Alternative Shape of Spar Platforms for Use in Hostile Areas
Authors: Haslum H.A. , Faltinsen O.M. 
Published: October 2008

Abstract
Motion response of spar platforms is studied, using a simplified calculation method. Classical spar platforms are vulnerable to heave resonance in sea states with long wave periods. Mathieu unstable pitch motion combined with extreme amplitude heave resonance is detected both by using this simplified method and in model tests. Alternative hullshapes with improved heave and pitch motion characteristics are proposed.

Introduction
The deep draft spar platform has been considered as a competitive alternative for deep-water field developments. So far, spar production platforms have only been installed in the Gulf of Mexico, but the concept has several times been proposed for fields in the Northern North Sea and West of Shetland.
By a 'classical spar' production platform is here meant a large circular cylinder with constant cross section and with a draft of approximately 200-meter. The idea behind this concept, or rather what is justifying the use of this enormous hull is that due to the large draft, the motion response of the platform should be adequately low to permit installation of rigid risers with dry wellheads. Therefore, the motion response (in particular heave and pitch) is crucial for the concept.
Motion response optimization of 'dry wellhead' platforms is an important issue. Extensive computational tools are often used in the design process as 'black box' analysis tools. Since physical understanding is important in design, it is desirable with supplementary simplified computational methods. Therefore several new, smaller and simpler computer programs were developed. Sensitivity of different hull configurations is easily verified without extensive input files. In addition, simplified calculation tools may be tailor-made to solve special problems such as the Mathieu instability. The pitch/heave instability problem, which is revealed in this work, could probably not have been found using state of the art commercial calculation tools.
The design philosophy behind deep draft floaters in general implies that the draft is adequately large to reduce 1.order heave excitation sufficiently. As a result, second order difference frequency excitation can be an important contributor to the total heave response. However, ordinary deep draft spar platforms have low damping and relatively low natural period. A combination of these two characteristics and swell may lead to linearly excited heave resonant motion of the spar. Consequently 1.order wave frequency effects become more important than 2.order difference frequency effects for the total heave motion. In a survival condition, wind is an important contributor to the total surge and pitch response. In this study only wave effects are taken into the optimization process.

Linear Wave Frequency Response
A simplified analysis method is developed. Assuming long wavelengths and linear damping, the linear equations of motion for surge, sway, heave, roll, and pitch are solved in the frequency domain. The heave motion is uncoupled while roll/sway and pitch/surge are coupled. Strip theory and frequency independent added mass coefficients are used. The damping is representing non-potential flow effects. No internal flow effects in the moonpool are considered (i.e. the spar bottom is closed). This simplified method is described in Ref.1.