1 1. MEMBERSHIP AND MEETINGS The membership of the ITTC Specialist Committee on Deep Water Mooring was as fol- lows: Dr. Christian Aage, Denmark (Chairman) Prof. Michael M. Bernitsas, USA Prof. Hang S. Choi, Korea Mr. Liviu Crudu, Romania Mr. Kazuo Hirata, Brazil Prof. Atilla Incecik, UK Prof. Takeshi Kinoshita, Japan Mr. Simen Moxnes, Norway (Secretary) Dr. John J. Murray, Canada (Secretary) Due to his change of employment Dr. Murray resigned from the Committee in 1997 and was replaced by Prof. Bernitsas. Dr. Mur- ray’s duties as Secretary of the Committee were taken over by Mr. Moxnes. Four Committee meetings have been held during the work period: • Trondheim, Norway, September 1996, in connection with the 21 st ITTC. • Tokyo, Japan, April 1997, at University of Tokyo after the OMAE’97 Conference. • Newcastle upon Tyne, England, December 1997, at University of Newcastle. A joint meeting was held with the ITTC Commit- tee on Loads and Responses. • Galati, Romania, October 1998, at ICE- PRONAV S.A. In connection with the meeting a Workshop on Deep Water Mooring and Related Topics in Offshore Engineering was arranged in a co-oper- ation between the University “Dunarea de Jos”, ICEPRONAV and the Committee. 2. COMMITTEE TASKS AND CONTENTS OF THE REPORT In 1996 the 21 st ITTC requested the fol- lowing tasks to be carried out by the Com- mittee: “Evaluate techniques and recommend procedures for the experimental and numerical simulation of moored vessels in wind, wave and currents.” The number of deep water moored off- shore vessels is growing rapidly, and hydro- carbon fields in water depths down to 3000 m are now seriously considered for floating pro- duction development. Physical and numerical modelling of such vessels with their extensive mooring lines and risers is a challenge to the ITTC Community. So the preparation of uni- form model testing and computational proce- dures is a highly relevant matter. The Committee has had to accept that a uniform coverage of the tasks above could not be obtained during the work period. While the numerical simulation of moored vessels has been rather well developed and documented in publications, this has not been the case for the experimental, physical model testing of moored vessels in very deep water. This state-of-the-art is reflected in the con- tents of the report. It is the Committee’s hope that the work can be continued and completed. The Specialist Committee on Deep Water Mooring Final Report and Recommendations to the 22 nd ITTC
Transcript
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1. MEMBERSHIP AND MEETINGS
The membership of the ITTC SpecialistCommittee on Deep Water Mooring was as fol-lows:
Dr. Christian Aage, Denmark (Chairman)Prof. Michael M. Bernitsas, USAProf. Hang S. Choi, KoreaMr. Liviu Crudu, RomaniaMr. Kazuo Hirata, BrazilProf. Atilla Incecik, UKProf. Takeshi Kinoshita, JapanMr. Simen Moxnes, Norway (Secretary)Dr. John J. Murray, Canada (Secretary)
Due to his change of employment Dr.Murray resigned from the Committee in 1997and was replaced by Prof. Bernitsas. Dr. Mur-ray’s duties as Secretary of the Committeewere taken over by Mr. Moxnes.
Four Committee meetings have been heldduring the work period:
• Trondheim, Norway, September 1996, inconnection with the 21st ITTC.
• Tokyo, Japan, April 1997, at University ofTokyo after the OMAE’97 Conference.
• Newcastle upon Tyne, England, December1997, at University of Newcastle. A jointmeeting was held with the ITTC Commit-tee on Loads and Responses.
• Galati, Romania, October 1998, at ICE-PRONAV S.A. In connection with themeeting a Workshop on Deep WaterMooring and Related Topics in Offshore
Engineering was arranged in a co-oper-ation between the University “Dunarea deJos”, ICEPRONAV and the Committee.
2. COMMITTEE TASKS ANDCONTENTS OF THE REPORT
In 1996 the 21st ITTC requested the fol-lowing tasks to be carried out by the Com-mittee:
“Evaluate techniques and recommendprocedures for the experimental and numericalsimulation of moored vessels in wind, waveand currents.”
The number of deep water moored off-shore vessels is growing rapidly, and hydro-carbon fields in water depths down to 3000 mare now seriously considered for floating pro-duction development. Physical and numericalmodelling of such vessels with their extensivemooring lines and risers is a challenge to theITTC Community. So the preparation of uni-form model testing and computational proce-dures is a highly relevant matter.
The Committee has had to accept that auniform coverage of the tasks above could notbe obtained during the work period. While thenumerical simulation of moored vessels hasbeen rather well developed and documented inpublications, this has not been the case for theexperimental, physical model testing of mooredvessels in very deep water.
This state-of-the-art is reflected in the con-tents of the report. It is the Committee’s hopethat the work can be continued and completed.
The Specialist Committee onDeep Water Mooring
Final Report andRecommendations to the 22nd ITTC
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3. DEEP WATER MOORED VESSELS
This section will give a presentation of thedifferent types of vessels and mooring systemsthat are presently used or planned for use indeep water developments. Moored vessels inthis context will normally be floating produc-tion units. Exploratory drilling units workingin deep waters are generally using dynamicpositioning for station keeping.
The work of the ITTC Deep Water Moor-ing Committee has been focused mainly onmethods for prediction of global responses, i.e.floater motions and positioning system loads.Vessels, mooring systems, their interaction,environmental excitation forces and the result-ing responses will be discussed.
3.1 Vessels
The following four main types of floatingproduction units, shown in Figure 1, will beconsidered:
• Monohulls• Semisubmersibles• Spar buoys• Tension leg platforms.
The four concepts above represent differ-ent design philosophies. There will of courseexist solutions that do not fit directly into anyof the listed groups. A thorough discussion ofthese concepts should, however, cover the mostimportant aspects related to their use asfloating production systems.
Common for all floating production unitsis that they utilize excess buoyancy to supportdeck payload. They will therefore be weightsensitive to some extent. This has, however,no direct impact on dynamic behaviour andwill not be the main focus of the present dis-cussion.
Dependent on the area and the sea state,ocean waves contain 1st order energy in therange 5-25 s. For a floating vessel the naturalperiods of the different modes of motion are
Figure 1 – The four main types of deep water moored vessels used for floating production(Frieze et al., 1997).
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therefore of primary interest, and in many waysreflect the design philosophy. Typical naturalperiods for the different vessels are presentedin Table 2 in section 3.6.
A common characteristic of all the floatersis that they are “soft” in the horizontal plane,which implies that they have natural periods inexcess of 100 s in surge, sway and yaw. Thefundamental differences between the vesselsare therefore related to their vertical motions,heave, roll and pitch. This will be discussedfurther in section 3.6.
Monohulls. The monohull is a ship-shaped structure characterized by a high pay-load capacity. Natural periods of heave, rolland pitch are all within the wave frequencyrange, leading to relatively large vertical wavefrequency motions. This necessitates the use offlexible riser systems. To reduce environmen-tal loads, partly or full weather-vaning is re-quired for permanently moored monohulls.
Semisubmersibles. The semisubmersibleconsists of three main structural elements, deck,columns and pontoons. Number and shape ofcolumns and pontoons vary with the differentdesigns. Semisubmersibles have smallwaterplane areas, which give natural periodslonger than 20 s, outside the range of 1st orderwave forces except for extreme sea states. Thisimplies small vertical motions compared to themonohull. Flexible riser systems are required,however, for this concept as well. Thesemisubmersible is very weight sensitive, i.e. ithas a low flexibility with respect to deck loadand oil storage.
