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DYNAMIC RESPONSE OF COMPLIANT OFFSHORE PLATFORMS TO
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ByOguz Yilmaz and A. Incecik
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Department of Naval Architecture and Ocean Engineering,
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University of Glasgow, U.K.
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INTRODUCTION
Increases in oil prices over the last ten years have made the small offshore oil
reservoirs in deep waters more attractive. Compliant offshore platforms are increasingly used in these oil fields due to their lower construction cost ,(compared with fixed platforms) and the fact that they can be towed to other oil fields to be used again.
Design of compliant offshore platforms operating in severe weather conditions has become a popular research topic both in the universities and in the offshore industry. Tension leg platforms and single point mooring systems are some of the examples of compliant offshore production platforms.
Compliant offshore structures can sustain severe weather conditions by moving under the environmental forces and adopting the position with minimum mooring loads. Compliant offshore structures are particularly sensitive to directionality and there are several advantages to including the directionality and taking into account the
probability of joint occurrence of various environmental events in design
calculations.[6] These advantages are:
It serves us as a sound basis for combining environmental events in a rational manner
It provides a framework for incorporating improved knowledge of the environment
It provides greater accuracy in design calculations
It allows a more consistent design approach in moving from one area to another
It avoids unintentional and implicit conservatism.
In this paper having briefly described non-linear time-domain analysis
techniques to predict dynamic motion response and mooring load characteristics of
Tanker-Buoy , Articulated Tower-Tanker and a Tension Leg Platform systems under wave , wind and current forces as they act from arbitrary directions the effects of
variations in environmental force directions and magnitudes on motion response and
dynamic mooring load characteristics of these compliant platforms are summarised.
2.
TIME DOMAIN ANALYSIS TECHNIQUES FOR COMPLIANT
OFFSHORE STRUCTURES
2.1 Tanker-Buoy System
In modelling the tanker-buoy system surge, sway and yaw motions of the
tanker and surge and sway motions of the buoy only were considered(See Fig. 1)[1]. Fluid reactive forces acting on the system were taken into account by using Cummins
technique [2]. Since the tanker was modelled as an elliptical cylinder all hydrodynamic forces acting on the tanker were calculated using Mathieu Functions. Morison's
equation was used in calculating the wave forces on the buoy. Wave drift forces were
calculated according to FaJtinsen's asymptotic theory [3]. Wind and current forces were
evaluated using semi-empirical formulas. ITTC friction resistance formula and the cross-flow principle were used to calculate current forces and moment. The Munk
moment was also included in the current yaw moment calculations [3]. Mooring forces
were calculated using catenary equations and the non-linear load-elongation
characteristics of hawser were taken into account in the prediction model [4].
The Motion responses of the tanker-buoy system were compared with
experimental measurements carried out at Hydrodynamics Laboratory of Glasgow
University. The results of predictions agree well with those of experimental
measurements. (See Figs. 2 and 3).
22 Articulated Tower-Tanker System
In order to predict the motion and structural response values of the coupled articulated tower-tanker system in waves, the system was modelled as a single degree of freedom system by assuming the tanker to be a rigid extension of the tower and that
the coupled system rotates about the articulating joint (See Fig. 4). The heave, pitch and
roll motions of the tanker were neglected. In formulating the wave forces and
hydrodynamic properties.the tanker was modelled as a rectangular box . The wave
forces and hydrodynamic properties of the articulated tower were formulated using
Morisons equation. The detailed derivations of the motion and structural response
equations are given in Ref. 5. Wave drift, steady current and wind forces and moments
were calculated according to the methods described in section 2.1.
2.3 Tension Leg Platform
In order to predict the dynamic motion response characteristics of the TLP described in Table i due to combined wave, wind and current forces, a simple
first-order motions of the TLP due to waves and steady motions due to wind and current were predicted using the Morison formulation [6]. The steady and slowly
varying displacements of a TLP due to waves were obtained follo'ing the procedure described by Pinkster in Ref. 7. The slowly varying oscillations of íFLP due to wind
/
were predicted by combining a wind spectrum which represents the air turbulence. aerodynamic admittance and the dynamic response characteristics of the platform to aunit wind gusting velocity. Tables 2 and 3 show the effect of variation in wave direction and sea State on the dynamic response characteristics of the TLP described in Table 1.
3.
