COMPARATIVE ANALYSIS OF TIME DOMAIN PROGRAMS … · Antonio Carlos Fernandes (Consultant at PETROBRAS) Mauricio Aratanha (PETROBRAS) S. Alejandro B. Kroff (Research Assistant at PETROBRAS)

COMPARATIVE ANALYSIS OF TIME DOMAIN

PROGRAMS FOR THE EVALUATION OF FPSOS AND

SPM HORIZONTAL PLANE DYNAMICS

Antonio Carlos Fernandes (Consultant at PETROBRAS)Mauricio Aratanha (PETROBRAS)S. Alejandro B. Kroff (Research Assistant at PETROBRAS)

Abstract —The present work compares critically two time domain programsthat are available for the analysis of ships on a Single Point Mooring (SPM).The emphasis is given on the response in waves. Examples with actual shipsunder interest by PETROBRAS indicate that both software may be useful

INTRODUCTION

PETROBRAS acquired two programs the TERM SIM II and later the

ARIANE^ somewhat unpretentiously. They were supposed to help in theanalysis and design of common operations involving ships on a SPM what ishappening throughout the Brazilian Coast. But suddenly, about three yearsago, the amount of investments for oil production in the deep waters ofCampos Basin increased dramatically. Since the field proven SemiSubmersibles hulls were scarce in the world, to have floating platform meantto have a FPSOs (Floating Production, Storage and Offloading) platformsbased on the more abundant ships on turrets. Later on, even the D1CASconcept using ships with smart moorings will be used. At the moment about20 development platforms are under construction around the world in placelike China, Spain, Singapore and Brazil. This situation increased the need ofreliable software tools.

For the referred FPSO platforms, the ships are not moving with an averageforward speed but instead, this speed is zero. The ship is to be kept in placewith enough compliance to face the environmental conditions due to waves,

Transactions on the Built Environment vol 29, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

206 Offshore Engineering

current and wind with a favorable heading. The so-called weather vaningimplied by the expected dynamic stability in the horizontal plane if effective,will lead to a behavior that is better than the excellent standards established inpractice by the Semi Submersible in the Campos Basin. The oil fields in theCampos Basin are in deep water but the weather is mild . This fact seems to bethe base for the success of several new developments that have been installed.

The present work will discuss some aspects of two time domain software thatare appropriate to simulate the horizontal plane dynamics. They are the

TERMSIM II' from MARIN and the ARIANE * from Bureau Veritas. Bothof them are commercially available and come from two conspicuousinternational companies with great experience in Naval Architecture

The work starts describing some characteristics of each software, stressing thedifferences between them. Typical examples of current PETROBRAS interestare processed and discussed. It is shown that some characteristics are verydifferent and may lead to very different results. It is also shown, however, thatthe damping loads may be used to bring the results closer.

THE TERMSIM II

The TERMinal SIMulator II program has been offered and maintained by theNetherlands' Ship Model Basin, the MARIN. The last version was handed toPETROBRAS in 1996. One of the great ideas of the program is the use of apre-processed data base that storage ship properties for interaction with thewaves, the current and the wind. The Program has a unique formulation sinceit aggregates the MARIN experience carefully developed along several years

as is well summarized by Wichers *. The data base that comes with theprogram set includes only three VLCCs (Very Large Crude Carrier) hullsallowing immediate application of some PETROBRAS actual cases. Newships may also be pre-processed and the data base may consequently beimproved. Non standards hull like the PP Moraes (President Prudente deMoraes) ship that was submitted to a jumboizing is a case that deserves aparticular pre-processing.

Probably the main contribution by this program is the development of amethod to deal with the dynamic effect that includes viscosity due to the shipmotion in a moving fluid.


Offshore Engineering 207

THE ARIANE

The ARIANE program, adequate to study Risers and Anchoring problems, ismore recent than the TERMSIM II. It has been implemented and maintainedby the Bureau Veritas, the French Classification Society. It seem to be evolvedfrom a static mooring line analysis program. In fact, due to the generality ofapplications and the user-friendliness, the Static of ARIANE is a highlight ofthe program. The lines properties may be non-uniform combining cables withchains with no restriction. The lines properties may be downloaded from abuilt in catalog. This is very helpful for typical Deep Water Mooring that haveto be non-uniform.

