Copyright 1999, Offshore Technology Conference This paper was prepared for presentation at the 1999 Offshore Technology Conference held in Houston, Texas, 3–6 May 1999. This paper was selected for presentation by the OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or its officers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented.

Abstract For the exploration and production in deeper water use may be made of semi-submersibles and ship shaped types of structures. In the production phase the floaters are normally permanently moored and the mooring system is designed to withstand the local extreme environmental conditions.

Due to the risers and mooring lines in deep water a considerable amount of damping can be induced to counteract partly the low frequency motions. The mooring system however has to take the ultimate forces to keep the vessel on station. In these water depths the length of the mooring lines may be considerable. The cost effect by reducing the mooring system in terms of less mooring lines or a lighter system by applying assisted DP is worth to consider.

As an example a 200 kDWT tanker based FPSO system moored by means of a turret system has been considered. A water depth of 1200 m has been taken. The heavy mooring system may withstand survival conditions e.g. 100-year storm condition.

The same tanker is now provided with a class 3 assisted DP system, consisting of 4 azimuthing thrusters. The size of the passive mooring system (no DP) can be reduced and may withstand a much lower seastate e.g. 1-year storm condition.

It will be shown that the light mooring system including the DP system may be equivalent to withstand the same survival condition e.g. the 100-year storm as the heavy passive mooring system. The results show the effectiveness and benefit in using DP to assist the mooring system in survival conditions. INTRODUCTION At present DP assisted tanker based FPSO units are used mostly for heading control. In these designs the location of the turret is located closer to midship than to the bow. Due to the

position close to midship the heading of the FPSO with regard to the environment may become unstable and heading control may be necessary, see Ref.1. For FPSO units with bow turrets permitting weathervaning, the application of DP assistance to reduce the mooring forces is worth to consider.

In deep and ultra deep water not only the costs of the long length of the mooring leg are large, but also the installation costs increase considerably with the water depth.

In applying assisted DP to reduce the mooring forces, the design of the mooring system may be reduced to a passive system to withstand the 1-year or 5-year storm. In higher seastate the DP system must be activated. The average percentage of times of the occurrence of seastates higher than e.g. a 1-year or 5-year storm is relatively small. If a passive mooring system is designed to cope with the 100-year storm, the mooring system will be a heavy one. This heavy system will encounter during the full life cycle a large number of oscillations and different load levels, effecting the strength and fatigue of turret and mooring legs.

In this paper an attempt is carried out to show the benefits of DP assisted turret moored FPSO units in deep water. For deep to ultra deep water computer programs are valuable design tools. In this paper for the study of the mooring system in 1200 m use have been made of the computer programs.

Before starting the study for 1200 m water depth first by means of the computer program DYNFLOAT a validation study on a passive bow turret mooring has been carried out on a 200 kDWT tanker (70% of loaded draft) in 350 m water depth and exposed to survival conditions. The mooring system consisted of ten radially spaced combi-lines. The results of the simulations agree well with the results of model tests.

After the proven liability of the computer program the water depth has been increased to 1200 m and the mooring system consisting of ten radially spaced combi-lines has been adapted accordingly. The same tanker, but now in 100 % loaded condition, was applied.

For a range of survival conditions the system was evaluated (step 1). A heavy mooring system was necessary.

In the next step (step 2) by placing an azimuthing thruster for each removed mooring leg, the number of legs was reduced. In this second step 4 legs were removed and 4 azimuthing thrusters close to the turret location were placed. The computations with assisted DP were, however, carried out with the program DPSIM. The program DPSIM has the same

OTC 10781

Benefits of using assisted DP for Deepwater Mooring Systems Johan Wichers (MARIN USA) and Radboud van Dijk (MARIN)

2 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

source as DYNFLOAT but in addition DPSIM has codes to compute the thruster actions and for the control system. The program DPSIM missed, however, the wave frequency motions. Comparing the result of DYNFLOAT with DPSIM for the (10 leg) passive mooring system, dynamic amplification factors for the turret and mooring leg load were derived and applied during this study.

