Stability of Deepwater Drilling Semi SubmersiblesArjan Voogt 1), Julian Soles 2)

1) MARIN USA IncHouston Texas USA

2) GlobalSantaFeHouston, Texas, USA

Abstract

Most stability standards for the design of semi-submersibles are based on quasi-static approaches.These methods do not take into account the dynamicwind and wave loading and the resulting platformresponse. Several model tests in recent years revealedthat stability criteria of drilling semi-submersibles areinfluenced by the existence of nonlinear wave loads.These wave loads appeared to be induced by shallowwater wave effects on top of the pontoons. This paperreviews these effects from model tests, from numericalcalculations and from field experience concluding thatfor increasing natural periods of roll, the low frequencyresponse increases. These motions reduce theavailability of the unit for drilling operations. Theauthors share this experience in hope that designers ofnew semi-submersibles will take these dynamics intoconsiderations.

Keywords

Stability; Semi-submersible; Operability; GM; Rollmotions; Nonlinear wave loads.

Introduction

Classically the major concern during semi-submersibledesign is to ensure that the vessel will have adequateintact and damage stability. With the advent ofwatertight upper decks and larger columns, the stabilityof some new semi-submersibles is governed by havingan intact GM greater than 0m, rather than the shape andarea under the GZ curve as was usually the case witholder designs. While this makes for a robust design froma stability aspect, it does not make for one from amotion point of view.

At low GM values, it has been observed that 5thgeneration semi-submersible designs typified byshallow drafts and large pontoons are susceptible tolarge angles of roll and pitch due to their long naturalperiods and subsequent low-frequency response [Voogt,2002]. Martin and Kuo [Martin, 1978] observed this

phenomenon for semi-submersibles in regular beamwaves. Takaki and Higo [Takaki, 1990] also observedlow-frequency sub-harmonic rolling motions duringmodel tests on a semi-submersible in regular waves.These motions were related to the steady tilt angle of theunit, increasing as the steady tilt angle increased.Despite the high level of research interest in steady tiltand low-frequency motions, until now there was littledocumented evidence of such problems occurring inpractice. This paper aims to bridge this gap betweenresearch and operational experience. After a review ofthe theoretical hydrodynamic background and thenumerical methods available to assess these phenomena,the operational experiences and implications will bediscussed.

Hydrodynamic Aspects

Submerged pontoons of a semi-submersible aresubjected to upward forces proportional to the wavedrift force [Pinkster, 80], [Molin, 79]. This forceincreases as the pontoon comes closer to the freesurface.In addition to this wave drift force-induced lift, anadditional lift force exists on submerged pontoons. Thislift force is due to currents and eddies being shed fromthe pontoons and columns. The impact of these eddies iswell known for horizontal motions of FPSOs(Galloping/Fishtailing) and Spars (VIM), but with lowrestoring moments these phenomena can also result inangular motions of the platform.

Tests in Regular Head Waves

In theory, in regular head seas there is no roll excitation,but the system is fundamentally unstable. If onepontoon (either pontoon) becomes slightly closer to thewater surface than the other, then the vertical wave driftforce on it will increase. The difference between thisvertical wave drift force and the vertical wave driftforce on the other pontoon will cause a static heel angle.Therefore, for a semi-submersible with low initialstability (low GM), the difference in vertical wave driftforces on the pontoons may provide an overturningmoment that is large enough to require a substantial

10th International Symposium on Practical Design of Ships and Other Floating StructuresHouston, Texas, United States of America 2007 American Bureau of Shipping

angle of heel to develop an equal restoring moment. Alarger value for initial stability will obviously reduce theequilibrium angle of heel. This angle of heel is onlyfound in regular wave tests in head seas or very close tohead seas. To demonstrate the dependency of angle ofheel on a representative design wave period, model testswere carried out with periods from 7 to 23 seconds andincreasing wave height [Voogt, 2002]. Figure 1 showshow the mean roll angle varied over these wave periodsat the operating draft with 2.5m GM in 3 knots current.From this data it can be concluded that the maximumlist for this configuration occurs at a specific wavefrequency of approximately eight seconds.

