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Dynamics of a Vertical Riser with a Subsurface Buoy

P.S.D. PereiraPetrobras R&D Center, Subsea Technology Division

Rio de Janeiro, R.J., Brazil

C.K. MorookaDept. of Petroleum Eng., Faculty of Mechanical Engineering, State University of Campinas

Campinas, S.P., Brazil

D.F. ChampiFaculty of Mechanical Engineering, State University of Campinas

Campinas, S.P., Brazil

ABSTRACT

A vertical riser sustained by a subsurface buoy is considered in the

current work. The physical riser terminates with a subsurface buoy near

the sea surface. From the buoy a flexible line is usually applied to make

the connection to a floating production facility. The present study

disregards the flexible line. Dynamic behavior of the system is

described and hydrodynamic forces due to current and waves are

evaluated. The solution in time domain is obtained and includes thetransverse motion of the system due to vortex-induced vibrations.

Discussions of systems motion are carried out in terms of riser and

buoy dynamics, for both, in-line (collinear with the external loads) and

transverse directions. The influence of buoy dimensions is also

analyzed. Comparisons with analytical solutions are carried out to

validate the solutions.

KEY WORDS:Offshore Risers; Hydrodynamics; Sea Wave; OceanCurrent; Vortex Induced Vibration.

INTRODUCTION

Nowadays, most of the petroleum discoveries in Brazil are located in

the deep and ultra-deep waters. Therefore, new concepts for offshoresystem and risers are needed to overcome the demanding challenges

presented by operations in deepwater. Many risers systems have been

presented in the literature (Serta and Roveri, 2001). Among those

systems, self standing hybrid riser system (Fisher et al, 1995; Dailey et

al, 2002) seems to be an attractive alternative. However, several

investigations are still needed for Self-Standing Hybrid Riser System

(SSHR) (Pereira et al, 2005).

Three main components compose a SSHR system: a) a long vertical to

tensioned steel pipe riser connected to a wellhead at the sea bottom, an

to a subsurface buoy near the sea surface; b) a subsurface buoy place

below the waterline, and; c) a flexible jumper. A floating productio

unit receives the upper termination of the flexible jumper and th

downward termination is connected to a gooseneck fixed to the top o

the subsurface buoy. The floatation of the subsurface buoy togethe

with the upward tension component due to flexible jumper at thconnection at the top of the buoy gives the necessary upward tension

which maintains the riser standing in the vertical configuration. Th

SSHR system is usually used to transport of oil and gas productio

from isolated petroleum well or for a set of wells linked by a manifol

at the seabed. It could be also used to export oil or gas production the

floating production unit to an offloading system.

In the present paper, the dynamic behavior of the vertical riser with

subsurface buoy as a part of SSHR system is presented. Combined

riser and subsurface buoy is commonly called a tower. Figure 1 show

an illustration of the vertical riser and subsurface buoy with th

respective possible tower displacements and motion. The towe

displacements are obtained through time domain integration of system

dynamics equations. Maximum and minimum envelop fodisplacements are shown for both in-line and transverse direction

respectively. Influence of parameters such as the ocean curren

velocity, the period of the wave, riser hydrodynamics coefficients

geometry of the buoy and internal fluid has been investigated. A

simplified analytical solution for riser free vibration is initially

described and, considerations of hydrodynamic forces for in-line an

transverse directions are also described.

Proceedings of the Sixteenth (2006) International Offshore and Polar Engineering Conference

San Francisco, California, USA, May 28-June 2, 2006

Copyright 2006 by The International Society of Offshore and Polar Engineers

ISBN 1-880653-66-4 (Set); ISSN 1098-6189 (Set)

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Fig. 1 Vertical riser with a subsurface buoy.

STATIC S OF THE VERTICAL RISER

The static configuration of a riser can be obtained from the equilibrium

of forces that act on the elements of the riser (Fig. 2). The equilibrium

of forces (Patel, 1989) including riser weight, axial force in the riser

length, the force produced by external and internal pressure, and the

external force produced by current velocity over the riser element,

result in the differential Equation (Eq.1) for riser static behavior.

dz

dxAAAF

dz

xdApApT

dz

xdEI

dz

diissnii )()( 002

2

002

2

2

2

++=+

(1)

Fig. 2 Forces in a riser element.

where, p0is the external hydrostatic pressure around the riser. p

is the internal hydrostatic pressure. A0is the cross-sectional are

of riser. Aiis the internal cross-sectional area of the riser and A

is the cross-sectional area of riser wall. i is the fluid specifiweight in the riser. 0is the specific weight of fluid surroundinthe riser (sea water) and S is the specific weight of riser wal(steel).