Knowing the dynamic amplification factors of the turret loads and mooring legs, computations with assisted DP were carried out with the mooring system consisting of the 6 radially spaced legs of the original heavy system. Computations were carried out with and without wind feed forward. The spring control coefficients of the thrusters were determined in such a way that the sum of the (horizontal) stiffness of the 6 legs and the stiffness of the control coefficient of the thrusters equals the stiffness for the passive 10 leg mooring system. In this manner a good comparing was possible on the effect on the thrusters on the behavior of the system. The results clearly show the favorable effect of the assisted DP. The results indicate that the 6 mooring leg system was overestimated.

In the following step (step 3) the 6 legs were significantly reduced in size, achieving a lighter mooring system. The thrusters were kept the same. In this condition the control coefficients were optimized to increase the effect of the assisted DP. In spite of the light mooring system the integrated system was able to withstand the same extreme survival condition in the parallel weather condition.

While in the passive mooring system the extreme storm conditions were applied in both collinear and oblique weather conditions, the assisted DP computations were carried out, however, in collinear extreme storm conditions only. The reason was for correct interpretation of the results.

Finally (step 4) computations were carried on the light mooring system as a passive mooring system (DP not active). The computations were carried out with the program DYNFLOAT. By means of the computations for a range of seastates both collinear and oblique, the operational limits of the light passive mooring system were determined.

In step 5 the results of the step 1 and step 4 were applied to the wave scatter diagram of West of Shetland for the period of the heaviest weather conditions (December-February). It turns out that the activation of the DP system is necessary for only in a small percentage of the mentioned period. The 5 mentioned steps including the validation are in more detail elaborated in the following sections. VALIDATION The validation computations were carried on a 60 % loaded tanker (70% of fully loaded draft) with a size of 200 kDWT. The water depth amounts to 350 m. The tanker was moored by means of an internal bow turret. The mooring system consists of ten radially spaced combi-lines. The main particulars of the tanker and position of the turret are given in Table 1, while the body plan is given in Figure 1. The environmental conditions are presented in Table. 3. The mooring pattern and weather directions are defined in Figure 3. For more details reference

can be made to Ref. 2. The computations were carried out with the MARIN time-

domain computer program DYNFLOAT. DYNFLOAT is a completely integrated program taking into account both the low and wave frequency dynamics of both the vessel and mooring system under action of wind, waves and current. For the wave drift damping and forces (including the current interaction effects) the theory as given in Ref. 3, 4 and 5 are taken into account. For the counter part of the wave drift forces being the low frequency hydrodynamic viscous reaction forces/moment, experimentally determined non-linear formulations (in calm water and in a current field) as given by Ref. 4 are implemented. For the dynamics of the mooring lines in calm water and in current including bottom friction and chain damping, reference is made to Ref. 5. The computation procedure is illustrated in Figure 2.

The results as directly computed by the program DYNFLOAT (no additional matching damping) is given in Table 4. The results of the model test are given in the same table. The computed loads in the mooring lines agree well with the results of the model tests.

THEORY DP ASSISTED General For the computations on the assisted DP use is made of the MARIN program DPSIM. As said in the introduction the program DPSIM has the same source, concerning the low frequency formulations, as DYNFLOAT but in addition DPSIM has codes to compute the thruster actions and for the control system. The program DPSIM missed, however, the wave frequency motions. This implies that comparison computations have to be carried out with DYNFLOAT to determine an estimate of the mean chain damping and the dynamic amplification factor for mooring leg and turret loads.

The computational procedures on the thruster action (thrust in a current field, thruster-thruster and thruster-hull interaction) are given in Ref. 7 and 8, while an example of the control system (PID-control coefficients, allocation algorithm) is described in Ref. 9. Propulsion Units For the azimuthing thrusters use is made of 5 mW azimuthing propulsion units. The particulars of the units are given in Table 1. The open water characteristics of the (Kamewa) units are given in Figure 6. An example of the thrust, torque and power for maximum nominal RPM and as function of low speed is given in Figure 7. PID-coefficients In this section as an example the estimate of the PD control coefficients as used for the assisted DP for the 6 heavy mooring lines will be presented.

The mooring pattern of the 10 leg and 6 leg mooring system with regard to the collinear weather condition is defined in the Figure 3 and 4. The assumption is that the stiffness of the 10 leg mooring equals the stiffness of the integrated stiffness (=stiffness 6 leg mooring + stiffness of DP

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 3

system). The example will be given for the surge direction only.