Fig. 1: Mean list angles observed in regular waves atdifferent periods, measured in 3 knots current

Low Frequency Roll Motions

In irregular (long crested) waves, the effect is much lesspronounced. The vertical wave drift force is notconstant and variations in force on each pontoon areequal to or larger than the force differences due to thepontoon immersion depth difference. However full scalemonitoring confirms that the effect of low GM can beseen in the actual roll motions a vessel experiences inhead waves. As shown in [Voogt, 02] these motionsincrease:

for relatively short waves (wave period 7s to10s)

not linearly or quadraticly with the wave height rapidly with current present with decreasing pontoon submergence

Figure 2 shows the measured roll motions in irregularhead waves during a 1-year Gulf of Mexico stormcondition (Hs=3m, Tp=8.2s) with 1 knot current for aGM of 2.5m. These roll motions mainly show a lowfrequency part at the natural period of 60 seconds.These motions are induced by nonlinear wave loads, asdiscussed in the section on the numerical background.

Fig. 2: Low Frequency Roll Motions measured for lowGM values in operational head waves

Effect of Stability

In an operational sea condition with significant waveheight of 3m and 8.2 seconds peak period, the rollmotions of the GSF Development Driller hull weremeasured for head waves with 3 knots parallel current.The standard deviation was shown for a GM of 2.5mand 5m. Additional research showed that the increase inthe roll motions is not linear with the change in stability(see Figure 3). These roll motions occur mainly aroundthe natural frequency of the semi-submersible. Forsmaller GM values this period increases, and thus thedamping and wave excitation change.

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Fig. 3: GM versus standard deviation of roll motions

Decay Tests

To assess the damping with different GM values, rolldecay tests were carried out. The natural periods anddamping values for each test were derived by theprocess of fitting the equations of motion with zeroexternal force to the measured positions and derivedvelocities ( ) and accelerations ( ):

0dispgGMbbI seclinxx

in which Ixx is the total roll inertia (including the addedinertia) and disp is the displacement in tonne. A lowpass filter is used right above the natural frequency forthe time derivatives of the roll motions. The estimatedtotal intertia provides the natural frequency and theestimated linear (blin) and quadratic (bsec) dampingterms can be used to calculate the equivalent damping(beq) as percentage of the critical damping (Bc) asfollows:

%100bbb seclineq

in which is the absolute roll velocity in deg/s.

The critical damping follows from:

displgGMI2B xxc ,

To find the optimum estimate for the damping, a leastsquare estimate is used.

The damping is given as a percentage of critical (Bc).The total absolute damping for a specific roll velocity ( ) equals:

cseclinceq BbbBbB with

displgGMI2B xxc ,

in which Ixx is the total roll inertia (including the addedinertia) and displ is the displacement in tonnes.

When reducing the GM from 5.0m to 2.4m, an increasein the natural periods from 40 to 65 seconds wasmeasured. For the cases with GM above 4m lineardamping could be fitted to the data, but for smaller GMsthe roll damping became more quadratic. For thosecases a least square fit with linear (equivalent) dampingonly is no longer accurate to reproduce the motionbehavior and is not accurate to predict the roll motionsin numerical calculations. Figure 4 shows how quadraticdamping terms are required to properly predict the rollresponse when the semi-submersible had low initialstability and a long natural period.

0 200 400 600 800 1000 1200 1400 1600-10

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5

10equivalent linear damping, beq= 2.82%, Tn = 62.3 s

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10linear and quadratic damping, blin= -1.26%, bsec= 11.44%, T n= 62.3 s

time [s]

Fig. 4: Measured roll decay at GM=2.4m with fittedequation of motions accounting for linear

damping (upper graph) or combined linear andquadratic damping (lower graph)

Numerical Background

Prior to the tests, a diffraction analysis on the vessel wascompleted for both drafts. This analysis demonstratedthat at headings just off 180 degrees the roll driftmoment was comparable to the vessel righting momentin the regular wave test at the survival draft. Thediffraction analysis also showed that for a headingslightly off from head seas (165 degrees) at operatingdraft the roll drift moment quadratic transfer function(QTF) is much smaller when compared to the survivaldraft (Figure 5). This characteristic has been attributedto the pontoons being immersed deeper into the water.This force is best known for causing hoveringsubmarines to rise to the surface [Wu, 93].