The same good words can not be extended to the Dynamic analysis ofARIANE which is much simpler than the TERMSIM II However, it allowsthe independent specification of coefficients, as the damping coefficients, thatmay be used to get better results. This requires practical experience that maybe gained with comparison with the TERMSIM II. An example is examinedlater. The ARIANE wave files are also pre-processed. Several hulls ofPETROBRAS interest have been already stored in the ARIANE input format.

Another noticeable difference is that the TERMSIM II starts presenting theresults only after 600 s of simulation time. The alleged reason for this is toavoid transient conditions, since the time integration starts the processing forany given initial condition. Meanwhile, the ARIANE starts the integrationfrom a quasi-static equilibrium that includes average environmental forces

THE EQUATIONS OF MOTION

Both the programs integrate a set of three second order differential equationsrepresenting the body 3 DOF (Degrees of Freedom ) Dynamics in thehorizontal plane. These equations are well known. For instance, followingWichers * and having Figure 1 in mind, the referred equations may be written

as:

=X (1)

Y (2)

N (3)

where the dots indicate time derivative and the inertial potential flowhydrodynamic properties (the added masses are indicated rby a^ ; i,j=l,2,6) are

made explicit and the generalized forces due to viscosity, interactions with



current, wind and waves are indicated by X, Y and N. Due to the usual hullsymmetry (a26=0=a 2), Equation (1), (2) and (3) simplifies to:

X (4)

Y (5)

(6)

Note that besides the added mass a^ terms, which are added to the

generalized masses, there is a term proportional to ( 22 -an) in Equation (6)

that is the so-called Munk moment. Since the motion is extremely slow thewaves are not essential unless in the average sense and the added massesabove may be considered the low frequency limit of the added masses whenthe free-surface is important. The double-body approximation that freezes thefree-surface is plainly justified. The environment forces to be include in theright hand side of the equations above are discussed next.

The current forcesThe ship moves in a body of water that is itself moving. For instance, if theship moves with the current in the same direction, there is no force on the shipat all. But as long as the relative velocity is different from zero, the currentforces starts to appear and depending on the direction, different hydrodynamiccharacteristics show up.

If the longitudinal motions are important, the problem is similar to the classicShip Resistance problem. Duly considerations should include both the frictionand the form drag However, as the ship starts to change the drift angle w.r.t(with respect to) the current, the so-called Cross Flow Principle (CFP) may beapplied. By the CFP the flow may be considered decomposed at each shipsection and the longitudinal component plays no role. The total forces areintegrated from the contribution at each section. The relative velocity shouldbe used for the calculation. Off course this is a desperate simplification (theadjective is meant to be as polemic as the CFP) since several interferenceeffects are not considered. Nevertheless, the CFD via the specification of thedrag coefficients may be used after calibration and seem to work whencompared with model tests. An alternative is to use the field-proven

hydrodynamic derivative formulation (Eda and Crane, 1965)^, available in

various versions (see for instance (Nishimoto, Brinati and Fucatu, 1995)*)and where all the cited interference effects are considered. However, anymethod should be carefully analyzed and verified. The technology used in a

Ship Maneuvering Simulator (Sphaier, 1997)* is a promising one, since itbrings the full scale into the problem via well experienced pilots.



Within the CFD, the TERM SIM II seems to be more complete since besidesthe quasi-static approach mentioned above considerations of the dynamicviscous effects is made. The necessary components are carefully calibrated

with model tests for key hull types *. The ARIANE do not consider theseeffects explicitly.

The wind forcesFor the wind, the problem is simpler because of the order of magnitude of thedensity and the cinematic viscosity. The air density is much less than the waterdensity (pwater /Pair =1000) and the added masses present in equations like (1),

(2) and (3)) are less significant. The difference in the cinematic viscosities(v water/^ir =100) is less prominent but, nevertheless, significant for the

viscous effects. Another aspect is that usually the superstructure forms havesharp corners and the separation occurs sooner, leading to non-varying form

drag coefficients. These are well estimated by the OCIMF^ work also madebyMARIN.

