STRUCTURAL ANALYSIS OF NORTH ADRIATIC FIXED OFFSHORE …

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Paul Jurišić, Croatian Register of Shipping, Marasovićeva 67, 21000 Split, e-mail: [email protected], Većeslav Čorić, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, I. Lučića 5, 10000 Zagreb, e-mail, [email protected]

STRUCTURAL ANALYSIS OF NORTH ADRIATIC FIXED OFFSHORE PLATFORM

Summary

The paper describes the strength of fixed offshore platform that is analyzed in order to determine its capability in withstanding the operating load with extreme environmental conditions. Critical conditions are taken into account, which include structure and equipment weight, operating load, wind load, hydrodynamic (wave & current) load using Morison equation. Stress analysis is performed by the finite element method. Structural joints, which are subject to long-period survey, are selected by stress level from SESAM result. Buckling of structural elements is checked using API Recommended practice for Fixed Offshore Platforms-Working Stress Design and ABS MODU Rules.

Key words: Fixed offshore platform, wave load, structural analysis, finite element model.

STRUKTURNA ANALIZA NEPOMIČNE PLATFORME SJEVERNOG JADRANA OSLONJENE O MORSKO DNO

Sažetak

Opisan je postupak analize strukture nepomične platforme oslonjene o morsko dno u namjeri da se odredi mogućnost takvog pomorskog objekta da podnese ekstremne okolišne uvjete u kombinaciji s radnim opterećenjima. Kritična stanja koja su uzeta u obzir uključuju težine same strukture i opreme, radne sile, sile vjetra i hidrodinamičke sile uslijed valova i morske struje koje su određene Morisonovim jednadžbama. Analiza naprezanja je izvršena metodom konačnih elemenata, a strukturni spojevi rešetkaste konstrukcije "jacketa" platforme koji se periodično pregledavaju su izabrani na osnovi rezultata iz SESAMa. Izvijanje svih strukturnih elemenata je provjereno upotrebom API i ABS pravila za platforme.

Ključne riječi: Nepomična pučinska platforma, valna opterećenja, strukturna analiza, model konačnih elemenata.

Jurišić, P., Čorić, V.: STRUCTURAL ANALYSIS OF NORTH ADRIATIC FIXED OFFSHORE PLATFORM

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1. Introduction

The present report describes the in-site structural analysis of fixed platform and the relevant structural checks carried out on the main structures of jacket structure. Static and dynamic loading are distinguished. The static loading on the structure originate from gravity loads, deck loads, hydrostatics loads and current loads. The dynamic loading originates from the variable winds and waves. Jacket structure has four cords in the sea depth of 40.8 m with two verticals and two inclining chords in way of maximum wave heading 180 degrees-široko, connected by horizontal and diagonal braces. Six conductor pipes are connected vertically from mud line to the top of jacket structure. Above truss structure are connected decks with living quarter, wellhead and other processing equipment. All analyses have been carried out with the data and procedure provided in [1], [2], [3], [4] and [5]:

Figure 1 Fixed offshore platform Figure 2 North Adriatic fixed offshore platforms location

Slika 1. Nepomična pučinska platforma Slika 2. Lokacija nepomičnih pučinskih platformi u

Sjevernom Jadranu

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2. Finite element structural model

The strength analysis of the jacket structure is performed by the finite element method employing the programming system SESTRA from the SESAM package, [6]. Since the structure is very complex a rather fine finite element mesh is required which is adapted to the structure topology as much as possible. The structure is modelled by beam elements in accordance with structure drawings. Each beam element consists of 2 nodes with 6 degrees of freedom.