Spar buoys. The Spar buoy is a longcylindrical structure floating vertically with alarge draft. Very small vertical motions makethe use of rigid vertical risers possible. TheSpar has a large oil storage capacity.
The Deep Draft Floater has also been pro-posed as a concept for deep water. It can bedescribed as a semisubmersible with a verydeep draft. Its dynamics and payload charac-teristics are similar to those of the Spar buoy.
Tension leg platforms. The tension legplatform, or the TLP, is a multicolumn structuremoored to the seabed by vertical tethers. It isthereby restrained from moving vertically andrigid risers may be used. The TLP is veryweight sensitive.
The TLP differs fundamentally from theother vessels. It may be argued whether theTLP is in fact a floating vessel, since it is thetether stiffness and not the waterplane stiffnessthat governs the vertical motion.
The Sea Star and the Tension BuoyantTower are other concepts that utilize a verticalmooring system.
3.2 Mooring Systems
Only passive station-keeping systems willbe discussed here. The station-keeping sys-tems can be divided into two main groups,compliant and rigid moorings:
• Compliant: Catenary mooringsTaut moorings
• Rigid: Vertical moorings.
This section will discuss the fundamentalphysics and dynamic characteristics of the dif-ferent mooring systems. Various system lay-outs will be presented briefly at the end.
The primary function of the station-keep-
ing system is to counteract the horizontal envi-ronmental forces so that the floating vesselremains within specified position tolerances.At the same time the system must be compliantenough to allow for the wave frequency motion,except for tethers in the vertical direction. Theenvironmental forces act in the horizontal plane,and the resulting horizontal forces must betransferred to the seabed. Since
Figure 2 – Components of a catenary mooringsystem at 1200 m water depth.
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Figure 3 – Components of a taut mooring system at 1200 m water depth.
these forces are acting at different levels, theywill introduce a moment Ms that is proportionalto the water depth:
Ms = Fh d (1)
where Fh is the horizontal force and d is thewater depth.
A mooring line cannot transfer any mo-ment, so the station-keeping moment must bebalanced by a vertical force couple. The funda-mental difference between catenary and tautmoorings is given by the way this station-keeping moment is balanced.
Catenary moorings. As illustrated inFigure 4, the buoyancy-corrected weight of thesuspended part of the mooring line must bal-ance the station-keeping moment in a catenarymooring system:
Ms = w s a (2)
where w is the buoyancy-corrected weight perunit length, s is the line length, and a is thehorizontal distance from the fairlead to thecentre of gravity of the suspended line. Thevertical force at the top will be equal to thebuoyancy-corrected weight of the suspendedline.
The compliance to allow for wave frequencymotions is ensured by a combination of geo-metrical and axial elasticity of the lines. Thelarge geometrical variations make these sys-tems susceptible to significant dynamic effects,mainly due to transverse drag forces.
Taut moorings. In a taut mooring systemthe lines are light compared to the line tension,w s << T, and the lines will be nearly straightbetween the anchor and the fairlead. In thiscase the vertical forces are taken up as anchorand vessel reactions directly, as seen in Figure5. The vertical force Fv is determined by:
Ms = Fh d = Fv a (3)
Note that the vertical force will decreasewith increasing mooring line length.
For a taut mooring line the compliance toallow for wave frequency motions must be pro-vided entirely by the axial elasticity. Tautmooring systems do not experience large trans-verse geometric changes to the same extent ascatenary systems, and dynamic effects due todrag loads are therefore moderate. To obtainsufficient elasticity and low weight, syntheticropes are often utilized in taut mooring systems.Such materials exhibit a more complexbehaviour than steel, including for examplehysteresis, which may give rise to importantdynamic effects.
Figure 4 – Force balance in a catenary mooring(Fylling, 1992).
Figure 5 – Force balance in a taut mooring(Fylling, 1992).
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Vertical moorings. Apparently a TLP structurecould be considered as a taut mooring systemwith vertical mooring lines. There is howeverone fundamental difference. TLP tethers areusually made of steel tubes with such massivedimensions that they cannot be considered asbeing compliant in the axial direction. TheTLP system acts as an inverted pendulum. Thestation-keeping forces are governed by the te-ther length and the pretension, the latter beingtypically 20% of the floater displacementweight.
Configurations. The configuration ofmooring systems regarding grouping andspread of the lines differs from one concept tothe other. There is a tendency, however, togroup the lines. This provides more spacingfor risers and a better system behaviour in dam-aged condition. Some typical configurations ofcatenary and taut mooring systems are illu-strated in Figures 2 and 3. TLP tethers willalways be vertical in the initial configuration.Any deviation from this will cause strongcouplings between horizontal translations andhorizontal axis rotations, e.g. surge and pitch.
3.3 Interaction of Vessel/Moorings/Risers
In the discussion of the interaction of thevessel, the mooring system and the risers, focuswill be on the global response of the vessel.The interaction effects can be divided into thefollowing groups:
The most obvious interaction effect is thehorizontal stiffness imposed on the vessel bythe mooring system, which is the primaryfunction of the mooring system. In a gooddesign the stiffness contribution from the risersystem should be relatively small.
An unwanted side effect of the mooringsystem is the coupling between horizontal dis-placement and rotation, e.g. between surge andpitch. The vertical components of the mooringline forces introduce heeling and pitching mo-ments. For vessels with small waterplane stiff-
ness and long moment arms, like semisub-mersibles, this coupling effect is significant.
The damping contribution from the moor-ing lines and risers will be significant, espe-cially in deep water. Since low frequency mo-tion is partly resonant, this damping is of greatimportance. The level of damping generatedby a mooring line is controlled by several para-meters, for example:
• The effective drag coefficient,dependent on possible velocityinduced vibration.
• The top end wave-frequencyexcitation.
• The mean tension level, given by thepretension and the low-frequencymotion.
Damping is the motion parameter wherethe interaction between different responsetypes is the strongest. For a given mooringconfiguration the damping effects willgenerally increase with water depth.
The inertia forces from the mooring andriser system will generally not have a signifi-cant influence on the global vessel response.As the water depth increases this could change,but compared to the drag-induced forces the ef-fect is expected to be relatively small.
The presence of current imposes drag for-ces on the mooring and riser systems, and asthe water depth increases, the exposed area andthereby the mean forces will increase. Thecurrent drag force is a function of the currentvelocity, which varies in both magnitude anddirection with depth. Ocean currents are vary-ing in time, as well. Assuming perfect correla-tion between these fluctuations at differentlayers, the excitation imposed on mooring linesand risers can be significant in deep water.Assuming no correlation, the forces due tofluctuation will tend to level out over the linelength.
In deep water the current forces can oftenbecome the dominant environmental loads onthe mooring system, contributing up to 75% ofthe mean drift forces on a floating productionsystem.
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3.4 Installation and Removal
The installation and removal of deep waterstructures by use of crane ships with longlifting cables becomes increasingly difficult asthe water depth increases. A typical dynamicalproblem is the possibility of resonance due tothe relation between elasticity of the liftingcables and the mass and added mass of thestructure. The natural period of the system cancoincide with the wave period, and thereforethe dynamics of the cable and the dynamics ofthe crane in operation should be considered inthe modelling of the system. Literature aboutthe subject is scarce and published full-scalemeasurements are lacking. Due to the complexgeometry of these structures, the numericalcalculation of added mass and damping is notalways an easy task. For a composition ofplates, pipes with a variety of combination andrelative distances and positions that can inter-fere with each other, the added mass and damp-ing coefficients are difficult to estimate.