The analytical solution for equation (Eq. 1) can be derive

straightforwardly if the distributed effect of riser weight is neglecteand replaced by a constant axial tension along its length and the rise

diameter and the flexural stiffness (EI) and the external current loa

(Fn) of the riser are all considered constant.

VERTICAL RISER FREE VIBRATION MODES

Analytical solutions for the risers natural frequencies and mode

considering uniform riser cross-section, material, with constant axia

tension through the riser length can be obtained. In the followin

results, riser terminations fixed at the sea bottom and free to rotate a

the connection with the subsurface buoy are used.

Therefore the equation of riser behavior free to vibrate can be describe

by the following equation:

02

2

2

2

4

4

=

+

t

xA

z

xT

z

xEI (2

The analytical solution (Champi, 2005) for the Eq. 2 is as follows:

)cos()sin()cosh()sinh( 24231211 zrCzrCzrCzrCX +++= (3

where, 442

142

knn

r ++= ; 442

242

knn

r ++= ;

42*

EI

Ak

= ; EITn /2 = ;

with the coefficients C1,C2, C3and C4obtained from the consideratio

of riser end conditions.

Numerical solution has been evaluated based on previous work (Ferrar

and Bearman, 1999, Martins et al, 2003, Morooka et al, 2003). In thi

case, the riser free vibration behavior can be represented in matrix

form, as follows:

[ ]{ } [ ]{ } 0)()( =+ txKtxM && (4

where, [M] is the mass matrix. [K] is the stiffness matrix.x(t)is thharmonic motion { } { } ).cos(0 = txx and is the phase angle.

The characteristic equation becomes:

[ ] [ ]( ) [ ] [ ] 0det 22 == MKMK (5

where, is the natural frequency of the riser.

x

weightAxial force

nF

External forceon the riser

CU

nF

External force External& internalPressures

External& internal

T+dT

T

V

V + dV

dx

dz

d+

zizo FF + xixo FF +

d

r

rdFn

z

DODi

W

x

weightAxial force

nF

External forceon the riser

CU

nF

External force External& internalPressures

External& internalExternal& internalPressures

External& internal

T+dT

T

V

V + dV

dx

dz

d+

zizo FF + xixo FF +

d

r

rdFn

z

DODi

W

Ucu

y (Transverse)

Wavevelocity profile

Uc

Wave Current Wave and Current

x(In-line)x

zy

u, Uc

Flow

D

z

Fy

z

Riser Cross Section

y

x

vortex

Fy

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IN-LINE HYDRODYNAMICS

The fluid force produced in the direction of the flow when the fluid

passes perpendicularly around the slender vertical riser with circular

transverse sectional area is usually composed by two terms (Sarpkaya

and Isaacson, 1981). The first term is due to the inertial effect produced

by acceleration of the fluid around the outer surface of the riser, and the

second one is the drag effect proportional to the fluid velocity.

Modified Morison equation has been used to compute in-line force onthe riser, as in follow:

( )xUuxUuACxuACuAF ccDDIAIx &&&&&& ++++= )( (6)

where, Fx is the in-line force per unit length, u is the wave particle

velocity, Ucis the current velocity, x& is the riser structure velocity inthe x direction, CD is the drag coefficient and CA is added mass

coefficient, respectively. Finally, AI =Do2/4, AD =Do/2, Do is the

external diameter and ois the seawater density.

In the present paper, for simplicity, Eq. 6 has been also applied to

estimate the in-line force on the subsurface buoy.

TRANSVERSE HYDRODYNAMICS

Transverse force happens when the fluid flow passes around the

vertical cylindrical riser producing variation in the pressure in the

transverse direction to the incoming flow. Pressure variation around

outer surface of the riser provokes separation of the flow and induces

vortex shedding. The presence of vortex shedding originates as an

unbalance of forces in time and produces an oscillatory transverse force

(FVIV) (Fig. 3). The consequence of this oscillatory transverse force

result in the vortex induced vibration (VIV) of the riser.

