by s.nallayarasu, s.goswami, j.s.manral, r.m.kotresh presenter: s.k. bhattacharyya dept. of ocean...

BYS.Nallayarasu, S.Goswami, J.S.Manral, R.M.Kotresh

Presenter: S.K. BhattacharyyaDept. of Ocean EngineeringIIT Madras

VALIDATION OF SPECTRAL FATIGUE ANALYSIS OF STRUCTURES IN MUMBAI HIGH FIELD

Historically, Bombay High Field of ONGC has several offshore platforms in the shallow water region of 50 to 80m water depth.

Most of these platforms are fixed template type structures with either main or skirt piles.

Many of these structures are as old as 20 to 30 years & have been designed as per API RP 2A guidelines.

These structures mostly produce oil & Gas and have both process & well head platforms.

These platforms have been designed against fatigue from cyclic wave loads.

Mumbai high field location

1. The field is located on the west coast of India and the wave approach is from south to north-west directions and the other directions are shielded from land.

2. Generally waves are approaching the platforms only from South, South-West, West and North-West. The directional distribution of waves used in the deterministic and spectral methods is shown in Figure

DIRECTIONAL DISTRIBUTION OF WAVES

Deterministic method of analysis

Seastate is discretised in discrete (deterministic) waves the scatter data based sea state specific information is used. Structural response to these discrete waves is then calculated

either with or without dynamic effects depending on natural period.

Spectral method of analysis

Seastate is characterised by the spectral energy. Further, the scatter data for different directions and wave

heights are used to simulate the seastate. The structural response is then calculated using stochastic

method of structural analysis. Dynamic analysis is performed to generate the dynamic

characteristics such as mode shapes and mass characteristics.

FATIGUE RESPONSE ANALYSIS

Wave scatter data and exceedance information used for the deterministic fatigue analysis is shown in Table 1 and 2.

The exceedance data has been converted to occurrence cyclic data with intermediate data range by interpolation

It has been summarised in Table 3.

WAVE SCATTER DATA

WAVE HEIGHT(M)

PERIOD (SEC)

S SW W NW

0.0-1.524 8.7 9.6 8.3 6.6

1.524 - 3.047 9.2 10.1 8.7 7.4

3.048 – 4.571 9.5 10.3 9.2 7.9

4.572 – 6.095 9.7 10.4 9.6 8.4

6.096 – 7.619 9.9 10.5 10.0 8.9

7.620 - 9.143 10.6 10.3 --

9.144 – 10.667 10.8 10.6 --

10.668 – 12.192 11.0 10.9 --

WAVE SCATTER DATA – Deterministic Table - 1

Wave Height (m)

Number of Waves Exceeding Specified HeightIn One Year

S DIR SW DIR W DIR NW DIR CUMULATIVE

0 1276045 770535 1015713 1220511 4282804

1.524 61704 219347 220985 69788 571824

3.048 3132 37929 31902 3764 76727

4.572 167 5878 4073 177 10295

6.096 11 869 493 8 1381

7.620 0 126 59 0 185

9.144 - 18 7 - 25

10.668 - 2 1 - 3

12.192 - 0 0 - 0


Wave Height (m)

W SW S NW

0.381 541944 359421 995444 928660

1.143 252784 191767 218897 222063

1.905 137022 128135 47802 53581

2.667 52061 53283 10770 12443

3.429 20503 22998 2409 2948

4.191 7326 9053 556 639

4.953 2656 3618 124 139

5.715 924 1391 32 30

6.447 322 538 11 8

7.239 112 205 0 0

8.001 39 78 0 0

8.763 13 30 0 0


The wave scatter data for spectral analysis obtained from National Institute of Oceanography is summarized in Tables 4 to 8 for south, south-west, west and north-west directions respectively.

