Methodology for dynamic analysis of offloading operations

METHODOLOGY FOR DYNAMIC ANALYSIS OF OFFLOADING OPERATIONS

Helio Mitio Morishita, Eduardo A. Tannuri, Tiago T. Bravin

Department of Naval Architecture and Oceanic Engineering of the University of Silo Paulo

Abstract: The relative positIOning between the Floating, Production, Storage and Offioading (FP SO) and the shuttle vessel during offioading should be analysed carefully, since the safety of the operation is of primary concern. In order to avoid collision, the shuttle vessel is kept away from the FPSO through the force of a tug-boat or by a dynamic positioning system. In both cases it is convenient to perform a preliminary study of their dynamics in order to obtain a guideline to set the best reference as well as a control approach . This paper presents a methodology for studying the dynamics and control of FPSO and shuttle vessel in tandem configuration systematically, using two software tools. The first tool allows the study of static solutions and the results have shown complex behavior, with a multiplicity of static equilibrium solutions the number and stability properties of which vary according to the combinations of the environmental conditions and vessel parameters. The second tool performs dynamic analysis of the FPSO-shuttle vessel, making it also possible to include a dynamic positioning system. Some results are compared with those obtained experimentally. Copyright © 2004 IFAC

Keywords: Offloading Operation, Dynamic Positioning System, FPSO

I.

INTRODUCTION

The FPSO systems have played an important role in the exploitation of deep-water oil in the Brazilian offshore basin. However those systems require a shuttle vessel to take the oil stored in the tanks of the FPSO to the shore from time to time. During the offloading operation the shuttle vessel and FPSO are connected to each other through a hawser in order to allow a safe oil transfer by a hose. Clearly a safe distance must be kept during this operation in order to avoid collision between the ships despite the forces due to current, wind and waves. The dynamics of the system is affected by the mooring system of the FPSO and among several alternatives, in this paper the Spread Mooring Systems (SMS) is taken into account.

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Regarding the tandem system both the equilibrium solutions and stability properties cannot be predicted easily since a set of twelve complex non linear differential equations has to be solved and their solutions depend on the relative directions and intensity of the current, wind and wave besides the parameters of the vessels (Souza Junior et aI., 2000, Morishita and Souza Junior, 2001, Morishita et aI., 2001a). In order to easily perform the static analysis of the system a special tool (software) was developed that solves the equations of the mathematical model numerically. This tool has allowed the study of the equilibrium points of the system systematically. Some of the fixed points obtained from the static analysis are either unstable or unacceptable (overlapping of the bodies). However convenient plot of all static solutions has been useful to understand the tendency of the stability properties

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(Souza Junior and Morishita, 2002). Once the fixed points are calculated the following analysis is the dynamics of the system for which a second tool was developed. The simulator, called Dynasim, can deal with multiple body systems, such as offioading shuttle-FP SOmono buoy configurations, taking into account risers and mooring line effects. It can also analyze the behavior of ships equipped with Dynamic Positioning Systems (DPS). The simulator comprises several models for environmental forces (current, wind and waves), and is able to analyze 6 degrees of freedom per body. Several experimental and numerical validations have been conducted and, nowadays, Dynasim is considered an important tool for design and analysis in the Brazilian oil industry (Nishimoto et aI., 200 I). Here must be emphasized that the main contribution of this methodology is to aid the selection of the shuttle tanker reference position and attitude properly. This means that keeping the ships in a safe position will require mInImum force from tug-boat or less fuel consumption of the DPS.

2.

MATHEMATICAL MODEL

Motions of the vessels in the horizontal plane are expressed in three orthogonal co-ordinate reference systems as shown in Fig. 1. The first system, OXYZ, is earth-fixed; the second and third ones, 01xlYIzI and 02X2Y2Z2, are body-fixed in the center of gravity of the FPSO and shuttle ship, respectively. The axes of each body-fixed co-ordinate system coincide with the principal axes of inertia of the vessel. The low frequency horizontal motions of each vessel are then given by: (m+m,,)zi = (m+m 22 )vr - (mx g +m 26 r

