Analysis of Dynamic Positioning System Performance for a Semisubmersible Platform

Analysis of Dynamic Positioning System Performance for a Semisubmersible Platform

Lei Wang, Liang Wang, and Shi-zhi Yang

State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University

Shanghai, China

ABSTRACT

This paper is concerned with a dynamic positioning system for a state of the art, ultra-deep water semisubmersible platform with 8 azimuth thrusters. The system meets the ABS class requirements for DPS-3. Hydrodynamic characteristics of the platform and the propulsion systems were measured at scale model and computer simulations were made. The correction factors to the open water thruster performance were developed from hull-thruster, thruster-thruster interactions, the forbidden zones were also provided for optimum thruster performance in the dynamic positioning control system. Thruster failure analysis is also covered and discussed. Numerical simulations were carried out for some specific examples.

KEY WORDS: Dynamic positioning system; semi-submersible platform; numerical simulation; model experiment. INTRODUCTION

Semi-submersible platforms are widely used in the exploration and development of ocean resources and many such platforms are now in operation. They are required to maintain a given position and to adjust this position under external forces of ocean current, wind and waves. With increasing depths, the conventional mooring positioned operation presents serious technical and economical limitations. A robust DP system can then improve position control ability, enhancing operational time schedule and making the operation economically feasible.

This works deals with the analysis of a Dynamic Positioning System (DPS) for a specific deepwater semi-submersible platform.

The Vessel is a four-column stabilized semi-submersible drilling vessel. The vessel is equipped with a fully redundant DPS-3 positioning system consisting of 8*4.6MW azimuth thrusters. In order to obtain accurate information of DP environmental loads, DP environmental loads on Semi are calculated and a 1:50 scaled model test was finished to prove the calculation; the wave drift force is mainly discussed, in which the calculation is based on the theory of near field integration and a new suit of measurement system is designed to fit for semi-submersible platform. Also, the effective thrust of 8 azimuth thrusters was calculated taking into interactions of current, thruster-thruster and

thruster-hull, and it reflected in the model test versus thrusters’ rpm.

The thruster interaction result in forbidden zones of 27.2 deg width，

and the zone which the thruster dependence on is labeled.

DP Capability Polar Plot and dynamic simulation are developed;

calculation and result analysis are carried out in some specific examples.

Thruster failure analysis is also covered and discussed.

VESSEL DATA

The semi-submersible platform's ' main particulars are included in the

Table 1. The draft of the semi-submerged platform is 19m.

A large scale model (Figure.1) of the vessel is constructed including

pontoons, columns, braces, and upper hull per the original arrangement

drawings.

Table 1. The detail parameters of the semi-submerged platform

Designation Unit

Fully

Model Length over all m 110.4 2.208

Width over all m 78 1.56

Elevation of box bottom m 30 0.6

Elevation of upper deck m 38.5 0.77

Length of pontoon over all m 110.4 2.208

Beam of Pontoon m 18 0.36

Height of Pontoon m 10 0.2

Length of column on pontoon m 20 0.4

Width of column on pontoon m 17.6 0.352

Corner radius of column m 4 0.08

Outer diameter of each circular cylinder

bracing

m 2.0 0.029

Elevation of each bracing above base line m 13.1 0.193

Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering Conference Osaka, Japan, June 21-26, 2009

Copyright ? 2009 by The International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-53-1 (Set); ISSN 1098-618

Fig.1. Model of the semi-submerged platform

The operating sea-state for drilling operation was defined as 0.99m/s current, 25.8m/s wind (10min average) speed and waves with 5.8m significant height and 10.8 seconds zero up-crossing wave period.

THRUST SYSTEM

As already explained, the platform will be equipped with 8 azimuth ducted thrusters. For simulation purposes, a series Ka propeller with a

19A nozzle, with 3.6m diameter has been used (Table.2). The 8 azimuth thrusters model represent units with 850kN effective thrust for

the situation without current (open water thrust). A review of the locations of the azimuth thrusters is given (Figure.2); also the nomenclature of the numbering of the propellers used in this paper is shown.

Table 2. Main parameters of the ducted propeller

Propeller Ka4-70

radius 3.6m

pitch ratio 1.1

blade area ratio 0.7

Duct NO.19A

radius 3.65m tip clearance 0.025m The main requirement for the controller is the ability to keep the platform at a pre-set position during drilling or standby operation; moreover, the DPS must be able to maintain vessel positioning even in the case of failure or maintenance of one or two thrusters during operation. Simultaneous inactivity due to failure or maintenance purposes is considered for pairs of thrusters, powered by the same power plant or controlled by the same switchboard section, namely: pairs 1-8, 2-7, 3-6and 4-5.