Fig. 3 Representation of the transverse VIV force at a risercross cylindrical section.

In the present study, transverse force has been estimated by semi-

empirical modeling and solutions are obtained in a 3-D fashion

dynamic behavior (Blevins, 1990, Ferrari et al, 2001) as follows:

)..2cos(..))((2

1 2 ++= tfCDUxuF StCVIV & (7

where,sf =(.St)/D, =

t

UdtU0

and Ctis the average amplitude o

transverse force.sf is the average frequency of the vortex shedding.

is the phase difference between the transverse riser response and force

St is the Strouhal number. U is the cumulative average velocity of th

oscillatory flow. U is the instantaneous oscillatory flow velocity.

DYNAMIC BEHAVIOR EQUATIONS

Equations for riser in-line and transverse dynamic behavior ar

described in this section. The riser motion for the in-line and transvers

directions in matrix form can be written as follows:

[ ]{ } [ ]{ } [ ]{ } { }xFxKxBxM =++ &&& (8

[ ]{ } [ ]{ } [ ]{ } { }yFyKyByM =++ &&& (9)

where, x is the riser motion in the in-line direction, y is for th

transverse direction which is perpendicular to the x direction. Th

direction of current and incident waves coincides with the in-line rise

direction. In Eq. 8 and Eq. 9, [ B ] is the risers structural dampin

matrix.

The hydrodynamic forces for the two directions can be described by th

following equations:

( ) xACxUuVACt

uACF IAcrDDIMx &&& ++

= (10

4444 34444 21&&&

ReactionFluid

IArDDVIVy yACyVACFF = (11

where, CMis the inertia coefficient.

Fig. 4 Relative velocity between riser structure

and fluid particle.

u,Ucu,Uc

FluidvelocityVortexformation

u,Uc

TransverseForce

ransverse direction

YVIV

F

xD xxDx&

xD xxDx&

u,Ucu,Uc

FluidvelocityVortexformation

u,Uc

TransverseForce

ransverse direction

YVIV

F

xD xxDx&

xD xxDx&

r

CU

uu &,

22 )()( yxUuV Cr && ++=

)( xUu C &+

rVy&

Transverse

In-line

r

CU

uu &,

22 )()( yxUuV Cr && ++=

)( xUu C &+

rVy&

Transverse

In-line

( ) ( )22

r yxUuV c && ++=

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Water Depth (m) 2800.0

Riser Length (m) 2700.0

Fluid density surrounding the riser (kg/3

m ) 1025.0

Fluid density inside the riser (kg/3

m ) 970.43

Density of riser material (kg/3

m ) 7846.05

Outer Diameter (m) 0.45

Inner Diameter (m) 0.41

Young Modulus (kPa) 2.1x108

CD-CA-Ct 1.2-1.0-1.2

The interaction between riser displacements in the in-line and

transverse directions, as in Eq. 10 and Eq. 11 take into account the

relative velocity explained in Figure 4.

RESULTS

Initial calculations have been performed to verify the numerical code

developed for the presented study that has been adapted from previous

developments (Ferrari and Bearman, 1999).

Table 1 shows main dimensions for the riser considered in thecalculations. Figure 5 shows a comparison of displacements and

rotation angles along the length of the riser, with buoy andwithout buoy. The comparison was derived from static behavior

calculations. The end conditions of the system are fixed at the

bottom and free at the top. On one curve the axial tension alongthe length of the riser is taken to be constant. As expected, the

ocean currents viscous effect is larger with the buoy than

without it. It can be noted that rotation angles along the lengthof the buoy are constant indicating that it is in almost vertical.

On the curve displaying displacement without the buoy, the riser

angle at its upper most extremes follows the general rotational

behavior of the riser.

Figure 6 shows a comparison between analytical and numerical

solutions for free vibration modes for two different riser lengths, 100

meters and 1000 meters, respectively. Calculations forthe riser without

the buoy by analytical solution and by numerical one are compared.

The risers axial tension is taken to be constant in this case, as in the

previous one. Normalized amplitudes for free riser motion modes are

shown. A good agreement can be observed in the comparisons.

