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DYNAMIC BEHAVIOR OF PIPELINES AND RISERS DUE TO

VORTEX-INDUCED VIBRATION IN TIME DOMAIN

C.K. Morooka 1, R.I. Tsukada

2

1,2 University of Campinas

Faculty of Mechanical Engineering & Center for Petroleum Studies

LabRiser - Offshore Systems and Risers

Abstract. Vortex-Induced Vibration (VIV) plays an important role in the design of oil

and gas production systems in offshore pre-salt fields in Santos Basin, Brazil. The

importance is represented by the large depth of petroleum reservoirs bellow the subsalt

layer, the ultra-deep waterdepth and the far distance of the oilfield from the coast. Very

aggressive fluid components like CO2 and SO2 present in the produced petroleum make

more complex the necessities for material of pipelines and risers. And, they will

increase the effects of the fatigue problems usually observed in risers and pipelines due

to the vibrations. The VIV in offshore structures is complex and it has still not been

completely understood, particularly in high Reynolds number (Re) currents. This paper

will describe a VIV simulation approach for the dynamic behavior of pipelines and

risers, in time domain. A semi-empirical approach is adopted to calculate the transversal

VIV force based on the lift coefficient and the Strouhal number. The fluid reaction force

opposing the riser’s motion due to VIV is evaluated by a Morison-type formulation. In

this attempt, two dimensional fluid flow is taken into account, and the shedding

frequency not locked onto the riser frequency of vibration is considered. The evaluation

of the proposed approach and the verifications of the adopted simplifications are carried

out through comparisons with experimental results.

INTRODUCTION

Most of petroleum discoveries in Brazil are located in offshore areas. Different offshore

riser systems are applied on the production phase of the petroleum field production. In

general, risers are slender and cylindrical pipes connecting the wellhead at the sea

bottom to a floating production platform at the sea surface. The riser is exposed to

environmental waves and current forces, and it is also forced by the platform motions.

Depending on the current velocity, periodic and alternate shedding of vortices appears.

This is the result of the boundary layer separation in the fluid flow around the riser

external surface. The forces due to the vortex shedding can cause vibrations on the riser,

and this phenomenon is normally called as Vortex-Induced Vibration (VIV).

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VIV is a very important effect and it should be taken into account in a design process of

offshore production systems. For instance, in cases with the presence of CO2 and SO2 in

the produced petroleum as observed in the pre-salt reservoirs Santos Basin [1],

aggressive fluid components could appear in the produced fluid. It can contribute to

reduce the fatigue life of a riser. Moreover, the oilfield commonly placed far from the

cost in ultra deep water depth demands longer risers and pipelines.

Denoting the current direction as the in-line direction (IL) and the orthogonal direction

to it as the cross-flow (CF), it is well known that the riser vibrates in both direction due

to the in-line VIV (IL VIV) and the cross-flow VIV (CF VIV). The IL VIV is caused by

the oscillation of the drag and it happens in a frequency two times greater than the CF

VIV [2], which is originated by the oscillation of the lift.

VIV has been intensively studied during the last decades resulting in many approaches

to estimates the forces resulted by this phenomena [2], and the influence of it in the

dynamic behavior of risers. Estimation procedures typically follow analytical, empirical

or numerical approaches, respectively. Each procedure has particular restrictions and it

is better than other according to the adopted assumptions.

Herein a semi-empirical approach will be presented and applied for different

configurations of risers and pipelines. In this case, the VIV forces are computed based

on a quasi-steady solution that makes use of empirical hydrodynamic coefficients, such

as the lift (CL) coefficient and the Strouhal number (St). The fluid reaction force

opposing the riser’s motion due to VIV is evaluated by a Morison-type formulation [3].

In this attempt, the in-line VIV is neglected, and the two dimensional fluid flow is taken

into account. Moreover, the shedding frequency is considered not locked onto the riser

frequency. However, it is well known that the in-line VIV has significant contribution in

the fatigue life, the 3D flow is observed [5] depending on the Reynolds number (Re),

and finally, for the reduced velocity nearby the five, the lock-in is commonly observed.

In order to verify the accuracy of the results following the presented approach, a set of

experimental model tests have been accomplished. They are results for a Top Tensioned

Riser (TTR), Steel Catenary Riser (SCR) and free-span pipelines, respectively,

previously published [3, 6, 7, 8, 9]. Very promising results, following the described

approach have motivated a continuous investigation.