2

where Xo and Yo are the components of the vessel's speed in the OX and OY axes, respectively, and ljI is the vehicle heading. The components U c and V c of the current are calculated as: (3)

where Vc and ljI c' are the velocity and direction of the current, respectively. The forces X and Y, and the moment N considered in this paper are due to current, wind, waves, hawser, yaw hydrodynamic damping and, in the case of the FPSO, mooring lines, Forces due to current are determined through a heuristic model based on a low aspect ratio wing theory with experimental validation (Simos et aI., 200 I) and the wind forces are calculated employing coefficients suggested by OCIMF (OCIMF, 1994). Forces due to waves are usually split in low and high frequency terms and the former can be considered as the sum of slow and mean drift forces. In particular, calculation of the mean drift forces considers corrections due to wave and current interaction. These forces are calculated based on sea spectra defined by their parameters, namely, significant height and period. The aero- and hydrodynamic interactions between the two vessels are not considered in this work. The forces produced by mooring lines and the hawser are calculated with catenary's equations. The high frequency components are expressed in terms of positions and attitude calculated taking into account the transfer function of the vessel and sea spectra. Therefore the total motion can be determined by adding the high frequency components to the low frequency components. y

+(mll-m' 2)vcr+X

(m + m ,, )v = (m " + m)ur - (mx g + m 26 } + (m" - m 12 " er + Y

(1)

(1 , +m 66 )r =- (mx g +m 26 Xv+ru)+ N

where m is the mass of the vehicle; m;,j ' i,j = I, 2, 6 are the added mass coefficients in surge, sway and yaw, respectively; u and v are the surge and sway velocities of the vehicle, respectively; U c and Vc are current speeds related to OX and OY directions, respectively; r is the yaw rate; Iz is the moment of inertia about the OZ axis; X, Y and N represent the total external forces and moments in surge, sway and yaw directions, respectively; X g is the co-ordinate of the vessel's centre of gravity along the OX axis and the dot means time derivative of the variable. The position and heading of each vessel related to the earth-fixed co-ordinate system are obtained from the following equations: Xo=UCosljI-vsinljl ; Yo=usinljl+cosljI; tft=r

460

(2)

x

o Fig. I. Body-fixed and earth-fixed co-ordinate systems

3.

STATIC ANALYSIS

In order to have a comprehensive knowledge of the dynamics of the system a preliminary and essential step in which the equilibria of the system are determined is required. These equilibrium solutions can be obtained by setting null all time derivative terms of the equations I and 2. This means the high frequency motion and

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slow drift forces are not considered in the static analysis. The solutions are the linear and angular positions of the vessels calculated for every set of independent parameter. These sets are defined by combining angles of incidence and speed of current and wind, angle of incidence and significant height and period of waves and the draft of the ships. Perhaps the most interesting results can be obtained by varying a specific independent parameter only within some reasonable range. For the sake of example the diagram of the equilibria of a shuttle vessel varying wind speed is shown in Fig. 2. Details of the particular of the ship are shown in Table I (Section 5). This picture, in which the fixed points are the heading, was assembled considering angle of incidence and speed of the current 180° and 1.0 mls respectively and angle of incidence of the wind 20°. Furthermore, wind and wave were assumed to have the same angles of incidence, and the significant height and period of the waves were assumed to be functions of wind speed only. The offioading operation is performed by the FPSO-bow hose connection.

r:~c:±::ll'··fR::~.·.~:;l• •

.z -50

, :..

,

:'

..... . -~.- . - ... ~- ., ---- ~ . . ---

-100 _____ __• _____ __ • ___

:

------~-.--.--;-------: ---- --

>t·. ~~.::?:_:~~;---"",.;.,-j~....~-----.

- 1500':-~--:1~O--:-':15:-----::2!:---::':25 0 :-----:3J!:---::':35:---c40 :':------::'45' Wind speed (m/s)

Fig. 2. Equilibrium map Fig, 2 reveals quite interesting results since for low speed of the wind (say up to 11 mls) there are two solutions only, being one stable and other unstable as shown in Fig. 3. For wind speed between 11 mls and 13.5 mls there are fold bifurcations and four solutions appear being two stable and two unstable fixed points. In Fig. 4 are shown the stable solutions for wind speed of 12.5 mls_ Increasing the speed of the wind the number of solutions is two. Slabl.

