Motion Reponses of a Semi-submersible:

Experimental Study

Y.Abbas

1, V.J. Kurian

1, N. Abu Bakar

1

1Civil Engineering Department, Universiti Teknologi PETRONAS

Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia

Abstract- Following a few catastrophic accidents involving

mobile offshore drilling platforms, various studies were carried out to investigate the adequacy of stability criteria applied to

offshore mobile platforms which was derived on an empirical basis considering service experience accumulated for ships over

many years. In this study, a twin hulled semi-submersible model sea-keeping performance was studied successfully in the wave

tank for regular and irregular waves in sea, quartering and beam orientations. Results showed that the model RAOs follow the same tendency for regular and irregular wave.

Index terms: Response Amplitude Operator (RAO), Mobile

Offshore Drilling Unit (MODU), Universal Tensile Machine

(UTM), Fast Fourier Technique (FFT).Frequency Domain (FD).

I. INTRODUCTION

As the search for oil & gas has extended to water depth

beyond continental shelf with increasing exploitations and gas

resources, many new types of floating productions and drilling

platforms in deep or ultra-deep water have been developed in

recent years [1,2]. An engineering idea is the minimization of the structure resistance to environmental loads by making the

structure flexible (compliant). Semi-submersibles are

compliant offshore structures. There are over 120 semi-

submersible platforms worldwide operating primarily as

exploration drilling vessels, although several semi-

submersibles are now dedicated to other tasks such as diver

support and fire fighting and as the surface vessels for offshore

hydrocarbon production systems. Indeed, for marginal fields in

deep water, a semi-submersible-based production system may

be the only viable economic alternative to conventional bottom

standing structures [3].

Semi-submersible platform consists of a deck, multiple columns and pontoons. They are “column-stabilized”,

meaning that the centre of gravity is above the centre of

buoyancy, and the stability is determined by the restoring

moment of the columns. This contrasts with the spar platform,

which achieves stability by having the centre of gravity below

the centre of buoyancy, and the TLP, whose stability is derived

from the tendons. Semi-submersible platform kept in position

by system of mooring lines anchored at sea-floor as shown in

Fig. 1.

Following a few catastrophic accidents involving mobile

offshore drilling platforms, various studies were carried out to investigate the adequacy of stability criteria applied to offshore

mobile platforms which followed an empirical basis

considering service experience accumulated for ships over

many years [4]. Sea keeping performance is of significant

importance in vessel design due to the stationary nature of

drilling and production platforms. For the purpose of the sea

keeping design, its response assessment to environmental

forces is evaluated using either physical experiments or

computational simulations. Traditionally, the evaluation of a

prototype vessel’s sea keeping performance was accomplished by physical experiments using scaled models in a towing or

wave tank. This approach requires a detailed model be built

incorporating the complete hull geometry and appropriate

scaling of the mass properties.

The primary purpose of this wave tank study is to obtain

reliable results by minimizing scale effects and measurements

error. Large scale is recommended to minimize the problem of

scale effect when Reynolds effect (such as presence of drag

force) is important. The common ranges of scale for studies

such as breakwater stability are 1:150 to 1:20 in two

dimensional (towing) tanks, and 1:150 to 1:80 in three

dimensional wave tanks. The desired range of the scale for offshore structures in two dimensional wave tanks is 1:100 to

1:10 [5]. The 1:100 scale model designed for this study is

considered similar in geometry and mass properties to

prototype. The model composes of eight columns and twin

pontoons with bracing members.

Figure 1: Semi-submersible & mooring lines systems.

II. OBJECTIVES

Although the available numerical methods for analysing

offshore structures provide acceptable results for the design of

the offshore structures, it is desirable to assess the effects of the

environmental forces such as wind, wave and current forces on

the vessel prior to its construction. The primary objectives of

this study were:

1) To determine the mooring line wire load extension

relationship utilizing the universal tensile machine

(UTM) to evaluate its modulus of elasticity and

breaking strength.

2) To construct a semi-submersible model with appropriate scale factor to simulate an operating

prototype platform.

3) To characterize the model responses in regular and

irregular waves with different heading angles for the

platform operating conditions.

4) To develop a computer code using Fast Fourier

Technique (FFT) to transfer the model responses time

histories to responses spectra in the tested frequency

range. III. METHODOLOGY

In many fluid flow problems, the gravitational effects

predominate, the effect of other factors, such as viscosity,

surface tension, roughness …etc is generally small and can be

neglected [6]. In this case, Froude’s model law is most

applicable. A general assumption is made here that the model

follows the Froude’s law.