TIME DOMAIN SIMULATION

A time-domain integration scheme or a frequency-domain analysis is usually applied for

the theoretical prediction of riser behavior for design purposes. Time-domain analysis

[3] is able to consider nonlinearities such as those related to riser material and

hydrodynamics of the sea current around the riser. Frequency-domain analysis [10] is

appropriate when the nonlinearities could be linearized. This approach is

computationally efficient, once complicated iterative convergence criteria can

commonly be avoided, and in general, it presents more conservative results.

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Today, time-domain analysis is a common practice to predict in-line riser behavior

under currents and waves forces, and forces induced by the floating platform motions.

The application of semi-empirical models for riser hydrodynamics has shown to be very

effective to provide reliable and practical solutions. Concurrently, Computational Fluid

Dynamics (CFD) appears as a useful tool for theoretical calculation of the VIV effect

[2, 5]. However, realistic reproduction of the VIV usually involves a huge

computational effort and reliable results are restricted for problems involving simple

geometrical configurations and flows. There is no common sense for which

methodology is more realistic to predict the riser Vortex Induced Vibrations (VIV). In

previous works, the importance of VIV in riser fatigue service life has been

demonstrated [11, 12]. Nevertheless, a clear understanding of the VIV effect and its

correct representation by a semi-empirical relationship to describe riser behavior for

design purpose is still needed and is fundamentally important.

In the present study, a semi-empirical relationship based on hydrodynamic coefficients

for cylinders from the literature is applied for simulations. Time-domain approach is

applied to estimate the in-line and cross-flow riser behavior. A Finite-Element Method

(FEM) is applied for the riser structure, and mass, stiffness and structural damping are

taken for each riser element.

TOP TENSIONED RISERS (TTR)

In general, a top tensioned riser (TTR) can be considered as a vertical slender pipe

excited at its upper end by the floating platform motions caused by waves, currents and

winds. The riser suffers direct action of sea current and waves along its length.

In the present approach, the riser motions for in-line and cross-flow directions

respectively can be taken independently for the two vertical perpendicular planes as the

scheme in Figure 1. The set of equations for the riser dynamic behavior in matrix form,

for the in-line and cross-flow directions are, respectively, as follows:

[ ] [ ] [ ] ( ) xACxUuVACt

uACxKxBxM IACrDDIMxxx

&&&&&& −−++∂

∂=++ (1)

[ ] [ ] [ ] ( )( ) ( )ϕ++−+−−=++ tf2πcosCDUxuρ2

1yVACyACyKyByM sLo

2crDDIAyyy

&&&&&&& (2)

where, [M] is the riser mass matrix, [B] is the riser structural damping matrix and [K] is

the riser stiffness matrix; CD and CA (= CM – 1) are drag and added mass coefficients,

respectively, CM is the inertia coefficient; Uc is the current velocity; u is the water

particle velocity due to the waves; AI = ρπD02/4, AD =ρD0/2, and D0 is the riser outer

diameter; finally, 22Cr y)xU(u|V| && +−+= is the relative velocity between the

external fluid velocity and riser structure, which couples riser behavior between the in-

line and cross-flow directions. Further, CL is the lift coefficient, ϕ is the cross-flow

force phase, St is the Strouhal number, and )y(x && , )y(x &&&& are the velocity and acceleration,

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respectively, of the riser in the in-line (cross-flow) direction. Finally, Sf is the mean

shedding frequency, with ( ) D/SUf tS ⋅= and ( )( ) ( )0t

0t CS tt/tdUxuU −∫ ⋅+−= & .

Equations (1) and (2) are solved by integration through discrete intervals of time, and

the motions of the entire length of the riser are obtained in a quasi 3-D fashion.

Figure 1. A typical scheme for an offshore production system with a top tensioned riser.

In order to verify the accuracy of computer implementations, comparisons with

experimental results in a wave basin for a top tensioned riser (TTR) model have been

carried out. A composite solid model made by Teflon coated brass was used in the

experiment. Geometric similarity was achieved from the outer diameter and length

relationship between model and prototype [6, 7]. Table 1 summarizes the main

dimensions of the riser model.

Model scale 1/50 was applied for the riser in this case. This model scale allowed the

representation of the main involved riser structural and hydrodynamics properties.