The percentage distribution for each combination of wave period and height will be used for the spectral representation of the seastate using JONSWAP spectra. Table-4 ( South)

Hs(m)

Mean wave period (s)3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 Total

0.0 - 0.5

0.38 0.77 0.00 0.00 0.00 0.00 0.00 0.00 1.15

0.5 - 1.0

0.00 5.00 17.31 18.85 11.54 1.15 0.00 0.00 53.85

1.0 - 1.5

0.00 2.69 10.77 15.00 1.92 2.31 0.00 0.00 32.69

1.5 - 2.0

0.00 0.00 2.31 2.31 2.31 3.85 0.77 0.77 12.31

Total

0.38 8.46 30.38 36.15 15.77 7.31 0.77 0.77 100.00

WAVE SCATTER DATA – Spectral

Hs(m)

Mean wave period (s)

3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 Total

0.0 - 0.5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.5 - 1.0 0.21 2.92 5.22 1.67 0.84 0.00 0.00 0.00 10.86

1.0 - 1.5 0.00 0.84 11.90 9.81 2.71 0.21 0.00 0.00 25.47

1.5 - 2.0 0.00 0.00 4.59 16.08 9.60 2.09 0.00 0.00 32.36

2.0 - 2.5 0.00 0.00 0.00 3.97 5.22 2.30 0.00 0.00 11.48

2.5 - 3.0 0.00 0.00 0.00 3.55 2.51 0.42 0.00 0.00 6.47

3.0 - 3.5 0.00 0.00 0.00 1.88 2.51 0.00 0.00 0.00 4.38

3.5 - 4.0 0.00 0.00 0.00 0.63 3.34 0.00 0.00 0.00 3.97

4.0 - 4.5 0.00 0.00 0.00 0.00 0.42 0.00 0.00 0.00 0.42

4.5 - 5.0 0.00 0.00 0.00 0.00 1.25 0.84 0.00 0.00 2.09

5.0 - 5.5 0.00 0.00 0.00 0.00 0.63 1.67 0.00 0.00 2.30

5.5 - 6.0 0.00 0.00 0.00 0.00 0.00 0.21 0.00 0.00 0.21

Total 0.21 3.76 21.71 37.58 29.02 7.72 0.00 0.00 100.00


Hs(m)


3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 Total

0.0 - 0.5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.5 - 1.0 0.28 1.83 1.83 0.00 0.00 0.00 0.00 0.00 3.94

1.0 - 1.5 0.00 1.69 4.22 0.70 0.00 0.00 0.00 0.00 6.61

1.5 - 2.0 0.00 0.42 9.00 2.81 0.00 0.00 0.00 0.00 12.24

2.0 - 2.5 0.00 0.00 6.05 5.63 0.56 0.00 0.00 0.00 12.24

2.5 - 3.0 0.00 0.00 2.39 12.80 0.84 0.14 0.00 0.00 16.17

3.0 - 3.5 0.00 0.00 0.14 9.00 3.66 0.00 0.00 0.00 12.80

3.5 - 4.0 0.00 0.00 0.00 3.52 6.33 0.14 0.00 0.00 9.99

4.0 - 4.5 0.00 0.00 0.00 0.14 9.85 0.00 0.00 0.00 9.99

4.5 - 5.0 0.00 0.00 0.00 0.00 6.61 1.69 0.00 0.00 8.30

5.0 - 5.5 0.00 0.00 0.00 0.00 2.53 3.38 0.00 0.00 5.91

5.5 - 6.0 0.00 0.00 0.00 0.00 0.14 1.27 0.00 0.00 1.41

6.0 - 6.5 0.00 0.00 0.00 0.00 0.00 0.42 0.00 0.00 0.42

Total 0.28 3.94 23.63 34.60 30.52 7.03 0.00 0.00 100.00


Hs(m)


3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 Total

0.0 - 0.5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.5 - 1.0 4.35 34.78 19.57 0.00 0.00 0.00 0.00 0.00 58.70

1.0 - 1.5 0.00 17.39 19.57 2.17 0.00 0.00 0.00 2.17 41.30

Total 4.35 52.17 39.13 2.17 0.00 0.00 0.00 2.17 100.00


RS-14 WELLHEAD PLATFORM

4 LEGGED PRODUCTION CUM DRILLING PLATFORM WATER DEPTH- 76.2 M 0 MAIN & 8 SKIRT PILES 16 WELL SLOTS & CONDUCTORS MODULAR DRILLING RIG HAVING RIG MAST, RIG