To determine the Dx control coefficient, the critical damping will be considered and is formulated as follows: Dtot= 2*β*√((M + a)*Ptot) in which: Dtot= total damping of integrated system β = relative damping (complete critical damping is taken, β=1) a = low frequency added mass in surge direction Ptot = total spring of the integrated system. For the heavy 10 leg mooring the total stiffness amounts to approximately 47 kN/m (displacement 100 m), see Figure 5. For the virtual mass was taken: Mv= 1.055*M=254110 ton.

As a result the total damping will be Dtot = 6910 kNs/m. Taken into account the current-, wave drift- and mooring-damping, as induced by the passive system, the Dx control coefficient as applied for the DP system in surge direction is assumed to be Dx= 6000 kNs/m.

The stiffness of the heavy 6 leg mooring system amounts to 27 kN/m (displacement 100 m), see Figure 5. The additional stiffness, which the control system has to deliver will be Px= 20 kN/m.

For the light 6 leg mooring system the DP control systems are further optimized by trial and error. By means of the PD coefficients the total required thrust forces based on the error displacement and velocities are computed and feed in the allocation algorithm. Allocation algorithm For an example of a description of an allocation algorithm reference is made to Ref. 9. The locations of the azimuthing thrusters, see Table 1, are in close proximity of the turret. The thrusters are working as one group. The control commands as given by the control system are based on possible wind feed forward and the error displacement and velocities of the turret with regard the earth bound set-point – compensating only forces caused by surge and sway deviations (no moments). The allocation algorithm distributes the total required thrust over de thrusters of the group. Deviation in direction of an individual thruster in the group may occur. The deviations are caused by the forbidden sectors of the jet direction of thrusters. The forbidden zones are defined in the allocation algorithm. The forbidden zones imply that the individual thrusters cannot interact in the mutual direction of the thrusters and a thruster and riser location. Thruster-hull interaction Figure 8 shows the computed static load-displacement relationship in surge direction (no mooring system). By applying static loads to the tanker in surge direction the thrusters have to find the reaction force. The required force has to comply with the Px control coefficient (in this case Px=50 kN/m). The actual delivered thrust is smaller than the

required thrust. The difference is the thrust loss due to thruster-hull interaction. The thruster-hull interaction amounts to approximately 4 %. It must be noted that in this condition no thruster-thruster action occurs - see locations of the thrusters, Table 1. COMPUTATIONS AND RESULTS The study is performed in 5 steps and is described below. • Step 1: Step 1 is the 10 leg mooring system with the tanker in fully loaded condition and exposed to a range of extreme weather conditions.

The particulars of the tanker are given in Table 1. The mooring system is defined in Table 2 and in Figure 3. The seastates are presented in Table 3. At the oblique weather condition the wind is turned by 45 degrees to portside with regard to the current and wave direction. The statistical analysis of the DYNFLOAT computations is given in Table 5.

From the results it can be concluded that the maximum forces in some of the mooring legs exceed the design forces to some degree. Reviewing the results the trend is that the turret displacements and associated forces increase with smaller peak periods of the wave spectra (Tp= 17.7, 15, 13.5 and 12 s) in spite of the decreased significant wave height, wind and current speed at smaller wave peak periods. The peak of the quadratic transfer function of the wave drift force is responsible for the increase of the motions and forces. The peak is close to 12 second. • Step 2: By means of comparison computations with DYNFLOAT and DPSIM on the existing heavy 10 leg mooring an estimate of the mooring line damping, current loads on the mooring lines and the dynamic amplification factor on the loads were determined. The results are given in Table 6.

The assumed dynamic amplification factors (DAF) based on the standard deviation of the horizontal force of the turret and mooring line were as follows: Fx-turret: DAF=1938/1605=1.21 Leg #1: DAF=780/627=1.24. An average DAF was taken, DAF=1.23 and applied for all DPSIM computations.

For the damping and the current loads on the mooring legs the total values were adapted according to the number of legs and diameter of the legs (step 3)

Next 4 legs of the heavy system were replaced by 4 thrusters. The remaining 6 legs were radially spaced as is indicated in Figure 4. From the results of step 1, see Table 5, seastate 4-parallel (Tp=12 s) was chosen as the worst seastate.

