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Abstract This paper describes the fatigue analysis of Kizomba 'A' FPSO based on the FPSO Fatigue Methodology Specification (FMS) [1] which is developed on the direct stochastic calculation. The FMS provides designers with technical guidance for fatigue control of newly built FPSO and can be characterized as integrated fatigue analysis to ensure the structural safety of all critical FPSO details by means of full stochastic analysis as well as component based one. At the cost of modeling complexity and computer resources, the full stochastic method gives the accurate fatigue damage for FPSO-specific details such as topside, piperack, flare etc., which are governed by hull-wave interactions. On the other hand, the component based one provides the cost-effective tools to screen the most fatigue prone area in topside supports for full stochastic analysis. Besides, the spectrum combination method that is suggested in order to consider both wave-line and wave-hull interactions, is adopted in fatigue damage calculation of the supports for FTL, OOL, riser and mooring. Apart from technical aspect, the interface management between other groups in charge of FPSO-hull, topside, riser and mooring system turns out very important due to tight project schedule. This paper proves the practical possibility and appropriateness of full stochastic fatigue analysis for FPSO and envisions its usefulness for other floating structures such as TLP, semi-submersibles and etc. The considered Kizomba 'A' FPSO to be installed on Angola Block 15 is 285 meters long, 63 meters wide, and 32 meters high, and can store 2.2 million barrels of crude oil in its lower hull facilities [2]. Introduction As the offshore oilfields shift into the deeper waters with little infrastructures, FPSOs have become the more popular solution. Currently one of the most active areas in FPSO

installation is the West Africa where the weather is benign and the swell from the south is dominant. Whereas strength of the FPSO in such a calm site is mostly controlled on towing route, the fatigue control is directly dependent on the site-specific environment. It should be ensured that FPSOs could stay for decades without drydocking for maintenance. ExxonMobil has developed FPSO Fatigue Methodology Specification (FMS) with DNV for providing designers with technical guidance for fatigue control of newly built ship-shaped FPSOs [3]. The aim of the fatigue control is to ensure that all critical structural details meet the fatigue design requirements. Also, the calculated fatigue lives form the basis of FPSO design and are used as inputs to the inspection plans during fabrication and in-service. The focus of the FMS is a full stochastic fatigue analysis method that gives the accurate fatigue damage for the FPSO-specific details like topside support, piperack, flare tower foundation etc. The structural behaviors of these supports are governed by wave-hull interactions and describable using linear analysis. The wave loads based on the metocean data of installation site are directly calculated and transferred to the structural model. Generally, full-ship structural model is utilized in the analysis. Figure 1 shows the general procedure of full stochastic fatigue analysis. For the fatigue analysis of hull-specific details such as toe and heel of longitudinal stiffener etc., component based fatigue analysis is used. Stress RAO is assumed as linear superposition of load RAO and stress influence factor, i.e., stress value due to unit load. This approach is popular for worldwide trading vessels because the non-linear effect due to intermittent wet and dry surface around still water line can be easily accounted for. Component based fatigue analysis is expanded in this project to screen the most fatigue prone connection out of many topside stools. Considering that there exists practical limitation in the number of thickness-based local FE models, it is important to screen where the most critical connection is. This kind of screening would be difficult and time consuming when the full stochastic analysis was used. One of the most difficulties in FPSO fatigue analysis would be to consider the wave-line and wave-hull interactions simultaneously. The details in this category are supports for FTL (Fluid Transfer Line), OOL (Oil Offloading Line), riser

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Fatigue Analysis of Kizomba 'A' FPSO using Direct Calculation based on FMS M.H. Oh, W.S. Sim and H.S. Shin, Hyundai Heavy Industries, Co., Ltd.

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and mooring system. Spectrum combination method can assess the fatigue damage in more accurate than conventional deterministic method could do when different sources of loads affect the structure concurrently. Principles of Fatigue Analysis The fatigue life may be calculated based on the S-N fatigue approach under the assumption of linear cumulative damage (Palmgrens-Miner rule). When the long term stress range distribution is defined through a short term Rayleigh distribution within each short term period for the different loading conditions, and bi-linear S-N curves are used, the fatigue damage expression can be given as,

