Coupling Effects for a Deepwater Spar
Authors: Colby Craig , Sødahl Nils , Katla Erling , Okkenhaug Siril 
Published: October 2008

Abstract
As production systems extend to water depths beyond 3,000 feet, the effects of mooring and riser become increasingly significant when predicting a Spar's response. For these water depths, the viscous damping, inertial mass, current loading and restoring effects from both the mooring and riser system should be included to accurately solve the system's motion response. For some systems, these effects can magnify the extreme response, but for Spar platforms, coupling the mooring and riser with the vessel motion typically results in a reduction in extreme motion response.
The ability to predict a significant reduction in the extreme motions can directly result in a smaller and less expensive mooring and riser system and indirectly in a lighter Spar platform through a reduction in payload requirements. Given the limitations of current model basins for deepwater Spar systems, quantification of the coupling effect of the mooring and riser system with the Spar hydrodynamic response can best be done through analytical software. This paper will describe recent efforts to predict and quantify these effects.

Introduction
The analysis results presented in this paper were developed for a comparative study organized by the Deepstar JIP. The comparative study involved analyzing a generic Spar structure for a GOM location with water depths of 3,000, 6,000, and 10,000 feet. The results presented are for a 100-yr. extreme hurricane condition. Coupling effects are identified and quantified by direct comparison of a coupled and de-coupled analysis.

Coupled vs. De-Coupled Analysis
Throughout this paper, the terms coupled and de-coupled analysis are used. These are defined as follows:Coupled analysis:Vessel forces including wave frequency and low frequency hydrodynamic forces are generated in the time domain using the program SIMO, Ref. 1, from previously calculated wave force transfer functions. These transfer functions were created from the wave diffraction program WADAM, Ref 2. The complete system of equations accounting for the rigid body model of the hull as well as the slender body model for the risers and mooring lines are solved simultaneously using a nonlinear time domain approach for dynamic analyses. The RIFLEX_C computer code, Ref. 3, is applied for all case studies reported in this work.De-coupled analysis:The vessel equation of motions are solved in the time domain similar to that described above using the program SIMO (i.e. the floater models applied in coupled- and decoupled analyses are identical). The effect of the mooring and riser system is included quasi-statically using nonlinear springs derived from the catenary solutions. In general, additional coupling contributions from damping as well as current loading on the slender structures need to be assessed and given as input to de-coupled analyses. However, no additional damping or current loading contribution from the mooring and riser system is included in de-coupled analyses reported in this work.
The above definitions will allow for quantification of coupling effects by direct comparison of results from coupled and de-coupled analyses, which is the main purpose of the present study.