A further observation from the diffraction analysis wasthat as the vessel heeled over the vertical wave driftforces for wave periods of around 7 seconds increasedeven further.

Fig. 5: Comparison of roll mean wave drift momentQTF at operating and survival drafts - wave

direction 165 degrees

The diffraction analysis was performed with the vesselheeled at 3 degrees, and the results shown in Figure 6when compared to the vertical drift forces at the evenkeel condition show a considerable increase. Whencomparing the roll mean drift moment QTF at even keelwith the rig heeled at 3 degrees, the peak of the QTF at3 degrees is almost 4 times higher with an increasedbandwidth also.

Fig. 6: Increase in the roll mean drift moment QTFbetween vessel at even keel and at three degree

roll angle

Therefore, it could be said that a small roll drift momentat even keel could cause a small list angle, subsequentlythe roll drift moment increases rapidly and the problembecomes significant. For comparison, the stability curveof the semi-submersible is shown in Figure 7. It can beseen that at 0 and 3 degrees heel the wave driftoverturning moment is greater than the rigs rollrestoring moment, and therefore causes the rig to heeluntil equilibrium is reached. It should be noted thatwithout the model tests to calibrate the diffractionanalysis results, it would be difficult to determinewhether this phenomena would actually occur or not.The diffraction analysis results would suggest a final listangle of greater than six degrees when compared againstthe roll restoring moment of the rig, particularly for thesix-meter wave height case. The reason the rig did notlist any further is that with a six degree list and a waveheight of six meters the top of the pontoon becomes

exposed, something that cannot be observed using thecalm water roll restoring moment curve.

Figure 7: Increase in the roll mean drift moment QTFbetween vessel at even keel and at three degree

roll angle

In essence, these results suggest that, at small heelangles, the higher pontoon experiences a greater steadyvertical force than the lower one, thus resulting in a netsteady moment. Equilibrium is achieved when there is abalance between this steady wave-induced heelingmoment and the hydrostatic restoring moment. If the righas very small initial stability (low GM) a large heelangle will be required to generate a restoring momentequal to the mean wave-induced heeling moment. But,as the equilibrium heel angle increases, the forceimbalance on the hulls increases, causing the heel angleto increase still further. In the worst case the heel anglewill continue to increase until the pontoon breaks thewater surface, a condition that was observed in the test.

Tests performed with a wave direction of 165 degreesstill showed a mean tilt angle, demonstrating that theeffect is still observed with slight changes in vesselheading. In fact for the effect to disappear, the headinghas to change sufficiently for the roll component of thewave to overwhelm the vertical wave drift forceimbalance. These results were verified by the diffractionanalysis. The effect will also disappear if the initialstability is sufficient to limit the initial heel angle andprevent the vertical wave drift force imbalance fromincreasing. Because the difference between verticalforces on pontoons for a given angle of heel is greaterthe closer the pontoons are to the water surface, theinitial stability required to eliminate the effect will beless as the pontoon submergence (draft) increases.

Operational Aspects

Deepwater Developments

The majority of todays deep-water developments arelocated in the Gulf of Mexico, Brazil, and West Africa.These are all areas with moderate environmentscharacterized by much lower wave heights than arefound in areas subject to harsh environments such as theNorth Sea and Eastern Canada. In these moderate

environments semi-submersibles show sufficient airgapand acceptable motion characteristics for stabilitycolumns with less height than their harsh-environmentcousins. This reduction in height of the stabilitycolumns significantly reduces the capital costs, but alsoinfluences the stability of the semi-submersible.