SUPPORT & LQ MODULE TOPSIDE WEIGHT- 6000 MT JACKET WEIGHT-3300 MT (GROSS)

SELECTED STRUCTURES

MNP PROCESS PLATFORM

EIGHT LEGGED 4 LEVEL TOPSIDES WATER DEPTH-72 M 16 SKIRT PILES 20 PRE-INSTALLED RISERS LAUNCH JACKET WEIGHT-7200 MT PROCESS HUB- TOTAL TOPSIDE WEIGHT-20000 MT 3 PROCESS GAS COMPRESSORS, 1

BOOSTER GAS COMPRESSOR. SUBSTRUCTURE SUPPORTS FOR 3

BRIDGES

SELECTED STRUCTURE

The calculation of cyclic stresses on the tubular joints shall include dynamic amplification. The effects of dynamic amplification can be ignored when the natural period of the structure is below 3 seconds as stated in API RP 2 A. This is due to the fact that most of the wave period inducing cyclic loads will be in range of 4 to 12 seconds.

The dynamic amplification factor (DAF) can be calculated using the following formula assuming a single degree of freedom system for the fixed type jacket structures.

where Tn is the natural period of the structure, T is the wave period and is the damping ratio( 2%). It can be shown that the the response and cyclic stress ranges can be linearly multiplied by the DAF and hence the total response can be calculated without going into the full fledged dynamic response of the structure against waves. However, the accuracy of the analysis depends highly on the descretization of the seastate and any simplification will lead to erroneous estimation of response and fatigue damage.

Where [K] is the stiffness matrix, {X} and {F} are the displacement and force vectors respectively. The above approach indicates a simplified method and is very easy to implement for practice. This method has been in use for several years for the prediction response of offshore structures.

2

2

2

1

(1 ) (2 )N n

DAFT TT T

[ ]{ } { * }K X F DAF

DETERMINISTIC ANALYSIS

Alternatively, the response and the cyclic stresses can be calculated using dynamic wave response including dynamic effects due to the above. This method of calculation involves procedures involving dynamic characteristics of the structure and performing the analysis in close intervals of frequency / wave period. However, the method of calculation involved several approximations and the discussion on these issues is outside the scope of this paper and can be found elsewhere.

(3)

Solution to the following equation will lead to Eigen modes and vectors. The dynamic analysis is performed to obtain the dynamic characteristics such as mode shapes and frequencies.

[ ]{ } [ ]{ "} 0K X M X

SPECTRAL ANALYSIS

Where X” is the Eigen frequencies and X is the displacements. The mode shapes and frequencies are then used in the subsequent wave response calculation in which the following equation is solved including the dynamic response of the system.

( 4)

The response is calculated as a transfer function to facilitate the computation of the fatigue damage for various waves in different directions. Typical wave response stress transfer function for base shear and overturning moment is shown in Figure 1 and 2 respectively

[ ]{ } [ ]{ '} [ ]{ "} { }K X C X M X F

SPECTRAL ANALYSIS FIG-1

TRANSFER FUNCTION FOR BASE SHEAR

SPECTRAL ANALYSIS FIG-2

TRANSFER FUNCTION FOR OVERTUNING MOMENT

SPECTRAL ANALYSIS

Selection of frequencies for the generation of transfer function is an important task such that the peaks and valleys of the response is not missed. Following the guidelines given API RP 2A, the frequencies near the natural period of the structure and its multiples shall be selected. The transfer function has been generated for various frequencies from 0.1 Hz to 0.5Hz (Typically from wave periods in the range of 2 to 10 seconds). The frequency interval is selected such that more number of points is generated near the natural period,

The transfer function and the response are generated for both maximum base

shear and maximum overturning moment cases and the worst case is used for the calculation of fatigue damage.

A wave steepness of 1/20 is used for the all the waves as recommended by API RP

2A for the calculation of wave height for each frequency. This has been used for the generation of the transfer function.

