Prediction of seakeeping and workability of offshore support vessels

2. Haagsteeg: P.O. Bo>. 28

6700 A V'ageningen. The Netherands

Teenone -- 31 6370 93011, Tee 45148 nsmo fli

T.

W88102 - KIVI-NVTS PREDICTION OF SEAKEEPING' CHARACTERI STICS AND

WORKABILITY OF

OFFSHORE SUPPORT VESSELS

By: R.P. Dallinga and A.B. Aalbers

Septenther 1986.

PREDICTION OF SEAKEEPING CHARACTERISTICS AND WORKABILITY

OF OFFSHORE SUPPORT VESSELS

Ir.. R.P. Dailinga and Drs. A.B.. Aalbers

MARIN, Ocean Engineering Division Wageningen, The Netherlands

effect of environmental factors like the frequency, and persistence of adverse weather conditions, and the. effect of operational

1. INTRODUCTION

1.1. General

The growing number of offshore constructions such as pipe lines, fixed platforms, under water manifolds etc. leads to an increasing demand for diving Operations for carrying out inspection and

main-tenance. These operations usually take place frotn a tobile basis: a

diving support vessel designed to stay on station by means of dy namic positioning. Such a ship is provided with one or more moon-pools and with cranes for handling diving bells and other equip-.

ment.

In the design phase of a diving support vessel it is useful to have a realistic insight in the motion behaviour, the station-keepi-ng capability and the acceleration levels on board of the ship. With respect to the diving operations it is alsO necessary to have early information on the behaviour of the moonpool. If for a certain area of operation the long term Sea cOnditions are known this informa-tion may be used to obtain a workability predicinforma-tion. This iS an

important factor ixi the economic evaluation of the project..

Computer calculation methods are available to make Such workability predictions fOr a. specific ôase as well as to investigate e.ffects

of changes in criteria, environmental conditions and ship

behav-iour.

In the present paper a set of criteria will be assumed valid for a hypothetical diving support vessel, calculation methods for mo-tions, acceleramo-tions, drift forces, wind and current forces, moon-pool relative motions and dynamic positiOning simulation are pro-posed. Thereupon a workability predictbn is made for a realistic

1.. Ship particulars

The. sections of a diving support vessel are showr in Figure 1. This

shape is used for the calculations and workability prediction. The main particulars of two alternative vessel sizes are shown in Table

1. An anti-roll tank is present in the smallest, vessel.

The moonpool is circular in shape and smooth walled. A thruster arrangement with two tunnel thrusters at the bow and two aimuthing

thrusters at the. stern was adopted.

l.3o Environment.

The NOrth Sea is chosen as the operational area for the diving sup-port vessel design. Environmental conditions of this area are

available in the form of wave scatter diagrams, water depth data, current data and information concerning the duration. of the sea conditions. In Figure 2 a typical wave scatter diagram is shown. Figure 3 shows a representative distribution of the length of good weather periods, Figure 4 indicates the average duration of these calm weather periods, and he average nuber of these periods per

year.

TheSe descriptions of the environmental conditions were compiled

2. WORKABILITY CRITERIA

2.l Ship motions and accelerations.

Lin4tations exist for the operation of equipment arid, cranes which can be expressed in ters of maximuth allowable accelerations and

ship mOtions (i.e. heave,, pitch and roll). For instance, a ditiamic

analysis of crane operations taking into accOunt shoOk loads and dynamic load amplification in the hoist wire and ax,rn.im allowable

side loads due to swing.

will lead

to criteria in terms of angular motionS and accelerations

at

the crane location. [5].

'Pubiishe4 of f shore experience of diving companies helps to select criteria, for ship motions [6 and 7].

'For the present paper the following Set of hip motion and acceler-. ation criteria was adopted:

Surge Sway Yaw

I

Heave. 3.0 rn Pitch 4.0 deg. Roll. . 6.0 deg.

.Vert.

acc. St. 1 2.5 rn/s2 (stern crane)

Vert. acc.. St. 8 1.8 rn/s2 (mOOnpool)

Transv. acc. St. 8 1.5 rn/s2 (moonpool tane) (1Q m above keel)

See dynamic positioning (Section 2.3)

The above limit values are the most probable single amplitude

2.2. Moonpool relative motion

The moonpool is used to lower equipment or diving bells to large depth. The relative water fnotions inside the moonpool may hamper diving bell passage [8 and 9]. Although application of aeration. will reduce the risk of slamming loads to a diving bell, a work-ability limit may still apply. For this study the criterion was set

at 2.5 in maximum single amplitude for 1000 oscillations.

2.3. Positioning accuracy

Irrespective of the accuracy of the dynanUc positioning reference system, the low frequency variations of the ship's position have to

be within certain limits. For diving operatiofis an overall accuracy of 2.5% of the water depth was assumed to be required. Furthermore,

it was assumed that the accuracy of the reference system iight lead to a pOsition deviation of 1% of the water depth, which has to be subtracted from the maximum allowable excursion. For constant wind and current, the maximum pOsition variatiOns in X and Y direction due to low frequency wave drift forces should be 1.5 in for 100 in water depth.

!4:. Oper tions scenario

For a workability assessment the operations scenario plays an im-portant role. The criteria given above may for instance be exceeded

somewhat before work. is actually stopped while the criteria must be

satisfied before work is resumed. Also, it is possible to have con-siderable inefficiency occurring after a bad weather period in

six coupled diffeential equations. _{In the present approach the.} following linear equations Qf motion _{are solved in the frequency}

domain: 6

z

j=1

(Mkj 1- ak.) cos(wt + c.) - w bk sin(wt + c.) +

= + 4)7()}

-6

iw E

j=l

j

aj

A. description of the numerical solution of the potential problem is given by Van Oortmerssen [10].

cos(wt +

J aj Fak cos(wt (1)

The hydrodynamic (motion-induced) reaction forces _{and the} (wave-induced) excitation forces are calculated by means of

_a

_cOmputer

program based on three-dimensional linear potential theory, _{In this} theory the. fluid is assumed to be ideal apd irrotationál.

t js assumed that in case of zero speed the flow .ield _{around the} moving body in waves can be described by a velocity potential:

X(Lt) =

_4(y)

exp(-iwt) ..