++

+= ∑

==

2

0ij

02

2

m0ij

2

0ij

01

1

m0ij

headings all seastatesall

1j1,iijd0

2m2S

2m1γ

a)2m(2

2m2S

2m1Γ

a)2m(2

rTνD

2

1

Where, Td = planned service life of FPSO in seconds ν0 = long term average response zero-crossing frequency ā1, m1=S-N fatigue parameters for N<107 cycles ā2, m2=S-N fatigue parameters for N>107 cycles Γ, γ= complementary incomplete gamma function and incomplete

gamma function rij= relative number of stress cycles in short term condition i, j So= stress range for which change of slope curve moij= zero spectral moment of stress response process

The fatigue design is based on the use of S-N curves that are obtained from fatigue tests. The design S-N curves are based on the mean-minus-two-standard-deviation curves for relevant experimental data. S-N curve for specific detail is selected based on its welding connection type as shown in Table 1. Table 1 Welding Connection Type and S-N Curve

S-N Curve Welding Connection Type

B Base material

C Weld toe (stress parallel to weld toe), Cut edges

D Weld toe (stress perpendicular to weld toe), Hotspot S-N curve

W Root cracking in fillets

The hotspot stress is regarded as principal stress at the distance of 0.5 times the thickness from intersection line in principal direction. In order to determine the hotspot stress, it may be necessary to perform several extrapolations depending on element types. In this project, 8 node shell element with a mesh size of t x t is used around hotspot region and the principal stress at the midnode along the element edge on the element surface is directly taken as hot spot stress without any extrapolation.

General Arrangement and Specifications General arrangement of Kizomba ‘A’ FPSO is shown in Figure 2. The FPSO will be installed at Block 15 in Angola offshore and main particulars are shown in Table 2. Table 2 Main Particulars of Kizomba ‘A’ FPSO

Item Dimension Unit

Length Overall 285.0 Meters Breadth 63.0 Meters Depth Moulded 32.3 Meters Draft (Fully Loaded) 24.45 Meters Displacement (Fully Loaded) 432,087 Tonnes Topside Weight (Operational) 35,860 Tonnes Mooring System Spreaded

with 15 lines -

Environment and Analyzed Loading Conditions The sea environment of installation area, ‘Angola Block 15’, can be characterized by swell dominant wave with minor wind-driven sea. The main direction of swell is assumed to come from 0º (SSW to NNE in magnetic North) with 75% probability and from +/-25º with 25% probability. In fatigue calculations, the swell is only considered. The swell scatter diagram is shown in Figure 3. In Specifications, the wave spectrum is defined as Ochi-Hubble (modified Bretschneider) spectrum with varying peak enhancement factor. The analysis has considered 4 loading conditions that are ballast, fully loaded, intermediate and towing draft condition. The first three are on-site operational draft conditions. Intermediate condition is included due to the large (16m) difference in draft between the ballast and fully loaded conditions. The time distribution of each draft is assumed as 25% for ballast, 25% fully loaded and 50% intermediate. Towing is a route-specific condition for re-locating the vessel from the construction yard in Korea to Block 15 in Angola. It utilizes different environmental data and is analyzed separately during 90 days through December, January and February. This period corresponds to the most severe environments in monthly-based scatter diagram. To combine the damage of operational condition with towing condition, the probability of towing condition is assumed as 1% that corresponds to 90 days and this is deducted from the probability of ballast conditions. Table 3 shows the distribution of analyzed load conditions. Table 3 Distribution of Analyzed Loading Conditions

Load condition Probability [%] Ballast 24 Fully loaded 25 Intermediate 50 Towing 1

Hydrodynamic Analysis Hydrodynamic analysis in full stochastic analysis is performed to transfer loads to the structural model directly. The structural model for global F.E. analysis is used for mass model. 3-dimensional linear potential theory has been applied in the

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hydrodynamic calculations. For inplace conditions, 9 wave headings from -90° to 90° with step of 22.5° are used to cover the short-crestness of swell waves. The directional distribution of short-crested waves is described by the cosine function to the power of 16 for swell. In towing condition, 12 wave headings from 0° to 360° with step of 30° and the directional distribution of short-crested waves described by the squared cosine function are used. The 25 regular wave periods are considered from 4 to 35 seconds. Non-linear Roll Damping Iteration The behavior of first order motions for a ship-shaped body is known to coincide well with the computational results from potential theory except roll motion. The roll motion is strongly governed by non-linear viscous damping, which is a function of roll angle, wave heading and wave frequency. To estimate these damping effects correctly, iteration procedure is performed for this project. Nonlinear roll damping is iterated based on Tanaka’s formula, harmonic linearization and the probability level of 10-4. The iteration process is quoted from FMS as followings: STEP: 1. Input a roll angle, θx

input, to compute non-linear roll damping.