It can be observed from Figure 1 and 2 that the maximum values of transfer

function occurs near the frequency of 0.4 which corresponds to a period of 2.5 sec. The natural period of the structures for MNP and RS14 is noted to be between 2.5 sec and 3 sec.

ESTIMATION OF FATIGUE DAMAGE

Fatigue damage has been calculated for all the tubular connections using Miner’s rule using cumulative fatigue damage model stated as below.

(5)

(6)

20

2 20

( ) ( )

( ) ( )

iRMS i h

iRMS

z

h

H f S f df

Tf H f S f df

where σ is the RMS (Root mean square value) of the stress calculated from the transfer function for a given Seastate, H is the transfer function and S is the spectral density of the seastate.

(7)

where n(s) is the number of applied cycles, L is the design life and Tz is the spectral mean period calculated above.Fatigue damage

(8)

where N(s) is the allowable cycles from the S-N curve and S is the stress range. Stress concentration factor (SCF) for the tubular joints has been calculated as per Effthimiou formulas as recommended by API RP 2A for tubular joints and the S-N curve has been adopted as per API RP 2A for tubular joints.

zT

mLsn )(

dss

sN

ssnD i

RMSi

RMS

)exp()(

)(2

2

02

ESTIMATION OF FATIGUE DAMAGE – (Contd.)

FACTOR OF SAFETY

FAILURE CRITICAL

API RP 2AONGCINSPECTABLE NON-INSPECTABLE

NO 2 5 2

YES 5 10 4

ONGC USE A FOS OF 4.0 FOR JOINTS BELOW TOW LEVELS OF JACKET FRAMING TO COVER FOR FATIGUE DUE TO WAVE LOADS

RESULTS AND DISCUSSIONS

MHN (Mumbai High North) field has been presented in Table 8 and 9 respectively. The fatigue life of major tubular joints along the jacket legs and X braces is presented. Fatigue life greater than 1000 years is marked as * since it is very high compared to the required design fatigue life of 50 years.

The fatigue life predicted by deterministic analysis for RS

14 well platforms seems to be on a higher side compared to the spectral fatigue analysis. In the case of MNP Process platform deterministic results are lower than spectral for lower three levels and reverse is the case for 4th and 5th level.

This is due to the fact that the Seastate has been condensed to discrete waves and the DAF has been treated approximately.

Table 8. RS-14 Well platformComparison of results of deterministic & spectral fatigue on selected joints

JOINT NO.FATIGUE LIFE

DIFFERENCE(D-S)DETERMINISTIC SPECTRAL

203L 74.71 17.84 56.87217L 31.17 31.79 0283L 968.58 473.76 494297L * 627.151 400201X * * 0303L 224.9 83.01 142317L 1039.15 215.84 824383L * 245.01 750397L 456.34 187.75 269301X * * 0302X 287.44 172.09 115303X 416.70 241.13 175303 * * 0304 * * 0305 * * 0403L 307.89 844.62 -417L 1287.7 * 0483L 369.62 90.76 278.86497L 118.87 32.14 86.73401X 23.18 5.32 17.86402X 4.11 0.87 3.24



403X * * 0404X * * 0503L 255.38 252.72 2.66517L 541.82 432.30 109.52583L 78.56 14.58 63.98597L 67.82 25.80 42.02501X 49.13 3.86 45.27502X 18.42 1.91 16.51503X * 655.58 345504X * * 0603L 145.32 141.13 131.19617L 273.35 12.08 261.27683L 160.99 19.34 141.65697L 28.88 7.21 21.67601X * 399.95 600602X * 398.85 600603X * 23.92 976604X * 24.27 976703L 1344.463 6.60 994717L * 6.055 994783L * 6.099 994797L * 5.54 994

Table 8. Continued

JOINT NO.