The azimuth and RPM of each thruster are controlled individually. Diameter of the thruster nozzle is 7.2cm at model scale (Figure.3), which equals 3.6m at prototype scale.

Figure.3. The model of thruster

These thrusters do not allow direct thrust or torque measurement; therefore the open water thrust of each thruster was measured versus RPM’s prior to installation into the model. This relation is used by the DP-controller to steer each thruster.

Thrust and azimuth of each azimuth thruster is determined by the thruster allocation algorithm. The total thrust of all thrusters matches the required thrust and moment, unless thruster saturation occurs.

Each of the thrusters is steered on RPM, in order to produce the required thrust, the relation between RPM and thrust of the propeller has been known by model test, the result is shown in Figure.4.

200

400

600

800

1000

050010001500 t

h

r

u

s

(

k

N

)

RPM(rad/s)

open water thrust vs RPM

maximum thrust …

The bollard pull thrust values have been corrected for the thrust degradation due to current inflow velocities (Figutre.5). These data were incorporated into the simulation.

0200400600800

10000

0.5

1

1.5

2

2.5

3

t h r u s t (k N )

surface current speed (m/s)

open water thruat vs surface current speed

maximumu thrust curve

Figure.5. Open water thrust to surface current speed relationship

Besides the thrust deductions current inflow velocities, it is noted that (Dang and Laheij, 2004) interactions among thrusters and thruster-hull are much more complicated for DPS than a normal sailing vessel or tugs. The thrusters close to the bow of the vessel will generate a water jet into the thrusters at the stern, it effectively increases the entrant speed into the downstream thrusters, resulting in thrust and torque reductions. For dynamic positioning, the thrusters are able to generate transverse thrust and also water jet in 360 deg. In many cases, there exist critical angles when the jet of one thruster will hit the other thruster with large influences. Mostly, this should be avoided. If not completely, this interaction should at least be known.

Due to the complexity of all iterations, there is still no good theory or calculation method available in order to predict the interactions accurately. In order to have an accurate prediction for interactions, model tests have been carried out. The results are shown in Figure.6.

1 &3

It is seen that the largest thrust loss due to thruster-hull interaction occurs at the situation when the thrust jet hits the vertical wall of the other pontoon. It is also seen from Figure.6 that when the water jet flows all the way from the bow to the stern under the hull bottom (at 0 deg) the thrust losses can be 18% due to mainly friction drag. When the jet is discharged close to the edge of the hull (say at 180 deg), the interaction is the lowest with a thrust loss somewhat around 10%. The largest thrust losses occur at the situation when the jet hits the other pontoon at the angle of 90 deg.

The thruster-thruster interaction is especially important in DPS, thrust loss is over 30% at some specific angles in this model test. For example, if thrusters 1 and 3 are producing thrust to stern, the downstream thruster (#3, in this case) would experience significant reduction off the beam direction, due to the wake of thruster #1 blowing into thruster #3.

In order to avoid thruster-thruster interaction, azimuth restrictions are imposed, see Table. 3. The centre angles are those of the force vectors. The ‘Thruster dep.’ (thruster dependency) column denotes the thruster on which the zone is dependent. If this particular thruster is not in use, the zone is neglected in the thruster allocation. The forbidden zones are calculated using a simple algorithm based on the results (Lehn, 1985) and were validated in model test.

Table 3. Thruster azimuth forbidden zones.

Thruster No. Zone No.

centre ψ

(deg) beam ψ(deg) Thruster dep. 1 1 -21.8 ±13.6 3 2 1 21.8 ±13.6 4 3 1 158.2 ±13.6 1 4 1 -158.2 ±13.6 2 5 1 21.8 ±13.6 7 6 1 -21.8 ±13.6 8 7 1 -158.2 ±13.6 5 8 1 158.2 ±13.6 6

ENVIRONMENTAL CONDITIONS

In order to obtain accurate information of environmental loads, environmental loads on the vessel are calculated and some tests are finished to prove the calculation.

Wind and current forces and moments associated with vessel yaw rotation were evaluated using an improved building block approach proposed by Sahin and Aybar (1984) and Walree (1991). The structure is built up of standard components with known force characteristics. Interaction effects like shielding are taken into account.

Wind load coefficients C XV , C YV and C MV are defined in the standard way by,

111222

;;126222V V V F C V F C V F C V XV a YV a MV a

ρρρ=== (1) which are presented in fugure.7. F 1V and F 2V are surge and sway component of wind force, F 6V is the yaw moment, ρa is air density; V is the mean wind velocity.

Figure. 7. Wind load coefficient

Current load coefficients (Figure.8), defined in the same way as the wind load coefficients.