Unstable

~

.Current

Shunle

Wind I Wave

Fig. 3. Equilibrium positions for 5m1s wind speed. Shuttle

,,~

"",/~ Wind/Wave

):

FPSO t

~~~ ~urrent Shuttle

"0

Fig. 4. Stable equilibrium positions for 12.5m1s wind speed.

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However, for a higher wind speed, the only stable solution is intrinsically safe. In this case additional forces can be recommended to reduce the amplitude of the oscillations or keep the positioning in case of sudden variation of the environmental condition. Here should be pointed out that the stability properties were determined through dynamic simulation.

4.

DYNAMIC SIMULATOR

Dynasim is designed to simulate multi body systems and different positioning systems such as, mooring lines, tug boats and dynamic positioning system (DPS) can e considered according to the sort of vessel. It includes validated models for all environmental agents, including non-uniform current profile along depth, mean wind forces and gusting, unimodal or bimodal waves and interaction between current and wave (wave drift damping) .

-+ui-l "'"

Cl)

Fig. 3 shows that for low wind speed the stable solution is not safe, due to the small distance between the ships. Fig. 4 reveals that for wind speed between 11,0 mls and 13,5 mls one of the stable solutions is unacceptable Furthermore, dynamic simulation has shown that such solution has a large base of attraction. The other stable solution, although safe, has presented a small base of attraction. Therefore in these cases, the utilization of a tug-boat or DPS is compUlsory.

Furthermore, the simulator includes simplified models for mooring lines and riser analysis, by means of catenary's equation or using pre-defined characteristic curves of each line. The 6 degrees of freedom of each body is simulated, and the visualization can be done by means of animations, time-series plots or statistical histograms. Concerning DPS simulator, three major blocks have been implemented, namely the wave filter, the controller and the thruster allocation, in order to represent a commercial DPS (Bray, 1998; Fossen, 1994) accurately. The wave-filter filters the highfrequency components due to first order wave forces . This filtering process is required since high frequency motions are oscillatory in nature and they should not be counteracted in order to avoid extra tear and wear of the thruster mechanism. Two types of wave filters have been considered: a conventional cascaded notch filter and a Kalman Filter. The controller determines the forces and moment required in the surge, sway and yaw directions based on the difference between reference and the filtered measurements. Dynasim allows the user to perform simulation choosing between two conventional control algorithms, namely a 3-axis uncoupled PID and a Linear Quadratic (LQ) controller. Additionally, a wind feed forward control is included. The control laws signals calculated by the controller

461

are sent to the thrust allocation that distributes control forces among thrusters. The allocation is based on a pseudo-inverse matrix technique.

the same velocity, the unstable equilibrium occurs at _ 50° (Figure 7). Wind 19, 6 m/s Wave Hs = 5,0 m Tp = 13,05

The simulator also includes models for controllable pitch propeller (cpp) and fixed pitch propellers (fpp), taking into account their characteristics curves, being able to estimate real power consumption and delivered thrust. It also evaluates time delay between command and propeller response, caused by shaft inertia (in case of fPp propellers).

I

~

Current 1,5 rn/s

More detailed description about the dynamic simulator can be found in Nishimoto et al. (2001) and Tannuri et al. (2003). Fig. 5. Case Study A 5.

RESULTS

350

In this section some illustrative results concerning the utilization of the tools during the analysis of offloading operations are presented.

300

-i? ~

Unstable

250 200

:r: ru

~

A real FPSO and shuttle tanker in an intermediate loading condition is considered, and their main dimensions are presented in Table I. The FPSO is moored by a Spread Mooring System (SMS), and the simulations are performed under typical environmental conditions encountered in Campos Basin.

c

r:.

~

,

-

150 100

Stable ,

50

Ul

Unstable

.....

· 50 ~ 100

0

10

15

20

25

30

35

40

45

Wind speed (m/s)