For the PD coefficients the values were used as described earlier. Computations with and without wind feed forward (WFF) were applied. Without WFF the results of the 6 heavy + 4 thrusters can be directly compared with the results of the heavy 10 leg mooring (same stiffness). The results are presented in Table 7. While the mean displacement remains the same, the standard deviation of the surge motions decreased considerably. The dramatic change is caused by the

4 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

additional damping generated by the thruster. Due the action of the spring of the thrusters the mean load on the turret reduced accordingly, while the standard deviation of the turret load and mooring leg reduced due to the mentioned increase of the damping. In applying WFF the balance between spring and damping is changed. More priority of the power is given to the mean displacement and less to the damping.

Assuming a design line force of 6979 kN (safety factor 1.67) it can be concluded that the design is overestimated. • Step 3: In step 3 the 6 heavy legs were replaced by 6 lighter lines. The particulars of the light system are given in Table 2. The diameter of all steel wire was reduced from 5.5 inch to 4 3/8 inch, while the diameter of the chain decreased from 5 inch to 4 inch. 300m decreased the length of the steel wire at the turret-side. The design load of the mooring leg reduces to 4680 kN (safety factor 1.67). As mentioned earlier the leg damping and current loads were adapted accordingly.

The assisted DP with the light mooring system were performed with WFF, while the PD coefficients were optimized and exposed to seastate #4-parallel. The results are shown in Table 7. Due to the softer spring of the passive mooring system, the effect of the DP system increases, resulting in lower forces for both the turret and mooring line loads. The mean power however increased from approximately 3000 kW to 3500 kW per thruster. • Step 4: In step 4 the limiting seastates for the light mooring in passive condition were determined. Therefore a number of lower seastates were chosen. The seastates applied are given in Table 3 (seastates #5, 6, 7, 8 and 9 both in collinear and oblique condition). The computations were carried with DYNFLOAT. The results are given in Tables 8. Except for the oblique seastate # 8 the line forces did not exceed the design value. • Step 5: The results of the steps 1 and 4 are indicated in the scatter diagram in Figure 9. Assuming that the heavy 10 leg mooring is equivalent to the 6 leg light mooring system including DP, the DP has to be active during less than 5 % of the average time during the worse weather season (December-February). CONCLUSIONS 1. The results of the fully integrated non-linear wave and

low frequency motion program DYNFLOAT shows good results compared to model test results. The program calculates all viscous damping due to the dynamics of hull and mooring system. No additional damping or “match” damping is necessary.

2. Comparing the result of a passive mooring system and the result of DP assisted mooring exposed to the same extreme storm conditions, the conclusion can be drawn that the effect of DP assistance is significant in reducing the mooring loads.

3. A 10 leg passive mooring system may be reduced to a 6 leg mooring, of which even the diameter and length can be decreased, and 4 azimuthing thrusters were placed close to the turret location (each removed leg replaced by an azimuthing thruster).

4. In comparing the costs of a lighter mooring construction versus the costs of an azimuthing thrusters, control system and personnel, also the costs for installation of mooring legs in deep water have to be taken into account.

5. Considering the scatter diagram in the worst season West of Shetland (December-February), the DP has to be active only during an average time of less than 5 percent.

6. The codes to compute the thruster actions and for the control system as present in DPSIM has to incorporated in DYNFLOAT for a consistent comparison of passive and DP assisted moorings.

REFERENCES 1. Aalbers, A.B. and A.A. Merchant: “The hydrodynamic

model testing for closed loop DP assisted mooring”, OTC paper #8261, 1996.

2. Wichers, J. and Chun Qun Ji: “Behaviour of turret moored tankers in combined extreme metocean parameters”, OTC paper # 8272, 1997.

3. Pinkster, J.A.: “Low frequency second order wave exciting forces on floating structures”, PhD, Delft University of Technology, 1980.

4. Wichers, J.E.W.: “A simulation model for a single point moored tanker”, PhD, Delft University of Technology, 1988.

5. Huijsmans, R.H.M.: “Mathematically modelling of the mean wave drift force in current: a numerical and experimental study”, PhD, Delft University of Technology, 1996.

