Marine Systems & Ocean Technology

, Volume 10, Issue 1, pp 26–37 | Cite as

The influence of wind-wave energy spreading on the riser system response of a spread-moored FPSO

  • Marcelo Caire
  • Carlos Eduardo Silva de Souza
  • João Paulo Ramos Cortina


Floating unit, mooring lines and risers comprise an integrated dynamic system that responds to environmental loading due to wind, waves and currents in a complex way. The riser system response of a spread-moored FPSO in deepwaters is greatly influenced by first-order wave motions, where the consideration of wind-wave energy spreading may have an important impact on the integrity assessment. A 5-year database generated by a numerical wave model (available from NOAA) provides a proper representation of the wind-wave spreading factor distribution for Santos Basin, offshore Brazil. Based on these data and considering a cos\(^\mathrm{2s}\) formulation for the spreading function, a short-term sensitivity study is performed to evaluate the spreading parameter \(s\) influence on the top tension response when the system is subjected to beam seas. The numerical simulations are carried out employing a simultaneous dynamic analysis of the vessel and slender structure system. Second-order loads, which may also be important by inducing mean and slow drift motions, are taken into account with a modification of Newman’s method, where the drift force coefficients are averaged with the squared surface elevation. The results show a significant influence of \(s\) on the riser response statistics.


Wave energy spreading Spread-moored FPSOs Numerical simulations Fully coupled analysis 

List of symbols


Unidimensional wave spectrum


Directional wave spectrum


Spreading function

\(\omega \)

Wave circular frequency


Significant wave height


Peak period

\(\gamma \)

JONSWAP spectrum enhancement factor

\(\theta \)

Propagation direction

\(\theta _0\)

Mean propagation direction


Spreading parameter


Spectral width

\(\mathbf {m}\)

Structural mass matrix

\({\mathbf {A}}\)

Frequency-dependent added mass matrix

\({\mathbf {B}}\)

Frequency-dependent potential damping matrix

\({{\mathbf {D}}_{\mathbf {1}}}\)

Linear viscous damping matrix

\({\mathbf {K}}\)

Hydrostatic stiffness matrix

\({\mathbf {x}}\)

Vessel position vector

\({\mathbf {q}}\)

Exciting force vector

\({{\mathbf {q}}_{{\mathbf {1}}}}\)

First-order wave forces vector

\({{\mathbf {q}}_{{\mathbf {2}}}}\)

Second-order wave forces vector

\({{\mathbf {q}}_{{\mathbf {EXT}}}}\)

Loads from coupling elements vector

\(\mu _\mathrm{x}\)


\(\sigma _\mathrm{x}\)

Standard deviation


Largest expected value



This work has been supported by SINOCHEM do Brasil through the ANP (National Petroleum Agency) investment clause in Research, Development and Innovation.


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Copyright information

© Sociedade Brasileira de Engenharia Naval 2015

Authors and Affiliations

  • Marcelo Caire
    • 1
  • Carlos Eduardo Silva de Souza
    • 1
  • João Paulo Ramos Cortina
    • 1
  1. 1.Instituto SINTEF do BrasilBotafogoBrazil

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