Table 1. FPSO and shuttle tanker properties Property FPSO Shuttle Length (L) Beam (B) Draft (T) Depth (D) Mass (M)

320.0 m 57.3 m 15.0 m 29.0 m 213000 ton

282.0 m 46.8 m 9.75 m 23 .3 m 98000 ton

Initially, the static analysis is performed for two cases without DPS, illustrating the effect of tug-boats forces in equilibrium position of the shuttle tanker. After that, dynamical simulations are performed for the same situations, in order to predict the oscillations of the ships during the operation. For such case, it is also presented an experimental result that presented a good adherence with the simulations performed.

Fig. 6. Case Study A: static analysis Stable

Fig. 7. Case Study A: equilibrium positions

The second part presents the dynamical result a similar case, considering now the utilization of a DPS. The experimental comparison is also performed, and some discrepancies will be analyzed.

Systems without DPS Fig.5 illustrates the first offloading condition (named condition A) analyzed. The static analysis was performed, considering wind speed varying from Om/s to 40m/s (Figure 6). For a 19,6m/s wind, the stable equilibrium position occurs for a shuttle yaw heading equal to 120 0 approximately (related to Ox axis). At

462

Fig. 8. Case Study A: (left) simulation result; (right) experimental result The dynamical simulation was then performed, and the results were compared to experimental results. The towing tank tests were carried out by the supervision of Petrobras, in a certified laboratory. As can be seen in the trace plot of Figure 8 and Table 2, there is a good

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adherence between the simulated motion and the one measured in the experiment, with small discrepancies in three motions. The hawser tension was also compared in Figure 9, with a difference of 17% in the mean value. Tabl e 2 Shutt Ie M otlOn . C ompanson X(m) Y(m) YawC) Experimental 226 -417 113 -419 Simulation 220 118

The second analyzed condition (B) is presented in Figure 11. Here, it is considered the simultaneous incidence of swell and local waves, typical condition encountered in Campos Basin. The static analysis predicted the shuttle stable equilibrium angle of 104°, and it was confirmed in the dynamical simulation (Figure 12 and Table 3). Again, the experimental results presented good adherence with simulation, even in the prediction of hawser force. Wind

Si mu la ti o n - M ea n F o r ce 611 k N

1~~::5 = 3,5 m Tp = 9,05

H5

2500

D Current

2000

1,0 rn/s '500 '000

Q

500

'4000

H5

Tp

Swell = 3, 0 m

=12,05

Experimental - Mean Force 734kN 3000 2500

Z

d:!o

2000

'(ji

c

CD

'500

~

'000

~CJ)

'"

I

M

500 0

0

2000

4000

T

~I

6000

8000

'0000

=212 kN

Fig. 11. Case Study B

'4000

'2000

T im e (s)

Fig. 9. Case Study A: Hawser forces The static analysis was also performed without tu~ force (Figure 10). As expected, the equilibriurr position does not present significant variations for wine. velocities greater than 10m/s, since in those cases, the environmental forces are stronger and the influence of the 100kN tug-force decreases. Indeed, the dynamical simulation confirmed this fact, with a general behavior similar to the simulation with the tug force . Of course, even for this case the tug boat is necessary during the operation, since sudden changes in environmental conditions may induce unsafe approximations of the ships.

Ta bl e3 . Sh utt 1e M otlOn an dH awser Force C ompanson X(m) Y(m) Yaw Hawser Force (kN) Exp. 149 -439 107 609 121 Simul. -441 631 103

e)

Such examples confirm that the numerical tools can be used with good accuracy to predict the behavior of passive offloading operation.

Unstable .

300

Fig. 12. Case Study B: (left) simulation result; (right) experimental result

g' 250 '0

~

200

~ !"

150

"

100

c55

50

§

System with DPS Stable ,

Unstable ·

·50

• 100 0

.

10

'.-.-------,.......,-,.....15

20

25

30

35

40

45

The same environmental condition of Figure 8 was tested for a DPS equipped shuttle tanker. In this particular case, the loading condition of the ships was altered, considering a ballasted shuttle tanker (M=75000ton; T=7.3m) and a full loaded FPSO (M=321000ton; T=21.2m) .

Wind speed (m/s)

Fig. 10. Case Study A: static analysis without tug-force