. (2)

This function is regarded as the linear sum of independent contri-butions due to diffraction from all modes of motion, the incident

3.2. Non-linear roll damping atid the anti-roll tank

F roll, the potential daping is very small so additional damping mechanisms have great influence on the motion response at reso-nance. These mechanisms comprise linear as well as noti-linear con-tributions. For the present calculations the following roll damping

contributions were considered:

=BF

+ _{BE Bw} + _BBK

being respectively the frictional, eddy, wave (potential) and bilge keel damping coefficients obtained after applying equivalent un-.

earization of the non-linear components. Since the calculations are

carried out for zero speed the contribution of the lift effects in the damping

is not

_{taken into accOunt. The damping contributions}

are

determined by means of empirical relations depending _{on the}

shape of the vessel as proposed by Ikeda et al. [ii].

For the 80 in long ship a U-type anti-roll tank was designed,

applying the theory given by Stigter [12]. Its dimensions are chosen such that the tank natural oscillation period is somewhat shorter than the natural roll period of the Ship, resulting in an

optimized roll reduction according to the findings of Van der aunt

[13].

The roil counteracting moment generated by the U-tank may be

ex-preSsed as an added inertia, a damping and a restoring coefficient

adaptation in the equation of motion of roll:

(M44 + a44 +

La44 )4

+

(B44 + b44)4

+. (c44 + Ac44 )4

= Fa4

cos(t +

o4)

(5)

The damping coefficient of the U-tank for the 80 m vessel is added to the effect of the additional dtnping mechanisms given in

equa-tion (4).

3.3. Moonpool relative rñotions

A mathematical model is used [14] taking into _{account. the coupling} of the fnoonpool relative motions with the local ship _vertical

mo-tion. The relative motion is found by solving:

{pA'('r + h) + %}h +bi + b2i i + pgAh +

+ + pA(T + h) + ah}z + (ehZ _{+ bh)z + pgAz = Fwh .} . . (6)

Non-linear terms are. present in this equation of motion so that it

is solved in the time domain using regular waves of a defined

am-plitude as input..

-From diffraction theory calculations with a separate facet repre-sentation [15] for the mbonpooi keel opening it is possible _to de-termine the wave forge acting on the water in the moonpool _{and the} interaction coefficients between local heave and relative _motions. In this approach a. frictionless, weightless and volueless piston is thought to lay flush with the ship keel in the moonpool, sepa-rating the moonpool cOntents from the outside.

The quadratic damping coefficient is estimated using model test results and literature [8, 14, 16, 17 and 18]. The quadratic damping depends on the internal configuration of the moonpool as

well as on the inflow and outflow energy losses. For this work the interior of the moonpool was chosen smooth walled so that the

3.4. Dynamic. positioning

For the low frequency motions the three equations of motion (surge,

sway and yaw) are being solved in the time domain. These equations include cOnstant added mass and damping terms (neglecting frequency

dependence)1 environmental forces (wind, waves and current) and

thruster forces. The Sway and yaw equations are coupled whereas the surge equation is coupled to the previous two mOdes by thruster

forces only.

The environmental forces are separated in wave, wind and current forces assuming there is no interaction between them. (Note that

experience with model test results shows that, fOr instance,

cur-rent can have a significant influence on wave drift forces).

The current forces are calculated using an empiricaL database of

model test data.

Wind forces are determined by dividing the structure above the waterline into geometric components. For the part of the hull below the upper cOntinuous deck wind resistance coefficients have been derived from [l9 arid 20]. Wind forces on the remainder of the supetStructure are added to the above values. These are found by adding the contributions of all superStrudture components taking

shadowing. effects, solidity effects and three-dimensional effects into account. This is done as set out in [21]. A realistic wind profile is assumed and the instantaneous wind direction with

re-spect to the ship's slow yaw drift motions is considered. The

effects of dynamic wind load variations are neglected.

The wave drift forces are calculated frOm quadratic drift force transfer functions obtained with the help of the diffractiOn theory computer program (see Section 3.1) applying the direct integration

functions are incorporated in the simulation program and the aver-age drift forces are computed by:

(2)

= 2f S(w) [F. (w a.)j (7)

0

For the dynamic behaviour the drift force spectral density func-tions are approximated f rpm the following relationShip [23, 24 an 25]:

(2)

8

_f

S(w) S(w + ii) [F' W±1i)]2 dw

0

ç

in which (similar to the Newman approach):

w+u)

!(2)(W

+, w+.)

I S I . (9)

Using the averages and the spectral densities of the low frequency

excitation a force record can. be generated. The procedure was- out-lined by Nierihuis [26]. The excitation forces in each time step are

calculated for the actual heading with respect to the waves.

The thruster forces present in the equations of motions are calcu-lated taking thruster/thruSter interactions into account [25]. Also

thrust degradation effects are considered1 due to:.

thruster-hull interaction (for bow thrusters, stern thruster as

well as if present - main propellers);

iifluence of cUrretit (using open-water diagrams fo main propel-lers and azimuthing thrusters) and.;

interaction between main propellers and stern thrusters - if

ap-plicable.

For this purpose use is made of theoretical calculations for

thruster-thruster interaction and model test data for the. other phenomena.

The control algorithm of. the D.P. simulation program is a schematic

representation of a real contrOl system. For _{every time step the} total required restoring forces (longitudinal and _{transverse forces} and the yaw moment) are determined using _{a PID controller. The} coefficients of Proportional and derivative terms of _{the controller}

are estimated using optirtum control theory [25].