6. Boom, H.J. van den: “Dynamic behaviour of mooring lines”, BOSS Conference, Delft, 1985.

7. Nienhuis, U: “Simulation of low frequency motions of dynamically positioned offshore structures”, Rina Sping Meeting, pare No.7, 1986

8. Nienhuis, U: “ Analysis of thruster effectivity for dynamic positioning and low speed manoeuvring”, PhD, Delft University of Technology, 1992

9. Wichers, J., S. Bultema and R. Matten: “Hydrodynamic research on and optimizing dynamic positioning system of a deep water drilling vessel”, OTC paper # 8854, 1998.

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 5

Table 1-Main particulars tanker and thruster

Main Particulars 200 kDWT Tanker Designation Symbol Unit Loaded Medium Ballast Length between perpendiculars Lpp m 310 Breadth B m 47.17 Depth D m 29.7 Draft T m 18.9 13.23 7.56 Displacement Volume � m3 234994 159698 88956

Center of gravity above keel KG m 13.32 11.55 13.32 Transverse radius of gyration Kxx m 14.77 15.02 15.3 Longitudinal radius of gyration Kyy m 77.47 77.52 82.15 Wind area frontal Af m2 1362 1177.1 1879

Wind area side As m2 4270 3641.5 7785

Turret location *) only at 350 m:

Longitudinal position of turret Xtur m 116.25 (145.85)*) 116.25

Particulars of the azimuthing thrusters Designation Unit Thr 1 Thr 2 Thr 3 Thr 4 Longitudinal pos. forward of st 10 m 96.25 96.25 106.25 106.25 Transverse position w.r.t. CL m 10 -10 17.5 -17.5 Diameter propeller m 4.1 4.1 4.1 4.1 Power kW 5000 5000 5000 5000 Time 0-151 (=max) RPM s 20 20 20 20 Time thruster turning 360 degrees s 30 30 30 30 Bollard pull kN 923 923 923 923

6 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

Table 2 Particulars of mooring system in 1200 m water depth

Designation Unit Heavy Light Pre-tension angle deg 59.5 58.7 Pre-tension kN 2060 2060 Chain table above sea bottom* m 1181.1 1181.1 Length of mooring leg m 2800 2500 Diameter turret m 10 10 Segment 1:spiral strand-steel wire Length at anchor m 600 600 Diameter inch 5.5 4.375 Mass in air kg/m 83 62.3 Weight in water N/m 660 484 Stiffness kN 1.15E+06 1.00E+06 Breaking strength kN 15990 9575 Segment 2: Grade 3, stud link Length m 800 800 Mass in air kg/m 353 226 Weight in water N/m 3015 1929 Stiffness kN 1.39E+06 8.90E+05 Breaking strength (RQ3) kN 11516 7816 Segment 3: Spiral strand-steel wire Length to turret m 1400 1100 Diameter inch 5.5 4.375 Mass in air kg/m 83 62.3 Weight in water in water N/m 660 484 Stiffness kN 1.15E+06 1.00E+06 Breaking strength kN 15990 9575

*) 100% loaded tanker

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 7

Table 3-Combined metocean parameters

Environmental conditions-350 m water depth Sea State Waves (JONSWAP, γ = 3.3) Current Wind

Hs(m) Tp(sec) dir(degr.) Vc(m/s) dir(degr.) Vw(m/s) dir(degr.) Collinear 15.4 14.7 180 1.8 180 60.6 180 Oblique 15.4 14.7 240 1.8 180 60.6 225

Environmental conditions-1200 m water depth Sea State Waves (JONSWAP, γ = 3.3) Current Wind

Hs(m) Tp(sec) dir(degr.) Vc(m/s) dir(degr.) Vw(m/s) dir(degr.) 1 16.0 17.5 180 1.2 180 50 180/225*)2 16.0 15.0 180 1.2 180 50 180/225 3 14.5 13.5 180 1.1 180 45 180/225 4 13.0 12.0 180 1.0 180 40 180/225 5 8.0 10.0 180 0.8 180 30 180/225 6 8.0 9.0 180 0.8 180 30 180/225 7 7.0 8.0 180 0.8 180 30 180/225 8 8.0 12.2 180 0.8 180 30 180/225 9 8.0 14.8 180 0.8 180 30 180/225

*) parallel case (180 degrees) and oblique case (225 degrees)

8 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

Table 4-Statistical results of turret moored tanker in a parallel and oblique seastate - measured and DYNFLOAT (350 m water depth)

