Abstract
Risers are used for carrying crude oil/gas from seabed to supporting platform. These risers experience various environmental loads while carrying the fluids. Generally, the length of the riser depends on water depth, type of the platform that is attached to, sea state and environmental conditions. The deformation characteristics of the risers shall be analyzed in order to assess the design parameters and safety operation. A nonlinear finite element analysis of the riser at 300 and 2000 m water depth has been performed under wave, current and wave + current loading in the present study. The riser is modeled as a two-dimensional beam element considering six degree of freedom which is suspended in the floating drilling platform and subjected to both axial and lateral forces. A straight riser at 300 m water depth is considered for the present study. As the J-Lay technique of the riser is easy and mostly used in the industry, a J-Lay at 2000 m is also analyzed. A MATLAB code ‘Riser Stat’ is developed to analyze the riser. The axial extensions of all the elements are estimated considering top tension, weight of the riser, internal liquid weight and buoyancy. Morison equation is used to estimate the wave force on the riser. The axial and horizontal displacements are at each node of the finite element model of the riser and are estimated due to the effect of top tension and wave force in a wave cycle. Series of analyses are performed on the J-Lay riser under wave height of 2.0 m and wave period of 5–15 s at and increment in wave period of 1 s. Linearly varying current velocity of 1.4 and 1.0 m/s at sea surface to 0 m/s at a depth of 200 m is considered to estimate the current loading. The effective tension along the length of the riser at 2000 m water depth is compared with the Lenci and Callegari (Acta Mech 178:23–39, 2005) [1]. The results are compared well. The response of the riser under the combination of wave and current showed more when compared with the response of the riser under only wave loading.
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Abbreviations
- A :
-
Cross-sectional area of the riser (m2)
- a :
-
Wave amplitude (m)
- C d :
-
Drag coefficient
- C m :
-
Inertia coefficient
- d :
-
Water depth (m)
- \( d_{\text{f}} \) :
-
Wave loading per unit length (kN/m)
- D :
-
Outer diameter of the riser
- E :
-
Modulus of elasticity of the riser material (N/m2)
- f :
-
Force vector
- g :
-
Acceleration due to gravity (m/s2)
- I :
-
Area moment of inertia (m4)
- k :
-
Wave number (m−1)
- \( K_{\text{E}} \) :
-
Elastic stiffness matrix
- \( K_{\text{G}} \) :
-
Global elemental stiffness matrix
- \( K_{\text{l}} \) :
-
Local elemental stiffness matrix
- L :
-
Length of the element
- \( l_{i} \) :
-
Length of the riser element
- \( S_{i} \) :
-
Curved length of the riser
- \( S_{\text{E}} \) :
-
Geometric stiffness matrix
- t :
-
Time step (s)
- T :
-
Transformation matrix
- \( T_{i - 1} \) :
-
Effective tension of the previous element (kN)
- \( T_{\text{Eff}} \) :
-
Effective tension in the element (kN)
- u :
-
Water particle velocity (m/s)
- \( u_{\text{c}} \) :
-
Current velocity (m/s)
- \( \dot{u} \) :
-
Water particle acceleration (m/s2)
- \( w_{\text{r}} \) :
-
Weight of the riser element (kg)
- \( w_{\text{i}} \) :
-
Weight of the internal fluid (kg)
- \( w_{\text{B}} \) :
-
Buoyancy of the riser element (kg)
- x :
-
Spatial location of the node in the direction of the wave
- \( x_{i} \) :
-
Spatial location of the riser in the direction of the wave
- \( y_{i} \) :
-
Spatial location of the riser in the direction of water depth
- z :
-
Elemental water depth (m)
- ρ :
-
Density of sea water (kg/m3)
- Δ:
-
Displacement vector
- \( \theta_{i} \) :
-
Angle of the riser with vertical axis
- σ :
-
Wave angular frequency (Hz)
References
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Madhuri, S., Kumar, B.N., Rao, K.V. (2019). Nonlinear Static Analysis of Offshore J-Lay Risers Using Finite Element Method. In: Rao, A., Ramanjaneyulu, K. (eds) Recent Advances in Structural Engineering, Volume 1. Lecture Notes in Civil Engineering , vol 11. Springer, Singapore. https://doi.org/10.1007/978-981-13-0362-3_44
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DOI: https://doi.org/10.1007/978-981-13-0362-3_44
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