The resulting required forces _{are divided over all available} prO-pulsors using an optimizing allocation routine. This routine

mm-imises the consumed power while satisfying _{all three force} con-straints (if within the limits of the propulsion system) _{and the} constraints imposed by maximum and minimum thrust for each

propel-ler.

The minimization process is based on the method of Davidon,

Fletcher and Powell; it includeS a penalty function approach tO ac-cOunt for the constraints.

Finally it may be noted that the D.P. simulation program accounts for time delays caused by e.g. filtering and thruster hardware as would be found on the prototype. In practice with _{a low-pass filter} it is neOessary to filter the position _{measurements, eliminating}

wave frequency contributions to avoid wave frequent thruster modulation.

3.5. Short-term statistics

For a

_{floating vessel in waves the frequencies of wave-induced}

motions and loads are reasonably narrow-banded. In that case the significant crest-to-trough value of the stochastically _varying

motion or load signal may be defined as:

al/3 '"uO - - .-,

'w,'w, - - (10)

g(v)

{F(VN)}N_l

_.

f(v)

in which the spectral density function

of the signal u is

ob-tained by spectral techniques from the response functions.

Generally,

the. stochastical signal u

is stationary and shows a

GauSsian distribution of the ensemble of Samples taken at constant

time intervals. The crest-to-trough values follow the Rayleigh

dis-tribution function and -the probability of exceedance Of one

indi-vidual amplitude Üa is given by:

u

-2

F()

F(ua>

= 1

-

f

f(ua)dua = exp(-

2m0

(11)

In a record of N amplitudes ÜaI the maximum value is defined as the

largest value in the ensemble

(u1

....

UN). Each element jn the

ensemble has a probability density f(u). When ordering the ensemble

as to the magnitude of the elements, the probability density

func-tions of the k-th element Vk is given by Ochi and Bolton, ref.

[27]:

g(v)

_{= f(vk)}

.

(){F(vk)}k{1

- F(Vk)

. .

(12)

in which

(1) is the probability that the element

is present in

the ensemble,

and

(2)

is the binomial distribution giving the probability

that the. value of

V

is indeed the k-th element in the

ordered ensentble.

The distribution of the maximum value of the ensemble (v1

is given by:

. . . .

(13)

According to Longuet-Higgins

tlie

most probable maximum value is

given by the value of vN for which

g(v) attains its peak value,

After some simplifications this requirethent _{leads to the familiar} expression for the most probable maximum in an ensemble Of N

val-ues:

Ua _{max. m.pr.} U1!3 v'½ in N ₍₁₄₎

This expression is used to relate the criteria given _{in Section 2.1}

to limit, values of the significant motions in a sea State.

Knowing the distribution function g(v) it is possible _{to indicate}

the confidence margins of a Rayleigh distribution. _{For a}

stochasti-cally varying signal with N oscillations the distribution _{of the} crest-to-trough values may be determined by statistical analysis

arid be plotted on Rayleigh distribution paper. _{At various}

probabil-N-k+1

-ity levels (= ) the function g(v) _{can be evaluated and -for}

instance 10%- confidence limits be indicated.

In the next section this analysis will be applied _{to the roll}

re-.ponse of sothe tested vessels in order to discuss the validity of _a Rayleigh distribution of these non-'lihear signals.

3.6. Wave. climate

Wave climate' information is Often available in terms of _{a so-called}

scatter. diagram which relates combinations of significant wave. 'height and average wave period to the _{elativè frequency of} occur-rence. If the operations with the vessel do not show "memory"

ef-fects

(if

_{e. the work can be stopped and resumed at any time without}

loss of efficiency) a Scatter diagram provides a means of calculat-ing' the average downtime due to weather. If, however, the occur-rence of downtime gives rise to inefficiencies (for instance, due to .the fact that part of the work has to be repeated or because extra work is generated) also the number of downtime periods

con-stituting the total downtime becomes _{an important factor in the} aSsessment of the workability of the vessel.

In the present Study the prediction Of the downtime is based on a

time domain realization of _{sea "states" (defined arbitrarily), each} defined by a (fixed) relation between wind speed, wave height and

average wave period The realizations, _{a "long-term" sequence of}

"short-term" Sea states of constant, duration were generated

accord-ing to a method proposed by Rothkopf _{{ 28]. At' the end Of each time} step (say 2 hours) the sea state for the next time step s

gener-ated.. The probability of going from _{one particular sea "State'1' to} any other sea "state" is given by a so-called, transition matrix; a tn-diagonal matrix, allowing only _{steps to adjacent sea "States",} was uSed. Rothkopf shows that the transition _{probabilities can be} derived simply from the average frequency of occurrence of each of the sea states, the average persistence _{of good (or bad) weather} and the duration of the individual time _{steps. The method is}

out-lined in Appendix I.

In recent years the application of this quantitative, method in the management of offshore operations has received considérablS atten-tion. One may refer to work by Shell'[2.9], _{'Hoffman [3o 31], chen}

[32,33], Hutchisori _{[34]., MacCallum [35'], Sánchez-Arcjila} [36] _and Kupras [37].

4. RESULTS

4.1. Ship motions

The heave and pitch motions may be determined from response func-tions applying spectral analysis techniques. For _{non-linear roll} this technique is not, readily applicable. However, after applying equivalent linearization on the expressions for the _{roll damping as} given by Ikeda. et al. [ii], it is possible to present the roll behaviour by carrying out speotral calculations for a ranqe of roll response functions each valid for a certain sinificant roil angle.

For the 80 m diving support vessel in beam seas the result of such an approach is shown in Figure 6. It may be concluded that non-linearity leads to relatively smaller ratios between roIl angle and wave height for increasing wave height at wave periods close to

roll resonance.

