En016 Icet 09 Carrol

7/31/2019 En016 Icet 09 Carrol

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Diffraction method for spar platforms

C.Y. Ng1,V.J. Kurian

2, M.A.W. Mohamed

3

1 Civil Engineering DepartmentUniversiti Teknologi PETRONAS, 31750 Tronoh, Perak, Malaysia

Tel: +6012-5714800, E-mail: [email protected]

2Faculty ofCivil Engineering Department

Universiti Teknologi PETRONAS, 31750 Tronoh, Perak, Malaysia


3Civil Engineering Departments

Universiti Teknologi PETRONAS, 31750 Tronoh, Perak, Malaysia


Abstract

This paper presents the numerical hydrodynamic analysis for the motion responses of spar offshore

platforms in regular sea waves using both Morison Equation and Diffraction Method. The spar was

modeled as a rigid body with three degrees of freedom restrained by mooring lines affecting the stiffness

values. Linear Airy wave theory and Morisons equation were used for calculating the wave forces on the

structure in the first case. The mass, damping and stiffness matrices were evaluated at every time step and

the equations of motion were formulated for the platform dynamic equilibrium. The equations were solved

using Newmarks Beta time domain dynamic analysis method. The results were obtained as Transfer

Functions in Surge. In the second case, the Transfer Functions were obtained using a linear diffraction

Method. The results were compared and conclusions arrived at. It was observed that the responses using

diffraction method were higher than that using Morison Equation for the low frequencies and vice versa for

the high frequency.

Keywords

Spar platforms, Hydrodynamic analysis, Degree of freedom (DOF), Morison modified equations,

Diffraction method, and Transfer function.

Introduction

Oil & gas industry has been blooming in

Malaysia for the last three decades. Fixed typeof offshore Platforms (Jacket type) has been

mostly used for the drilling and production of oil

& gas. Now, the industry is moving towards

depths of 500 m to 1500 m (deep) and above

1500 m (ultra deep) due to the depletion of near-

shore resources of petroleum. Spar Platform is

one type of deepwater platform widely being

used.

Spar platform can be described as a floating

platform with a deep draft cylindrical hull.

Classic spar comprises of a single cylindrical

hull whereas the truss spar has an upper buoyantcylindrical hard tank and a keel ballast soft tank

connected at the midsection by a truss system

[1]. Recently, even more advanced concepts of

spar platform have been developed such as

geometric spar [2], cell spar and cell truss spar

[3,4].

Wave force calculation is one significant step in

the design of any offshore structure. Basically


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wave forces on offshore structures could be

determined by three methods, namely Morison

equation, Froude-Krylov theory and Diffraction

theory, for different conditions [5].

The objective of this paper is to presents the

numerical hydrodynamic analysis for the motion

responses of spar offshore platforms in regular

sea waves using both Morison Equation and

Diffraction Method. Transfer functions of

classic spars were determined by both Morison

Equation and Linear diffraction and the results

were compared.

Methodology

Analysis model

Classic spar platform was modeled as a rigid

cylinder with three degree-of-freedom at its

origin. The mooring lines attached to thefairleads near the center of gravity, connected the

platform to the seabed for providing stability to

the spar. Spar platform is always stable because

the center of gravity is below the center of

buoyancy [6]. Figure 1 shows a typical offshore

Classic Spar Platform.

Source from Globalsecurity.org

Figure 1 - Typical Offshore Classic SparPlatform

Five classic spars were considered in this study.

Each of the spar platforms was connected by

four mooring lines to the seabed at depth of 800

m. The typical dimensions of these five classic

spars for the determination of respective transfer

functions are presented in Table 1.

Table 1 Typical Dimension of Classic Spars

Spar Diameter Hull Length Draft

CS1 30.0m 205m 190m

CS2 32.5m 205m 190m

CS3 35.0m 205m 190m

CS4 37.5m 205m 190m

CS5 40.0m 205m 190m

Morison Equation

In Morison equation, wave force computation is

a summation of inertia force and drag force.

Inertia coefficient and drag coefficient to be used

for the wave force calculation have been

determined primarily based on experimental

studies. Morison Equation is basically suitable

for structures which are relatively small as

compared to the water wave length.

Morison Equation elaborated wave force as a

summation of inertia force and drag force,

uuD

CuD

CF

FFF

DM

DI

2'

4

2 +=

+=

Where

F = the wave force;

FI = inertia force;

FD = drag force;

u = water particle velocitynormal to the cylinder;

u = the water particle

acceleration normal to the

cylinder, calculated with the

selected wave theory at the

cylinder axis;

= the seawater density;

D = member diameter;

CM, CD = inertia and drag coefficient;

Equation 1 - Morison Equation

By adopting the linear wave theory, the water

particle kinematics was determined by the

following equations [7]:

cossinh

coshu

kd

ks

T

H=

Equation 2 - Horizontal water particle velocity


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sinsinh

cosh2'u

2

kd

ks

T

H=

Equation 3 - Horizontal water particle

acceleration

Where,

S = y+d;

= kx- t;

k = (2/L);

d =water depth;

T = wave period;

y =height of the point of evaluation of

water particle kinematics;

x = point of evaluation of water particle

kinematics from the origin in the

horizontal direction;

t = time instant at which water particle

kinematics is evaluated;

L = wave length;H = wave height and d was water depth.

In this study, CM and CD values were selected

based upon the test data conducted by

Charkrabarti [5] for a smooth circular cylinder in

waves. Mean curves were prepared for CM and

CD value from the tests as shown in Figures 2

and 3.