Following the calculations, dynamic behavior of the vertical top

tensioned riser with a subsurface buoy has been simulated in a very

deepwater condition. Table 2 shows main dimensions for the riser and

Table 3 for the buoy. The riser has been considered fixed at the bottom

end and fixed at the top to the buoy that is free to move. The considered

water depth is 2800 meters, and the subsurface buoy is submerged 100

meters below the surface.

Two different ocean current profiles have been applied: first constant

along the entire riser length extending to the buoy, and the second

constant only along the buoy length. Riser is considered fixed at the sea

bottom and at the buoy.

Table 1. Vertical riser in the initial calculations

Fig. 5 Riser displacement and rotation angle through the

riser length, with and without the subsurface buoy,

with constant riser axial tension.

Fig. 6 Riser free vibration modes.

Table 2. Main dimensions of the riser

Table 3. Main dimensions of the buoy

Length (m) 37.0

Outer diameter (m) 6.4

Young Modulus (kPa) 2.1x 1013

CD-CA-Ct 1.2-1.0-1.2

Length (m) 100

Outer Diameter (m) 0.25

Inner Diameter (m) 0.21106

Top Tension (kN) 178.0

Young Modulus (kPa) 2.1 x 108

Current Velocity (m/s) 1.0

Density of water (kg/ 3m ) 1025

Drag Coefficient (CD) 0.7

0

20

40

60

80

100

-1 0 1

1st

4th

3rd0

200

400

600

800

1000

-1 0 1

1st

2nd

3rd

Distancefromt

hesea

bottom[

m]

NumericalAnalytical

Normalized Amplitude

2nd

0

20

40

60

80

100

-1 0 1

1st

4th

3rd0

200

400

600

800

1000

-1 0 1

1st

2nd

3rd

Distancefromt

hesea

bottom[

m]

NumericalAnalytical

Normalized Amplitude

2nd

0

20

40

60

80

100

120

0 10 20

0

20

40

60

80

100

120

0.0 0.2 0.3

With buoy

No buoy With buoy

No buoy

Displacement [m] Rotation [rad]

Analytical Numerical

150

Distanc

efromt

heseabottom[

m]

150

Direction In line

0

20

40

60

80

100

120

0 10 20

0

20

40

60

80

100

120

0.0 0.2 0.3

With buoy

No buoy With buoy

No buoy

Displacement [m] Rotation [rad]

Analytical Numerical

150

Distanc

efromt

heseabottom[

m]

150

Direction In lineIn-line

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The numerical simulation results are presented in terms of envelops of

maximum and minimum amplitudes of the riser displacement along its

length. Mean displacement is shown and dynamic motion of the riser is

assumed to happen around this position. Parametric calculations have

been performed using the geometry of the buoy such as its diameter

and length to determine their influence over the involved

hydrodynamics coefficients. Other factors influence the hydrodynamic

coefficients like internal fluid, the current velocity and the wave period.

Figure 7 shows envelop of the maximum displacement when the ocean

current velocity is varied. Ocean current is present only along thesubsurface buoy length. For the in-line direction, riser displacement due

to static current load is visible. However, none is observed for the

transverse direction. As it was expected, when the current intensity

increases, larger displacements are observed in the in-line direction due

to drag. On the other hand, transverse riser motion is in general

decreased due to viscous drag damping. However, due to larger VIV

force around the buoy, the amplitude of displacement of the system

around the buoy is increased.

Figure 8 shows riser behavior in the presence of only waves. Various

wave periods have been used. For both in-line and transverse

directions, the amplitude of the riser motions increase with larger wave

periods.

Fig. 7 Envelop of maximum amplitudes for displacement

(only current with different velocities).


(only wave case, wave height of 4.0 m).

Figure 9 shows envelops of amplitude in the in-line and transvers

directions. The current velocity of 1.2 m/s only along the buoy length i

used with various diameters of the buoy. The riser axial tensio

increases with larger buoy diameter due to the larger buoyancy. Th

VIV force of the buoy is increased when the buoy diameter increases

In the result of Figure 9, the in-line motions are reduced and transvers

ones are increased when the buoy diameter increases.

In the same way, Figure 10 shows result for the riser in current with

constant velocity profile of 0.3 m/s along the riser and the buoy length

In this case, buoy length is varied and the same tendency stated abovis observed. In general, it could be observed that when the buoyancy o

the buoy increases through an increment of the buoy diameter o

length, riser in-line displacement and motion are diminished and th

transverse riser motion is increased.