The effect of the U-type anti-roll tank is indicated in Figure 5. Due to the increase in damping the resonance peak in the roll

response. is practically diminished arid as a consequence the non-linearity in the curves is smaller. The magnitude of the roll motions of the Stabilized vessel i.s considerably less than for the unstabilized vessel. See Fiure 6. It was considered necessary to investigate whether the roll motions of this type of ship follows a

Rayleigh distribution, in order to be able to use Longuet-Higgins' expression for the most probable maximum, equation (14).

In Figure 7 is shown that the measured roIl, crest-to-trough

dis-tribution for two of the three investigate.d vessels lies, within the

10% confidence margins of the theoretical Rayleigh distribution, while the third measured distribution is somewhat at the low side. This lead to the conclusion that by applying equation (14) to re-late the most probable maximum criterion value to a significant roll limit is not unjustified but may lead to somewhat conservative

results. On the other hand it is made quite clear that the actual

maximum value encountered in an arbitrary ensemble may differ con

.siderably frOm the most probable.

In Figure 8 a comparison has been made of the pitch motiOns of, _the

80 in vessel and the 110 in vessel in bow quarterin seas. The effect

of increasing the size of the ship is most prohounced in _{the lower}

sea states with short period waves.

4.2. Moonpool relative motions

For head sea cOnditions the moonpool response function was

calcu-lated for two wave amplitudes: 1.0 m and 3.0 in. The results are

shown in Figure 9 for the 80 m vesse1 Since the relative motion is

governed by a combination of wave force, interaction effects and non-linear reaction forces, the wave height effect in the behaviour is different at different frequencies because the phase differences between the contributions vary with frequency.

Due to the reasonable symmetry of the ship with respect to the nioonpool location, the moonpool response is assumed identical for head-on and stern-on waves as well as for bow- quartering and stern

quartering waves.

It is clearly shown that the -highest relative motions may be

expected in beam sea conditions.

For the 110 in vessel the same conclusions are valid although the reduced heave motions in the shorter wave period range will

-4.2. Climate characteristics

Characteristic parameters in the present simulation procedure are the average duration of good (or bad) weather periods, their fre-quency of occurrence and the frefre-quency of occurrence of the indi-vidual sea states. Figure 10 shows the relation between the wave height and the above parameters. They were derived from the data in Figures 3 and 4 and data.presented by Vik et al. [4] and Mo ét al.

[2]. The data agree very well as far as the. number of severe storms is concerned.

Figure 11 shows the distributiOn of the duration of good weather periods as derived frOm the simulations. The results indicate a considerable spreading in the duration of good weather periods.

This tendency is reflected iti all results of the present

investiga-tion. This is also illustrated in Figure 12, in which a typical example of a climate realization is shown. The transition matrix on which the simulations ae based is shown in Table 2.

Figure 11 also Slows that if for a certain job interruption.s have very serious consequences and should be avoided, a very high aver-age operability is required.. For instance, limiting the average number of interruptions to one per thonth requires 98% average operability.

The spreading inthe results indicates that a largeaniount of reli-able data is required for a validation of the above method (or simi1ar simulation procedures). Figure 13 shows a comparison of the cumulative distributions derived from field data and simulations.

The results show considerable discrepancies, especially at the longer durations.

Wave hindcast data published by Bales [3.8] can be used to check one

of the baSic assumptions underlying the, simulation procedure. In this procedure the probability P(iI1) to remain in a particular sea

state is independent of the history of the process. The probability of exceeding a. duration of N* _{steps in this particular sea state}

becOmes:

P(N > N* ₌ epNmn(uI

i))

yielding an exponential distribution _{for P(N >} N*).

In Figures 14 and 15 hindcast data for the _{North Sea are shown.} Especially the lOwer sea states _{show distributions of duration} which correspond very well with the _{above distributions. The} tran-sition probabilities P(ili) derived _{from these data agree very well} with thOse derived from the data in _{Figure 4 as far as the lower}

5. WORKABILITY PREDICTION

As outlined in the foregoing, a workability prediction is based on a large number of data and assumptions. The input information

con-sists of:.

Ship data:

- dynamic positioning characteristics;

- frequency response functions for all required quantities;

- wave climate informatiOn in terms of the frequency of occurrence of sea .tate _{and the frequency or average duration of workable}

sea states.

Operational data:

a set of criteria for operable weather conditions;. - a stt.ategy for the operation.

One of the basic assumptions in the wo;kability prediction _method is the applicability of the Rayleigh distribution for the predic-tion of extreme values. This assumppredic-tion was discussed in Secpredic-tion 4

and in ref. [39 and 4.0].

It is essential to realize that the output information (the down-time, job duration, etc.) must be regarded as a stochastic vari-able. If the operational scenario is very complex and the simula-tion time is restricted statistical tests _{may be required. to judge}

the significance of the results [41].

5..l.Workability in beam seas

A rough indication of the downtime in beam seas can be obtained by disregarding the effects of the operations scenario, See Figure _16. It shows that the roll response limits operations over nearly the entire wave period range prevailing in the scatter diagram. In

short period waves the relative wave elevation in the moonpool iS a limIting factor. The acceleration limitS are not indjcated in Fig-ure 16 because these appear not to be a determining factor in the workability prediction. The average workability and the effect of

the anti-roll tank is indicated below:

80 m diving support vessel average workability in beam seas

Stabilized 47%

Unstabilized 33%

Consideing the operational limitS impoed by the relative wave elevation in the present moonpool design, it must be concluded that it is no use to further decrease the roll response -if

possible-for it will not yield a larger operability.

In Figure 16 also the limiting sea states for dynamic positioning are indicated. Two values of the available thruster power are

i-n-vestigated and the results.