Figure 3 Structure drawing of fixed platform Figure 4 Layout of model topside nodes

Slika 3. Konstrukcijski nacrt fiksne platforme Slika 4. Raspored čvorova nadgrađa na modelu

In order to maximise the load on the piles, the conductors are not connected to the soil and are considered only as elements applying to the jacket horizontal components of environmental loads (non-structural beam). To avoid too complex FEM model, the structure of topside is not included in the model. The reaction forces due to the weight of the topside are used as loading of the model top nodes (1904, 1905, 2108, and 2101), see Figure 4. FEM model particulars are given in summary of data from input and load interface files. The super-element has 237 sub-elements, 144 nodes, 840 internal (free) degrees of freedom, 24 retained (super) degrees of freedom, 5 load-cases with node loads, line or point loads for 2-node beams or point loads and gravitational load. The basic elements are given as 233 2-node beam elements (BEAS) and 4 1-node spring elements (GSPR). Mechanical properties of the steel used for the jacket are defined in table 1: Table 1 Material properties:

Tablica 1. Svojstva materijala

Material EN 10025 S345 JO API 5L X52 SR5 Young's modulus, N/mm2 206000 206000 206000 shear modulus, N/mm2 78400 78400 78400 Poisson's ratio 0.3 0.3 0.3 thermal coefficient, 1/K 0.00001 0.00001 0.00001 weight density, N/mm3 0.000077 0.000077 0.000077 minimum yield stress, N/mm2 335 345 360 allowable stress, N/mm2 240 240 245 minimum tensile strength, N/mm2 510 510 520


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Characteristic of jacket structure is changing along the jacket lengths. Dimensions and sectional properties of the main structural beam elements are given in the table 2: Table 2 FEM model main particulars

Tablica 2. FEM model glavne dimenzije

PIPE section 1 (ch. sec.) 2 (chords) 3 (diagonals) 4 (el. brac.) DY-Outer diameter of tube, m 1.690E+00 1.630E+00 7.000E-01 5.080E-01 T-Thickness of tube, m 4.500E-02 1.500E-02 2.000E-02 1.270E-02 SFY-Factor modifying shear area, Y-direction 1.000E+00 1.000E+00 1.000E+00 1.000E+00 SFZ-Factor modifying shear area, Z-direction 1.000E+00 1.000E+00 1.000E+00 1.000E+00 A-Cross section area, m2 2.326E-01 7.611E-02 4.273E-02 1.976E-02 IX-Torsional moment of inertia about shear centre, m4

1.574E-01 4.963E-02 4.943E-03 6.093E-04

IY-Moment of inertia about Y-axis, m4 7.872E-02 2.481E-02 2.472E-03 3.047E-04 IZ-Moment of inertia about Z-axis, m4 7.872E-02 2.481E-02 2.472E-03 3.047E-04 IYZ-Product of inertia about Y and Z axes, m4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 WX,MIN-Min.torsional sect. modulus about shear centre, m3

1.863E-01 6.089E-02 1.412E-02

2.999E-03

WY,MIN-Min. section modulus about Y-axis, m3 9.316E-02 3.045E-02 7.062E-03 1.499E-03 WZ,MIN-Min. section modulus about Z-axis, m3 9.316E-02 3.045E-02 7.062E-03 1.499E-03

3. FOUNDATION BOUNDARY CONDITIONS

Jacket structure deformation mode and connection with the environment result as the model boundary condition on the seabed. Property foundation stiffness matrices define the model boundary conditions. These matrices have been defined on the basis of loads applied to the pile top [5]. In the table 3 the stiffness matrices values are compared with the ones resulting by the pile analysis for the forces on pile top. To express the boundary conditions in the form of foundation stiffness matrices in PRERFAME model the command "Spring to ground" is used, [7]. Elements 101, 104, 105, and 108 are connected to an existing single node, see Figure 6. The linear elastic structural jacket analysis and the non-linear pile-soil analysis are executed successively, resulting with the unbalanced axial force, shear and bending moments of foundation area. Table 3 Foundation stiffness matrices

Tablica 3. Matrice krutosti temelja

F (kN) 78936 395827

M (kNm) 395827 3162837

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Figure 5 Model of boundary conditions "Spring to ground" Figure 6 Layout of model foundation nodes

Slika 5. Model s rubnim uvijetima "Tlo kao opruga" Slika 6. Raspored čvorova na temeljima modela

4. LOADS ON THE JACKET STRUCTURE 4.1 Gravity load of structure

Gravity load consists of jacket structural weight and weight of equipment. All gravity loads from the topside are transferred to the jacket structure through 4 points in the model. The basic load conditions have been analyzed:

• Jacket dead weight as calculated by SESTRA : 5839 kN • Deck dead weight included crane and flares weight: 4065 kN • Operating loads on deck: 5014 kN • Equipment dry weight: 2183 kN • Live loads on deck: 6505 kN • Dead and live loads of the living quarter: 5827 kN

4.2 Wind load

Wind forces act on the deck and living quarter along platform main axes. The force is relevant to operating conditions. The values of wind speed and direction were measured, [4]. The wind load on the model is divided into two portions: the wind load on the hull and the wind load on the legs. Both are calculated together.