PARAMETRIC STUDIES AND DISCUSSION OF RESULTS
A group of simulation studies for the tanker-buoy system were carried out using a non-linear time domain simulation computer program based on the prediction method
described in Section 2.1. At the beginning of each simulation the tanker was placed along the x axis with a zero yaw angle and the hawser was unstretched. Results of the parametric study are tabulated using the steady and oscillatory motion responses of the buoy and the tanker, which were obtained through a F.F.T analysis of the time domain simulations. During the simulations the effects of directionality of wave, wind and
current force were investigated and the results of these simulations are given in Table 4. These indicate that maximum steady and oscillatory sway and yaw motions occur when
wave and current forces make a 90 degree angle with the wind forces. Similarly
maximum sway motions of the buoy occur when wave and current forces make a 90
degree angle with the wind forces. Another conclusion which can be drawn from Table
4 is that wind direction does not significantly affect the motions and that mean sway displacement and yaw angle increase as the current direction changes from O to 90 degrees. However maximum oscillatory sway motion of the buoy occurs when wave force direction makes a O degree and wind and current directions make a 45 degree angle with the horizontal axis. Maximum steady and oscillatory surge motions of the
buoy and ship occur when wave, wind and current forces act co-linearly.
A group of simulation studies was carried out for the articulated tower-tanker system. In Table 5 the yaw angle (in degrees) corresponds to a steady angle after the
articulated tower-ship system reaches an equilibrium state under wave, wind and current forces. Surge and sway values given in Table 5 indicate the amplitude of
oscillations about the equilibrium state. Similarly, oscillatory components of the axial and transverse yoke forces, as well as the steady forces at the base joint, are given in
Table 5 shows that wave excitation is the dominant environmental force in the prediction of steady yaw angle and surge and sway motion amplitudes. Examination of Table 5 also reveals that maximum axial and transverse yoke forces occur when the
direction of wave approach makes a 90 degree angle with wind and current directions. Parametric studies carried out with the TLP Platform shows that with an increasing wave angle from O to 90 degrees total surge response decreases by 3-4% and that maximum yaw response occurs when the wave angle of attack is 60 degrees (Tables 2-3).
CONCLUSIONS
Maximum steady and oscillatory sway and yaw motions of the tanker in the CALM system occur when wave and current forces make a 90 degree angle with the
wind forces. Similarly maximum sway motions of the buoy occur when wave and current forces make a 90 degree angle with the wind forces. It was found that the mean mooring line forces were not generally sensitive to changes in current and wind
loading, and that there was not a linear relationship between the wave height and the
response values or the mooring forces of the CALM system.
Maximum axial and transverse yoke forces in the SALM system occur when the direction of wave approach makes a 90 degree angle with wind and current directions. It was also found that neither the wind and current speed nor their directions had a significant effect on axial and transverse yoke force predictions.
Since the motion displacements due to steady wind and current as well as second-order wave and dynamic wind forces contribute significantly to the total surge response the effect of variation of wave direction on total surge displacements is not significant. However as the direction of wind and current varies from O to 90 degrees the total surge response decreases by about 25%.
REFERENCES
Yilmaz, O. & Incecik A., 'Identification of Non-linear Effects in Predicting the Motion Response of a CALM System', Proc. of the Eleventh International Conference on Offshore Mechanics and Arctic Engineering, Calgary, 1992.
Cummins, W.E. 'The Impulse Response Function and Ship Motions',
Schiffstechnik, Vol. 9, No. 47, 1962.
Faltinsen, O.M. , Kjaerland, O. , Liapis, N. and Walderhaug, H. Hydrodynamic Analysis of Tankers at Single Point Mooring Systems', Proceedings of the Second International Conference on Behaviour of Offshore Structures, No. 59, London, 1979.
Yiimaz, O. & Incecik A., 'Non-Linear Dynamic Time Domain Simulation of Moored Floating Systems', Proc. of the Tenth International Conference on Offshore Mechanics and Arctic Engineering, Stavanger, 1991.
Helvacioglu, I.H.H. 'Dynamic Analysis of Coupled Articulated Tower and
Floating Production Systems', Department of Naval Architecture and Ocean
Engineering, University of Glasgow, 1990.
Incecik, A. 'The Effect of Joint Occurrence of Wave, Wind and Current Loading on Dynamic Response of a Tension Leg Platform', To be presented at the
International Conference on OMAE '93, Glasgow.
Pinkster, J.A.' Mean and Low Frequency Wave Drifting Forces on Floating Structures', Ocean Engineering, Vol. 6, 1979.