Drag coefficient has been varied for the riser and buoy, as shown in th

results in the Figure 11. When the drag coefficient is increased, in-lin

riser displacement is increased due to drag. On the other hand

transverse riser motion is decreased due to the increase of drag which

acts to dampen this direction.


(only current, 1.2 m/s along the buoy length).


(only current, 0.3 m/s along the riser and buoy length).

0

400

800

1200

1600

2000

2400

2800

-2 0 2

0

400

800

1200

1600

2000

2400

2800

0 50 100 1 50Distancefrom

theseabottom

[m]

In line Transverse

Displacement [m]

Current velocity : 0.3 m/s 0.8 m/s 1.2 m/s 1.5 m/s

0

400

800

1200

1600

2000

2400

2800

-2 0 2

0

400

800

1200

1600

2000

2400

2800

0 50 100 1 50Distancefrom

theseabottom

[m]

In line Transverse

Displacement [m]

Current velocity : 0.3 m/s 0.8 m/s 1.2 m/s 1.5 m/s

0

400

800

1200

1600

2000

2400

2800

0 50 100 150

0

400

800

1200

1600

2000

2400

2800

-2.5 0 2.5Distancefrom

theseabottom

[m]

In line Transverse

Displacement [m]

Buoy diameter: 5.5 m 6.0 m 6.4 m 7.0 m

0

400

800

1200

1600

2000

2400

2800

0 50 100 150

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

In line Transverse

Displacement [m]

Buoy diameter: 5.5 m 6.0 m 6.4 m 7.0 m

0

400

800

1200

1600

2000

2400

2800

-0.2 0 0.2

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

In line Transverse

Displacement [m]

Period : 11.5 sec. 12.0 sec. 12.5 sec.

0

400

800

1200

1600

2000

2400

2800

-0.2 0 0.2

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

In line Transverse

Displacement [m]

Period : 11.5 sec. 12.0 sec. 12.5 sec.

0400

800

1200

1600

2000

2400

2800

0 50 100

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distancefrom

theseabottom

[m]

In line Transverse

37 m 45 m 55 m

Displacement [m]

Length of the buoy :

0400

800

1200

1600

2000

2400

2800

0 50 100

0400

800

1200

1600

2000

2400

2800

0 50 100

0

400

800

1200

1600

2000

2400

2800

-2 0 2

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distancefrom

theseabottom

[m]

In line Transverse

37 m 45 m 55 m

Displacement [m]

Length of the buoy :

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(only current, 0.5 m/s along the riser and buoy length)


(only current, 0.5 m/s along the riser and buoy length).



Figure 12 shows simulation results for in-line and transverse motion othe riser and buoy where different values for added mass coefficien

have been used. No significant variations can be noted for thi

simulation for the in-line riser displacement and motion in current du

to dynamic nature of the added mass effect. For the transvers

direction, when added mass coefficient is increased smaller motion ar

observed for the riser along its length. Constant current profile of 0.

m/s is considered along the riser and buoy lengths.

In Figure 13, maximum amplitudes for displacement are shown for th

riser and buoy in current with constant current profiles of 0.5 m/s. It i

noted that if the transverse force coefficient Ctis increased, almost n

variation is noted for the in-line displacement of the riser, however, a

increase in the transverse riser motion can be observed as it wa

expected.

Figure 14 shows the effect of the presence of petroleum fluid in th

riser. In this case, the presence the internal fluid affects the effectiv

tension and in consequence the overall stiffness of the riser. With th

petroleum fluid in the riser, its displacement in the in-line direction a

the riser motion in the transverse directions appear a little bit bigger i

compared with without the internal fluid case.

Figure 15 shows the time history from numerical simulations for th

vertical riser and subsurface buoy dynamics. In-line and transvers

motions are from the follow locations: 2700 meters (top of th

submerged buoy), 2663 meters (bottom the buoy), 1440 meters (on th

vertical riser) and 890 m (on the vertical riser). Only a current of 0.

m/s along the buoy length has been considered for this case. For the inline directions, motion is derived from the mean (static) displacemen

of the system. Larger displacements were found for the transvers

direction than in the in-line direction for this case which only consider

current. Larger motion is observed in the transverse direction close t

the buoy. For the in-line direction, displacements were bigger in th

risers mid length.