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The shuttle tanker is equipped with 1 main propeller, I tunnel stem thruster and I tunnel bow thruster. It is

463

used a 3 axis uncoupled PlO, associated with a cascaded notch wave filter. The set-point position is (X=125m; Y=-380m; Yaw=IOOO).

accuracy of the models included in the tools except in the case of propeller forces ofDPS. 7.

In Fig. 13, it can be seen that in the simulation and in the experiment, the ship was kept close to the set-point position. However, the experiment presented larger oscillations around mean position.

ACKNOWLEDGEMENTS

The authors are grateful to the support of Petrobras, in special to Dr. Isaias Q. Masetti, due to the initial motivation and the permission to use the experimental results. The second author is grateful to FAPESP (Proc. no 02/07946-2 and 04/02402-0). 8.

Fig. 13. Case Study C: (left) simulation result; (right) experimental result Propellers forces are also analyzed. For example, Fig.14 contains the thrust of main propeller. It can be seen that experimental forces presents larger values than simulation results, with a discrepancy of 26% in the mean value. FM:e Prop. t (kN ) '~I.-~----~----~--~====

"

• •

1000 I •

-,

-.

" ~"

'

-"i ' , '

.'.

t·

\

2500

3000

3500

4000

4500

E.p.

_Sim .

",: ':

5000

5500

;

6000

nme(s)

Fig. 14. Case Study C: thrust of main propeller. Possible causes for the significant differences between experiments and simulations are still being analyzed, but it can be cited the difficulties associated with propeller forces measurement. They are estimated using the rotation of the propellers, and, in model scale, they are extremely small (approximately IN). 6.

CONCLUSIONS

The methodology applied in this paper to analyse the dynamics and control of offloading operation involves static and dynamical analysis. The fixed point diagrams have shown that some unexpected solution can arises depending on combinations of the environmental agents. The static solutions are then analysed in the dynamical simulator in order to predict stability properties. In this paper illustrative examples were shown and some of then were compared with experimental results. The comparison has shown a good agreement between theoretical and experimental results confirming the

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REFERENCES

Bray, D. (1998), Dynamic Positioning, The Oilfield Seamanship Series, Volume 9, Oilfield Publications Ltd. (OPL). Fossen, T.!. (1994), Guidance and Control of Ocean Vehicles, John Wiley and Sons, Ltd Morishita, H.M., Souza Junior, 1.D.R. (2001), Dynamical features of an autonomous two-body floating system, Dynamical Systems and Control, FE Udwadia, and HI Weber (Eds), Gordon and Breach, London. Morishita, H.M., Souza Junior, 1.D.R., Comet, B.1.1. (2001a), Systematic investigation of the dynamics of a turret FPSO unit in single and Tandem Configuration, OMAE'2001 - 20th International Conference on Offshore Mechanics and Arctic Engineering, Rio de Janeiro, Brazil. Nishimoto, K., Fucatu, C.H., Masetti, !.Q. (2001), Dynasim - A Time Domain Simulator of Anchored FPSO, Proceedings of the 20 th International Conference on Offshore Mechanics and Artic Engineering, OMAE, Rio de Janeiro, Brazil OCIMF (1994), Predictions of wind and current loads on VLCCs, Oil Companies International Marine Forum. Simos, A.N., Tannuri, E.A., Leite, A.J.P., Aranha, 1.A.P.(2001), A quasi-explicit hydrodynamic model for the dynamic analysis of a moored FPSO under current action, Journal of Ship Research, Vol.45, No.4, December, pp289-30 1 Souza Junior, J.D.R., Morishita, H.M. (2002) Dynamic Behavior of a Turret FPSO in Single and Tandem Configuration in Realistic Sea Environments, OMAE '2002, 21 st International Conference on Offshore Mechanics and Arctic Engineering, Norway. Souza Junior, J.D.R., Morishita, H.M., Fernandes, c.G., and Comet, B.1.J. (2000). Nonlinear Dynamics and Control of a Shuttle Tanker, Nonlinear Dynamics, Chaos, Control and Their Applications, Vol. 5, JM Balthazar, PB Gon9alves, RMFLRF Brasil, IL Caldas, and FB Rizatto (Eds), Chapter 2, pp 137-14. Tannuri, E.A., Bravin, T.T., Pesce, c.P. (2003), Development of a Dynamic Positioning System Simulator for Offshore Operations, 17th International Congress of Mechanical Engineering, COBEM2003, November 10-14, Sao Paulo, Brazil.

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