3.5 Sources of Excitation
A thorough discussion of excitation andresponse of floating vessels is outside the scopeof this Committee’s tasks. The Loads andResponses Committee will cover these aspectsin more detail. However, a brief overview ofexcitation mechanisms will be given in thissection.
For a deep water mooring system, all theenvironmental loads, except the current forces,can be considered as acting at the water surface.Only current has a variation with depth, andcurrent forces may be of significant magnitudeall the way to the bottom. This is reflected inthe level of discussion. Resulting responses ofthe different types of vessels as well as therelative importance of the different excitationmechanisms are discussed in section 3.6.
Waves. Wave forces are usually dividedinto the following categories:
• 1st order forces at wave frequency (WF)
• 2nd order forces- mean wave drift forces- forces at sum frequencies (HF)- forces at difference frequencies (LF)
Wind. Wind forces may be divided intothe following three categories:
• Mean wind loads• Fluctuating wind loads, due to
fluctuations or gusts in the wind field• Vortex induced vibrations (VIV), due to
structure/wind interference.
Current. As for the wind, current forcesmay be divided into the following three cate-gories:
• Mean current loads• Fluctuating current loads• Vortex induced vibrations.
The nature of vortex induced vibrations isactually a strong coupling between excitationand response. It will mainly affect mooringlines and risers. The primary effect with re-spect to global vessel response is the increasedline and riser drag due to transverse oscillations.This will increase both the mean forces and thedynamic forces.
The current velocity vector varies in bothtime and space. Considering the large volumeoccupied by a deep water moored structure,maybe several km3, the complete description ofa current field for a specific structure is verycomplicated. Ideally it should comprise thefollowing information for a volume grid withsufficient resolution:
• Mean velocity and direction• Depth dependent velocity profile• Time dependent velocity profile• Direction and depth dependent
fluctuation spectrum• Information on spatial correlation.
Environmental specifications do not usu-ally comprise such information. A typical spec-ification defines a unidirectional depth depend-ent constant-velocity profile with a given returnperiod.
Ice. Structures in arctic waters will besubjected to ice. The ice loads will act directlyon the vessel and produce a mean drift force in
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the drifting direction of the ice field. Any fluc-tuations will most likely have very long periods.
3.6 Resulting Responses
The 1st order wave forces will be the domi-nant dynamic loads, orders of magnitude largerthan any other dynamic loads. The globalbehaviour of offshore structures may thereforebe classified by the motion characteristics ofeach rigid body mode of motion under wavefrequency excitation. Modes having a naturalperiod below the wave periods are usually de-noted as restrained, while modes with a naturalperiod above the wave periods are denoted asfree.
Table 1 - Modes of motion of deep water moored vesselsVessel Modes of motion: Free (F) or Restrained (R)
Surge Sway Heave Roll Pitch YawShip F F F F F FSemi F F F F F FSpar F F F F F FTLP F F R R R F
Table 2 - Natural periods of deep water moored vesselsVessel Natural periods (s)
Table 1 summarizes the global behaviourof the four main types of deep water mooredvessels, while Table 2 lists the typical naturalperiods of their six modes of motion. The dis-cussion will focus on:
• Motions: Mean offset, WF and LF• Mooring system forces:
Mean, WF, LF and HF (for TLPs)• Depth sensitivity. The motions of importance to a floating
production system, moored in deep water, are:
• Horizontal translation• Horizontal rotation• Vertical translation• Vertical rotation. The horizontal translation and rotation
(surge, sway and yaw) must be limited due tothe capabilities of the riser system. The maxi-
mum allowable offset will typically be 10% ofthe water depth.
The vertical translation (heave) determineswhether rigid risers may be used or not. Theuse of rigid risers is often desirable since itmakes the use of dry wellheads possible.
Vertical rotation (roll and pitch) is a limit-ing factor in the function of the on board pro-cess equipment.
Depth sensitivity is mainly connected withthe horizontal motions, whereas the verticalmotions are almost independent of the waterdepth. Figure 6 shows the relative magnitudesof the different components of horizontal mo-tions for typical moored structures.
The following observations regardingdepth sensitivity are more or less valid for allmoored structures. Except for very shallowwater the wave frequency motion can be con-sidered as being independent of the water depth.Mean offset and low frequency motions willtend to increase with increasing water depth fora given mooring configuration. This is due todecreasing horizontal stiffness of the mooringsystem. Mean offset and low frequencymotions thereby tend to be more and moreimportant for the extreme offset as the waterdepth increases.
Figure 6 - Horizontal motions of moored structuresat different water depths, composed of wave
frequency motions (WF), low frequency motions (LF), and mean offset (M).
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Figure 7 – Heave transfer functions of a semi, sparand ship with a North Sea storm wave spectrum.
Monohulls. Due to the large superstruc-tures of the floating production units, and theiractive or passive weather-vaning ability, thewind forces will often be dominant relative tothe current forces, at least for shipshapedfloaters.
The natural periods of all vertical modes ofmotion of a monohull are in the 1st order wavefrequency range. This implies significant wavefrequency motions, as indicated in Figure 7.
Monohulls will experience significant LFresponse in the horizontal plane only. Ship-shaped floaters may be particularly sensitive tosurge excitation since the viscous hull dampingis very low. This sensitivity is reduced withincreasing water depth since the damping con-tribution from mooring lines and risers in-creases.
Fishtailing, an unstable coupled yaw and
sway motion excited by wind and current, is aparticular challenge in the design of monohullmoored vessels. The horizontal stiffness of themooring system is a governing parameter, andfishtailing may thereby be a growing problemwith increasing water depth.
For catenary systems the wave frequencymotions will introduce dynamic mooring forces
that will tend to increase in deep water due toincreased transverse drag forces. Taut mooringsystems are not subjected to the same level oftransverse motions, and they will thereby actmore quasi-statically. Dynamic forces willtend to decrease with increasing water depthfor such systems, since the elastic length of themooring lines increases.
Semisubmersibles. Compared to the ship-shaped floaters the current forces will be largeron semisubmersibles due to the bluff shapes oftheir underwater columns and pontoons. Windloads will still dominate the mean drift forces,except in calm areas with strong currents.
The semisubmersible is characterized byhaving free modes of motion only, whichmeans that all natural periods are above therange of natural wave periods. Despite thisfact, the wave frequency motions are not insig-nificant, especially in extreme conditions, asindicated in Figure 7.
Large semisubmersibles at 100,000 t dis-placement or more are naturally less sensitiveto WF action, and for such structures the LFresponse may dominate the roll and pitch mo-tions.
Catenary moored semisubmersibles mayalso experience significant dynamic mooringforces due to WF response. The discussionperformed for the monohulls is also valid here.
Spar buoys. With a typical draft of 200 mthe spar buoy has a very large area exposed tocurrent forces and with a cylindrical shapeleading to separated flow, the current force isusually the dominant mean drift force on a sparbuoy. Low-frequency vortex induced vibra-tions may increase the effective drag leading toeven higher mean current forces.
The spar buoy is characterized by havingfree modes of motion, only. The natural heaveperiod is well above the range of 1st order waveperiods. In addition, the spar buoy has a lowlevel of vertical wave excitation due to its largedraft, which exploits the fact that the 1st orderwave motions and dynamic pressures decayexponentially with depth. This results in verysmall heave motions, as seen in Figure 7,which makes the use of rigid vertical riserspossible.
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Low frequency motions will dominate theresponse with respect to horizontal translationsas well as horizontal and vertical rotations.Current fluctuation may be a significant motionexcitation force on a spar buoy. Depth corre-lation is a central issue when determining thelevel of such excitation.