5.2. Workability in bow quartering waves

Figure 17 indicates that the roll motions in bow quartering seas are, like it was in beam seas, a major factor limiting the opera-tions of a diving support vessel. In short period waves the pitch response becomes a limiting factor. As in the beam seas case the accelerations are not a determining factor for the workability. Disregarding the operations scenario the workability becomes as

Average workability

in bow quartering waves

Vessel _{80 m 80 m}

110 m

Anti-roll tank _{no yes no}

Criteria: roll only

pitch only heave only

roll, pitch and heave

The dynamic positioning simulations

for bow quartering waves reveal

that the reduction in thruster power from (0.8 _{0.8 MW) fore and}

(1.5 + 1.5 MW) aft to (0.4 _{+ 0.4 MW) fore and (1.0 +}

1.0 MW) aft is

hardly affecting the workability of the 80 m vessel since _{the roll}

and pitch requirements prevail _{(see Figure 18).}

The limit sea State for _{the lowest thruster power configuration in}

the. long wave period _{range is about 4 m significant}

wave height,

mainly due to the associated wind speed. In the Short wave period range the wave drift forces _{are dominant and the limiting}

condi-tions become lower with decreasing wave period

Weather simulations for workability _{in bow quartering waves}

Assuming a job which requires _{240 hours to complete in ideal}

weath-er conditions, simulations _{were made to predict the}

characteristics

Of the actual job durations in _{the North Sea wave climate.}

The re-sult

are ifidicated in Table 3 and Figures 19 and 20. The limit sea

state serving as start and _{stop criterion was derived}

from the

limiting Sea states in Figure _{17. It was assumed that work could be}

stopped without loss of efficiency _{and could be resumed without} delay as the starting/stopping _{criterion was met.}

45% 71% 97%

66% 66% 78%

93% 93% 96%

The spreading in the düratiôn of the workable periods is _reflected in the duration of the jobs. Operating at a w average workability

drastically increases the spreading of, the. job durations leading to. occurrence of excessive job durations.

5.4. Scenario.

A penalty on the interruptior of a job is an example of a. sitnpie

operational. scenario. The simulation for the stabilized 80 m vessel in bow quartering Seas. was repeated with a. penalty of 24 hours on

every interruption due to adverse weather. In Figure 21 arid Table 3

the cumulative, distributions of the job durations are compared. It is shown that te average job duration. increases by some 60% be-cause the good weather periods of short duration give no progress in. the work. Also the spreading is wider, i.ea 10% of the jobs 'wOuld last lOnger than 1070 hours, whereas the simulations without penalty indicate a job duration of only 5 hours at this 10% ex

6. CONCLUSIONS

Regarding the results of the preSent investigation _{the following}

conclusiOns seem justified:

The roll respOnse of diving support Vessels.is _{a major factor in} limiting diving operations. Installation of _{an anti-roll tank}

may be very useful in reducing the downtime.

The duration of workable periods of time _{Shows a very large} spreading1 which. is reflected in all results. This phenomenon may lead to large differences in job completion time between

otherwisS similar veSsels on similar jobs.

Although simulation procedures based on the tn-diagonal transi-tion matrices are widely used, the basic assumptransi-tions _uhderiing the procedure have not been validated thotoughly. In this re-spect the neglection of physical wave growth and decay _processes

REFERENCES

1., _{K. HaSselman et al.:}

"Measurements of wind-wave _{growth and swell decay during}

the

Joint NOrth Sea Wave Project _{(J0N5wAP)1'. Deutsches}

Hydrograph-isches Institut Hamburg, 1973.

K. Mo, I. Vi]c and O.G. _Houinb:

"Wave statistics at Station _{"M" with speciai reference}

to

du-ratioh and frequency of _{sea states". The Ship Research,}

Insti-tute, Norway, 1978.

L. H&land, Q.G. Houmb and B. _Pederson:

"Long term distribution of _{North Sea Waves". Norwegian}

Mari-time Research, Vol. 1, No. 1, 1973. I. Vik and O.G. HOumb:

"Wave statistics of Utsira with Seciai reference to duration and frequency of storms". The _{Ship Résearöh Institute, Norway.}

P. Holland:

"Operational, environmental and design _{considerations for} heavy lift offshore cranes". _{RINA Symposium on offshore}

trans-port and installation, London, 1985.

A.J. Beveridge Star:

"Marine operations for platform _{maintenance and repair". EUR}

75, EUROPEC London, 1978. D. Hoffman and G. Petrie:

"Sequential simulation of vessel _{performance during extended}

offshore activities". SSPA Sympsiuirt _{on Ocean Engineering and} Ship Handling, Gothenburg, 1983.

S. Spangeberg and B. Kof$d Jacobsen:

"Reduction of the water motion in _{the moonpool", MARINTEC,}

1983.

J. Treider and, T. Mellern:

"Measuring of hydrodynamic forces _{acting on a diving bell".}

DNV Technical report 78-059, 1978. G. van Oortmerssen:

"The motions of a moored ship in waves". _{Thesis, Deift Univer} sity of Technology, 1976.

11

Y. Ikeda, Y. Himenô and N. _Tanaka:

"A prediction method for ship _{roll damping". Report No.00405} of Dept. of Navy Arch. of _{Osaka Prefecture, 1978.}

C. Stigtèr:

"The performance of U-tanks as a passive anti-rolling device". Report No. 81S, Netherlands _{Ship Research Centre, T.N.0.}

J.D. van der Bunt:

"The design of U-tanks _{for r011 damping of ships".}

Report

No.124S, Netherlands Ship _{Research Centre, ToN.0.}

A.B. Aalbèrs:

"The water motions in a moonpool". Ocean Engineering, Vol. 11, No. 6, 1984.