Therefore, material properties such as EI, EA, mass per length, and geometry were

adjusted by available materials for the riser model in order to represent the prototype

behavior.

In the experiments the riser model is tensioned at the top by constant weights and

horizontal forced oscillation device was installed in the water channel [6, 7]. Two sets

of underwater cameras were used to measure riser displacements, and both ends of the

riser, top and bottom respectively, are free to rotate.

x

Wind

Wave

Riser

Floating Production

z y

Current

Sea

Current

IN LINE

CROSS-FLOW

Wellhead

X

Y Z

g

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Table 1. Comparison between prototype and model parameters [7]

Properties Real Scale Model (1/50)

Teflon Brass core

Outer Diameter (m) 0.25 0.0050 0.0017

Inner Diameter (m) 0.21106 0.0018 -

Modulus of Elasticity (N/m2) 2.1x1011 0.4x109 1.006x106

Density of Material (kg/m3) 7860 2170 8600

Water Depth (m) 100 2.0

Riser Length (m) 120 2.4

Top Tension (N) 5.0x105 3.092

mLTTop (N/kg) 21.15 21.15

3mLEI (N/kg) 0.058 0.0502

mAρ 0.2554 0.2555

mDLρ 156.08 156.17

Mass per Length (kg/m) 197.01 0.08244

Comparisons of numerical simulations with experiment have been carried out to

validate the numerical computer program, as shown in Figure 2. Furthermore,

validations against API 16J Bulletin [13] results have been also carried out. Good

results have been observed in these comparisons [14].

0

In-line

20

40

60

80

100

120

-2 -1 0 1 2

Displacement (m)

Dis

tan

ce f

rom

Bo

tto

m (

m)

Numerical Experimental

Cross-Flow

0

20

40

60

80

100

120

-0.5 -0.25 0 0.25 0.5

Dis

tan

ce f

rom

Bo

tto

m (

m)

Displacement (m)

Numerical Experimental

0

In-line

20

40

60

80

100

120

-2 -1 0 1 2

Displacement (m)

Dis

tan

ce f

rom

Bo

tto

m (

m)

Numerical Experimental

Cross-Flow

0

20

40

60

80

100

120

-0.5 -0.25 0 0.25 0.5

Dis

tan

ce f

rom

Bo

tto

m (

m)

Displacement (m)

Numerical Experimental

Figure 2. Numerical simulation result compared with experimental data aiming

numerical code validation for a top tensioned riser (TTR) [14].

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SUBSEA PIPELINES WITH FREE-SPAN

Following the same mathematical model for the riser in above, it was applied for

horizontal subsea pipeline presenting free span as shown in Figure 3. The fundamental

difference between the pipeline and the riser cases, in general, is the direction of

pipeline weight, and the difference between internal and external pressures. In the

pipeline’s case, the external pressure is almost constant in all length and it could be too

large when compared with the internal pressure for deepwater regions. These

corrections were included in the solution [15]. Improvements to consider the soil effects

on each termination of the free spans were also included [16].

CrossCross--flowflow

InIn--lineline VorticesVortices

CurrentCurrent

PipelinePipeline

SoilSoil

CrossCross--flowflow

InIn--lineline VorticesVortices

CurrentCurrent

PipelinePipeline

SoilSoil

Figure 3. A typical scheme for a free-span pipeline.

A pipeline model experiment was conducted in the IPT towing tank [8]. Uniform

incident current to the pipeline was produced by towing it through the 220 meters long

water tank. A pipeline model was assembled in the towing carriage (Fig. 4) and it was

moved in the still water conditions with controlled constant towing carriage velocities.

Carriage

VR 1 to 10

Still water

276 m

aluminum pipe

Carriage

6 m

4 m

rail

End Plate

0.5 m

Y

X

Y

Z

Carriage

VR 1 to 10

Still water

276 m

aluminum pipe

Carriage

6 m

4 m

rail

End Plate

0.5 m

Y

X

Y

Z

Figure 4. Scheme of the pipeline model experiment [8].

The pipeline model was made by aluminum and attached to the moving carriage with

universal joints at the both ends, modeling a pinned-pinned boundary condition. The

experiments were carried out for two conditions: the first, for the pipeline perpendicular

to the moving direction, and the second tilted 30°. The carriage velocity was varied to

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achieve a range of reduced velocities (VR) from 1 to 10. Table 2 presents the pipeline

model properties. The achieved range of Re varies nearly from 430 to 3500.

