A STUDY ON THE EFFECT OF SEMI-SUBMERSIBLE DRILLING RIG MOTIONS WITH VARIATION IN MOORING LINE PRE-TENSION TO THE SAFETY OF DRILLING RISER

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1 A STUDY ON THE EFFECT OF SEMI-SUBMERSIBLE DRILLING RIG MOTIONS WITH VARIATION IN MOORING LINE PRE-TENSION TO THE SAFETY OF DRILLING RISER Arda 1, Djatmiko E.B. 1, and Murdjito 1 1 Department of Ocean Engineering, Faculty of Marine Technology, Institut Teknologi Sepuluh Nopember (ITS) Kampus ITS Sukolilo, Surabaya 60111, Indonesia ebdjatmiko@oe.its.ac.id ABSTRACT A study has been carried out to evaluate the effect of semi-submersible drilling rig motions with variation in the mooring line pre-tension to the safety of the incorporated drilling riser. Semi-submersible motions in the 6-degree of freedom were predicted by means of a mathematical model based on the diffraction theory in frequency domain, for a number of wave headings. Results of the motion analysis were then applied as a primary input data to run a time domain simulation of the moored semi-submerible equipped with drilling riser. The semi-submersible was designed to be operated in Natuna Sea, with a peculiar 10-year return period of wave appropriately to model the maximum operating condition. During the simulation, the 8-mooring line configuration was set to have pre-tensions increased between 400kN up to 000kN, at 400kN intervals. Simulations under all pre-tensions give satisfactory results in term of the tensions developed on the mooring line, where the lowest safety factor is.44 when it is weighed against the criteria required by API-RPSK. Up to the pre-tension of 800kN, the maximum angle of deflection of the drilling riser flex joint is about 6.deg, with the mean value of 4.8deg, which is in fact exceeds the criteria as imposed by API-RP16Q. The criteria in this guidance is also vanquished with regards to the von Mises stresses arise on the drilling riser when the pre-tension was set 100kN or lower, with maximum reaching 369MPa or some 0.8 times of the yield stress, at 400kN. Considering these results, for the safety of drilling riser operation, it is suggested therefore that the pre-tension should be set higher than 100kN. Keywords: semi-sumersible, motion, mooring pre-tension, flex joint angle, riser stress, safety 1. INTRODUCTION The limited oil and gas resources in shallow waters have urged operators to intensively shift their activies to exploit the deep water territories. In this regards the operation of fixed offshore structures becomes more technically complex and is no more considered as economical, especially when related to drilling operations where most of the time requires the rigs to have flexible mobility from one field to another. Realizing this, floating structures with such flexibility are then more widely used, and play important roles in exploitation of deep water oil and gas fields. A large number of floating drilling rigs are now in operation worldwide with various types of structural configurations [1,]. In the early development of deep water activities in the 60s operators commonly employed single hull vessels to support the drilling operation [3]. These types of floating structure are recognized to have drawbacks especially in their seakeeping characteristics when excited by reasonably large waves. Whereas the deep water largely are located in more open seas with considerably harsher environmental conditions. Researches were then intensively programed by many institutions to obtain new innovative platforms which can be operated benignly when exposed to severe seas. One among those newly invented platforms in the 70s is designated as semi-submersible. This type of floating structure is acknowledged by its excellent seakeeping characteristics, chiefly when equipped with dynamic positioning system [4]. During the main drilling operation a floating offshore platform should be capable of keeping its intended stationary position, or shortly referred to as the stationkeeping. One way of accomplishing this is by activating its incorporated dynamic positioning system. However, at certain harsh environments such a system would not be effective to maintain its position with only a limiting allowance to drift. Therefore, the traditional way of station keeping by means of mooring system, which is considered more reliable, is still customarily employed. Acknowledging that mooring system will represent as a crucial element in the success of drilling operation thorough analysis is mandatory to be performed prior to the deployment, hence to attain appropriate and safe system. The scope of study and analysis on mooring system as well as its effect on the safety of riser on drilling rigs is relatively broad. This could range from the VIV evaluation to predict fatigue life of the mooring and riser system [5], the introduction of torsion actuator to control riser angle and vibrational reduction [6], control system for riser end angle due to ice load [7], and so on. On the study as reported in this paper the analysis of mooring system on semisubmersible drilling rig has been established by considering the vessel motion effects and a range of mooring pre- 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 1/11