Figure 2 - Inertial Coefficient vs. KC for a

smooth circular cylinder in waves

Figure 3 - Drag Coefficient vs. KC for a smooth

circular cylinder in waves

Source: Hydrodynamics of Offshore Structures [5]

Transfer function of the above mentioned models

were determined by Morison Equation. The

transfer functions in time domain were

determined by MATLAB program based upon

Newmark Beta Method.

Diffraction Theory

When the structure is large compared to the

wave length, Morisons Equation is no longer

applicable. This is mainly due to wave field near

by the structure would be affected when the

structure is large enough; and diffraction of the

waves from the surface of the structure is to be

taken into account into evaluation of the wave

forces. In the case, Diffraction Theory is

applicable for computing the wave force. [5]

Transfer functions of the spar platforms by

diffraction method were adopted with

commercial structural analysis software.

Data input for linear wave diffraction was as

shown in Table 2.

Table 2 Data for diffraction method

Description Value

Water Depth (m) 800

Sea water Density (MT/m3) 1.035

Origin Orientation (vertical axis) +z

Frequency range (Hz) 0.05 0.20

Wave height (m) 1Mooring

line

Cross section area (cm2) 128.68

Elastic Modulus

(1000kN/cm2)

10.409

Numerical Results and Discussions

Transfer function of the classic spar models were

determined numerically by time domain analysis

as well the linear wave diffraction analysis. All

the response results at the origin are presented inthis paper.

The transfer functions for surge response of the

models are compared in Figures 4 to 8. For the

time domain analysis, the transfer function was

determined as the ratio of response height to the

wave height.


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Surge Response For Classic Spar 1

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.05 0.10 0.15 0.20 0.25

Frequency, Hz

Surg

eResponse,m/m

Morison's Equation Linear Diffraction Figure 4 - Transfer Function for Classic Spar 1

in Surge motion


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.08.0

9.0

0.00 0.05 0.10 0.15 0.20 0.25

Frequency, Hz

SurgeResponse,m/m


in Surge motion


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.05 0.10 0.15 0.20 0.25

Frequency, Hz

SurgeResponse,m/m


in Surge motion


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.05 0.10 0.15 0.20 0.25

Frequency, Hz

Surg

eResponse,m/m


in Surge motion


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.08.0

9.0

0.00 0.05 0.10 0.15 0.20 0.25

Frequency, Hz

SurgeResponse,m/m


in Surge motion

Through the study it was found that, theapplication of Morison equation is simple and

easy as it involves only determination of the

water particle kinematics and substitution into

the equation. In other hand, the application of

diffraction method involves very cumbersome

solutions. Nonlinearities can be easily

incorporated into Morison equation while

nonlinear diffraction method is extremely

complicated. Morison equation can be applied

using normal computer programming while

diffraction method needs very costly software

like SACS. Because of these reasons, it can be

observed that majority of the research papers that

deal with such studies resort to using the

Morison equation even for large cylinders where

diffraction method is the only correct method.

From the above figures, it is obvious that

responses from Morison equation (time domain)

gave much smaller values of transfer function for

frequencies below 0.05 Hz and higher values for

frequencies above 0.05 Hz. For large members,


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as the size of the structure was expected to alter

the wave field in the near by area, diffraction at

the vicinity has to be taken in to account [5].

The wave diffraction analysis provides a reliable

and accurate result of transfer function for deep

water structure such as spars and semi

submersibles.

Conclusion

1. The results of this analysis showed that the

responses using diffraction method were higher

than that using Morison Equation for the low

frequencies and vice versa for the high

frequency.

2. The maximum amplitudes of the spar

platforms obtained by both methods are shown

in Table 3:

Table 3 Maximum amplitude for classic spars

Classic Spar Linear Diffraction Morison Equation

CS1 8.942 3.760

CS2 8.381 3.123

CS3 7.899 5.400

CS4 7.478 5.015

CS5 7.084 6.153

Acknowledgment:

The authors would like to gratefully

acknowledge the civil engineering department

and management department of Universiti

Teknologi PETRONAS (UTP) for their support

and encouragement.

References

[1] Kurian V.J., Montasir O.A.A and Narayanan

S.P., Numerical and Model Test Results for

Truss Spar Platform, Proc 19th

Intl. Offshore

and Polar Eng, ISOPE, Japan, 2009.

[2] Wang Y., Yang J.M., Hu Z.Q., Xiao L.F.,

Theoretical Research on Hydrodynamics of a

Geometric Spar in Frequency and Time

Domains, Journal of Hydrodynamics, 2008,

20(1), 30-38.

[3] Zhang F., Yang J.M., Li R.P., Chen G.,

Numerical investigation on the Hydrodynamic

Performances of a New Spar Concept, Journal

of Hydrodynamics 2007, 19(4), 473-481.

[4] Zhang F., Yang J.M., Li R.P., Chen G.,

Coupling Effects for Cell Truss Spar Platform:

Comparison of Frequency- and Time Domain

Analysis with Model Tests, Journal of

Hydrodynamics 2008, 20(4), 424 432.

[5] Chakrabarti S.K., Hydrodynamic of

Offshore Structures, WIT Press, 2001.

[6] Agarwal A.K. and Jain A.K., Dynamic

Behaviors of Offshore Spar Platforms Under

Reguar Sea Waves, Ocean Engineering 2003,

30, 487-516.

[7] Kurian V.J.,Wong B.S., and Montasir

O.A.A., Frequency Domain Analysis of TrussSpar Platform, International conference on

Construction and Building Technology 2008.

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En016 Icet 09 Carrol