Strain gauges were attached into the pipeline model external surface and bi-directional

accelerometers were provided to measure the movement in the in-line and cross-flow

direction. Load cells were also assembled in the both ends of the pipeline to measure

forces at the two directions already mentioned.

Table 2. Pipeline model properties [8].

Parameter Symbol Value (Unit)

Length L 4.57 (m)

External diameter D 0.02 (m)

Internal diameter 0.0184 (m)

Pipe mass per unit length 0.135 (kg/m)

Added mass (free oscillation) 0.314 (kg/m)

Added mass coeff. (free oscillation) CA 1.001

Total oscillating mass m 0.715 (kg/m)

Pipe stiffness EI 132.75 (Nm2)

First mode natural frequency (air) 2.358 (Hz)

First mode nat. frequency (immersed) fn1 1.025 (Hz)

Figure 5 presents a comparison of numerical results with the experiment for the pipeline

cross-flow vibrations. It is for the pipeline perpendicular to the moving direction.

In the numerical simulations, CL was estimated from the force measured by the load-

cells [8]. And for simplicity, CD and CA, both were taken equal to1 and constant with

Reynolds number, as presented in Table 2.

The results have shown that for low VR (before lock-in region), the proposed VIV

approach presents good agreement with the experimental. However, for larger VR the

simulation results were more conservative. Perhaps, it could be related with the change

of the vortex pattern from 2S to 2P [2, 17], which is not taken into account in the

present VIV approach.

STEEL CATENARY RISER (SCR)

The proposed VIV approach was also extended for simulations of the dynamic behavior

of free catenary risers [4]. The main considerations were:

1) to consider three dimensional non-linear structural model;

2) corrections for angles of the incidence at each time step due to large changes of

the catenary riser shape with the vibrations and the incident flow.

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0

0.4

0.8

1.2

0 1 2 3 4 5 6 7 8 9 10

Reduced Velocity (VR)

Cro

ss-F

low

(Ap

eak/D

)

Cross-Flow Response

Numerical

Experimental [8]

2.0

1.0

00 1 2 3 4 5 6 7 8 9 10

Reduced Velocity (VR)

Cro

ss-F

low

(f/f

n1)

Figure 5. Comparison of the cross-flow response for the pipeline in the perpendicular

condition [8].

Then, a numerical procedure was implemented to calculate the cross-flow VIV forces in

a three dimensional non-linear riser solution in time domain program [18]. The FEM is

being applied for the statics and dynamics analysis, respectively. And three dimensional

beam elements are being considered for the numerical simulations.

In VIV problems the incident fluid flow can be decomposed into normal and tangential

components to the cylinder axis. For straight beams geometries, as the case of vertical

risers, the tangential component is usually very small when compared with the normal

component. Therefore, good result is possible to obtain with the use of the incident fluid

flow velocity to evaluate the VIV force. However, it is not long validity for curved riser

beam geometries, like in catenary risers. In these cases, the tangential component can

reach not negligible values depending on the angle between directions of fluid incidence

and riser longitudinal axis. Very often, two dimensional sections perpendicular to the

cylinder axis is assumed. And, only the normal direction component of the flow at each

riser beam element is considered as an approximation [5]. Experiments were

accomplished with straight and inclined rigid cylinders to the incident fluid flow

demonstrating this approach [19].

A model test with a SCR was carried out in the IPT towing tank [9]. Improvement of

the understanding for the global SCR dynamic behavior with the VIV was intended with

the experiment. In order to obtain this, a large reduction scale factor of 250 was adopted

to keep Froude similarities. Finally, mass and stiffness of the riser model are very small.

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The tested Re ranged from 400 to 600. This range was calculated considering the

experimental model diameter and the range of velocity of the towing carriage.

The experimental set up is shown in Figure 6, and the main characteristics of the SCR

model in Table 3. The SCR model consisted of a 4 millimeter made by porous rubber

solid cylinder covered by silicone. External diameter of 8 mm and the distributed mass

per length have been adjusted.

Four pairs of single axis micro-accelerometers measured the experiment. Accelerations

for the cross flow direction in Y axis as in Figure 6, and for the direction normal to the

model in the SCR plane have been obtained. Positions of the accelerometers are

presented in Table 4. The tension at the top of the catenary riser model was taken

through ring type load cells with capacity to measure up to one kilogram-force.