2 tensions, and further to look at the impact on the riser behaviors. The manipulation or line adjustment is viewed as an essential phase to assure the integrity of the mooring system. This set of analysis eventually is outlined by understanding the primary objective of the drilling operation with floating structure, which is to minimize the riser angles on the wellhead part and at the top joint [8]. Specifically the operation of drilling riser is related to physical limitation of the components, say the maxium deflection angle of the flex/ball joints, the platform offset, and the allowable stress of the riser, as shown in Fig. 1. In the end the level of system safety for semi-submersible drilling operation would be judged against a certain accepted criteria [9].. METHODOLOGY Figure 1 Loads on the riser of a semi-submersible system [10] The study reported herein was carried out in conjunction with the recent activity projected by Conoco Phillips to drill 11 offshore wells in the Natuna Sea, Indonesia. For this activity Conoco Phillips has hired Essar Wildcat, a semisubmersible drilling rig owned and operated by Essar Oilfield Services (EOSL), a global company under Essar Group home based in India [11]. Essar Wildcat is an Aker H-3 Class, semi-submersible of nd generation built by Aker Verdal at Norway Shipyard delivered in By the time it was commencing the service to Conoco Phillips the vessel was just out of Keppel Shipyard in Singapore after accomplishing a periodical maintenance and repair. z O x y Figure Semi-submersible model configuration 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 /11

3 Table 1 Principal dimensions of the semi-submersible Description Unit Quantity Length Overall m Breadth (moulded) m 7.0 Large Colum Diameter m 8.0 Small Colum Diameter m 5.8 Corner Colum Diameter m 5. Height of Pontoons m 6.7 Operating Draught m 1.3 Transit Draught m 6.4 Operating Displacement ton 4170 Transit Displacement ton VCG (Operating) m 17.8 VCG (Transit) m 4.0 GM (Operating) m.7 GM (Transit) m 75.6 In the first stage of the study, an ample data and information related to the semi-submersible, operational supporting system, and the corresponding environmental conditions have been collected. Figure exhibits the basic configuration of the semi-submersible with principal dimensions as depicted in Table 1. The supporting facilities include the mooring system and drilling riser are listed in Table and Table 3, while the mooring configuration is illustrated in Figure 3. The mooring configuration as sown in this figure comprises of eight spread mooring line. The direction of environmental excitation is also defined in the figure. Table Mooring properties for the semi-submersible Description Quantity Chain Type Studlink chain R4 Chain size 76 mm diameter Length of chain 100 m (approximate) Chain break load tonnes Chain weight in air 0.16 tonnes/m Chain weight in water tonnes/m Anchor type 8x15000kg HY -17 anchor. Number of line 8 Figure 3 Mooring line configuration and heading convention Table 3 Drilling riser system Description Quantity Number of tensioner 1 Length between riser joint m (30 ) Length between pup joint m (10 ) 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 3/11

4 Outside diameter m (1 ) Riser pipe thickness m (0.5 ) Yield strength MPa (65 ksi) Weight of riser joint in air.95 ton Weight of riser joint under water.57 ton Weight of pup joint in air 1.5 ton Weight of pup joint under water 1.3 ton Weight of slip joint 5.3 Ton The environmental data for the Natuna Sea, location where the semi-submersible is in operation, is presented in Table 4, comprises of water depth, wave, current and wind intensities. The latter three data is based on the 10-year return period, which is considered appropriate to model the maximum or severest condition for drilling operation. Table 4 Environmental data for Natuna Sea Parameter Water depth Wave: Significant wave height, (Hs) Peak period, (Tp) Maximum wave height, (Hm) Mean period, (Tm) Spectrum Current: Surface velocity Mid-depth velocity Bottom velocity Wind: Wind speed 10-yrs Return Period 90 m 4.6 m 10.1 s 8.4 m 9.3 s JONSWAP 0.85 m/s 0.66 m/s 0.48 m/s 1.36 m/s Based on the the preliminary dimensions and technical drawing that is available a numerical model of the semisubmersible hull was then generated using a CAD tool. The hydrostatic properties of the model hull were further validated against the primary data from the reference, as shown in Table 5.1. Referring to the data in this table the difference of all the hydrostatic properties are below 1.0%. Therefore, the model is considered appropriate to be analyzed further. Table 5 Model validation.1 Motion Analysis Parameter Unit Operating Draft Selisih m (%) Reference Model Displacement ton KM m GM m LCB m VCG m The second stage of the study has been arranged to perform the motion analysis of the vessel in free floating condition. For this purpose, the general equation of coupled floating structure motion in the 6-degree of freedom was applied, as follows: 6 e i M t jk A jk k B jk k K jk k Fj ; j, k n1 (1) where M jk = matrix of mass and mass moment of inertia of the semi-submersible, A jk = matrix of hydrodynamic added mass coefficients, B jk = matrix of hydrodynamic dammping coefficients, K jk = matrix of restoring coefficients, F j = matrix of exciting forces (F 1, F, F 3 ) and moments (F 4, F 5, F 6 ) in complex function, j,k = 1,,3,4,5,6 for surge, sway, heave, roll, pitch and yaw, = motion displacement of the k th mode, k k = motion velocity of the k th mode, 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 4/11