0

400

800

1200

1600

2000

2400

2800

-3 0 3

0

400

800

1200

1600

2000

2400

2800

0 50 100Distancefrom

theseabottom

[m]

Displacement [m]

In line Transverse

0.6 1.0 1.3 2.0CA :

0

400

800

1200

1600

2000

2400

2800

-3 0 3

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

Displacement [m]

In line Transverse

0.6 1.0 1.3 2.0CA :

0

400

800

1200

1600

2000

2400

2800

0 2 4 6

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distance

from

theseabottom

[m]

In line Transverse

Displacement [m]

Without internal fluid With internal fluid

0

400

800

1200

1600

2000

2400

2800

0 2 4 6

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distance

from

theseabottom

[m]

In line Transverse

Displacement [m]

Without internal fluid With internal fluid

0

400

800

1200

1600

2000

2400

2800

0 75 150

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distance

from

theseabottom

[m]

In line Transverse

Displacement [m]

1.20.80.5 2.0:DC

0

400

800

1200

1600

2000

2400

2800

0 75 150

0

400

800

1200

1600

2000

2400

2800

-2 0 2Distance

from

theseabottom

[m]

In line Transverse

Displacement [m]

1.20.80.5 2.0:DC

0

400

800

1200

1600

2000

2400

2800

-5 0 5

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

Displacement [m]

In line Transverse

1.2 2.50.1:tC

0

400

800

1200

1600

2000

2400

2800

-5 0 5

0

400

800

1200

1600

2000

2400

2800


theseabottom

[m]

Displacement [m]

In line Transverse

1.2 2.50.1:tC

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(a)

(b)

Fig. 15 Time history of the amplitude of riser displacements

from numerical simulations for four different locations:

(a) In-line direction and, (b) Transverse direction.

CONCLUSIONS

Numerical simulations for the vertical riser with a subsurface buoy as a

part of a SSHR system have been carried out. Fundamental equations

for the system behavior and hydrodynamic loads have been described.

Simulation results have been compared with analytical solutions and

time domain simulation results have been shown for a very deep water

case. Parametric simulations have been undertaken. Particular attention

has been taken to VIV effects.

The hydrodynamic model used in this study for in-line and transvers

directions has shown to be practical with the coupling of the tw

directions in a 3-D fashion dynamic system behavior.

The subsurface buoy needs a special care regarding its structural an

geometric aspects, because it demonstrated great influence in th

overall vertical riser dynamics.

The influence of internal fluid flow affects its axial tension

consequentially, the stiffness of the system. This fact needs particula

attention in further studies regarding riser fatigue.

The hydrodynamic coefficients in the in-line and transverse direction

are very important for the investigations of dynamic behavior of

SSHR. Therefore, the correct determination of these values i

fundamental for numerical simulations.

ACKNOWLEDGEMENTS

The authors would like to acknowledge CNPq and PETROBRAS fo

their support for the present study.

REFERENCE

Blevins, R., 1990, Flow-Induced Vibration, 2nd Edition, KriegePublishing Company.

Champi, D.F., Morooka, C.K., Pereira, P.S.D., 2005, Numerical Stud

of Self Standing Riser System, 18th International Congress o

Mechanical Engineering (COBEM2005), Ouro Preto, Minas Gerai

Brazil.

Dailey, J.E., Healy, B.E., Zhang, J., 2002, Truss Riser Tower in Deep

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-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

2700 m from the sea bottom




Time (s)

Time (s)

Time (s)

Time (s)

Displacement

(m)

D

isplacement

(m)

Displacement

(m)

Displacement

(m)

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300

-0.01

0.00

0.01

800 900 1000 1100 1200 1300





Time (s)

Time (s)

Time (s)

Time (s)

Displacement

(m)

D

isplacement

(m)

Displacement

(m)

Displacement

(m)

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300





Displacement

(m)

Displacement

(m)

Displacement

(m)

Displacement

(m)

Time (s)

Time (s)

Time (s)

Time (s)

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300

-1.80

0.00

1.80

800 900 1000 1100 1200 1300





Displacement

(m)

Displacement

(m)

Displacement

(m)

Displacement

(m)

Time (s)

Time (s)

Time (s)

Time (s)

43

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