TABLE 1: GEOMETRICAL CHARACTERISTICS OF THE TLP
HULLLENGTH 510 m NUMBEIROFHULLS 4 HULLDIAMETER 13.6 m COLUMN DIAMETER 25.0 rn COLUMN SPACING 76.0 rn COLUMN HEIGHT 63.0 m DRAUGHT 37.5 m WATER DEPTH 310.0 rn TOTAL WEIGHT 590, 080.0 kN TENDON PRETENSION 448, 281.0 kN TENDONAXIALRIGIDITY 1, 014 MN/rn LONG.DECKAREAEXP.TO WIND 7,000 m"2 TRANS. DECKAREA EXP. TO WIND 12000 m"2
TABLE 2: Motion Response of the TLP due to Co-linear Wave, Wind and Current
TABLE 3: Effect of Wave Direction on the Motion Response of the TLP
15 dog 30 deg 45 deg 60 deg 75 dog 90 deg
Cormtant values: Current speed 1.5 rn/s. wind angle O deg and current angle O dog
ARETORCR REStY'sE SECOND ORDER RESPONSE TOT. RESP
Wind speed
[mis]
Damp Cool. HsWave [m[ Surge As [m] Sway As [m[ Yaw As [Deg] Offset r [m] Offset ]rrl[ )ynamic Winc
[[
S o. waves]m] Steady drift [m] Total Surge [ml 1000 15 00 20 00 30 00 0.05 0 10 0 15 0.20 201 4 74 8 49 19 05 0.36 0.53 0 85 2 26 0,00 0 00 0.00 0 00 000 0.00 0 00 0 00 336 3 70 4 18 5 55 000 0 00 0.00 0.00 0.42 0.73 1.05 1 89 0.01 0.18 0.98 6 64 0.01 0 05 0 12 0,35 392 4 66 5.97 13 16F1RETORIR RESPOfSE SECOND ORDER RESSE TOT RESP
Wind speed Damp Cool Hs Wave Surge As Sway As Yaw As Offset r Offset iDynamic Win So, waves Steady drift Total Surge
[misi [m] [m[ [m] [tDeg] [m[ [irr] (m] [m[ [m] [m]
1000 0.05 201 020 0.20 467 3.36 000 0.42 0.01 0.01 3.83 15 00 0 10 4.74 0.38 0.09 6.55 3.70 0.00 0.73 0.18 0.05 4.58 20.00 0,15 8 49 0.74 0.22 7.07 4.18 0.00 1.05 0.98 0.12 5.91 3000 0.20 1905 2.16 0.62 7.31 5.55 0.00 1,89 6.64 0.35 13.13
AREl OR RESPONSE SECOND ORDER RESPONSE TOT. RESP
Wind speed Damp Cool. Hs Wave Surge As Sway As Yaw As Offset r Offset i)ynarmc Winc So, waves Steady drift Total Surge
[m/s] [m] [m[ [m] [Deg] [m[ [ml [m[ ]m[ [m[ [m[
1000 0.05 2.01 0.09 0.05 4.95 3.36 0.00 0.42 0.01 001 3.79 15.00 0.10 4.74 0.24 0.17 7.38 3.70 0,00 073 0.18 0 05 4 53
20,00 0 15 8.49 0.63 0.41 8.00 4.18 0.00 1 05 0.98 0.12 5.87
30.00 0.20 19.05 1 93 1.67 8.28 5.55 0.00 1.89 6.64 0.35 13,06 F1RETORLR RSE SECOND ORDER RESPONSE TOT. RESP.
Wind speed Damp Coat. Hs Wave Surge As Sway As Yaw As Offset X Offset z)ynamic Wax So, waves Steady drift Total Surge
[mis] [m] [m] [ml [Deg[ ]m] [m] [m] [m] [m[ [m) 10.00 0.05 2.01 0.03 0.06 2.20 3.36 0.00 0.42 0.01 0.01 3.79 15.00 0 10 474 0.19 0.20 2.76 3.70 0.00 0.73 0 18 0.05 4.52 2000 0.15 8.49 0.53 0.54 3.06 4.18 0.00 1,05 0 98 0.12 5.83 30.00 020 19.05 1 60 1.61 3.31 5.55 0.00 1.89 6.64 0.35 12.98 FIRET ORDER R'SE SECOND ORDER RESPONSE TOT. RESP
Wind speed
[mis]
Damp. Coot. HsWave
[ml Surge As [m] Sway As [m] YawAs [Dog] Offset r [m] Offset [m] Jynamic Winc Irrt] S.o. waves [m] Steady drift [m] Total Surge [m] 10.00 15.00 20.00 30.00 0.05 0.10 0.15 020 2.01 4.74 8.49 19.05 0 02 0.15 0.48 1 16 0.13 0.28 0.65 1,94 482 7.50 8 53 9.12 3.36 3.70 4.18 5.55 0.00 0.00 0.00 0.00 0.42 0.73 1.05 1.89 0.01 0.18 0.98 6,64 0.01 0.05. 0.12 0.35 3.79 4.51 5.81 1289
RRET ORDER RESCNS SECOND ORDER RESPONSE TOT. RESP
Wind speed
[mía]
Damp. Coot Ha Wave
[m[ Surge As Im] Sway As [m] Yaw As [Dogi Offset X [m] Offset [m] )yrramnic Winr [m] So, waves [m] Steady drift [m] Total Surge [m] 10.00 15.00 2000 30 00 0.05 0.10 0.15 0 20 2,01 4.74 8.49 19,05 0.01 0.08 022 0 61 0.24 0.40 0.76 2.17 4.92 7.15 8.03 8.52 3.36 3.70 4,18 5.55 0,00 0.00 0.00 0.00 0.42 0.73 1.05 1.89 0.01 0.18 0.98 6.64 0.01 0.05 0.12 0.35 3.79 4.50 5.75 12.82 ARETOR0R6r'SE SECOND ORDER RESPONSE TOT. RESP.