Due to very low wave frequency motion,the spar buoy is generally not subjected to largedynamic mooring line forces.
Tension leg platforms. The TLP is basic-ally free in the horizontal plane (surge, swayand yaw), but restrained in the vertical plane(heave, roll and pitch).
The TLP will thereby experience wavefrequency motions in the horizontal plane thatare of the same order of magnitude as those ofa semisubmersible of comparable size. In thevertical plane, however, the TLP will behave asa fixed structure with practically no wave fre-quency motion response. Wave frequencyforces are directly compensated by the stiffnessof the tether system.
Higher order wave forces at different sum-frequencies may introduce resonant (springing)or transient (ringing) responses in the verticalmodes. These effects may give significant con-tributions to the tether loads.
Due to the tether system the TLP will movealong a spherical surface. This gives rise to theset-down effect, which is a kinematic couplingbetween the horizontal surge and sway motionsand the vertical heave motion. Set-down is ofimportance to the wave airgap.
4. NUMERICAL MODELS
Numerical modelling is getting increasing-ly important for verification of moored systemsas the water depth increases. This because nophysical model test facilities can accommodateall water depths and mooring line spreads thatare being developed today. Even if largeenough model basins do exist, the designer willusually benefit from a combined approach,using both numerical and physical modelling.Furthermore, a theoretical understanding of thebehaviour of the complex vessel/mooring/risersystem is necessary for the development of hy-
brid model testing methods that can take careof the inevitable truncations of the mooringsystems in the model basin.
For these reasons, numerical approachesare continuously progressing, in this area as inmany others. Numerical modelling of deepwater mooring systems poses large demands oncomputer power, and many numerical prob-lems still need to be solved.
4.1 Dimensional analysis
It is not easy to describe the overall behav-iour of mooring systems connected to offshorestructures, because the behaviour is affected bydiverse factors that are specific to the systemunder consideration. A convenient way to un-derstand the underlying mechanism may be touse dimensional analysis. It is well-known thatthe results of this method are not unique butmanifold, depending on the aim of the analysisand also on the choice of reference parameters.For example, Webster (1995) obtained the di-mensional relation for the tension of a uniformmooring line, which is undergoing imposedsinusoidal motions at the top in associationwith mooring damping, as follows:
�
����
�
�
=
s
cfsssf
s
s
s
hm
s
hd
wDU
,HA
,wl
AE,
wg,
Hg
,AI
,AA
C,DD
C,Ha,
wHT
,Hl,t
fwHT
2
20
22ρ
ρπτ
τ (4)
Since the meaning and role of these non-dimensional parameters are comprehensivelyexplained in Webster (1995), we cite hereinonly those parameters related to the waterdepth H. The geometric parameter l/H is theratio of the mooring length to the water depthcalled the “scope” of the mooring line. Theparameter T0 /wH represents the static preten-sion of the mooring line divided by the buoy-ancy compensated weight of a length ofmooring line equal to the water depth. Thesetwo parameters govern the geometry of themooring line when no motions are imposed.
Furthermore a/H denotes the motion am-
plitude relative to the water depth, Hg
πτ2
the
ratio of the period of the excitation to that of apendulum of length H, whereas the charac-teristic cross-sectional dimension relative to the
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water depth is given by HAs . In the case ofdeep water, it is obvious that these three para-meters tend to zero and lose their effectiveroles.
On the other hand, the dynamic parameterEsAs /wl is indirectly related to the water depthcorresponding to the relative stiffness of themooring line. It is recognized that the dynamictension of the mooring line is significantlyinfluenced by this parameter, and that it nor-mally increases as the water becomes deeper.Hence, the relative stiffness plays a leadingrole in deep water, as found by Papazoglou etal. (1990 a). This is particularly the case fortaut mooring systems, which are being increas-ingly deployed in deep water. Taut mooringsystems are characterized by having very largevalues of T0 /wH and EsAs /wl.
4.2 Mathematical modelling
The behaviour of a mooring system is di-rectly influenced by the floater at the top, withequations of motion as expressed by Lee et al.(1998):
thrustmooringwave
currentwindviscous
memoryrrARB
FFFFFF
FννCννCνM
)t()t()t()t()t()t(
)t()()(
++++++
=++�
with vηJη )(===
=====� (5)
where M is the mass matrix including addedmasses, while vvCRB )( and rrA ννC )( are the
Coriolis force and the centripetal force, respect-ively. The velocity v is referred to the body-fixed coordinates, which are transformed fromthe earth-fixed coordinates through the relationgiven above with the help of the rotation matrix
)( ηJ ===
= . The relative velocity vector is denotedby rν .
External forces consist of the wave radia-tion force, the viscous damping, the wind force,the current force, the wave exciting force, themooring force and the thruster force, if themooring system is assisted by a dynamic posi-tioning system. The wave radiation force con-
tains time memory effects, which can be esti-mated most conveniently from the wave damp-ing, as explained in Choi et al. (1994).
The horizontal floater motions can be divi-ded into the following three componentsclassified by their time scale:
• Mean offset resulting from the steadycurrent force, mean wind and meanwave drift forces.
• Low frequency offset resulting from theslowly-varying wind and wave driftforces.
• Wave frequency motion in directresponse to the waves.
The mean offset of a moored system isdetermined statically. Generally speaking, thelow frequency offset can also be predicted bythe same method as a sequence of steady off-sets because of the long periods. However, thewave frequency excursion can only be appro-priately predicted by a dynamic approach.
In accordance with these motions, themooring line displays quasi-static and/or dyna-mic behaviour, which in turn affects the floaterin a coupled fashion. Depending on the as-sumptions and simplifications made, differentmethods have been developed. A variety ofreferences are available dealing with differentkinds of floaters and cables, combined or sep-arate. In this section, we confine our discus-sion to numerical models of the mooring linesystems.
The first step in the numerical modelling isto model the mooring line as either a continu-ous line or a lumped-mass-spring system. Thestatics and dynamics of cables are classicalsubjects treated in several books and papers.Irvine (1981) gives a broad overview and ahistorical perspective. More recently, Trianta-fyllou (1994) and Howell (1991) treated thecontinuous cable without considering bendingstiffness. Garrett (1982) derived the flexibleslender structure model by using beam or rodelements including the bending stiffness.Paulling and Webster (1986) expanded thistheory to include the stretch of the cable to-gether with various loads acting on it. Themore popular lumped-mass-spring model hasseveral advantages in terms of straightforward-ness, economy and versatility at the expense of
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accuracy. Among many others, Huang (1994)developed a numerical method for dynamicanalysis of marine cables. Huang (1992) andChucheepsakul et al. (1995) derived a varia-tional formulation for marine cables based onthe work-energy principle. The next questionis to which extent the material and strengthproperties are included, such as axial, bendingand torsional stiffness, structural damping, lin-ear or non-linear elasticity, uniformity and ho-mogeneity of the line. Depending on this, aclass of different methods is developed.
4.3 Quasi-static Modelling
Neglecting the dynamic excitation due towaves, the variation of current in time and thevortex-induced vibration, mooring lines may betreated statically. A number of different ap-proaches have been undertaken to solve theproblem. The main issue hereby is the dimen-sionality, the elasticity and the current drag, asseen in Huang and Vassalos (1993).
Mooring lines basically show a three-dimensional shape, but the assumption of co-planar configuration reduces the complexity ofgeometric descriptions. The static solution isoften insensitive to elastic deformations andthus the cable may be modelled as inelastic inmany practical situations. The governing equa-tions of an inelastic cable are of course simplerthan those of an elastic cable. The current dragacting on the cable is proportional to the squareof the relative velocity, and hence it is non-linear.