5 k = motion acceleration of the k th mode, = exciting force or moment of the j th mode. F j The solution of the above equation of motion is accomodated in a frequency domain numerical tool based on the diffraction theory. Pressure on the hull surface was computed by applying the panel method which incorporates the translating-pulsating source distribution, as described in [1]. The primary results of this numerical modeling are the six mode of motion amplitudes extracted from the correponding steady-state oscillations [13]. These motion amplitudes were then related to the incident wave amplitudes in the form of response amplitude operators, RAO = k0 / w0, for each incremental wave frequency, [1-14]. Accompanying output data so obtained are hydrodynamic coefficients which have been compiled as input data necessary to run the subsequent numerical model for the mooring system.. Mooring Analysis The third stage of the study was focused in modeling the behavior of the moored semi-submersible. Formulation of the moored semi-submersible is established on the basis of equilibrium force equation which accounting for the slowly varying excitations due to current, wind and waves against the reactions brought about the body motion and mooring lines, in accordance with references [15-0], as follows: () M( x Dx ) X X X X () where x ( x, x, x 1 6 ) T H W M 0 0 M 0 M I 0 0 x D 0 0 x X H = vector of hydrodynamic reaction and current forces, X W = vector of wind force, X M = vector of mooring line force, and X () = vector of wave drifting force or the nd -order wave force. M A time domain approach is adapted in this numerical model, where the above equation is formulated as a set of Eulerian equations combined with the non-linear external excitation of current, wind and wave loads. The mathematical model is further executed by taking into account constant frequency dependent as well as frequency independent hydrodynamic coefficients. The well known Cummins approach is used to derive the frequency independent coefficients through the application of impuls response function. Current and wind loads could be treated as steady or unsteady excitation as necessary, whereas the wave is considered as random to realistically model the mooring behaviors. In case of Natuna Sea it is considered that JONSWAP sea spectra is approriate, with the following equation [13]: 5 4 exp 0 0 S g exp 1,5 0 (3) where = 0.076(X 0 ) -0. or when X 0 unknown, g = acceleration due to gravity, = wave frequency, = modal frequency = (g/u w )(X 0 ) -0.33, = peakedness parameter, = shaped parameter (0.07 for 0 and 0.09 for > 0 ), X 0 = fetch length, and U w = wind velocity. The input data required to run the time domain simulation comprises of semi-submersible hull model, mooring and riser properties, boundary condition due to the vessel motions as represented by the RAOs, loads brought about mooring line pre-tension, and the environmental conditions. The output data yielded from the simulation ranges from the dynamic mooring tensions, system offsets and riser reponses as described in the next sub-section. In order to check the safety of the mooring system, the output data are then compared with the criteria as required by API-RPSK as depicted in Table 6. 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 5/11

