the production fluid flows internally from one end to the other, inside the conductor along the transversely deflected riser loaded by the environmental forces. The fluidparticles of the internal flow experience the dynamic force of centrifugal and Coriolis accelerations as they travel inside the curved path along the deflected riser. The fluid dynamic force exerts periodically against the interior wall of the conductor along the riser. The force is integrated into the vibration of the riser. Or worse yet, the vibration may be locked-in by that of vortex shedding and together they resonate. This, in turn, will fail the riser system prematurely. For the general knowledge of the centrifugal and Coriolis accelerations, readers may refer to any text book of engineering mechanics or Hibbeler (2).
An aerodynamic force induced vibration on a horizontal pipeline supported at intervals above ground, has been observed and analyzed by Housner (3). He has concluded that the internal fluid velocity causes a dynamic coupling of the simple modes of vibration of the pipeline. At low fluid velocities there is negligible effect upon the vibration of the pipeline, and at a certain high critical velocity the internal fluid flow causes a dynamic instability. The fluid velocity contributes the centrifugal and Coriolis accelerations in the deflected pipeline.