The principal components act in the nor-mal directions both in the plane and out of theplane. The latter components are caused byvortex shedding and invoke the need to treatthe problem dynamically in three dimensions.The simplest model is to assume an inelasticco-planar cable without external forces, whichleads to the classical catenary equation.
Most mooring chains may be well approx-
imated by the catenary equation. But the tradi-tional catenary equation is cumbersome for ev-aluating the force-deflection relation, because itrequires a number of intermediate steps. Flory(1997) suggested a new form of the catenaryequation to overcome this difficulty. By usinga co-ordinate system based on the undeflectedposition of the cable, the catenary top excur-
sion can be directly calculated when the exter-nal force is imposed.
Huang and Vassalos (1993) developed asemi-analytical method, which predicts the sta-tic behavior of a three-dimensional cable undera given distribution of point loads, for exampledue to current. They derived an exact solutionas a function of the internal force vector at theend point along the cable. Since the internalforce is determined as the solution to theproblem, this scheme must be implementediteratively.
Huang (1992) and Chucheepsakul et al.(1995) analyzed the quasi-static behavior ofmarine cables based on a hybrid formulation, inwhich the variational principle is applied forthe virtual horizontal displacement coupledwith an equilibrium equation in the tangentialdirection. With this formulation, they investi-gated the effect of axial deformations on theconfiguration and tension of the cable andfound that, the displacement and strained arclength increase with decreasing extensibility inthe case of given top tension, while the tensionvariation decreases. Chucheepsakul et al.(1996) reformulated the problem in polar co-ordinates in order to circumvent the limitationinvolved with the use of rectangular co-ordi-nates that may cause problems when the slopeat the bottom end of the cable becomes verysmall.
4.4 Dynamic Modelling
It is generally believed that the maximumattainable value of the dynamic tension in deepwater happens within the wave frequency range,and thus is invoked by linear motions of afloater at the top. Therefore, the need toincorporate a dynamic approach for mooringapplications in deep water has been addressedin several works, e.g. by Bergdahl and Rask(1987) and Fylling et al. (1987). This work haseventually led to a modification of the designrules and guidelines of various organizations(DNV, 1989 and API, 1995). Based on the con-clusions drawn by a task group on this topic,API (1995) strongly recommended using a dy-namic analysis for permanent mooring systemsin deep water. The task group undertook aparameter study to compare predicted line ten-sions obtained from quasi-static and dynamicanalyses for various conditions.
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Figure 8 - Parameter study of dynamic relative tostatic line tensions for a drillship and a semisub-
mersible with all-chain and combination moorings(Kwan, 1991).
Figure 8 from Kwan (1991) shows themaximum tension from the dynamic analysisdivided by the maximum tension from thequasi-static analysis for a drillship and a semi-submersible, respectively, connected to an all-chain or to a combination mooring system in astorm environment. In this figure, the largestand smallest ratios in three wave headings havebeen selected. The results indicate that a drillship with an all-chain mooring system is themost dynamically excited system, and that itstensions increase by 20-60%. The combinationmooring system is amplified by 10-50% for adrillship. It should be noted that the dynamicamplification is much less for the semisubmer-sible, due to its inherent damping.
4.5 Non-linear Time Domain Analysis
The dynamics of the mooring cable isnormally involved with non-linear loadings andinteractions among slowly varying drift mo-tions, fast varying wave induced motions, andvortex induced vibrations, which makes the dy-namic analysis a difficult task. There are fourprimary non-linear effects that have an impor-tant influence on the mooring line behaviour:
• Non-linear stretching of the line. Thelongitudinal stiffness of the line is afunction of the tension level.
• Change in over-all geometry associatedwith the shape deformation of the line.
• Fluid loading proportional to the square
of the relative velocity.
• Bottom effect. The interaction betweenthe line and the seafloor is not fullyclarified.
The bottom effect has been investigated byWung et al. (1995), who developed a numericaltool for the anchor-chain-soil interaction andcarried out centrifuge tests. They concludedthat a significant amount of energy is dissi-pated through the embedded mooring line.
Chatjigeorgiou and Mavrakos (1997) in-vestigated the non-linear effect on mooring ten-sions at the top including bending effects andtime variation of the strain along the mooringline. They compared the numerical results withexperimental data as well as with those ob-tained from simplified methods, in which thedynamic tension was assumed to be constant orits variation along the line was neglected.They found that the fully non-linear modelmore closely predicts the experimental data. Itwas also found that contributions arising fromtime differentiation of the dynamic quantitiesin the compatibility relations might be signifi-cant in predicting the dynamic behaviour of anelastic cable even for small excitation ampli-tudes.
It is well-known that the dynamic analysiscan be made either in the time domain or in thefrequency domain. All non-linear terms areproperly accommodated in the time domainanalysis, whereas they must be more or lessapproximated by equivalently linearized onesin the frequency domain. Mavrakos et al.(1989) compared experimental results with nu-merical predictions based on both time and fre-quency domain analyses for deep water moor-ing lines with submerged buoys. They foundthat the experimental data showed good cor-relation with numerical predictions,particularly with those based on time domaincomputation. They argued that discrepanciesbetween theory and experiment originatemainly from inaccurate treatment of theinteraction between cable and bottom.
Ran et al. (1998) calculated non-linearcoupled responses of a moored spar in randomwaves with and without current both in timeand frequency domains. The mooring dyna-mics were solved based on a generalized co-ordinate finite element method. In the time do-
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main analysis, Morison's equation was used toestimate mooring line drag force, which actsboth as wave excitation force and as viscousdamping. In the frequency domain analysis thenon-linear forces were stochastically linearized.Comparisons show that the time-domain analy-sis produces larger wave-frequency and slowlyvarying responses and also higher mooringtensions, except for wave-frequency top ten-sion, than the frequency-domain analysis.They postulate that it is because the viscousdamping is likely to be overestimated by sto-chastic linearization in the frequency-domainanalysis. They also found that the heave re-sponse and top tension increase in the presenceof current.
Chucheepsakul et al. (1995) investigatedthe effect of axial deformation on the naturalfrequencies of the in-plane vibration of marinecables. They used the Galerkin finite elementmethod to obtain the mass and stiffness matri-ces and then solved the eigenvalue problem.They found that the natural frequencies in-crease with an increase in the top tension aswell as elastic modulus. Newberry and Perkins(1996, 1997) propose a new mechanism for thedynamic tension as a consequence of the coup-ling between lateral and tangential deforma-tions.
The stability of a non-linear system maybe examined by bifurcation theory to producecatastrophe sets in the design space definingregions of qualitatively different system dyna-mics. Catastrophe sets have been derived nu-merically by system search for bifurcationwithout waves by Chung and Bernitsas (1992)and with waves by Bernitsas and Kim (1998).Here it is shown that resonance with the naturalfrequencies of a mooring system represents on-ly one of the mechanisms that are responsiblefor large amplitude slow motions of a spreadmooring system. The authors indicate a varietyof bifurcations that are caused by mean orslowly varying drift forces and suggest theappropriate design criteria. In Bernitsas et al.(1999) a review of mooring design based oncatastrophes of slow dynamics is presented.