10 leg mooring system-350 m water depth Mean St.dev. Min Max

Designation Unit Test*) Comp.**) Test Comp. Test Comp. Test Comp. Parallel weather condition

Surge m -47.75 -48.78 13.54 13.39 -94.49 -101.7 -10.81 -13.59Heave m -0.8 0 5.07 4.46 -19.07 -13.4 16.53 12.64Pitch degrees 0.24 0 1.91 1.62 -7.27 -4.6 6.29 4.93Fx-turret kN 5158 5014 2336 2368 166.2 969 16602 17797Fz-turret***) kN -10308 -10429 3487 2517 -31138 -22578 -1501 -2318My-turret kNm -16004 -14009 9989 10195 -66919 -73392 12196 14042L-1***) kN 3156 3254 1071 1024 681 659 9361 9390L-2 kN 2517 2694 912 783 361 474 8256 7022L-10 kN 2590 2594 910 783 445 473 8514 7046

Oblique weather conditions Surge m -37.46 -32.20 7.59 7.40 -65.01 -57.9 -13.78 -7.4Sway m -24.67 -26.2 9.98 12.52 -65.96 -79.5 2.92 1.72Heave m -0.97 0 5.01 4.69 -20.29 -13.81 13.59 14.24Roll degrees -0.96 0 1.55 1.03 -6.79 -3.69 5.98 3.66Pitch degrees 0.21 0 1.87 1.7 -5.86 -5.03 6.79 5.01Yaw degrees 34.18 39.68 2.54 4.39 24.12 26.82 43.75 55.35Fx-turret kN 4385 3974 1835 1788 123.4 -2062 14788 12272Fy-turret kN 72 487 1037 1554 -243.3 -3937 7208 12971Fz-turret kN -9819 -10084 3321 2683 -29873 -24391 -1569 -2176Mx-turret kNm 2416 4468 3899 5599 -13262 -10695 32896 49577My-turret kNm -13170 -10731 7802 7474 -60318 -46440 14390 17978L-1 kN 2443 2273 697 600 525 104 6460 5417L-2 kN 2773 2800 920 803 365 290 9365 6953L-3 kN 2158 2460 915 841 285 115 9471 9098L-4 kN 1331 1553 558 572 242 0 5891 7026L-5 kN 771 821 294 326 205 0 2871 3275L-6 kN 531 515 180 232 185 0 1752 1744L-7 kN 921 508 161 231 608 0 2027 1866L-8 kN 596 676 244 296 136 0 2084 2478L-9 kN 872 960 361 382 126 0 2785 2942L-10 kN 1491 1482 533 483 227 0 3791 4405*) Test = measurements **)Comp. = DYNFLOAT computer program-no additional lf damping ***) including pre-tension

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 9

Table 5-Statistical analysis of DYNFLOAT results - 10 leg heavy mooring system in 1200 m water depth

10 leg mooring-heavy system-1200 m water depth DesignationQuantity Unit Mean st.dev. min max mean st.dev. Min max

Seastate #1 seastate #2 Parallel survival condition

Surge m -98.4 14.5 -142 -63 -114 24 -189 -64 Fx-turret kN 3738 1131 -688 7747 4681 1651 401 11811 L-1*) kN 3639 568 1491 6411 4001 799 1140 7301 L-2 kN 3287 515 1097 5807 3551 679 749 6458

Oblique survival condition Surge m -102 18 -158 -61 -119 29 -225 -59 Sway m 4 7 -16 22 9 11 -30 50 Yaw degrees 23 5 6 36 19 7.4 -11 38 Fx-turret kN 3495 1209 -1490 7674 4422 1867 -947 13872 Fy-turret kN -1672 866 -6882 599 -2035 1691 -14636 4054 L-1 kN 3731 680 1269 7258 4141 966 1049 8304 L-2 kN 3311 558 1031 6244 3555 778 672 7327 L-3 kN 2496 448 60 4794 2520 520 0 5092 L-4 kN 1761 442 0 3814 1690 437 0 4061 L-9 kN 2589 558 42 5129 2757 628 0 5932 L-10 kN 3396 661 748 6771 3771 888 568 7938