FATIGUE LIFEDIFFERENCE

(D-S)DETERMINISTIC SPECTRAL

404X * * 0503L 255.38 252.72 2.66517L 541.82 432.30 109.52583L 78.56 14.58 63.98597L 67.82 25.80 42.02501X 49.13 3.86 45.27502X 18.42 1.91 16.51503X * 655.58 345504X * * 0603L 145.32 141.13 131.19617L 273.35 12.08 261.27683L 160.99 19.34 141.65697L 28.88 7.21 21.67601X * 399.95 600602X * 398.85 600603X * 23.92 976604X * 24.27 976703L 1344.463 6.60 994717L * 6.055 994783L * 6.099 994797L * 5.54 994

Table 8. Continued

Table 9. MNP Process platformComparison of results of deterministic & spectral fatigue on selected joints


DIFFERENCE(D-S)

DETERMINISTIC SPECTRAL

203L 52.41 108.38 -56207L 9.47 34.14 -24213L 9.26 21.43 -12217L 78.80 127.34 -49283L 52.93 129.05 -77287L 11.55 81.14 -70293L 11.14 69.06 -58297L 43.65 88.38 -45204X * * 0205X * * 0206X * * 0207X * * 0208X * * 0209X * * 0210X * * 0211X * * 0212X * * 0213X * * 0203L 52.41 108.38 -56207L 9.47 34.14 -24213L 9.26 21.43 -12217L 78.80 127.34 -49

JOINT NO.

FATIGUE LIFEDIFFERENCE

(D-S)DETERMINISTIC SPECTRAL

303L 20.89 202.21 -182307L 70.45 508.03 -438313L 69.36 806.51 -737317L 18.49 302.99 -284383L 19.56 267.49 -248387L 197.60 485.68 -288393L 253.92 783.73 -530397L 18.97 358.24 -339304X * *305X * *306X * *307X * *308X * *309X * *310X * *311X * *312X * *313X * *403L 149.07 * -851407L 20.62 200.44 -180

Table 9. Continued

JOINT NO.


417L 156.09 72.32 84483L 185.24 163.23 22487L 168.31 147.37 21493L 140.70 132.46 8497L 135.05 118.97 16404X * *405X * *406X * *407X * *408X * *409X * *410X * 96.67 903411X * 513.86 486412X * 125.03 875413X 429.95 21.49 409503L 104.71 0.88 104507L 24.17 0.06 24513L 23.69 1.07 22517L 153.88 0.85 153583L 301.03 0.87 300

Table 9. Continued

JOINT NO.


587L 73.39 0.89 72593L 156.72 1.01 155597L 181.49 0.69 180501X * 127.26 873502X * 136.83 864503X * 234.38 760504X * 115.94 884505X * 108.49 892506X * 233.61 767507X * 1.42 999508X * 1.57 999509X * 1.42 999510X * 0.21 999603L 151.58 0.57 151607L 99.52 1.18 98613L 184.74 1.21 183617L 370.08 0.56 369683L 206.42 0.70 205687L 105.74 1.20 104693L 180.44 1.13 179

Table 9. Continued

Based on the results obtained from the fatigue analysis of platforms in Mumbai High North and South platforms, following observations are made.

Generally both methods predict fatigue life reasonably well for most of

the joints except for some joints at the bottom of the jacket, the deterministic method predicts the fatigue life lower than the spectral methods. This is due to the fact that the dynamic response of the structure over-predicted by deterministic method by approximate calculations of DAF due to course discretisation of wave periods.

However, the joints near the top of the jacket, the predicted fatigue life

using deterministic methods seems to be higher than the spectral methods. This is due to the fact that the wave load and associated cyclic stresses are only due to the local wave loads rather than the dynamic response.

It is recommended that spectral fatigue analysis be used for large

platforms to assess the fatigue life since the inaccuracy introduced due to the treatment of dynamic amplification factor.

CONCLUSIONS

API RP 2A Recommended Practice for the Design and Construction of fixed offshore platforms, working stress design.

Fatigue User Manual, SACS Software, EDI

Identification of wave spectra for Mumbai offshore region, National Institute of Oceanography, December 2007.

References

by s.nallayarasu, s.goswami, j.s.manral, r.m.kotresh presenter: s.k. bhattacharyya dept. of ocean...

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