4.6 Coupled or Uncoupled Models
The low frequency motion of a floater indeep water is significantly influenced by thecurrent load and the damping of slendermembers like mooring lines and risers. Fully
coupled floater/mooring/riser analysis yieldinga consistent representation of these couplingeffects as described by Ormberg et al. (1997)will require a huge amount of computationalpower. In order to gain computational effi-ciency and flexibility, alternative analysis stra-tegies are proposed by Ormberg et al. (1998),using a combination of uncoupled and coupledanalysis. They examined three alternatives tothe fully coupled system analysis and appliedthem on a turret-moored tanker with a tautmooring system. Based on the comparison ofthese results with those obtained by a fullycoupled analysis, they concluded that a coupledvessel motion analysis could be a practicalalternative to the fully coupled system analysis.A simplified model of the slender structures,moorings and risers, is still catching the maincoupling effects in terms of restoring force anddamping. Slender structure responses are thenevaluated in detail in subsequent slender struc-ture analyses, where critically loaded mooringlines and risers are analysed one by one con-sidering vessel motions as forced support dis-placements.
4.7 Mooring Damping
As the water depth increases, the dampinginduced by the mooring lines increases rela-tively to other sources of damping, affectingthe motion response of the vessel considerably.Thus an accurate estimate of mooring induceddamping is critical to a realistic simulation ofdeep water moored vessels. Huse and Mat-sumoto (1988, 1989) and Huse (1991) havetreated this problem by means of the dissipatedenergy model with an iterative use of mooringequations.
Wichers and Huijsmans (1990) extendedthe model to a finite element method in orderto include the dynamic effects of cables. Adirect time-domain simulation was performedby Dercksen et al. (1992).
Webster (1995) carried out a systematicparameter study based on a non-linear dynamicsimulation, where both the cross-flow drag andthe internal damping of the mooring line wereconsidered. He found that the damping de-pends strongly on transverse motions andtherefore increases drastically with the stiffnessof the mooring line, because a stiff cable ismore prone to undergo large transverse oscil-lations.
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Figure 9 – Low frequency damping from tanker,mooring lines and risers (Hwang, 1998).
Hwang (1998) simulated damped oscilla-tions of a surging tanker in still water, in cur-rent, and in current with regular and irregularwaves, similarly to decay tests in a model basinto evaluate the mooring damping. Figure 9shows the contributions of tanker, mooringlines and risers on low frequency damping forwater depths of 70 m and 860 m. It is observedthat the mooring line damping constitutes 32%of the total low frequency damping in the 70 mshallow water case. This contributionincreases to about 58% in the 860 m deepwater case.
4.8 Validation
Numerical methods should be verified by ademonstration that the original equations canbe recovered from their discretized version, asthe grid spacing tends to zero. For linearinitial-value problems, stability is the necessaryand sufficient condition for convergence in thelight of the Lax equivalence theorem. For non-linear problems, however, it is hardly possibleto prove the stability and convergence of a nu-merical method in an analytical form. There-fore, a convergence test is usually conductedby repeated computation on a pre-designed setof different grid systems. For the mooringanalysis in deep water, such a systematic ap-proach has not yet been found in the open lite-rature.
On the other hand, there are ample works,in which numerical results are compared withexperiment. For example, Papazoglou et al.(1990 b) suggested a scaling procedure for
mooring experiments. In order to satisfy thedynamic similitude, they introduced elasticsprings in the mooring line model. Theprocedure was validated by comparison of full-scale and scaled-down numerical results withexperimental measurements. Figure 10 showsthe dynamic tension amplification at the top ofthe mooring line and directly below theattached lower buoy. As observed in the figure,the numerical results show good agreementwith experiments.
Figure 10 - Dynamic amplification of line tensionat the top of the mooring line and at a submerged
buoy (Papazoglou et al., 1990 b). Legend:───⊗ , ─ ─ ─ numerical results, frequency domain
As pointed out by Leite and Fernandes(1998), conventional catenary mooring systemsare becoming impractical in deep water. Tautmooring systems with polyester synthetic ropesare regarded as an effective alternative andhave been deployed more frequently in recentyears. Further studies are needed of the dyna-mic behaviour of this system and of themechanical behaviour of synthetic ropes undersevere environmental conditions (Fernandes etal., 1998).
Turret moorings assisted by dynamic posi-tioning systems are widely employed for drill-ships and FPSOs, so it is strongly recom-mended to investigate the combined effects of
15
mooring lines and thrusters, as done by Kim etal. (1997), Strander et al. (1997), and Nakamu-ra et al. (1994).
The dynamic behaviour of the embeddedmooring line on the sea floor is a long-standingresearch topic. A description of in-plane andout-of-plane cable motions at the seabedcaused by vortex shedding has been made byPesce et al. (1997). Further investigation intothis important subject is recommended.
5. PHYSICAL MODELS
Experimental testing by means of physicalscale models in a model basin has been the tra-ditional way of investigating the behaviour ofmoored offshore vessels for nearly fifty years.Model testing of complete systems is recog-nized as the most reliable method for verifica-tion of floating offshore structures with respectto global responses such as vessel motions andmooring loads. Physical models have the ad-vantage, compared to numerical models, thatthey to some degree can bridge a gap of incom-plete knowledge of the many factors influen-cing the behaviour of these complex systems.As at sea, all laws of nature are obeyed in themodel basin, albeit only in model scale.
The scale effects, that are an unavoidableproblem in any physical model test, play a rolein model testing of deep water moored vesselsas well. But with different weighting of thedominant physical factors, model testing ofdeep water moored structures makes other de-mands on test facilities and scale ratios thanmodel testing of floating structures in moremoderate water depths. ����������������������� ���� ����� �� ��� ����������������������������������������������� ��� ����� ���� ����� � ������������������������������������������������������������������������������������������������������������ ������������ ���������� ������������ ���������������� ���� ��� �������������������������������� ������ ���� �������� ��������� ���������� ���� ������������ ������� ����� ��� ����������������������������������� ���� ��� ��� ����� �������������
Physical models of deep water mooredsystems require very large model basins. Evenwith a scale ratio of 1:100, which is tradition-
ally considered very small and indeed unac-ceptable to many model basins, modelling of afull-scale water depth of 3000 m does require a30 m deep model basin. At MARIN in Wage-ningen, the Netherlands, a new offshore basinis under construction with a maximum waterdepth of 30 m in the central pit (Buchner et al.,1999), which will allow model testing of ver-tical mooring systems (TLPs) at these extremewater depths. But spread mooring systemshave a footprint of about five times the waterdepth, in this case 150 m in all directions. Noexisting or planned model basin can accom-modate a spread mooring system at this waterdepth with traditional scale ratios.
Three different approaches have been pur-sued to circumvent this problem. One ap-proach is to do the model testing �������“�������”������������������������������������������� A second approach is touse extremely small scale ratios. A thirdapproach is to truncate the mooring lines andrisers at the model basin walls and bottom andthen simulate the truncated parts by passive oractive mechanisms, the so-called hybrid me-thod.
5.1 Natural Model Basins
Over the years, several laboratories havebeen using fjords, lakes and rivers as “natural”model basins for special research projects.Very large test dimensions can be achieved bythis approach. But due to the non-control-lability of the environmental test conditions,waves, wind and current, such facilities cannotbe used on a routine basis.
5.2 Ultra Small Scale Model Testing
At MARINTEK in Trondheim, Norway, acomprehensive and very interesting test serieshas been carried out to investigate the feasibi-lity of model testing at ultra small scale ratios(Moxnes and Larsen, 1998).
The Ocean Laboratory model basin at MA-RINTEK measures 80 m by 50 m with a maxi-mum water depth of 10 m. These dimensionsallow for a full modelling of a catenary moor-ing system up to 1000 m water depth with tra-ditional scale ratios. To extend this limit by theuse of ultra small model scales, a comparativemodel test series was carried out with twomodels of the same floating production unit
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(FPSO) at the model scales of 1:55 and 1:170.Scale ratios around 1:55 have been used formany years in model testing of moored off-shore vessels, and their reliability in relation tofull scale is well established, which makes thelarge model a suitable benchmark object.