Both the TERMSIM II and the ARIANE also allows for fluctuating windspeed for several user specified wind spectra.

The wave forcesAs discussed in the next section, the only significant restoring mechanism is

due to hawser tension. It may be shown * that the typical period for the casesunder study are of the order of 1500s. The realistic wave system leads toexciting periods in the 6-10s range, where the energy is concentrated. Hence,the wave system for the horizontal plane dynamics will be felt mostly by theaverage drift force. The second order effects on the dynamics seems to bemuch less important than in a usual mooring line problem. Some evidences are

shown latter on in an Example. Nevertheless, the Newman's Approximation''

which introduces an error of the order of {(1/1500)* } should be more thanenough for the SPM problem.

Besides the wave exciting force, due to the presence of the waves, thedamping in the slow dynamics is increased with the so-called WDD (WaveDrift Damping). In the SPM problem, there is no MLD (Mooring LineDamping) hence the WDD seems to be very significant. This effect iscalculated in the TERMSIM II but in the ARIANE, it should be consideredimplicitly via a damping coefficient that includes other damping effects.



DYNAMIC STABILITY

As said before, for the case under focus here, the only restoring mechanism isdue to the hawser connected by its turn to the mono-buoy whose effect issmall for the case under study (see discussion in (Fernandes and Sphaier,

1997)*. The hawser is usually very stiff, that is, its elasticity may beconsidered infinite. The same for the deep water mono-buoys. Hence, thetension like restoring mechanism seems to be the most important. However,this area of knowledge, can not be fully understood without the DynamicStability analysis. Since the ship motions is not stable even for a constantcurrent, one would better know what is happening in general terms, that is, notonly via time series analysis. The position of the hawser fairlead, the hawserlength and the average hawser tension are properties that control the finalbehavior.

Fortunately it may be shown^ that this complementary analysis is not difficultonce few hydrodynamic derivatives are known. This kind of analysis launchessome light to the time domain responses that sometimes may be obscure. TheFigure 2, exemplify this praxis. It corresponds to the analysis of a tanker on aSPM. In order to construct this figure, the fairlead has been considered at thebow (a/L=0.5) and the limit tension that separates a stable region from an

unstable one was calculated as shown in (Fernandes and Sphaier, 1997)*The points that are in the figure corresponds to TERM SIM II simulations. Thestable or unstable behaviors observed with the TERMSIM II are veryconsistent with the predictive stability analysis in Figure 2.

EXAMPLES

The present work choose to show one example from a comprehensive study

that has been finished at PETROBRAS '. The focus in on thePETROBRAS' Henrique Dias VLCC that has been adapted to became aFPSO after about 20 years of service. The main characteristics are shown inTable 1. The behavior of this hull has been studied when moored on a SPMarrangement with the buoy shown in Table 2 and when submitted to aincoming wave train (H% = 4.5m; T% = 9.0s) 50 degrees from North.

Only the yaw is shown to illustrate the cinematic behavior, while the dynamicsare illustrated by the hawser tension time history. The Figures 3 and 4 showthe Henrique Dias results with the original data base from the TERMSIM IJ.Some statistics are sown in Table 4.



VesselLpp (length between perpendiculars)(m)B (beam) (m)T (draft) (m)

V (displacement) (m-*)WD (water depth) (m)

Henrique320.00

54.5021.67314000

400

Dias

Table 1 - Henrique Dias main characteristics

Diameter (m)draft (m)6 legspretension (kN)WD (water depth) (m)

15m2.36chain 3 inch diameter

500400

Table 2 - Mono-Buoy main characteristics

The next simulation has been obtained with the same wave train on the sameHenrique Dias hull. However, this time the data base was modified from theoriginal one by taking zero off-diagonal terms in the QTF (QuadraticTransfer Function). There is no need to show the figures with the timehistories since they are very similar to the Figures 3 and 4. The statistics ofcourse resulted also similar and is shown in Table 3.

meanstandarddeviation

TERMSIM IIOriginalData Base

v|' (dg)5022

T(kN)540200

ZeroOff-Diagonal

QTFY (dg)5221

T(kN)527197

ARIANERecommended

Damping

M> (dg)49.22.3

T(kN)

25316

ModifiedDamping

M> (dg)50.323.3

T(kN)493291

Table 3. Statistical values of TERMSIM II and ARIANE processing theHenrique Dias in a incoming wave train (H%= 4.5m; TV, = 9.0s) 50 degrees

from North; last columns statistics taken from t=3000 s .

