For the evaluation of extreme loads and the assessment of the fatigue life of flex risers, use is made of discrete element models. Most of the models describe the fluid forces by means of empirical formulations using coefficients from 2-D cylinder tests. Recent research has shown that the fluid force modelling should incorporate lift forces perpendicular to the incoming flow. Moreover, model tests on typical flex riser sections have proven that the 2-D cylinder formulations are not applicable and may lead to significant errors. In this paper a new fluid model formulation is presented. This formulation is derived from both model tests and theoretical vortex simulations. Results of systematic drag tests for riser sections are discussed. Capabilities of vortex simulations are evaluated.


Flexible risers have proven to be a key item for cost effective floating production systems. Most problems involved with the application of rigid risers, such as restricted horizontal floater motions and heavy and costly heave compensators, can be eliminated with the application of flexibles. Many flow lines have already been used in mild environments and for limited exposure times. In harsh environments such as the North Sea, the large diameter and relatively stiff flexible risers for permanent floating production (Fig. 1), require extensive design and engineering analysis. Riser systems have to be evaluated for extreme conditions as well as fatigue life. To this end analysis of the dynamic behaviour of the riser system is of prime importance. Typical items of investigation are:

  • extreme motions;

  • interference with mooring or other risers;

  • minimum bending radii;

  • end-connector loading;

  • dynamic tension;

  • dynamic torsion;

  • flow induced vibrations.

The motions of the riser and the forces are primarily excited by floater motions, direct wave forces on the riser and by current. These exciting forces are counteracted by the riser-end forces, the internal forces (bending, stretch and torsion) and the fluid reactive forces due to the riser motions relative to the water. During the last four years several computational methods have been developed for the analysis of the dynamic behaviour of riser systems. Discrete element techniques such as the Finite Element Method (FEM) and the Lumped Mass Method (LMM) are nowadays available for the design, engineering and operation of flexibles (see amongst others refs. [1] and [2]). These techniques utilize a spacewise discretization of the riser (Fig. 2) describing the relevant forces on each of the elements and nodes. Knowing the forces and mass properties of each section the accelerations can be solved and numerically integrated to velocities and excursions. Although in reality the fluid force-riser motion mechanism is both complicated and important, the fluid load models used in the discrete element methods are normally rather simple and inaccurate. The models are generally based on the well-known Morison approach using relative fluid velocities. Constant drag and inertia coefficients are derived from 2-D cylinder tests. Flexible risers, though slender in overall dimensions, comprise 3-D curvature, subsea buoys, tethers and buoyancy beads in various shapes. These features provide 3-D flow ensuing not only large in-line drag forces but also lift forces perpendicular to the incident flow. Correlation studies [3J have clearly demonstrated that use of conventional 2-D cylinder data may lead to e.g.significant under estimation of tensions.

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