The FPSO models were turret-moored at a
full-scale water depth of 385 m. The practicalproblems related to constructing an FPSO mo-del with turret and mooring lines at scale 1:170were considerable. At this scale ratio, 1 tonnefull scale becomes 0.2 grammes in model scale,and extreme care is needed in the building, in-strumentation and ballasting of the model.
The two models were exposed to identicalwave, wind and current conditions. Great carewas taken to make the input wave time seriesidentical in both scales, which was actuallyachieved to a high degree, as seen in Figure 11,where four independent realisations of the
same test are displayed, two at each scale ratio.Figure 11 - Four independent realisations of the
same FPSO model test, two at scale 1:55 and two atscale 1:170. The four time series are almost
identical for waves as well as responses.(Moxnes and Larsen, 1998).
The results with respect to global
behaviour, vessel motions, mooring line ten-sions and turret forces are almost identical. Itshould be underlined, however, that scale ef-fects on the viscous forces and damping maystill be significant, but obviously without muchinfluence on the global behaviour for this typeof structure.
It can be concluded that, model testing ofmoored floating offshore vessels in waves canbe carried out successfully at a scale ratio of1:170 with results very similar to those ob-tained at scale ratio 1:55. Practical problemsrather than scale effects seem to be the limitingfactor for this type of model testing, but a scaleratio of 1:170 is indeed very close to the prac-tical limit with today's model basin technology.
5.3 Hybrid Model Testing
When even the most extreme scale ratiosdo not allow the modelling of complete deepwater mooring and riser systems, hybrid modeltesting is an interesting option. The hybridmethod takes its name from its combination ofphysical and numerical models. Hybrid model-ling is being developed at several institutions,but few results have been published yet.
Hybrid model testing normally means acombination of physical and numerical modelsthat are working on-line during the model test.The truncated parts of the mooring lines and ri-sers are simulated by mechanisms at the sidesand bottom of the model basin. The mechan-isms can be either passive or active. A variantof the method is the numerical reconstructionmethod, where the model test time-history isreconstructed after the test in a numerical simu-lation model that comprises the parts missingin the physical model.
While hybrid methods are usually intro-duced because of the limited model basin di-mensions, the method also offers an interestingsolution to the well-known scaling law conflict.If the parts of the mooring system that are mosttroubled by scale effects are replaced by actu-ators coupled to on-line computational modelswith full-scale properties, the complete systemcan to some extent be free of scale effects.
Watts (1999) has discussed the principlesof hybrid hydrodynamic modelling. Some pro-mising results from an on-going joint industry
project at Haslar are presented. It is concludedthat hybrid hydrodynamic modelling presentsthe only viable alternative to the constructionof ever deeper, more expensive wave basins.
Buchner et al. (1999) have described thedevelopment of passive and active hybrid mo-del mooring systems, presently going on inconnection with the construction of the newOffshore Basin at MARIN. The basin measures45 m by 36 m with an overall depth of 10,5 m.It has a central pit of 30 m. The proposed ac-tive hybrid system is seen in Figure 12.
Figure 12 - The active hybrid mooring system beingdeveloped at MARIN (Buchner et al., 1999).
Passive Hybrid Systems are mechanismsthat simulate the truncated parts of the mooringlines and risers by a system of springs, massesand mechanisms connected to the floater.Clauss and Vannahme (1999) have described apassive cam-controlled model testing mechan-ism that can simulate arbitrary non-linearitiesof the truncated mooring lines. Typically, thehorizontal mooring stiffness and thereby thelow-frequency motions of the vessel can bemodelled quite well by passive hybrid systems,whereas mooring damping and mooring linedynamics cannot be modelled correctly.
Active Hybrid Systems simulate the trun-cated parts of the mooring lines and risers bycomputer-controlled actuators that must be ableto work in model-scale real-time. The motionsof the floater and other important system com-ponents are measured and fedback into thecomputer simulation, which delivers the con-trol signals to the actuators. With an activehybrid system, dynamic mooring line beha-viour can be simulated, including damping andsoil mechanical aspects.
Numerical Reconstruction is an interestingvariant of the hybrid modelling technique,where the physical model test and the numeri-cal simulation are decoupled in time. A nume-rical model is calibrated to reconstruct the timehistories from the model test with the truncatedsystem. The calibrated model is then used toextrapolate the behaviour of the complete sys-tem to full water depth with all truncated partsof the system included. This can be done byuse of coupled analysis tools as described byOrmberg et. al. (1999). Methods for experi-mental estimation of hydrodynamic coeffi-cients, important for the reconstruction phase,are described by Stansberg et al. (1998).
The numerical reconstruction is more thanjust a calibrated numerical simulation. Themethod acts as a correction to and extra-polation of the model test, adding thecharacteristics of the mooring system thatcannot be modelled correctly in the physicalmodel, while still containing the true non-linearor even chaotic behaviour of the floater, whichcannot be modelled correctly in the numericalmodel.
6. EVALUATION OF NUMERICAL ANDEXPERIMENTAL TECHNIQUES
6.1 Introduction
This section gives the results of an evalu-ation carried out in order to establish the state-of-the-art procedures used in numerical andexperimental simulation of deep water mooredvessels in wind, waves and current.
In this respect the Committee has decidedto carry out a survey to identify the currentprocedures employed by ITTC member organ-isations as well as non-member organisationsinvolved in the analysis of deep water mooredsystems. The organisations responding to thequestionnaire are listed below.
1. China Ship Scientific Research Centre,China.
2. David Taylor Research Centre, USA.3. Defence Evaluation and Research Agency,
UK.4. El Pardo Model Basin, Madrid, Spain.5. Global Maritime Ltd., UK.
18
6. Hyundai Maritime Research Institute,Korea.
7. ICEPRONAV S.A., Galati, Romania.8. Ishikawajima-Harima Heavy Industries Co.
Ltd., Japan.9. Krylov Shipbuilding Research Institute,
Russia.10. MARIN, Wageningen, The Netherlands.11. Marine Design & Research Institute of
Japan.13. MSC International (UK) Ltd., UK.14. NRC Institute for Marine Dynamics,
Canada.15. Offshore Technology Research Centre,
USA.16. Osaka Prefecture University, Department
of Marine System Engineering, Japan.17. Ship Research Institute, Japan.18. University of Glasgow, Department of
Naval Architecture and Ocean Eng., UK.19. University of Michigan, Dept. of Naval
Architecture and Marine Eng., USA.20. University of Newcastle, Department of
Marine Technology, UK.21. VBD, Duisburg, Germany.22. W.S. Atkins Oil and Gas, UK.23. Yokohama National University, Japan.
6.2 Results of the Questionnaire
The responses to the questionnaire wereanalysed and the percentage-wise results to-gether with comments (in italics) are summa-rised on the questionnaire form as shown in thefollowing. 1. Which of the following mooring concepts
can be modelled using your mooringanalysis tools/experimental facilities?
Num. Exp.a) Combination of wire-chain
system 60% 68%b) Combination of wire-chain-
submersible buoy system 60% 45%c) Combination of wire-chain-
polyester system 50% 32%d) Comb. of wire-submersible
buoy-polyester-chain system 50% 32%
2. Are your tools suitable for uncoupled aswell as coupled vessel mooring system in-vestigation?a) Yes 83%b) No 17%
3. Do you consider the effect of loading,stiffness and damping of a riser system onthe vessel and mooring system behaviour?
Num. Exp.
a) Yes 45% 55%b) No 55% 45%
4. Which of the following effects do you con-sider when you carry out uncoupled analy-sis/experimental investigation of vesselmotions of a vessel-mooring-riser system?