The Table 3 also includes statistics of the ARIANE results obtained with twodamping coefficient sets. The first set, that is called recommended, has been

obtained from an ARIANE correlated document^. The recommendation inthe latter is to use the following formulae for the diagonal damping matrix:

bi,=0.01M.f (7)



(8)

(9)

The Table 4 shows the results of the latter formulae, together with another setthat has been obtained by trial and error with the purpose of matchingTERMSIM II and ARIANE results. The Figures 5 and 6 are the results of theARIANE simulation (yaw and hawser tension) with the recommendeddamping matrix. The Figure 7 and 8 the same with modified damping. TheTable 4 shows that the latter results are much closer to the TERMSIM IIstatistics. The time series in the Figures 7 and 8 are also closer to theTERMSIM II ones shown in Figures 3 and 4.

b

b

b

11

22

66

(t/s)

(t/s)

(m4/s)

RecommendedDamping

563

2730

23198 xl()3

ModifiedDamping

206

1001

8500x103

Table 4 - Damping used in the ARIANE processing.

CONCLUSIONS

The exercises just presented with waves and others that investigate the current

and wind loads ™, indicate that it is possible to combine the qualities of thetwo programs to reach more reliable results. A conclusion that is valid for theprediction of the behavior of the ship on a SPM. Complementary bifurcationmaps such as the one summarized in Figure 2 are also possible and straight-forward. PETROBRAS has all the programs available. Hence, it is possible tosuggested the following methodology:

a) Perform Static Mooring analysis with the ARIANE, calculating themooring lines restoring capabilities of the Monobuoy;

b) Feed the TERMSIM II program to obtain preliminary dynamics;c) Check the consistency with the bifurcation maps as the one shown in Figure

2;d) Reprocess ARIANE with varying damping coefficients trying to match withTERMSIM II results;

e) Once the match is reached, extract the statistical properties useful forfurther design;

f). Stops one all results match consistently.



It is expected that this results are helpful for further software developments.To have an open software with the source code available is, however, a goalthat should be alternately pursued

ACKNOWLEDGMENTS

The Authors would like to thank PETROBRAS for this great opportunity.The usual but essential thanks also go to Andre Leite and othersGETINP/GESEM Engineers, for their help on creating the present productiveambiance at this E&P department. It give us great pleasure to participate inthis historical effort in the Campos Basin. This is likely setting a world recordon simultaneous field developments.

REFERENCES

[1] Mann, 1994, "TERMSIM II. User's Guide", Mann, Oct..

[2] Bureau Veritas, 1992, "ARIANE. User's Guide", Version 3.0, BureauVeritas, France, Jan..

[3] Wichers,J.E.W , 1988, "A Simulation Model for a Single Point MooredTanker", Marin publication n. 797

[4] Eda,H. and Crane Jr.,L., 1965, "Steering Characteristics of Ships in CalmWater and Waves", Trans. SNAME, Vol. 73, pp 135-177.

[5] Nishimoto, K., Brinati, H.L. and Fucatu, C.H , 1995, "Analysis of SinglePoint Moored Tanker Using Manouvering Hydrodynamic Model",OMAE, International Conference of Offshore Mechanics and ArtieEngineering, Copenhagen.

[6] Sphaier, S., 1997, "Analise da Operagao de Navios Aiiviadores. Base deDados para Dois Navios Petroleiros", Relatorio Tecnico paraPETROBRAS, COPPE/UFRJ, Maio.

[7] Marin, 1993, "Prediction of Wind and Current Loads on VLCC's AnUpdate", Marin Report zOl 1524-2-OE; to OCIMF; Oct..