The wind force is calculated in accordance with the following equation: ApF ⋅= (1)


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F - wind force, kN A - projected area of all exposed surfaces, m2 p – pressure kN/m2

For the wind pressure the following equation is used: shk CCfvp 2= (2)

f – mass density of air (=1.225 kg/m3 for dry air) vk – wind velocity (=55 m/s) Ch – height coefficient (=1.1), [1] Cs – shape coefficient (=1.0), [1] Resultant load in x direction: 659 kN Resultant load in y direction: 560 kN

Figure 7 Model with combination of gravity and wind loads Slika 7. Model s kombinacijom gravitacijskih opterećenja i sile vjetra

4.3 Wave and Current Loads

In the sea depth 40.8 m the wave load is defined according to the wave characteristics obtained by the Hydrographic Institute, [4]. Using the deterministic approach for the wave load calculation, the structure is exposed to a directional, periodic wave with the characteristic in table [4].

Table 4 Wave heights and directions (100 year return period)

Tablica 4. Valne visine i smjerovi (100 godišnji povratni period)

Wave height H, m 14 7.9 Wave period T, s 14.5 9.2 Heading angle α , deg 180 (široko) 45 (bura)

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z

x

D

dz

z + d

dF

The design waves are specified by their wave period T, the wave height H and the wave heading angle measured counter-clockwise from the global positive X-axis to the propagation direction of the waves. Stocke's 5th wave theory is used for the mathematical model of the waves. The loads are calculated in the time domain that is calculated at given time instants or phase angles of the wave cycle. At each time instant loads are calculated up to the instantaneous water surface, [8]. In addition to surface waves the structure is also exposed to current. Current is superimposed to the wave particle velocity. On the steel water level the current velocity is taken as 0.81 m/s and 25m below water surface it is taken as 0.6 m/s and as 0.5 m/s in the mud level. The velocity of current follows the linear law. The hydrodynamic forces are calculated according to Morison's equation with non-linear drag formulation. It is assumed that the forces may be divided into a sum of an inertia component due to the fluid acceleration and a drag component due to the fluid velocity. Morison's equation assumes that the pressure gradient across a member diameter is roughly constant and the diffraction (scattering of the wave) is negligible, [9] and [10]. According to the Morison's equation the calculated force intensity are included in this equation:

Figure 8 Model for result calibration Morison's equation Figure 9 Maximal horizontal force on monopod Slika 8. Model za kalibraciju rezultata Morisonovih jed. Slika 9. Maksimalna horizontalna sila na modelu

monopodne platfome

),(),(21),(

4),(

2

trvtrvDCtraCDtrF nndnmn ρπρ +⋅⋅= (3)

where: - ρ − water density, kg/m3 - D - member diameter at the load calculation point, m - Cm - inertia coefficient matrix, - Cd - drag coefficient matrix, - vn - undistributed velocity component of the fluid normal to the member at the time and

point in question (including both wave and current), m/s - an=dvn/dt - undistributed acceleration component of the fluid normal to the member at the

time and point in question, m/s2 - r - global coordinate of the load calculation point, m - t - time, s

0 1 2 3 4 5 6

3000

2500

2000

1500

1000

500

500

1000

1500

2000

2500

3000Ftotal (kN)

rad

kN

3000

3000−

2137−

2251

f 011 Θ( )

f 010 Θ( )

f 09 Θ( )

6.30 Θ


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The coefficient matrices are defined by: ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

Z

Y

X

CC

CC

000000

Where: C represents the hydrodynamic inertia or drag force coefficient in the member local

coordinate system. The hydrodynamic coefficient of jacket structural member are Cd = 0.7 and Cm=2.0. Drag coefficient Cd=0.735 (+5%), has been used for submerged jacket members, where sacrifice anodes are provided, [8], [9] and [10].