Num. Exp.a) Mean current forces on
mooring lines 41% 41%b) Mean current forces on risers45% 50%c) Low frequency damping
effects due to mooring lines 23% 36%d) Low frequency damping
effects due to risers 23% 41%e) Mooring mass 50% 59%f) Riser mass 50% 63%g) Mooring stiffness 59% 59%h) Riser Stiffness 45% 50%i) Please add other effects that
you consider:Riser pretension 4% 4%
5. In your uncoupled analysis tools, are the
motion response equations of the vessel inthe vessel-mooring-riser system based on:
a) Linear frequency domain equat.? 60%b) Non-linear time-domain equat.? 40%
6. Is your dynamic mooring analysis in theuncoupled system based on:
a) Analytical modelling? 32% b) Lumped-mass modelling? 53%c) Finite-element modelling? 32%
7. Do you have coupled analysis tools for:
a) Vessel-mooring systems? 100%b) Vessel-mooring-riser systems? 60%
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8. Are your coupled dynamic analysis toolsbased on:
a) Linear frequency-domain equat.? 53%b) Non-linear time-domain equat.? 47%
9. How do you obtain maximum/extremedesign parameters?
Num. Exp.
a) Through deterministic anal. 14% 23%b) Through statistical analysis 64% 58%c) Depending on the parameters
we may use, both 22% 19%
10. If you have answered (c) at question 9,please give details.
No details given.
11. Have you validated your uncoupled vesselmotion and dynamic mooring analysistools through:
a) Model testing? 24%b) Numerical simulations? 18%c) Model testing as well as
numerical simulations? 54%d) Full scale measurements? 4%
12. Have you validated your coupled vesselmotion and dynamic mooring analysistools through:
a) Model testing? 38%b) Numerical simulations? 15%c) Model testing as well as
numerical simulations? 47%d) Full scale measurements? 0%
13. In defining the environmental designcriteria for deep water moored vesselbehaviour and mooring loads, how doyou specify wave, wind and currentconditions?
Num. Exp.a) 50-year return concurrent
conditions 26% 32%b) 100-year return concurrent
conditions 26% 26%c) 100-year wind and wave
plus 10-year current 21% 21%d) 100-year wave and current
plus 10 year wind 11% 21%e) 100-year wave and associated
wind and current 21% 37%f) 100 year wind and associated
wave and current 16% 32%g) Steeper waves than associated
with 100-year wave height 21% 21%h) 1-year wave
and 100 year current 16% 26%i) N year response 21% 26%
14. Do you assume that waves, wind andcurrent act on the moored system:
a) Colinearly? 47% 51%b) Non-colinearly? 53% 49%
15. If your answer is (b) at question 14, howdo you select the angles between waves,wind and current, and how many differentangles do you consider?
Typically two or three; Decide inco-operation with metocean people;Customer specifies; Typically twelvedirections specified from the analysisof metocean data.
16. If you are to simulate the behaviour of amoored deep water vessel (depth greaterthan 1500 metres) experimentally, whichof the following test strategies would youchoose?
a) Testing a small scale model in an
existing basin? 41%b) Testing a traditional scale model
at sea? 0%c) Testing a complete model of the
vessel with simplified models ofmoorings and risers? 36%
d) Testing elements of the system inexisting basins at traditional scaleand synthesising the completesystem by numerical simulations? 41%
e) Constructing a new experimentalfacility? 14%
17. Further comments and/or suggestions?
Expression of interest to carry out com-parative studies using numerical simu-lations under the auspices of the ITTCDeep Water Mooring Committee.Further development of hybrid modeltesting techniques.
6.3 Conclusions of the Survey
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The results of the survey indicate the needfor the development of numerical tools for theanalysis of:
• Mooring systems, which consist of thecombination of wire-chain-polyester orwire - submersible buoy - polyester-chain systems.
• Coupled vessel, mooring and riserssystem behaviour.
• Low frequency damping of mooringlines and risers.
The results of the questionnaire analysisalso indicate the need for:
• Validation of uncoupled/coupled analy-sis tools through physical or hybridmodelling.
• Further development of hybrid modeltesting techniques.
7. GENERAL TECHNICALCONCLUSIONS
The number of deep water moored off-shore vessels is growing rapidly, and hydro-carbon fields in water depths up to 3000 m arenow seriously considered for floating produc-tion development. Physical and numericalmodelling of such vessels with their extensivemooring lines and risers is a challenge to theITTC Community.
Physical models of floating vesselsmoored in extreme water depths require testingat extreme scale ratios. Model testing ofmoored floating offshore vessels in waves hasbeen carried out successfully at a scale ratio of1:170 with results very similar to those ob-tained at scale ratio 1:55. Practical problemsrather than scale effects seem to be the limitingfactor for this type of model testing, but thescale ratio of 1:170 is close to the practicallimit with today's model basin technology.
Even at such extreme scale ratios, however,no existing or planned model basin can accom-modate a full model of a catenary mooringsystem at 3000 m water depth. In addition tothe correct water depth, such a basin shouldhave horizontal dimensions at least five timesthe water depth in any direction. Systems foraccurate generation of uniform and non-uniform current as well as multidirectional
waves and wind all over the basin will berequired. When a basin is too small for a fullmodel, truncations or simplifications of thephysical model will have to be made.
Testing in “natural” model basins such asfjords, lakes and rivers can be considered forspecial research projects. But due to the non-controllability of the environmental test condi-tions, such facilities cannot be used on a rou-tine basis.
Hybrid models are physical models wherethe necessary truncations or simplifications ofe.g. the mooring system are simulated by com-puter-controlled mechanisms. A hybrid modelcan be an interesting solution, when neither aphysical nor a numerical model of a compli-cated system can be made. A reliable hybridmodel will require a good numerical model ofthe behaviour of the truncated parts, which canbe operated in model-scale real-time. Even ifsuch hybrid models have not been successfullymuch developed in the past, the necessarybuilding blocks are at hand.
Numerical models of floating offshore ves-sels moored in deep water have been developedfor many years. Some of the problems in-volved in the numerical modelling of suchcomplex systems are amplified in extremewater depths, and the relative importance ofcurrent-, wave-, and wind-driven forces aredifferent compared to the more usual waterdepths.
Generally, the more simplified numericalmodels that work satisfactorily in less complexproblems, have had to be abandoned. Dynamicmodelling is used instead of quasi-static model-ling. Non-linear time-domain analysis is usedinstead of frequency-domain linear modelsbecause of the strongly non-linear behaviour ofthe anchor lines regarding stretching, catenarygeometry, fluid loading and bottom friction.Finally, coupled instead of uncoupled modelsof vessel, anchor lines and risers are desirable,but also extremely computer demanding. Aworkable solution to this problem is a de-coupling into slow motion dynamics (man-oeuvring and memory effects) and fast motiondynamics (wave frequencies).
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8. RECOMMENDATIONSTO THE CONFERENCENone.
9. RECOMMENDATIONSFOR FUTURE WORK
Work should be continued to incorporateother positioning systems than moorings aswell as the hydrodynamic aspects of physicaland numerical modelling of systems beingdesigned for deep and ultra deep waters.
Development of recommended procedures,including procedures for hybrid model testing,should be further pursued.
Verification and validation of physical aswell as numerical models should be furtherpursued.
The possibilities of obtaining metoceaninformation and do environmental modelling ofdeep waters, especially of the currents down to3000 m water depth should be investigated.Systematic information on current velocities,profiles, directions as function of depth andtime, etc. is needed.
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