G. van Oortmerssen:

"Hydrodynamic interaction between _{two structures floating in}

waves". BOSS Conference LOndon, _{No. 26, 1979.} P.W. Bearman en J.M.R. Graham:

"Hydrodynarnical forces _{on cylindrical bodies in oscillatory} flow". BOSS Conference London., _{No. 24, 1979.}

J.O. Flower. and W.AK. Sabti Aljaff:

"Kryloff-Bogoliubo.ff's _{solution to decaying oscillations. in.} marine systems". ISP, Vol. 27, No. 313, 1980.

G!F. KnOtt and J.0. Flower:

"Measurement of energy losses _{in oscillatory flow through a} pipe exit". Applied Ocean _{Research, Vol. 2, No. 4, 1980.}

"Prediction of wind and current _{loads on VLCC's". Oil}

Compa-nies International Marine Forum, 1977. R.P. Isherwood:

"Wind resistance of merchant ships". RINA, 1972.

"Rules for the construction and classification of mobile off-shore units", Det Norske Veritas, 1975 (reprint 1980) and 1983..

J.A. Pinkster:

"Low frequency second order. wave exciting forces on floating structures". Thesis, Delft University of _{Technology, 1980.}

J.A. Pinkster:

"Low frequency _{phenomena aSsociated with}

vesSels moored at

sea". Paper SPE 4837, _{EUropa Spring Meeting}

of SPE-AIME, Amsterdam, 1974..

J.A. Pinkster:

"Dynamic positioning _{of vessels at sea".}

Course No. 105,

Department of Experimental _{Methods in Mechanics, Udine,}

1971.

H.J.J. van den Boom and _{U. Nienhujs:}

"Hydodynamic analysis of _{dynamically Positioned}

vessels".

Workshop on ship and platform _{motions, Berkeley, 1983.}

26.. _{U. Nienhujs:}

"Simulations _{.. Of low frequency motions of dynamically}

posi-tioned offshore structures". RINA Spring Meeting, _{Paper No. 7,} 1986.

M.K. Ochi and W.E. Bolton:

"Statistics for prediction _{of ship performance in}

a seaway, Part I, II and III".

International Shipbuilding Progress, Vol. .20, 1973.

M.H. Rothkopf, J.K. _{Carson and S. Fromovitz:} "A weather, model for _{simulating offshore}

conStruction alter-natives". Managethent. Science, Vo1 _{20, No. 10, 1974.}

RoC. Shell and A.H. Masso:

"Rough weather drilling _vessel

simulation". Offshore Tech nology ConferenOe, Paper Z9l7 _{Houston, May 2-5, 1977.}

D..Hoffman and V.ic. Fitzgerald:

"System approach _{to offShore crane ship}

operations". SNAME

Transactions, VOl. 86, 1978. D. Hoffman and G. Petrje:

"Sequential simulation of _{vessel performance during}

extended offshore activit.ies' _{Second Ifltenationalsynposi}

on, Ocean

Engineering and Ship _{Handling, Gothenburg, 1983.}

H.T. Chen: .

"Long-term prediction of _{offshore vessel responses}

for design

and operability evaluation". _{Offshore Technology}

Conference, Paper 3800, Houston, 1980.

33. H.T. cien and P. Rawston:

"System approach to offshore construction project, planning

and scheduling". Marine, Technology, Vol. 20. No. 4, October 1983.

34. B.L. Hutchison, B.L.:

"Risk and operability in the marine environment". SNAME Trans-actions, Vol.. 89, 1981.

35.' K.J. MacCallum and J. Bollard:

"The use of transition matrices for weather simulation". Marine Technology, Vol. 23, No. 3, Pp. 238-244, July 1985. A. Sânchez-Arcilla:

"On the sequential behaviour of sea states". International

Conference on Coastal EngineerIng, Houston, 1984.

L.K. Kupras and P.M. Kupras:

"SimulatiOn and performance analysis of floating drilling, i

operations". To be published in International Shipbuilding

Progress, 1986.

S.L. Bales, W.T. Lee arid J.M. Woe'lke:

"Standarized wave and wind environment for NATO operational areas". DNSRDC/SPD-O919-0l, July 1981.

R.B. Inglis, J.G..L. Pij'fers and .J.H. Vughts:

"A unified probabilistic approach to predicting the responses of offshore Structures, including the extreme response". BOSS

Conference, DeIft, 1985.

A.B.. Aalbers arid R.P. Dallinga:

"Model measurements and design calculations for the transport

of a jack-up' on a barge". RINA Symposium on Offshore transport and installation, London', 1985.

S.K.T. Boersma and T. Hoénderkamp:

. "Simulatie, een moderne onderzoSksrnethode". Academic Service,

APPENDIX I

Definitions and notations in _{the climate description}

Each climate record is _{regarded as a sequence of}

short-term sea "states" in which the _{environmental conditions}

are assumed to be stationary. Each "state" _{can represent an arbitrary}

combination of

wind speed and direction, _{current speed and direction,}

wave height

and, period, spectral shape _{and direction. rn the}

present method,

sea states are defined following the Beaufort scale and _assuming so-linear wind and waves.

Workable or "good" weather _{of class i is defined as a period of} time in which the waves are lower than those in _{class i (those of}

class 1 to i-i). The trafisitjon _{from one individual}

sea -state i to

the sea state in the _{next time step is given by}

a tn-diagonal transition matrix, which allows _{the continuation of}

sea state i, increasing the sea state _{to state 1+1 or decreasing}

the sea state to i-i. The related _{probabilities are. denoted}

as

P(iIi),

_P(i+lJi)

and P(i-lJi).