111222;;126222

C C C F C C F C C F C C XC w YC w MC w ρρρ=== (2)

F 1C and F 2C are surge and sway component of wind force, F 6C is the yaw moment, ρw is water density; C is the mean wind velocity.

Figure. 8 Current load coefficient

The wave drift force (F wd ) (Figure.9~11) is mainly discussed, in which the calculation is based on the theory of near field integration (Pinkster, 1980; Huijsmans and van Walree, 1991) and a new suit of measurement system is designed to fit for the vessel.

Figure. 9 Wave-drift load confidents, surge

Figure.10 Wave-drift load confidents, sway

Figure. 11 Wave-drift load confidents, yaw

To validate the results of numerical calculations of the second order wave forces, the measurement of wave drift forces utilizing a passive

restricted system (Figure.12) proposed by Pinkster(1980).

Fig. 12. Passive restricted system

Fig.13 presents an illustrative example of such coefficients for a 45 deg wave-heading angle, 5.8m significant height of wave. Second order slow drift forces were evaluated time domain and the results are compared with the results of model tests. In this condition, the mean wave drift forces are 802.2kN (calculation) and 842.8kN (model experiment), the error is 5.06%.

Figure. 13 Results of wave drift forces of calculations and experiments.

The Pipe drag (F cp ) is defined as the current force distribution along the pipe and buffer (F cp ), induced by the relative current velocity (V C(Z)), where the relative current velocity is the pipe element velocity (V S ) relative to the surface or subsurface current velocity profile (Brink and Chung, 1981). Among the force components for the given operational and environmental requirements, the F cp and F wd are the largest force components and are in the same order of magnitude for the stationkeeping mode with no choice of headings. For the given requirements, the F cp remains the same regardless of the ship heading. The F cp values vary along the pipe length as a function of V C(Z) and the vertical variation of the subsurface water properties. The assumed mining velocity range can place the pipe drag coefficients (C D ) along the pipe near the subcritical to critical Reynolds number (Re) range. In other words, the F cp values can be quite different at an instant between the top- and bottom-end sides of the lift pipe. Furthermore, steep slope and ambiguity of the C D versus Re curve in this Re range can pose problems on accurately estimating the contribution of total pipe drag at different ship velocities to the ship thrust allocation (Figure. 2 for details) and possibly for the ship thruster control. The latter will be further discussed in conjunction with the control simulation results. If the top end of the lift pipe is connected to a point far from the ship c.g., the pipe drag vector can require significantly large restoring moment in the ship thrust allocation.

STATIONKEEPING CAPABILITY

Brink and Chung (1981) was the first one to introduce azimuthing thrusters to dynamic positioning as improvement over Glomar Explorer's fixed thruster efficiency, and the improvement of the Glomar thruster system and control logic was a guide of our work. In this paper the control mechanism of the simulation program is a feedback system using position data and includes a wind feed-forward system. Based on the position signals the total required thrust vector is determined with a PID controller:

int int

int int int int

i

tx X

X c x b x

xdt X treq e tx tx wff T T

i ty Y Y c y b y ydt Y treq e ty ty wff T T

i t N

N c b dt req e t t wff T T ψψψψψψψ=?+Δ+Δ+Δ+∫=?+Δ+Δ+Δ+∫=?+Δ+Δ+Δ+∫&&& (3)

In which X e is the average environmental force vector, T int is the integration time and Δx, Δy, Δψ are the position deviations, see Figure. 14. X wff is the wind feed forward force vector. c t, b t and i t are

Fig. 14 Sketch map of DP control

Solving the allocation of required forces (equation (2)) is a non-linear problem due to the possible presence of forbidden sectors for azimuthing angles. Furthermore, the solution of the location should be optimal in the sense of minimal fuel consumption. This is achieved by defining a penalty function which uses the square of the thrusts.

Forces in x and y direction for each azimuthing thruster is used to build a objective function:

[,,...,]

12x x x x N = (4)

where N is the number of azimuthing thrusters, x 2i-1 is the surge force of azimuthing thrusters, x 2i is the sway force of azimuthing thrusters.

And the azimuth of thruster is defined as:

2arctan(

21

x i i

x

i α=? (5)

The objective function which must be minimized is defined as:

22()()2121

N

f x x x i i

i =+∑?= (6)

The constraints can be divided in equality and inequality constrains.

The three equality equations are determined by the equilibrium of forces in the surge, sway and yaw directions, i.e. the forces of the allocation solution must be equal to the forces required by the controller:

()0121

1()0221

1()0321,21,11

N

g x X x treq i i N g x Y

x treq i i N N

g x N x l x l treq i y i i x i

i i =?=∑?==?=∑?==?+=∑∑??== (7) in which l yi and l xi are distances in x and y between thruster and rotation

center of the platform.