A deep-water semi-submersible must have high deckload capacity because deepwater developments tend tobe far offshore, where re-supply is expensive. Efficientcompartmentation and placement of down floodingpoints allows the high deck loads required to perform indeep water to be carried with relatively low initialstability (small GM values). Small initial stability valuesincrease angular motion natural periods and may reducepitch and roll motions in waves. A shortcoming of lowinitial stability at operating draft is that it may benecessary to reduce variable deck load at survival draftbecause the stability rules intact 100 knot wind criteriabecomes more onerous than the damage criteria.

Roll motions in short Waves and Currents

The low frequency roll motions seen during model testshave also been observed during actual operations in lowperiod waves combined with current. With the vessel inhead seas, larger than expected roll motions have beenobserved. The period of the roll motions, approximately40 sec, is the same as the vessel natural roll periodwhich confirms that these roll motions are due to lowfrequency forcing. It should be noted that to date, whenthe low frequency roll has been experienced, themagnitude of the roll motion has not been significantenough to hinder drill floor operations. It should benoted that due to the model tests discussed above,design changes were made to the hull prior toconstruction that significantly reduced these motionsalthough not completely removing them.

To manage the vessel when this does occur, the crewfound that by changing the vessel heading by 30-45degrees the roll motion can be completely removedwithout the addition of any pitch motion. This supportsthe conclusions arrived at during the model testsdiscussed above, in that the vertical wave drift forcesacting upon the pontoons are sufficient to cause lowfrequency roll motions in head seas.

Also of significance is the fact that the vessel draftaffects the low frequency roll phenomenon, althoughtypically a heading change is all that has been required,and draft changes have never been utilized to removethis phenomenon.

Crane Operations

The deepwater developments on which 5th generationsemi-submersibles are working involve major logisticalplans to ensure that the well construction processcontinues 24hrs per day. These logistical plans involvehandling items of various shapes and weights, ranging

from a 0.5 tonne work basket to 75 tonne subseaproduction trees or manifolds. Typically cranes installedon these semi-submersibles have increased in size toaccommodate these larger payloads, which significantlyhelps the operator simplify planning issues and reducecosts associated with hiring alternate vessels tocomplete the infrastructure that the drilling vessel isconstructing.

The cranes used to handle these large payloads havelong and heavy booms. Figure 8 shows how the vesselangle of heel/trim varies for the same load and distancemoved with GM. It can be seen at GM values less than2 or 3m the angle of heel/trim will be much greater thanat GMs larger than this The load and distance isrepresentative of a 150 tonne static load rated cranewhich has a 50 tonne boom with center of gravityapproximately 30m from the crane pedestal.

GM v Angle of heel/trim(Boom movement (Equivalent Weight moved = 50 tonnes @ 30m), Displacement = 50,000)

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Fig. 8: GM versus Angle of Heel/Trim

Therefore, depending on the cranes selected for thevessel, the GM limit imposed for operations shouldconsider that the weight of the boom alone could causethe vessel to heel/trim unacceptably.

Rig Floor Pipe Handling

As discussed above, a consequence of installing largercranes is that they come with much larger booms. Thedownside to this is that when handling small loads withthe crane, which represent 95% of all lifts the crane willmake, the rig will have a greater tendency to roll/pitchdue to the crane movement when compared to a lesscapable crane which could equally perform these smalllifts. This can impact drill floor operations where pipebeing passed through the rotary needs to be keptcentrally located. Due to the crane movement, which istypically going on 24hrs per day, the rig will have atendency to heel/trim which results in the drillersneeding to be more careful when setting the slips(Figure 9) on pipe to ensure the pipe is not resting onone side which may cause the slips to not set properly.The consequence of not setting the slips correctly can bedropping pipe in the hole that must be avoided. Inaddition with the pipe not centrally located it can dragon the side of the slips causing premature wear on thedies that grip the pipe.