The average duration of _{a period of workable weather}

equals the total amount of time _{spent in workable sea states}

divided by the number of workable periods. If the frequency of occurrence of each

sea state is given by f(i,) it is given _by:

i-i Z f(j) = j=1

-GWP''

-NGWP (i) with:

NGWP = average nurtber of workable periods _{per unit of time}

= average duration of workable periods

GWP

i-i

E _{f(i) = fraction of time spent in workable}

sea states. i=l

The probability of starting or ending a period of workable _weather

at an arbitrary time step equals _{the ratio of the average number} Of

workable periods per unit of _{time and the number of}

simulation steps per unit of time:

(i)

PGW(1)

₌

_l/t

t _{1 . . . .}

1-2

It. equals the probability of entering _{a workable period, down from}

sea state i to i-i Or -leaving a workable period _{from sea State i-i} up o Sea state i:

GWP = f(i)

P(i-lIi)

=f(i-l)

P(iI

The average duration Of _{a period of downtime (time steps with sea}

states i, i+1, _{..., n) follows froth the total amount of time spent} in _{non-workable, periods and the average number of non-workable}

periods: -i-i f(j) 1 - E. f(j) Ci) ,-BWP -

-BWP

Nw

with _{representing the average numTber of non-workable periods}

per unit of time; which 'of, course equals the _{average number of}

wOrkable periods NGWP!

Based on information on the average number of workable weather win dows or their duration the transition probabilities _{follow from:}

p(i-iJ

i) (t-3) 1 E _f(j) =-1 PGWP(1+l)

t

,(i+l) P(i+lIi) - ,-, GW f(j)

_fU)

Gwp(i+l) f(i) tNGwP(1) :

f(i) f(i) _{DGWP(1) f(i)}

-(I-5a)

P(.iJi)

1 - P(i+lJi)

_P(i-j.Ij)

Keeping in mind tha _{Ue average nUmber of}

workable periods equals the average number of downtime periods the above can also be ex

pressed in terms. of the _{average length of the downtie}

periods: P(i+1

Ii)

P(i-iJi) = PBwp(+1)

_BwP'

f(i) _f(i) DBWP PBWP(1)

Lt.wp(i)

f(i) f(i) BWP

or:.

P(i-lIj)

=P(i!j-l) . . . . . . . (I-Sc) and.: n E _f(j) j=t±1 f(i) n Z f(j) f(

U

(1-6)

(I-7a) (r-.7b)

P(iji) = 1 -

P(i+lIi)

-

_P(i-lji)

1+1 Sea i

state

_i-i

Time

Figure I-A - Climate S _{ulation procedures}

Downtime Downtime

Sea state at t+t bra *

Figure I-B - Transition matrix

1 2 3 i-I i i+1 n-i n

1 2 3 i-i i i+1 ñ-1 -n

(I)

P(112) P(2i) P(212) P(2J3) P(32) P(313) P(4f P(i-21i-1) P(i-lk-1) P(i-1i)

-pciliii

P(ili) P(ili+i) P(i+lIi) P(I+iJi+1) _P(i+21j+i) P(n-21n-1) P(n-1n-1) P(n-lIn) P(nln-1) P(n!n) + Sea State at t bra

PP power anti-roll tank in 0 110 B m 16.2 22.3 P. rn, 4.4 _6.0 - 0f7 0.7 v 3992 10303 in 1.5 1.5 9.6 13.1 in water - 0.36 0.36 -- 0.25 0.25 Iloonpool; diameter in 6.0 6.0 locatiOn - St. 8, St. 8,

centre -line centre .1-me

Thrusters: Bow tunnel;

locations - St 18 5 and 19 St 18 5 and 19

diameter rn 2.0 _2.0

power - MW 0..8 0.4

Stern thruster:

locations - St 1, 4 0 rn St 1, 4 0 in

from centre line from centre line

diameter in 2.2 2.2 power MW 1.5 - 1.0 Bilge keels: length in 0.35 L 0.35 height in 0 45 0 45 Ahti-roll tmk: type -. U-tank length 'in _8.0 duct height m _0.8

wing tank width in 2 5

volume . rn3

-Table 2 - Transition matrix 1 0.944 0.056 _{0.000 0.000 0.000 0.000 0.000 p.000} 2 0.031 0.919 0.050 O.000 0.000 0.000 0.000 0.000 3 0.00O 0.085 0.849 0.066 0.000 0.000 0.000 0.000 4 0.000 0.000 _0.134 0.786 0.080 0.000 0.000 0.000 0.000 0.000 0.000 0.177 0.739 0.084 0.000 0.000 0.000 0.000 0.000 0.000 0.228 0.664 0.108 0.000 000O 0,:000 0.:000 0.000 0.000 0.323 0.524 0.152 8 0.000 0.000 0.000 0.000 0,000 0.000 0.913 0.087

Sea Séã state T+2 (hours)

state T

TabIe _{3 - Effect of roll stabilization aid ship size onworkability}

Scenario: job duration calm water : 240 hours

Criteria for Stopping/resuming operations: _{2+1,3 = 6 deg.} Heading : bow quartering seas

Desôription _Unit 80 m vessel

unstabilized 80 m vessel stabilized 110 m vessel unstabilized Climate characteristics:

I4miting wave height m 1.6 2.2 2.2 2.8

Average duration wokable periods hrs 49.3 71.1 71.1 103.8 Standard deviation düràtion

workable periods hrs 33.1 63.8- 63.8 94.5

Nuiner of workable periods per year - 80.3 92.0 92.0 66.0

Job óharacteristics:

Penalty on interrupting operations hrs 0 0 ₂₄ 0

Average duration hrs 529.2 356.5 569.3 30.7

Standard deviation duration hrs 285.4 188.1 325.7 157.7

Duration with 10% exceedance hrs 805.0 512.0 1070.0 410.0

12 0 0 0 0 11 94 17

/

8 .73 0

11/

K1

0 0 0

>7

0 8 12

Mean Zero-UpCrosSing period T2 (s)

Figure 2 Wave climate scatter diagram

11(

49 58 61 12 23 11 4 25 6 2 20

100 50 c3 !11 <1:rn: <4 m <5 rn <. rn <7 rn 10 20 50 Duration (hours) 100 200 500 1000

Figure 3 - Cumulative distribution Of good weather periods during

10000 5000 1000 DGWP 500, (hours) 10 0 Number of periods Duration _GWP 2 £ Mo et al. [2]

Viketal. (4]

* In house data

Figure 4 - Number of good weather periods per hour and average

duration as a function of wave height (North Sea)

10 3 5 6 8 9 10 ç113 (m) 500 50 GWP (1/hour) S 100 50

-15 for a1/3 = 10 deg.