The first set of inequality constraints are given by the maximum power

per thruster.

()04max,1()0

3max,g x T g x T N

N ==+M

The second set of inequality constraints is given by the forbidden zones. All azimuthing thrusters may have one forbidden zone which can be chosen by the user. The forbidden zones are characterized by their lower(a l,i ）and upper （a u,i ）bounds. One can write these constraints as follows:

2

2

()022l u u l g αααααα+???

??

????=??≥?????

??

?The NLPQL algorithm (Lootsma, 1979) solves such constrained nonlinear programming problems.

And the stationkeeping capability of the vessel during drilling operations determines the required thruster loads at various environmental conditions - expressed in wind speed, current speed, pipe drag and wave drift forces (Srinivasan and Sen, 2003). Active thrusters as well as thrusters out of service are considered. The performance prediction is determined in accordance with the requirements of Reference 1. The DP stationkeeping capability plots are provided for the following operating modes: z I ntact System - all thrusters functional.

z Damaged System - DPS-2 (one thruster out) and DPS-3 (one

main power plant/switchboard out).

DP capability analyses are generally used to establish the maximum weather conditions in which a DP vessel can maintain its position and heading for a proposed thruster configuration. The environmental forces and moments are increased until they are exactly balanced by the maximum available thrust offered by the thruster configuration. Thus, a limiting weather condition is obtained as a combination of a mean wind speed, significant wave height and a sea current speed. Wind, current and waves are normally taken as coming from the same direction. By allowing the environmental components to rotate in steps around the vessel, the results of a DP capability analysis can be presented by means of a limiting mean wind speed for a discrete number of wind angles of attack.

The results are presented in polar plots recommended by Reference 10 (2000) indicating the required thrust levels as a fraction of the maximum available thrust as well as the required thruster torque as a fraction of the maximum allowable torque for the two groups of thrusters.

Each plot represents:

　a selected environmental condition

　a selected number of active thrusters (or plants powering the thrusters)

The following cases for the intact condition and failure modes were considered in the computations:

Case 1.

This is the intact case. All thrusters are available at full load. This is the

normal operating condition (Figure.15).

Case 2.

Thruster No. 2 is out (DPS-2 condition). Due to the longest moment arm, it is the most critical thruster for vessel heading control 0

10

Case 3.

One switchboard section is out (DPS-3 condition). In this mode, thrusters 1 and 8 are out (one of other switchboard sections out, is treated similarly) (Figure.17).

010

The simulation results are summarized in Table 4 showing the limiting weather conditions at the most unfavorable wind directions.

Table. 4. Limiting conditions at most unfavorable wind directions.

Case no.

Wind

direction(deg)

Wind

speed(m/s)

Current

speed(m/s)

Significant

wave height

(m/s)

1 305 31 0.99 13.1

2 70 27 0.99 10.3

3 290 25 0.99 9.7 The results of the stationkeeping capability plots lead to the following conclusions:

Intact Condition: The static holding calculations indicate that the vessel

is capable of keeping position during drilling conditions.

DPS-2 Notation: The static holding calculations for the vessel indicate that the vessel is capable of keeping station during drilling conditions after loss of a critical thruster. Hence it complies with the DPS-2 notation requirements of Reference 1.

DPS-3 Notation: The static holding calculations indicate that the vessel

is capable of keeping position after loss of one power plant during the drilling conditions. Hence it complies with the DPS-3 notation requirements.

Time simulations for a normal case (30 deg incidence) are shown in Fig. 18, the displacements in axis, as well as the reference point trace are presented. As expected, the DPS works well, presenting a motion of

CONCLUSIONS

A comprehensive and up-to-date case-study analysis of a Dynamic Positioning System to be installed in a semi-submersible platform has been successfully carried out. In order to feed a numerical simulator, a 1:50 scale model has been conducted, addressing wave forces and thrust of azimuth thrusters. Numerical simulation used a simple and validated model taking into account current (at low speed and large drift angles), waves (including current interaction) and wind forces. Thrust allocation was also implemented. Propeller failure analysis was carried out.

Two methods for DP capability analysis, i.e. DP Capability Polar Plot and DP Dynamic Simulation, are introduced, calculation models of them are developed, and calculation and result analysis are carried out in some specific examples. Based on two methods introduced above and some other factors like failure model and economic performance, the DPS complies with the ABS DPS-2 and DPS-3 requirements for drilling conditions.

ACKNOWLEDGEMENT

The model tests were conducted by State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University, and financially supported by National High Technology Research and Development Program of China (863 Program, Grant No. 2006AA09Z327). Their technical and financial supports are truly appreciated. REFERENCES

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