[8] Fernandes,A.C. and Sphaier, S., 1997, "Dynamic Analysis of a FPSOSystem", ISOPE 97, International Symposium on Offshore and PolarEngineering, Honolulu, May



[9] Fernandes,A.C. and Aratanha,M., 1996, "Classical Assessment to theSingle Point and Turret Dynamic Stability Problem", OMAE, InternationalConference of Offshore Mechanics and Artie Engineering, Florence.

[10]Fernandes,A.C. and Kroff, S.A.B., 1995, "Critical Analysis of theTERMSIM II Program", Report to PETROBRAS. Depart. Eng. Naval eOceanica, USP, Nov..

[ll]Fernandes,A.C. and Kroff, S.A.B., 1997, "TERMSIM II and ARIANECombined", Report to PETROBRAS. Depart. Eng. Naval e Oceanica,USP, JuL

[12]Bureau Veritas, 1995, "Quasi-Dynamic Analysis of mooring Systems",Recommended Practice, Oct..

[13]Aranha, JAP and Fernandes, AC , 1995, "On the Second-Order SlowDrift Force Spectrum", Applied Ocean Research 17 311-313, TechnicalNote. Elsevier Science Limited.

[14]Abkowitz,M.A., 1980, "Measurement of Hydrodynamic Characteristicsfrom Ship Maneuvering Trials by System Identification", Trans. SNAME,Vol.88, pp 283-318.

Figure 1 - System of reference OXYZ Is right-handed and fixed in space;Gxyz is fixed on the ship; \I/<.,M'V andxi/^, stand for current, wind and wavedirection; Uc,Uv and H^,^ are the current and wind intensity and the wave

significant wave high and up-zero-crossing period.



0.060

a/I = 0.5

0.040 —

0.020

0.000

5.0

Figure 2 - T-f Stability diagram as proposed in (Fernandes and Sphaier,

1997)* for a 260 m tanker on a SPM with a fixed mono-buoy; the pointscorresponds to TERMSIM II simulations with different current values; nowaves neither wind are present; the Hawser length is 200 m; (Abkowitz,

1980)'* VLCC data has been used; the time series are consistent with theposition in the diagram; the instabilities are limit cycle type; T, , the limiting

hawser tension, is made non-dimensional with -



' M l ' M M M M i ' I? ^ s l l i ° ° i

time (s)

Figure 3. Henrique Dias yaw time history as predicted by TERMSIM II withan incoming wave train (H^=4.5m; T% = 9.0s) 50 degrees from North; the

original data base from the TERMSIM II package is used; the processingstops at 10800 s due to tthe program imposition.

time (s)Figure 4. Henrique Dias hawser tension time history as predicted byTERMSIM II with an incoming wave train (H,. = 4.5m, T% =9.0s) 50 degrees

from North; the original data base from the TERMSIM II package is used; theprocessing stops at 10800 s due to tthe program imposition.



'1•d• -

Figure 5 - Henrique Dias yaw time history as predicted by ARIANE with anincoming wave train (H^=4.5m; T^,=9.0s) 50 degrees from North

Recommended Damping (see table 4) is used.

Figure 6. Henrique Dias hawser tension time history as predicted by ARIANEwith an incoming wave train (H % = 4.5m; T% = 9.0s) 50 degrees from North

Recommended Damping (see table 4) is used.



time (3)i I

Figure 7 - Henrique Dias yaw time history as predicted by ARIANE with anincoming wave train (H% =4.5m; T% = 9.0s) SO degrees from North. Modified

Damping (see table 4) is used.

time (s)

Figure 8 - Henrique Dias hawser tension time history as predicted by ARIANEwith an incoming wave train (H^ = 4.5m; 7% = 9.0s) 50 degrees from North

Modified Damping (see table 4) is used.


Documents

COMPARATIVE ANALYSIS OF TIME DOMAIN PROGRAMS … · Antonio Carlos Fernandes (Consultant at PETROBRAS) Mauricio Aratanha (PETROBRAS) S. Alejandro B. Kroff (Research Assistant at PETROBRAS)