2. Perform vessel motion analysis including damping from STEP 1.

3. Calculate long-term roll motion, θxupdate, with 10-4

probability, using design wave scatter diagram. 4. If θ4

update from STEP 3 is equal to θxinput in STEP 1, stop the

iteration. Otherwise, set θxinput = θx

update, and go back to STEP 1.

Global FE Analysis The global FE analysis is performed with loads that are directly obtained from hydrodynamic analysis. The global FE model for the structural analysis is presented in Figure 4. The lower hull as well as FPSO-specific system such as topside, riser, flare etc. is modeled to consider the global stiffness more accurately. The global FE model has a 3-2-1 fixation simulating a simply supported beam. The restraints are applied at three nodes in the FE model, which have a relatively high stiffness, typically at bulkhead intersections. The geometry of the global FE model is defined using 4-node and 3-node shell elements with membrane and bending properties for plates. The 2-node beam element is used for modeling of longitudinal stiffeners, web flanges etc. In order to verify global FE analysis, several items must be checked. Mass balance between loading manual and mass model, comparison of excitation and reaction forces and stress level at the main deck due to unit bending moment are typical examples. As the displacement from global FE analysis is transferred to local FE model, getting the realistic displacement in global analysis is very important for correct analysis. To verify that that stiffness of coarsely modeled support system in global model is compatible with local FE model for topside, piperack

and flare systems, force-displacement comparison on simple static analysis is performed. In the comparison, the same model extent and boundary condition are used. Screening Analysis Screening analysis for the topside support structure is performed based on simplified component based method. This approach is simpler than normal component based method in that the phase difference in load component and the long-term stress distribution are roughly assumed. Nevertheless, this approach gives the efficient and reasonable result for screening purpose. The fatigue damage is calculated on following formula with assumed Weibull shape parameter.

+= ∑ h

m1qaTD

km

1

d0 1Γν

Where, Td = planned service life of FPSO in seconds ν0 = long term average response zero-crossing frequency ā1, m1=S-N fatigue parameters h = Weibull stress range shape distribution parameter q = Weibull stress range scale distribution parameter k = number of load conditions Γ(1 + m/h) = gamma function that can be found in mathematical

handbooks The Weibull scale parameter is defined from the stress range level, ∆σ0, as

( ) h/10

0

nlnq σ∆=

Where, n0 is the number of cycles over the time period for which the stress level ∆σ0 is defined.

In this analysis, stress amplitude, σ0, is defined as following formula.

vxxvvvvv RAccARAccA ⋅⋅+⋅⋅=0σ

ZBMKRAccA hullgmxxm /⋅+⋅⋅+

Where Av = stress influence factor, stress from unit vertical force at

topside supporting column Am = stress influence factor, stress from unit moment at topside

supporting column Kg = stress concentration factor for unit x-displacement. Accv = vertical acceleration of 10-4 level Accx = longitudinal acceleration of 10-4 level BMhull = vertical hull girder bending moment of 10-4 level Rvv = vertical reaction force due to unit vertical acceleration Rvx = vertical reaction force due to unit longitudinal acceleration Rmx = reaction moment due to unit longitudinal acceleration Z = section modulus of hull girder system

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The screened locations for FPSO-specific details are shown in Figure 5. Local FE Analysis Local FE analysis using sub-model technique is performed to calculate fatigue lives for the selected concerned connections. Sub-model is composed with 8 node shell elements with t x t mesh size at hotspot region. The sub-model should be compatible with the global model. This means that the boundaries of the sub-model should coincide with the elements in the global model. The local FE model is modeled sufficiently large to avoid the boundary effects. In case of topside and piperack support, the structural behaviors are governed by wave-hull interactions and full-stochastic method gives the accurate fatigue life. Typical FE model and minimum fatigue life is shown in Figure 6 and 7 for topside fixed support and piperack support respectively. The dominant load turns out to be hull-girder bending moment and the shape of bracket toe in longitudinal direction is the most important design factor for fatigue control. It should be noted that this reasoning has its validity for FPSO in West Africa. Spectrum Combination Method On the other hand, spectrum combination method is used for the FPSO-specific items such as FTL, risers, OOL and mooring lines that may be governed by non-linear line dynamics as well as wave-hull interactions. Stress spectrums from wave-hull interactions and line load dynamics are combined on following formula.