4.4 Buoyancy

The buoyancy of all the submerged members is included in calculations. However, a separate load condition due to buoyancy force only has also been analyzed and used in combination with gravity loads to determine the load distribution when environmental actions are present.

Resultant load from SESTRA : 661 kN

4.5 Marine growth

Increased diameter and roughness heights are specified to account for additional forces due to marine growth locally. The given marine growth is added to the member diameter at the load calculation points before calculating the viscous drag forces. The roughness height is used to specify varying hydrodynamic coefficients. The density is equal as the seawater and is used to calculate the weight of the marine growth as static load, and additional mass for use in subsequent dynamic structural analysis as horizontal component only.

The data of marine growth are taken on safe side 20 cm.

Table 6 Sum of global forces and moments on jacket structure for all load combinations with wave characteristics: H=14m, T=14.5s, α=0 deg.

Tablica 6. Suma globalnih sila i momenata na strukturu jackteta za sve kombinacije opterećenja s valnim karakakteristikima H=14m, T=14.5s, α=0 deg. LOADCASE: FX [kN] FY [kN] FZ [kN] MX [kNm] MY [kNm] MZ [kNm] 1. GRAV.JAC.+WIND 1.247E-11 1.989E-12 5.839E+03 2.303E+02 1.488E+03 8.412E-12 2. G.TOPSIDE -7.400E+02 -6.400E+02 1.776E+04 -2.411E+03 -2.411E+03 8.640E+01 3. BUOYANCY 7.677E-07 1.833E-06 -6.608E+02 -2.661E+01 -2.747E+02 3.761E-05 4. WAVE F.+CUR.+3. 5.826E+03 -1.382E+00 -1.210E+03 2.643E+01 -9.515E+04 -1.026E+02 5. WAVE M.+CUR. +3. 5.397E+03 9.050E+00 -8.810E+02 3.040E+01 -1.042E+05 2.568E+02 6. 1.+2.+4. 6.802E+03 -6.413E+02 2.239E+04 4.416E+03 -9.607E+04 -1.620E+01 7. 1.+2.+5. 6.373E+03 -6.309E+02 2.272E+04 4.420E+03 -1.051E+05 3.432E+02

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5. Structural response of the model All the elements of the main structure have been checked against the requirements of

[1], [2] and [3] for strength, stability and yield. Stress levels in the jacket structural elements are not to exceed the allowable stresses and the figures 10-15 show the result of the structural response from XTRACT (displacements and stress tensor components), [11]:

Figure 10 Displacements [m] of model for load Figure 11 Displacements [m] of model for case 7 (H=14m, T=14.5s, α=0 deg.) load case 7 (H=14m, T=14.5s, α=180 deg.) Slika 10. Pomaci [m] modela za slučaj Slika 11. Pomaci [m] modela za slučaj opterećenja 7 (H=14m, T=14.5s, α=0 deg.) opterećenja 7 (H=14m, T=14.5s, α=180 deg.)

Figure 12 Displacements [m] of model for load Figure 13 Displacements [m] of model for load case 7 (H=7.9m, T=9.2s, α=45 deg.) case 2-topside weight Slika 12. Pomaci [m] modela za slučaj Slika 13. Pomaci [m] modela za slučaj opterećenja 2 opterećenja 7 (H=7.9m, T=9.2s, α=45 deg.) težina topside-a


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Figure 14 Bending stress-σzx [kN/m2

]due to moment Figure 15 Bending stress-σzx [kN/m2 ]due to moment

z-axis for load case7 (H=14m, T=14.5s, α=0 deg.) z-axis for load case 7 (H=7.9m, T=9.2s, α=45 deg.) Slika 14. Savojno naprezanje-σzx [kN/m2

]za moment Slika 15. Savojno naprezanje-σzx [kN/m2 ]za moment

oko z-osi za sl.opt.7 (H=14m, T=14.5s, α=0 deg.) oko z-osi za sl.opt.7 (H=7.9m, T=9.2s, α=45 deg.) 5.1 Elastic stability (buckling) and yield check of jacket tubular section