Seastate #3 Seastate #4 Parallel survival condition

Surge m -106 29 -201 -46 -95 31 -218 -39 Fx-turret kN 4436 1889 65 12756 3998 1938 471 13789 L-1 kN 3818 820 1118 7548 3578 780 1474 7637 L-2 kN 3412 665 1037 6605 3229 611 1399 6524

Oblique survival condition Surge m -111 35 -226 -38 -101 38 -253 -37 Sway m 10 13 -30 56 9 16 -36 71 Yaw degrees 15 9 -15 36 11 10 -20 38 Fx-turret kN 4280 2170 -1042 14897 4006 2298 78 16704 Fy-turret kN -1697 1786 -13817 5064 -1102 1860 -16182 5311 L-1 kN 3962 990 1159 8494 3729 988 1491 9286 L-2 kN 3408 777 910 7160 3255 749 964 7270 L-3 kN 2447 449 0 5049 2404 383 198 4954 L-4 kN 1680 346 0 3748 1706 266 0 3227 L-9 kN 2715 531 274 5597 2626 457 844 6624 L-10 kN 3644 867 1000 8296 3439 838 1563 9404 *)line forces are including pre-tension; Fline design=6979 kN (f=1.67)

10 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

Table 6-Comparison results of DYNFLOAT and DPSIM

Sea state 4-parallel-10 mooring lines-heavy system DYNFLOAT DPSIM Quantity Unit

LF+WF LF LF+WF Surge m mean -95.4 -93.2 -93.2

m stdev 30.7 30.9 30.9 m min -218 -180 -180 m max -39 5 5

Fx-turret kN mean 3998 3920 3920 kN stdev 1938 1605 1966 kN min 471 -220 -270 kN max 13789 8477 10385

leg # 1 kN mean 3578 3509 3509 kN stdev 780 627 768 kN min 1474 2034 1702 kN max 7637 5489 6724

Table 7-Statistical analysis of DPSIM results - 4 mooring systems

10 mooring lines 6 mooring lines + 4*5 MW thrusters Heavy lines Heavy lines Light lines Sea state 4

parallel No thrusters No WFF*)**) WFF*)**) WFF*)***)

Quantity Unit Quantity LF+WF LF+WF LF+WF LF+WF Surge m mean -93.2 -95.9 -76.0 -83.6

m stdev 30.9 15.5 18.6 23.5 m min -180 -144 -138 -161 m max 5 -55 -30 -34

Fx-turret kN mean 3920 2402 1796 1506 kN stdev 1966 591 670 577 kN min -270 1649 893 843 kN max 10385 4703 4415 3571

leg # 1 kN mean 3509 3487 3117 2775 kN stdev 768 410 433 280 kN min 1702 3405 2986 2872 kN max 6724 5731 5532 4439

Thruster 1 kN mean 422 562 635 Thruster 2 kN mean 421 561 635 Thruster 3 kN mean 422 563 635 Thruster 4 kN mean 421 561 635

*)WFF = wind feed forward **) Px + Cx (6 lines static) = Cx (10 lines static) in which Px = control coefficient ***) optimized PD coefficients

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 11

Table 8 Statistical analysis of DYNFLOAT results - 6 leg light mooring system in 1200 m water depth

6 leg mooring-light system-1200 m water depth Designation Unit Mean st.dev. min max mean st.dev. Min max mean st.dev. Min max

Seastate #5 Seastate #6 Seastate #7 Parallel survival condition

Surge m -92 25 -176 -34 -88 21 -144 -40 -73 15 -117 -40Fx-turret kN 1753 554 445 3984 1657 446 492 3090 1370 315 576 2420L-1*) kN 2880 267 2134 4148 2837 208 2200 3660 2710 142 2300 3240L-2 kN 2479 161 1971 3067 2456 138 2030 2930 2380 84.9 2130 2680

Oblique survival condition Surge m -107 33 -183 -31 -106 34 -186 -22 -86 23 -144 -38Sway m 8 23 -37 55 9 27 -48 60 8 23 -144 -38Yaw degr. 9 12 -16 30 8 14 -19 32 10 13 -16 31Fx-turret kN 1910 745 164 4080 1867 761 45 4260 1480 514 237 2970Fy-turret kN -425 785 -2220 1270 -384 890 -2160 1540 -385 758 -1940 1190L-1 kN 3020 343 2050 4230 3008 340 2050 4340 2820 207 2330 3630L-2 kN 2500 265 1820 3280 2485 267 1910 3330 2390 211 1910 3100L-3 kN 1660 140 1310 2160 1668 160 1320 2130 1720 135 1420 2110L-4 kN 1420 144 1080 1960 1426 150 1090 1960 1510 107 1240 1800L-5 kN 1740 161 1370 2280 1754 168 1340 2200 1800 141 1460 2210L-6 kN 2610 249 1890 3420 2612 275 1970 3390 2510 221 2000 3140