Auxiliary

Platform

Oscillator

Wave

3.60 m

3.30 m

Test Platform

Ls= 5.20 m

RubberSilicone

D=8 mm 20º

Z

X

YZ

X

Y

Current

Accelerometer

A

B

C

D

Figure 6. Experimental Setup of the SCR Experiment [9].

Table 3. Main Characteristics of the SCR Model [9]

Linear Mass [kg/m] 6.28 x 10-2

Bending Stiffness [N.m2] 5.5 x 10

-5

Axial Stiffness [N] 13.75

Table 4. Accelerometers position in the model [9].

Accelerometers (pair) Depth [m]

Accel. A 1.238

Accel. B 2.264

Accel. C 2.898

Accel. D 3.431

Figure 7 are the results for current velocity of 0.07 m/s measured in the experiment by

the accelerometers A and C, respectively, compared with numerical simulations.

Comparisons have been extended for others accelerometers measurements results which

have shown good agreement with the calculated by numerical simulations. As it is

possible to observe from Figure 7, experimental results presented some peak

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frequencies that could be understood as the harmonic responses of the SCR model. The

first peak measured by the cross-flow accelerometer should happen due to the VIV.

And, the third one is interpreted as resulted by hydrodynamics forces from different

vortex shedding pattern as previously described in [20, 21]. Others peaks probably are

unexpected component of the acceleration due to misalignment of the very small

accelerometers in the experiments and other difficulties of the setup and measurements

in the SCR model with very small dimensions.

Cross-Flow Acceleration's FFT (Accel. A)

Numerical

Accel. A (Experimental [9])

0

0.016

0 1 2 3 4 5Frequency [Hz]

Cro

ss-F

low

Acc

eler

atio

n [

ms- ²

]

Cross-Flow Acceleration's FFT (Accel. A)

Numerical

Accel. A (Experimental [9])

0

0.016

0 1 2 3 4 5Frequency [Hz]

Cro

ss-F

low

Acc

eler

atio

n [

ms- ²

]

Cross-Flow Acceleration's FFT(Accel. C)

Numerical

Accel. C (Experimental [9])

0

0.016

0 1 2 3 4 5Frequency [Hz]

Cro

ss-F

low

Acc

eler

atio

n[m

s- ²]

Cross-Flow Acceleration's FFT(Accel. C)

Numerical

Accel. C (Experimental [9])

0

0.016

0 1 2 3 4 5Frequency [Hz]

Cro

ss-F

low

Acc

eler

atio

n[m

s- ²]

Figure 7. Comparison of the cross-flow acceleration measured in the model test and

calculated by numerical simulation [4].

Multi modal response is usually expected for a SCR model experiment. Verifications

were conducted in order to verify this [4], and it was observed that the frequency of the

cross-flow VIV force varies between nearly zero at the bottom riser model and up to

1.6 Hz at the riser top. Therefore, the peaks at 2.7 and 4.05 Hz in the SCR response are

unlikely to be vibration modes excited by cross-flow VIV forces of a multi modal

response. This is evidence for the former conjecture that these peaks are caused by

others considerations in the hydrodynamic forces, not accounted in the cross-flow VIV

approach as described in above.

Finally, it can be observed that the numerical simulations give a good estimation of the

first peak of the VIV response from comparisons with experiments. This confirms the

importance to consider the normal component of the fluid flow velocity to the cylinder’s

local axis for the VIV forces estimation. For the prediction of the third peak response in

the results, further investigations are needed to take it into account.

CONCLUSIONS

A numerical simulation procedure for the cross-flow VIV has been presented for

deepwater riser and pipeline behavior under the incidence of the current. A set of model

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experiments for different risers and pipeline configurations have been presented

following previous works, and numerical simulations procedures have been evaluated.

Comparisons between numerical simulations and experimental results showed that the

proposed VIV approach can predict the dynamic behavior of a horizontal subsea

pipeline with a free span and risers for all Reynolds number range achieved in the

model tests. Continuing effort through the numerical and experimental approaches are

intensively demanded, in order to clarify and to give reliable the hydrodynamics

modeling for the VIV forces to give a good prediction of service lifetime of risers and

pipelines for design purposes.

ACKNOWLEDGMENTS

The authors would like to thank CNPq and Finep (CTPetro), Capes, Fapesp, PRH/ANP

and Petrobras for the continuing support of the present investigation.

REFERENCES

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