6 Table 6 Criteria and safety factor for mooring line [1] Case Analysis Tension Limit Equivalent Method (% of MBS) SF Intact (ULS) Dynamic Damaged (ALS) Dynamic Riser Analysis Principally the prediction of riser behaviors has been included in the time-dimain simulation as previously described. Nonetheless it is considered necessary to put forward the underlaying approach that has been adopted. As outlined in [13] the basic horizontal equation of motion of the riser as a flexible cylindrical member including its internal forces, surface and body forces may be written in the x z coordinate system as: ( x x x x EI z) T ( z) w( z) m ( z) f ( z, t) e x (4) z z z z t The first term in the left hand side of this equation is the horizontal reaction from the flexural rigidity, the second term arises from the effective tension, Te, the third term is owing to the bouyant weight, w, whilst the last term is the inertia of the riser accelerating in horizontal direction. The effective tension is related to the actual tension, T, of the riser by T z) T ( z) A ( z) p ( z) A ( z) p ( ) (5) e ( 0 0 i i z where A 0 and A i are the external and internal cross-sectional areas of the riser, and p 0 and p i are the corresponding fluid pressures. The right hand side of eq. (4) is the forcing function which may be expressed by the modified Morison equation. Having accomplished this equation riser responses can be derived including the von Mises stress. The acceptability of the riser so designed may be examined against the appropriate criteria, such as from API-RP16Q as shown in Table 7. Tabel 7 Criteria for drilling riser [] 3. RESULTS AND DISCUSSIONS Design Parameter Riser Connected Drilling Non-Drilling Riser Disconnected Mean Flex/Ball Joint Angle (Upper & Lower).0 deg N/A N/A Maximum Flex/Ball Joint Angle (Upper & 4.0 deg 9.0 deg N/A Lower) Allowable Stress 0.67σ y 0.67σ y 0.67σ y The results of this study are presented in this section, covering the RAOs of semi-submersible when modeled in free floating condition, the mooring system responses, as well as responses of the corresponding drilling riser system. The RAOs of the semi-submersible for all the six-mode of motions are exhibited in Figure 4. It is shown here the semi-submersible has been modeled under excitation of waves propagate in five directions, ranging from 0deg up to 180deg at 45deg interval. As expected, the surge motion is pronounced when the semi-submersible is excited by the following (0deg) and head waves (180deg), gradually reduces in oblique waves (45deg and 135deg), and practically almost deceases in beam waves (90deg). In the contrary to the surge, the sway mode of motion is pronounced when excited by the beam waves, gradually decreases in oblique waves, and nearly diminishes in following and head waves. The two horizontal motions, surge and sway, demonstrate a common trend of harmonically excited dynamic system without stiffness, where the responses tend to approach unity at very low or zero frequency. With regards to heave mode an interesting fact is acquired, that is the responses are almost similar in all wave directions. Although the responses in following and head seas are found to be the largest, but the difference with those in oblique and beam waves is comparatively small. The maximum RAO of heave is found about 0.94m/m in very low frequency. The first rotational motion, ie. roll, as can be predicted is dominated by the beam waves, steadily lessen in oblique seas, and diminish in following and head seas. The peak value of roll RAO is approximately 0.78deg/m. The trend of pitch motion is similar to the surge mode, where higher RAO occurs in head and following seas, reduces in oblique waves and much lower in beam seas. The pitch RAO reaches a maximum value of approximately 0.51deg/m in head seas, whilst the maximum in following seas is only slightly lower, ie. about 0.49deg/m. In the case of yaw motion the trend seems to be in between the roll and pitch modes, where higher responses occur in either aft (45deg) or fore (135 deg) oblique waves. As can be seen in the figure, the peak yaw RAO is about 0.1deg/m, which is much lower order in comparison to roll or pitch modes. All the peak values of the RAO in 6-degree of freedom at any wave heading are presented in Table 8, together with the natural frequencies of the vertical mode of motions. Considering the result where the peak RAOs are all below unity, it may be then regarded that the quality of semi-submersible motions are 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 6/11

7 excellent. Eventhough these results represent the condition in idealized regular waves. Therefore checks still need to be carried out further by implementing a spectral analysis to draw full conclusions on the platform behaviors in real seas. (a) (b) (c) (d) (e) (f) Figure 4 RAOs of the semi-submersible in free floating condition: (a) surge; (b) sway; (c) heave; (d) roll; (e) pitch; (f) yaw Table 8 Maximum value of RAOs and natural frequencies Mode of Motion Maximum RAO 0deg 45deg 90deg 135deg 180deg Natural Frequency (rad/s) Surge Sway Heave Roll Pitch Yaw th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 7/11

8 The next result, as shown in Figure 5, is a typical output data obtained from the time domain simulation, that is a plot of time history of the upper flex joint angle due to the excitation of a certain random waves. Other output data which are generated by the simulation includes the maximum mooring line tensions, the maximum offset, the angle of lower flex joint, as well as maximum stresses on the drilling riser, as function of the incremental mooring pre-tension. All simulations have been conducted by imposing a random wave characterized by Hs=4.6m and Tp=10.1sec, propagates at five different directions as was done in the case of free floating motions. Summary of all the results are then presented graphically as in Figures The horizontal red lines in the figures represent the limiting criteria as required appropriately. Figure 5 Time history of the upper flex joint angle of the drilling riser at the mooring pre-tension of 400kN induced by a random wave of Hs=4.6m, Tp=10.1sec and=90deg Figure 6 Maximum mooring line tensions Maximum tension of the mooring line increases linearly with the increasing of pre-tension, as displayed in Figure 6. From all variation of the pre-tension which has been induced, that is from 400kN up to 000kN at 400kN increment, eventually the maximum tensions so generated are reasonably lower than limiting criteria as stipulated by API-RPSK. The lowest safety factor, with reference to MBS of 6000kN, is found to be.44. This value is well above the minimum requirement on safety factor, ie (a) (b) Figure 7 Maximum offset: (a) x-axis and (b) y-axis 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 8/11