A twin hulled semi-submersible model was built to a scale

of 1:100 in accordance with the drawings shown in Fig. 1. The

model was placed in the wave tank by using 1.5 ton mechanical

crane as shown in Fig. 2. The semi-submersible consisted of

two rectangular pontoons each with four circular columns. The

reason for choosing this particular geometry for the semi-

submersible model was because it is the conventional type and

has a similar configuration to the Ocean Ranger which had

sunk to the bottom of the ocean with the loss of all 84 of its

crew (Dudgeon, 1984), this model is for a Tankagi MODU

prototype operating in the north sea. The model was painted in

a high visibility colour (yellow) for video shots purposes and

draft marks with measurements scale were added for accuracy

and visual purposes.

The twin rectangular hulled semi-submersible members are made of acrylic plastic sheets by Globe Plastic Industries

(IPOH) SDN. BHD. The model members were cut using laser

techniques and these members were connected by melting and

cooling using chloroform compound. Special ballast containers

were placed in the corner columns to ballast the model to the

desired draft. The weights inside these ballast containers could

be placed vertically so as to adjust the center of gravity of the

model for the desired metacentric heights. The principal data

for the prototype and the model are given in Table 6.

Modelling of moored vessels involves modelling not only

the floating structure but also the mooring system. Several types of mooring are used with floating structures. The most

common of these are mooring chains, wires and hawsers. In

this study, a multi component mooring system was utilized for

Stationing the model composed of aluminium alloy wire

and distributed clump weight made of steel chain as shown in

Fig. 3 having physical characteristics presented in Table 2.

Four typical mooring lines were connected to the model at

fairlead points according to the drawing shown in Figure 4. It is

worth mentioning that the pretension on the mooring lines was

maintained by small buoys designed to provide the desired net

buoyancy and attached near the mooring fairleader as in the

mooring line part. The stiffness of the wire was determined by

placing a specified length of the mooring line in UTM and

measuring its elongation at various loadings [7]. For the generation of regular and irregular waves, the wave

maker paddles were oscillated with a constant and variable

frequency and stroke. The range of stroke periods of regular

oscillation varied from 0.4 s to 2.5 s [8]. The tests in regular

waves were carried out in order to obtain RAOs of the semi-

submersible applying following Equations 1 & 2 for linear

system [9]. A high quality video camera was used to record the

model motions in sea, quartering and beam waves. The data

were collected in time domain for regular wave tests and all

were filtered. The irregular wave responses were processed by

FFT to represent collected data in FD.

������ = � �� … (1)

����� � = ��(�)�(�) … (2)

WhereAR= Response amplitude, A�=wave amplitude , SR(f)=

response spectrum energy at wave frequency (f) and S(f)=wave

spectrum energy at wave frequency (f).

I. RESULTS AND DISCUSSION

The uni-axial tension tests were conducted for three

specimens of the mooring line wire made of aluminium alloy in

1.55 mm diameter and 100 mm length to construct the load-

extension and stress-strain relationships for the mooring line

wire as shown in Fig. 5. It was found that the test specimens

behave as perfectly elastic for lower strain values with average

elasticity modulus of 3600 MPa and breaking tensile load of

800 N.

Fig. 6 shows the surge response for a regular wave. Surge

amplitude of 18 mm was obtained for a wave of 18 mm height and 2.5 s period. By comparing theoretical and observed wave

profile for regular waves, it is noted that the wave diffraction

effects is significant for wave frequency above 1.8 Hz.

Fig. 7 shows the surge RAOs for irregular waves, a

maximum of 4 m/m was noted. Fig. 8 shows the heave RAOs

for irregular waves, a maximum of 2.5 m/m was shown.

Finally, Fig. 9 shows the pitch RAOs for irregular waves with a

maximum of 0.0105 rad/m. Regular wave RAOs were

measured for the purpose of comparisons with RAOs of

irregular waves. Results showed that the model ROAs follow

the same tendency for regular and irregular wave.

a.

b.

c.

Fig.1: General arrangement of the semi-submersible model.

a. Model plan. b. Section 1-1. C. Section 2-2.

(All dimensions are in mm.)

Figure 2: Perspective view of the semi-submersible model.

Figure 3: Mooring System configuration.

Figure 4: Mooring System Setup plan.