Fig. 9: Hydraulic Slip

Figure 9 shows a set of hydraulic slips with a drillingguide mounted on top. The drilling guide was designedto keep the drill pipe centrally located within the slips toensure that the pipe does not rest against one side,which can cause the slips not to set properly.

Vessel Ballasting

Without the drilling guide the rig is required to trim thevessel frequently to try to keep the pipe centrallylocated, something that is not practical in day-to-dayoperations.

Typically semi-submersibles do not routinely transferballast between pontoons. Although this is not a classrule it has been adopted as a best practice within theindustry from lessons learned from previous incidents.Having the ability to routinely transfer ballast betweenpontoons would make keeping the vessel level muchsimpler though, since you would not need to beconcerned with keeping a constant vessel draft as theballast remains onboard throughout the process.

Therefore to level the vessel you must take on ballast inone pontoon and remove ballast from the other, while atthe same time keeping the vessel draft constant.Performing this task constantly on a vessel with lowinitial stability is not ideal. Therefore a semi-submersible should be designed with adequate stabilityto prevent this requirement as existing stability ruleswill not prevent this from occurring.

The VDL trade-off

The key requirement for these rigs is a high variabledeck load (VDL) due to the type of deepwaterdevelopment work that they are being scheduled for asdiscussed above.

The conflict when deciding the vessel VDL is that theaim of the vessel designer is to maximize VDL whileensuring the vessel meets all Class stabilityrequirements. Vessel designers have been able to meetall Class stability requirements with GM>0m being the

limiting factor, and as can be seen from Figure 8 provesimpractical, which has been the case since the firstfloating vessels were designed. The trade-off for thedesigners and owners asks the question, What is anacceptable range of stability (GM) values to use whenthere are no Class requirements governing?

The vessels designers must address the answer to thisquestion, but the vessel owners must be very aware ofthe decisions behind the VDL limit imposed on thedesign. Recently the methods outlined in this paper havebeen used to limit the VDL on newly- built semi-submersible designs where practical considerations havegoverned over Class requirements.

Conclusions

In short waves and high currents, the vertical lift loadson the pontoons of the semi-submersibles result in rollmotions in head seas. These roll motions occur mainlyaround the natural frequency of the semi-submersible.For smaller GM values the period increases and the rolldamping becomes more quadratic. This process resultsin an increase of the standard deviation of roll fordecreasing GM.

The methods and considerations outlined in this papershould aid designers and owners in determining howand when to limit the VDL of the vessel in order toprovide a safe and practical working platform.

References

Atlar, M. "Towards the Understanding of Steady TiltPhenomenon in Semi-Submersibles", 6th Int. Symp.and Exhibition, Offshore Mechanics and ArcticEngineering (OMAE87), Houston, Texas, 1987.

Dev A.K., "Viscous effects in drift forces on Semi-submersibles", Ph.D. Thesis, Technical Universityof Delft, 1996.

Martin, J. and Kuo C. "Calculations for Steady Tilt ofSemi-Submersibles in Regular Waves", RoyalInstitution of Naval Architects, London, April 1978

Molin B. "Second-order diffraction loads on three-dimensional bodies", Applied Ocean Research,1979, 1: 197-212

Pinkster J.A., "Low frequency second order waveexciting forces on floating structures", Ph.D. Thesis,Technical University of Delft, 1980.

Takaki, M., and Higo, Y., A Control of an UnstableMotion of a Semisubmersible Platform with a LargeList Angle, Proc. 4th Intl. Conf. Stability of Shipsand Ocean Vehicles (STAB90), Naples, 1990.

Voogt A.J., J.J.Soles and R.v.Dijk., Mean and lowfrequency roll for semi-submersibles in waves,ISOPE 2002, Kyushu, Japan, 2002.

Wu, Tong-Ming. " Effect of Second Order Forces onSteady Tilt Behaviours and Some Applications inDynamic Positioning Aspects of Twin HulledMarine Vehicles", Ph.D. Thesis, University ofGlasgow, Scotland, U. K., 1993.