9 Maximum offset in the longitudinal or x-direction, as shown by Figure 7a, occurs at the mooring pre-tension of 400kN, brought about the following and head waves, reaching as much as 6.3m or about 7.0% of the water depth. Whereas the maximum offset in the transverse or y-direction, as shown by Figure 7b, occurs also at the mooring pretension of 400kN, but it is brought about the beam waves, reaching as much as 7.9m or about 8.8% of the water depth. In accordance with reference [0] generally the maximum offset is allowable within the range of 8.0% up to 1% of the water depth. Therefore in term of either longitudinal or transverse offset the operation of the semi-submersible could be regarded as acceptable. (a) (b) Figure 8 Upper flex joint angles of the drilling riser: (a) maximum value and (b) mean value (a) (b) Figure 9 Lower flex joint angles of the drilling riser: (a) maximum value and (b) mean value Considering the criteria as set by API-RP16Q, the maximum and mean angle of flex joint should not exceed 4deg and deg, respectively. In the case of upper flex joint, as can be seen in Figure 8a, the maximum angle criteria is violated when the pre-tension is lower than some 740kN. In the case of lower flex joint, as can be seen in Figure 9a, the maximum angle criteria is violated when the pre-tension is lower than some 500kN. Looking at the mean angle on either upper or lower flex joint, the criteria will be violated when the pre-tensions are lower than about 90kN and 800kN, as exhibited in Figures 8b and 9b, respectively. In all cases the largest flex joint angles are due to beam waves. In order to attain safe operation, with reference to criteria of the flex joint angle, it is therefore concluded that the minimum pre-tension imposed should then not be less than 1000kN. Figure 10 Maximum von Mises stresses on the drilling riser 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 9/11