TABLE 1

SEMI-SUBMERSIBLE GEOMETRY AND DYNAMIC DATA FOR PROTOTYPE AND MODEL

(λ=100)

Variable Prototype Model Scale

factor Scaled Actual

Pontoon Length (m) 110 1.10 1.10 λ

Breadth (m) 015 0.15 0.15 λ

Height (m) 008 0.08 0.08 λ

Column

spacing

Longitudinal 024 0.24 0.24 λ

Transverse

(m)

060 0.60 0.60 λ

Column diameter (m) 10&8 0.10 & 0.10 λ

No of bracing members 16 16 16 1

Bracings diameter (m) 1.0 0.010 0.011 λ

Water depth (m) 110.000 1.100 1.100 λ

Draught (m) 16.000 0.160 0.160 λ

Displacement (Kg) 30000E+03 30.000 30.020 λ 3

GM values Roll (m) 2.880 0.0288 0.0280 λ

Pitch (m) 2.360 0.0236 0.024 λ

Radii of

gyration

Roll (m) 34.300 0.343 0.340 λ

Pitch (m) 35.300 0.353 0.350 λ

Yaw (m) 40.600 0.406 0.410 λ

Regular wave height (m) 6.600(1) 0.066 0.066 λ

Regular wave period (m) 8.700(1) 0.870 0.870 2/1λ

The max. water particle

velocity (m/s)

2.385 0.239 0.240 2/1λ

Significant wave height (m) 3.300(2) 0.033 0.033 λ

Notes:

1) 100 year storm criteria for Peninsular Malaysia

Operation (PMO)-Appendix (G)-PETRONAS

Technical Specifications PTS 20.073.

2) Regular and irregular waves were designed for wave

headings of 0°, 45° and 90°.

Figure 5: Universal Tension Machine (UTM) stress-strain

curves for mooring wire specimens (d=1.55 mm.)

TABLE 2

MULTI-COMPONENT MOORING LINE PROPERTIES

Description Prototype Model

Scaled Actual

Horizontal pretension component (Kg). 70000 70E-3 70E-3

Angle of inclination at fairlead point

(Deg.).

30 30 30

Effective diameter of the

mooring/anchor lines (mm).

150 1.50 1.55

Effective area of the clump weight

(mm2).

1057 10.57 10.50

Submerged unit weight of

mooring/anchor lines (kg/m).

20000 0.020 0.021

Submerged unit weight of clump weight

kg/m.

83000 0.083 0.083

Mooring line length (m). 120 1.2 1.2

Anchor line length (m). 50 0.5 0.5

Clump weight length (m). 100 1.0 1.0

Water depth (m). 110 1.1 1.1

Height of fairlead point (m). 105 1.045 1.045

Elasticity modulus of mooring/anchor

lines KN/m2.

360E+3 3.6E+3 3.594E

+3

Anchor average holding capacity (Kg). 7250E+0 7.25 7.26

Figure 6: surge response for regular sea wave

(H=32 mm, f=0.4 Hz)

Figure 7: Surge RAOs for sea waves

0

1

2

3

4

5

0.6 1.1 1.6 2.1

Su

rge R

AO

(m

/m)

Wave period (s)

RAO(regular) RAO(irregular)

Figure 8: Heave RAOs for sea waves

Figure 9: Pitch RAOs for sea waves

II. CONCLUSIONS

The station-keeping experimental tests have been

conducted in the Universiti Teknologi PETRONAS offshore

laboratory for a semi-submersible model in scale of 1:100

using Froude’s modeling law. Model responses to regular and

irregular waves were evaluated and assessed numerically.

From this study, we can conclude the following:

1) The response RAOs obtained by regular waves of

different periods agreed very well with the RAOs

obtained by a single irregular wave using FFT

technique.

2) By comparing theoretical and observed wave profile

for regular waves, it is found that the wave diffraction

effect is significant for wave frequency above 1.8 Hz.

3) The maximum response RAOs were 4m surge, 2.5m

heave and 0.0105 radians pitch for a unit sea wave.

ACKNOWLEGEMENT

The support provided by the Universiti Teknologi

PETRONAS is gratefully acknowledged.

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Industries, Inc. Plainfield, Illinois 60544-8929, USA (2005).

0

1

2

3

4

0.55 1.05 1.55 2.05

Hea

ve R

AO

(m

/m)

Wave period (s)

RAO(regular) RAO(irregular)