The results of analysis are shown in the figures 16-19 as the structural response obtained from FRAMEWORK, [12] (buckling check with "hot spot" identification). Combined axial compression and bending is controlled according to [3]:

Usage factor: 111

2

'

2

'

≤⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

⋅+

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

⋅

+=b

e

ax

bzmz

e

ax

bymy

a

ax

FFffC

FffC

Ff

UsfTot (4)

where: fax- computed axial compressive or tensile stress fby- computed compressive or tensile stress due bending Fa - allowable axial compressive stress Fb- allowable bending stress F'e- Euler stress dived by factor of safety

According to [2] the expression (5) is to be satisfied to avoid buckling:

11 '

≤

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅+

be

a

bm

a

a

FFf

fCFf

(5)

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Figure 16 Stability check for load case 7 Figure 17 Stability check for load case 7 (H=14m, T=14.5s, α=0 deg.) (H=14m, T=14.5s, α=180 deg.) Slika 16. Provjera izvijanja za sl.opt. 7 Slika 17. Provjera izvijanja za sl.opt. 7 (H=14m, T=14.5s, α=0 deg.) (H=14m, T=14.5s, α=180 deg.)

Figure 18 Stability check for load case 7 Figure 19 Yield check for load case 7 (H=7.9m, T=9.2s, α=45 deg.) (H=7.9m, T=9.2s, α=45 deg.) Slika 18. Provjera izvijanja za sl.opt. 7 Slika 19. Provjera tečenja za sl.opt. 7 (H=7.9m, T=9.2s, α=45 deg.) (H=7.9m, T=9.2s, α=45 deg.)


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6. CONCLUSION

Numerical model of fixed offshore platform exposed to environmental and operating

load has been analyzed in this paper. The obtained result shows that selected sizes of construction are in accordance with [1] and [2] rules. Environmental parameters are defined carefully and the unit is able to withstand the extreme conditions. On the basis of calculated stress levels it has been found that only few beams (tubular joints) approach the limit stress levels or even overcome it (hot spots). A detailed study of these beams (tubular joints) shows that these tubular joints are exposed to high stress level only in extreme environmental condition. The calculated results have been validated by the comparison with designer's numerical model (Tecon-Milano). This comparison shows similar stress levels in position of tubular joints of lower diagonals and joints of main jacket columns with foundations. These beams (tubular joints) are to be permanently examined during the classification survey of jacket structure. Marin growth is to be permanently monitored during life time cycle because of possibility of significant increase of stress level in hot spots. However, there is still some place for improvement. This refers to the modelling of boundary conditions due to foundation and will be the meter of future work, as well as fatigue analysis of the whole structure.

REFERENCES

[1] ..:“Rules for classification of fixed offshore installation”, Det Norske Veritas, 1995. [2] ..:”Rules for Building and Classing-Mobile Offshore Drilling Units”, American Bureau of Shipping, 2001 [3] ..: “Recommended Practice for planning, designing and constructing fixed offshore platforms-working

stress design”, API-2A WSD (RP 2A-WSD), American Petroleum Institute, 2002. [4] Report of Republic of Croatia – State Hydrographic Institute "Oceanographic and meteorological data for

the area of north Adriatic-Ivana Gas Field-Extreme values", Split, 1996. [5] Report of Tecon-Milano, 380200 BOCS 41613 – Non Linear Pile Analysis, Milano, 1998. [6] ... SESTRA, SESAM User's Manual, Det Norske Veritas, Oslo, 2005. [7] …PREFRAME, SESAM User's Manual, Det Norske Veritas, Oslo, 2004. [8] ... WAJAC, SESAM User's Manual, Det Norske Veritas, Oslo, 2004. [9] ZIENKIEWICH, O.C.: “Numerical methods in Offshore Engineering”, University College Swansea

Press, Swansea, 1978. [10] CHAKRABARTI, S.K.: "Handbook of offshore engineering", Planfield, Illinois, USA, 2005. [11] ... XTRACT, SESAM User's Manual, Det Norske Veritas Oslo, 2005. [12] ... FRAMEWORK, SESAM User's Manual, Det Norske Veritas Oslo, 2004.

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