10 The von Mises stresses which develop on the drilling riser as presented in Figure 10 seem to exceed the criteria as required by API-RP16Q, when the mooring pre-tensions are set at values of 400kN up to 100kN. The largest von Mises stress occur due to the excitation by beam waves and at mooring pre-tension of 400kN, where the value is as high as 369MPa or 0.8 times the yield stress (ie. 448 MPa). The criteria in this respect requires the maximum stress should be less than 0.67 of the yield stress, which could be met if the mooring pre-tension is set not to be less than 100kN. 4. CONCLUSIONS A study has been comprehensively carried out to evaluate the effect of the semi-submersible drilling rig motions with variation in the mooring line pre-tension on the operational safety of the corresponding drilling riser. The study is based on the Essar Wildcat semi-submersible to be operated in Natuna Sea. Referring to the results of the analyses that have been performed some conclusions could be drawn, as follows: The semi-submersible is found to have excellent motion characteristics in free floating condition as proven by the RAO values which are generally below unity. Although this finding is based on the regular wave excitation, but as an initial indicator this seems to be amenable. If the RAOs are then interrelated to wave spectra it could still be expected that the motion behaviors in real seas would be in moderate levels. Considering the behavior in the maximum operating environmental condition, that is due to the wave of Hs=4.6m and Tp=10.1sec the mooring line tension would not violate the criteria even if the pre-tension is set as low as 400kN. For the corresponding maximum random wave and pre-tension of 400kN, the maximum offset in the longitudinal and transverse directions are found to be approximately 6.3m and 7.9m, or about 7.0% and 8.8% of the water depth, respectively. Both maximum offsets are considered safe with reference to the generally accepted limiting criteria. The angle of flex joint is largely influenced by the excitation of beam waves. Considering the mean value of the upper flex joint, which is more vulnerable than the lower flex joint, the related criteria will be exceeded if the pre-tension is below 1000kN. Looking at the von Mises stresses so developed on the drilling riser brought about the corresponding random wave, the criteria will be violated if the pre-tension is less than 100kN. Therefore, for the safety of the operation it is recommended that the mooring pre-tension is to be set higher than that value. ACKNOWLEDGEMENT The authors would like to convey their sincere gratitudes to PT Global Maritime for the permission granted to use the various data for this study. REFERENCES [1] Buslov, V.M. and Karsan, D.I. ( ), Deepwater Platform Designs: An Illustrated Review (3 parts), Ocean Industry, Oct (Part 1), pp. 47-5, Dec (Part ), pp , Feb. (1986) pp/ 53-6 [] Abbot, P.A., D Souza, R.B., Solberg, I.C. and Eriksen, K. (1995), Evaluating Deepwater Development Concepts, Journal of Petroleum Technology, Vol. 47, No. 4, pp , Apr. [3] Collier, C.L. and Hammett, D.S. (1974), Dynamic Stationed Drill Ship SEDCO 445, Proceedings of Offshore Technology Conference, Paper No. OTC-034, Houston, Texas, May [4] Hammett, D.S. (1977), The First Dynamically Stationed Semi-Submersible SEDCO 709, Proceedings of Offshore Technology Conference, Paper No. OTC-97, Houston, Texas, May [5] Jeans G. (003). West of Shetland Drilling Operations - Validating Riser VIV Fatigue Life Predictions Meeting Report, Journal of the Society for Underwater Technology, Vol. 5, No. 4, pp [6] How, B.V.E., Gea, S.S. and Chooa,Y.S. (009), Active Control of Flexible Marine Risers, Journal of Sound and Vibration, Vol. 30, Issues 4-5, pp [7] Nguyen, D.H., Nguyen, D.T., Quek, S.T. and Sørensen, A.J. (011), Position-Moored Drilling Vessel in Level Ice by Control of Riser End Angles, Cold Regions Science and Technology Vol. 66, Issues -3, pp [8] Nguyen, D.H., Nguyen, D.T., Quek, S.T. and Sørensen, A.J. (010), Control of Marine Riser End Angles by Position Mooring, Control Engineering Practice, Vol. 18, Issues 9, pp [9] Vazquez, A.O., Ellwanger, G.B. and Sagrilo (006), Reliability-Based Comparative Study for Mooring Lines Design Criteria, Applied Ocean Research, Elsevier, Vol. 8, pp [10] Stokvik, C., (010). An Investigation of Forces and Moments From Drilling Risers on Wellheads, M.Sc Thesis, NTNU [11] The Economic Times (011), Essar Shipping Bags $11M Contract from Conoco Phillips, Nov. 9 [1] Djatmiko, E.B. (199), Hydro-Structural Studies of SWATH Type Vessel, PhD Thesis, University of Glasgow, UK [13] Chakrabarti, S.K. (1987), Hydrodynamics of Offshore Structures, Computational Mechanics Publication, Springer- Verlag, Southampton 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 10/11

11 [14] Bhattacharyya, R., (1978). Dynamics of Marine Vehicles, John Wiley & Sons. [15] Wichers, J.E.W. and Huijsmans, R.M.H. (1984), On the Low Frequency Hydrodynamic Damping Forces Acting on Offshore Moored Vessels, Proc. of Offshore Technology Conference(OTC), Paper No. OTC-4813, Houston, Texas, USA, May [16] Wichers, J.E.W. (1986), Progress in Computer Simulations of SPM Moored Vessels, Proc. of Offshore Technology Conference (OTC), Paper OTC-5157, Houston, Texas, USA, May [17] Wichers, J.E.W. (1987), The Prediction of the Behaviour of Single Point Moored Tankers, Proc. of Workshop on Floating Structures and Offshore Operations, Wageningen, the Netherlands [18] Wichers, J.E.W. (1988a), Simulation Model for Single Point Moored Tanker, MARIN Publication, No. 797, Wageningen, the Netherlands [19] Wichers, J.E.W. (1988b), Wave-Current Interaction Effects on Moored Tankers in High Seas, Proc. of Offshore Technology Conference (OTC), Paper OTC-5631, Houston, Texas, USA, May [0] API (001), Recommended Practice for the Analysis of Spread Mooring Systems for Floating Drilling Units. API Recommended Practice P (API-RPP) [1] API (005), Design and Analysis of Station Keeping Systems for Floating Structures. API Recommended Practice SK (API-RPSK), 3 rd ed [] API (1993). Design, Selection, Operation and Maintenance of Marine Drilling Risers Systems, API Recommended Practice 16 Q (API-RP16Q) 8 th International Conference on Marine Technology, Kuala Terengganu, Malaysia, 0 October 01 11/11