I

/

/

/

/

,

6 al/3 10 deg. = 15 deg. 0.5 1.0 1.. 5 w (rad/s)

Fiure 5 - Roll response fr 80 i diving uppor-t vessel in regular

beam waves

10

E

-w

C) 30 20 10 0 Stabilized ----Unstabilized 10.2-11..1 / / / / / /

1/

/

/

/

i' .6 5.6 6.5

/7//,

i1i '/7

/.

0 5 10 15 ZW1I3 (m)

102 99 90 70 50 C) 14 U S ₃₀ U C) S (0 C, .0, C, C) '4-4 0 >1 -4 .0 I0 .0 0 14 1 0.1. 0 V S.

'

Research vessel

Diving support vessel

I

Pilot vessel

-'

/

igure 7 - Distribution of measured crest-to-trough values for roll

in .i.rregular beam seas (resonance conditions)

10

5

Bow quartering seas - JONSWAP

80 spectra - in vessel 110 in vessel 5.6-6.5

_6.5-7.5/

8.4 10.3

/

10.3

/

.1

Ii ;',1"

/

-

Il/ri t

I,,,, /

1/1/

,T2=4.6s

0 5 10 15 w1/3 (rn)

in in 2. 0 4th 0 in L 4.) 0 .0 0. 0 3. 0

Ca1cuation for 1 tn wave amp1itue

Cculai for 3mwaveàmplitude

Beam waves 6'

1g,7j...

it.

-\

\

\

..

/

\

'-

.!___-...'

.

--'

ii

. Head waves - / ¼.' .%

\

\

0 05 1.0 1.5

Wave frequency (rad/s)

Fiure 9

MOorpoo]. response functions for 80 tin diving support

2 5 5.0 7.5 w1/3 max. (in)

14 a) 100 0.1 -

---1-H

F---2.8 2. 2 1 .6 -Lih-i ting wak7e height (m) 10 100 1000 10000 Duration (hours)

6 2 0-0

'u

a

ma

a

a,

--

---

---U

LA

uauaasaumaaaaaaaaaai

amaaaaaaaaaaaaaaaau

uaaaaaaaaaauaaaaaaaa

ammamamanaimammamu

10 10 20 20 30 30 40 40 0 10 20 30 40 Time (days)

Figure 12 - Sample climate. rea1.zations

8

6

4

2

1000

-

aon

--Field data

10 - 100 1000 10000

Duration (hours)

Figure 13 Cumulative distribution, of duration of good weather periods

1.0

05

0 2 a) c

01

a) 0.05 x a). 141 0 0.02 a) 0.01 0.005 0.002 0.001 0 w1'3 = 2-3 in o

'

_1-2xn A Duration (hours)

Figure 14. - Cumulative distribution f duration, of individual sea

states .

1.0 0.5

02

0.i

a, 0.005 0.002

0.00i

8-9 in ' o 6-7xn a =5-6ni-A 4-5m b 3-4m -I' 0.05 l.i 0 0.02 -a, 0.01-0 12 24 - 36 48 60 72 84 Dutation (hours)

Figure 15 - Cumulative distribution of duration Of individual sea

12

0

Beam seas - V5 = 0 kn. - JONSWAP spectra

High power thrusters 0 0

1

_0: Low power thrusters 4 Transverse

::::ti01.1

0 -i-Heave Roll: stabilized Lunstabjljzed

&I

.. . '4I _{20 4} 5 55 58 49 23 1 4

(

it

o'

8 12 16

Mean zero-uperossing period T2 (s)

12

Bow quartering seas - 0 kn. JONSWAP spectra

80 vessel vessel

---110

in in

o'

o

o4jo

(stabilized) i \ 0 1 0 4 i o (unstabilized)

I

\\ \

_o1

Pitch 0 i7 'S

256

1

\

11 12 61 94

\__._;__'

82 31 29 0

3O

Heave 5 5 0 0 16 120 141 73

2o-4-2---crt

Roll (unstabilized) 5

5558492311

4 2 1 0 0 4 8 12 16

Mean zero-uperossing period Cs)

Figure 17 -. Workability of 80 m and 110 n diving support vessel in bOw quartering seas

:..

.wA10

3.

5

1 O

S

11 4 2 1

Low power thrusters

Pitch 80 m vessel 110 m vessel High power thrusters Roll: stab iii zéd uristabilized 12 4

Bow quartering seas _- V = 0 kn. JONSWAP spectra

Mean zero-uperossing period

2

Figure 18 Workability of 80 m diving support vessel in bow

quartering seas

0.4 0.3 0.2 110 in vessel. unstabilized 0.1 >1 C) C) 0 I, -C) 0.2 80 rn vessel 0.1 stahi lizéd 0.2 80 in vessel 0.1 unstàbilized 200 400 600 800 1000 1200 1400

Job duration (hours)

1.0 0.00.1 80 in vessel stabi 1 izéd 110 In vessel unstabilized 8.0 th vessel uristabilized

Excess duration (hours)

Figure 20 Cumulative distribution of job duration

(exöess o 240 hburs daith water duration)

1.0 w C) C 0.1 C) a, U.' 0 >1 C) C a, 0.01 a, 0.001 24 hOur penalty on interruption of operations 0 penalty 80 in vessel stabilized 0 250 500 - 750 ₀₀₀

Excess dürat-jon (hours)

Figure 21 - Cumulative, distribution of job duration (excess of 240 hours cairn water duration)