∑ ⋅+= − std_lineloadkstd_inducedwavestd_comb FAσσ

( 2inducedwave

2std_inducedwave

std_combcomb

1−− ⋅= νσ

σν

)2lineload

2std_lineloadk ))(average()FA( ν⋅⋅+ ∑

Where,

σcomb_std = standard deviation of combined stress spectrum σwave-induced_std = standard deviation of wave-induced stress

spectrum, i.e. wave-hull interaction Flineload_std = standard deviation of line load spectrum Ak = stress influence factor, i.e. stress from unit load νcomb = zero-crossing frequency of combined stress spectrum νwave-induced = zero-crossing frequency of wave-induced stress

spectrum vlineload = zero-crossing frequency of line load spectrum,

The stress spectrum for wave-hull interactions comes from full stochastic fatigue analysis and line load spectrum comes from other interface groups in charge of riser, OOL and mooring system. This spectrum combination method can be regarded as conservative approach because the possible stress reduction from phase difference is ignored. In case of risers in port side around midship region, the fatigue damage from line load is negligible because the riser system in

port side is flexible one and has the small dynamic load. On the contrary, the hull-girder effect on platform structure that is continuous in longitudinal direction is significant. Therefore, the end connection of platform structure is designed to have the soft bracket toe as shown in Figure 8. In case of OOL that are located in bow area of the FPSO, hull-girder or sea pressure effect is negligible. However, OOL is not flexible system and governed by significant line dynamic load. As a result, the OOL structure is designed with bracket for fatigue control as shown in Figure 9. Conclusion This paper presents a very brief and selective review of the extensive experiences gained from Kizomba ‘A’ FPSO fatigue analysis according to FMS. The FPSO-specific details are only described and the hull-specific details are excluded in this paper. The conclusions can be summarized as followings: Full stochastic fatigue method of FPSO-specific details is

applied for on-going project. Practical possibility and usefulness of full stochastic

fatigue analysis is verified. By means of spectrum combination method, fatigue

damages from wave-hull and line dynamic load are considered more accurately. Non-linear roll damping is iterated to consider its

variations from roll angle, wave heading and wave frequency. Analytical screening procedure is set up to select the

most fatigue prone connection for refined fatigue analysis Interface management between other groups in charge of

FPSO-hull, topside, riser and mooring system is very important due to tight project schedule.

FPSOs will be seen in the most of the offshore sites after FPSOs are allowed in the Gulf of Mexico and the stricter requirement for fatigue proof design is expected. The experiences and technique obtained from Kizomba ‘A’ FPSO fatigue analysis will be the key references for the new demands of offshore market. References 1. “FPSO Fatigue Methodology Specification, FMS”, Rev. 5,

ExxonMobile Development Company & Det Norske Veritas, June 2000

2. “FPSO Hull and Marine Systems Design and Construction Specifications (for Kizomba FPSO)”, Brown and Root Energy Service, Oct. 2000.

3. “DNV Classification Note No. 30.7, Fatigue Assessment of Ship Structures”, Det Norske Veritas, September 1998

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Figure 1 Full Stochastic Fatigue Analysis Procedure Flowchart

Figure 3 Swell Scatter Diagram for Angola Block 15

Figure 4 Global FE Model of Kizomba ‘A’ FPSO

Figure 2 General Arrangements of Kizomba ‘A’ FPSO

Piperack

Topside Modules Accommodation and Heli-deck

FTL Caissons

Crane Pedestal

Fire Pumps

Flare Tower

Hydrodynamic model

Global FE model

Local FE model

Hydrodynamic analysis

Global structural analysis

Local structuralanalysis

Mass information

Fatigue analysis

Reporting

Displacements transfer

Drawing, loading manual, applicable scatter diagram, etc…

Loads transfer

Screening

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Figure 6 Minimum Fatigue Life for Fixed Topside Support

Figure 7 Minimum Fatigue Life for Piperack Support

Figure 8 Minimum Fatigue Life for Riser in Port-side

Figure 9 Minimum Fatigue Life for OOL(Oil Offloading Line)

Figure 5 Selected Locations from Global Screening Analysis

Weakest connection

Weakest connection

87 years

Weakest connection

85 years Weakest connection 204 years

53 years