Wind speed Damp. Coot Ha Wave Surge As Sway As Yaw As Offset r Offset iJynamic Winc So, waves Steady dritt Total Surge
(m/s] [m[ [m] [m] [Deg] [m] [m] [m] [m] [m] [m] 10.00 005 2.01 0.00 0.36 0.00 336 0.00 0.42 001 0.01 379 15.00 0.10 4,74 0.00 0.54 0.00 3.70 0.00 0.73 018 0.05 4 49 20.00 0.15 8.49 0.00 0.85 0.00 4.18 0.00 1.05 0.98 0.12 5.73 30.00 0.20 19.05 0 00 2.26 0.00 5.55 0.00 1.89 6.64 0.35 12.80
Table 5: Effect of Directionality of Environmental Forces on the Motion Response of the SALM System
Simulation No
Direction of Variables MEAN SHIP MOTION RESPONSE Mean Hawser
Tension(kN) Wave Current Wind Surge(m) Sway(m) Yaw(deg)
1 0 0 0 342.80 0.00 0.00 2674 2 0 90 0 331.80 73.06 16.70 2585 3 15 90 0 312.50 128.70 25.10 2802 4 30 90 0 283.00 185.30 29.72 2617 5 45 90 0 254.17 224.50 33.85 3874 6 60 90 0 219.60 259.57 43.50 2518 7 75 90 0 183.40 288.90 52.33 5571 8 90 90 0 146.20 311.10 62.30 6522 9 0 45 0 323.90 6389 2.24 2838 1 0 0 45 15 320.80 78.77 1.76 2947 11 0 45 30 317.10 91.35 2.31 3039 12 0 45 45 314.60 104.20 3.91 3099 13 0 45 60 315.60 105.50 5.59 3036 14 0 45 75 317.30 104.10 7.07 2953 15 0 45 90 322.30 91.82 8.36 2783 1 6 0 1 5 0 290.10 21.69 2.06 2990 17 0 30 0 313.70 45.98 1.10 2857 18 0 45 0 323.90 63.89 2.24 2838 19 0 60 0 325.53 73.11 7.49 2786 20 0 75 0 327.90 69.73 12.08 2681 Simulation No
Direction of Variables Yawing
Angle(deg) Axial Yoke F.(MN) Transverse Yoke F.(MN) Steady Joint F.(MN) Wave Current Wind
i O 0 0 0.00 6.60 0.00 2.60 2 0 0 90 6.97 6.60 1.00 2.50 3 30 0 90 28.16 6.60 0.30 2.30 4 45 0 90 37.93 6.50 1.10 1.70 5 60 0 90 49.25 6.50 1.60 1.40 6 90 0 90 73.40 6.70 2.40 2.20 7 0 90 0 17.20 6.80 2.40 2.50 8 0 90 30 18.06 6.80 2.50 2.50 9 0 90 45 18.28 6.90 2.60 2.50 10 0 90 60 18.76 6.90 2.60 2.50 11 0 90 90 19.49 7.00 2.70 2.50 1 2 0 30 90 9.70 6.50 1.40 2.70 13 0 45 90 12.48 6.50 1.80 2.50 14 0 60 90 15.18 6.70 2.20 2.50
10m
Buoy 0.6 E o E 0.5 o I.-. 0.4 = C, w 0.3 = 0.2 0.1 0.0 175 m X Hawser10m
x14m
V.' 310 m Tanker 170 m Mooring lines///////////////
Fig. 1 CALM System
I] MEASUREMENTS
FREQUENCY DOMAIN SIMULATiON TIME DOMAIN SIMULATION
0 4 0.6 0.8 1.0 1.2 1.4 1.6
FREQUENCY (Hz)
DIA 127rn S.W.L.1 69m i ¿9m i 2.m 0.4 I-= 0.3
o
w = 0.2 0.1 0.0 192-7mFREQUENCY DOMAIN SIMULATiON
a TIME DOMAIN SIMULATION
Fig. 3 Surge response of the buoy (Current Force=0.06 N.)
PAYLOAD 16MN 91. rn 5L. mr YOKE 22 m 3L.m'-
-r-315m
0-0m SEA BED.... 1/.5 -2m .-.---- 2-/.m 21m FORE PERPENDICULAR D[A15-Om t3066m
Fig.4 Articulated tower and tanker geometry
EXPERIMENTAL TANKER 20-35m