Seastate #8 seastate #9 Parallel survival condition

Surge m -90 28 -180 -28 -74 15 -116 -33Fx-turret kN 1710 610 252 4310 1390 367 361 2800L-1 kN 2870 307 1880 4430 2730 204 1870 3580L-2 kN 2470 191 1690 3260 2390 160 1570 3120

Oblique survival condition Surge m -95 36 -215 -29 -78 20 -137 -33Sway m 10 16 -24 62 7.5 9 -21 38Yaw degr. 14 8.5 -12 31 20 5 5 32Fx-turret kN 1670 859 -35 5560 1290 451 111 3040Fy-turret kN -571 583 -3000 1210 -657 345 -2020 355L-1 kN 2940 449 1740 5490 2770 249 1690 3880L-2 kN 2420 259 1540 3350 2350 195 1450 3130L-3 kN 1680 144 857 2350 1730 139 970 2380L-4 kN 1470 170 791 2270 1540 148 600 2370L-5 kN 1790 161 1230 2520 1810 155 901 2610L-6 kN 2580 264 1600 3990 2480 207 1490 3530*) line force including pre-tension; Fline design=4680 kN (f=1.67)

12 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

Fig. 1-Body plan of 200 kDWT tanker Fig. 2-Computational procedure

Fig. 3-Layout of 10 leg mooring system in Fig. 4-Layout of 6 leg mooring system in 1200 m 350 and 1200 m water depth water depth

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 13

Static Load

0

1000

2000

3000

4000

5000

6000

7000

8000

0 20 40 60 80 100 120 140 160 180 200

Excursion [m]

Load

[kN

]

Total 10 lines heavy system

Total 6 lines heavy system

Total 6 lines light system

Fig 5-Static load (100% loaded tanker) of 10 and 6 leg mooring systems

Open Water Chart

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8J

Kt-t

ot, K

t-n, 1

0*K

q, e

ta-0

Kt-tot Kt-n 10*Kq eta-0

Fig 6-Thruster characteristics

14 JOHAN WICHERS AND RADBOUD VAN DIJK OTC 10781

Thrust & Power vs. current velocityThruster @ 151 RPM

0

100

200

300

400

500

600

700

800

900

1000

0 1 2 3 4

Vc [m/s]

Thru

st [k

N]

0

1000

2000

3000

4000

5000

Pow

er [k

W]T (thrust) [kN]

P (power) [kW]

Fig 7-Thrust and power (MCR) as function of speed at 151 RPM

Static Load DP-system only(Px = 50 kN/m)

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50 60 70 80

Excursion [m]

Thru

st [k

N]

required thrust

delivered thrust

max Thrust

Fig 8-Computed static load-displacement; required and delivered total thrust

OTC 10781 BENEFITS OF USING ASSISTED DP FOR DEEPWATER MOORING SYSTEMS 15

AREA 9 (West of Shetlands)Direction = West (perc. of obs. = 22.04%)Dec to FebSea states 1 to 9

997> 14 1 1 213.5 1 1 1 312.5 1 1 1 1 411.5 1 2 2 2 1 810.5 1 3 4 3 1 12

Hs 9.5 2 5 6 4 2 19[m] 8.5 1 4 9 10 6 2 1 33

7.5 1 7 16 15 8 2 1 506.5 3 14 26 21 9 3 1 775.5 6 26 39 27 10 2 1104.5 1 13 43 52 29 9 2 1493.5 3 26 64 57 24 6 1 1812.5 8 45 72 44 13 2 1841.5 1 18 51 44 16 3 1330.5 3 12 12 4 1 32

< 4 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 > 13Tz [s]

12

34

567

6 leg light system + DP or 10 leg heavy system 6 leg light system

Fig. 9-Scatter diagram - limiting conditions