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**VALIDATION OF SPECTRAL FATIGUE ANALYSIS OF STRUCTURES IN MUMBAI HIGH FIELD**

BY S.Nallayarasu, S.Goswami, J.S.Manral, R.M.Kotresh Presenter: S.K. Bhattacharyya Dept. of Ocean Engineering IIT Madras

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**Mumbai high field location**

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.

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**DIRECTIONAL DISTRIBUTION OF WAVES**

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. 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

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**FATIGUE RESPONSE ANALYSIS**

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.

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WAVE SCATTER DATA 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.

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**WAVE SCATTER DATA – Deterministic Table - 1**

WAVE HEIGHT (M) PERIOD (SEC) S SW W NW 8.7 9.6 8.3 6.6 9.2 10.1 7.4 3.048 – 4.571 9.5 10.3 7.9 4.572 – 6.095 9.7 10.4 8.4 6.096 – 7.619 9.9 10.5 10.0 8.9 10.6 -- 9.144 – 10.8 – 11.0 10.9

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**Number of Waves Exceeding Specified Height**

WAVE SCATTER DATA – Deterministic Table - 2 Wave Height (m) Number of Waves Exceeding Specified Height In One Year S DIR SW DIR W DIR NW DIR CUMULATIVE 770535 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 7.620 126 59 185 9.144 - 18 7 25 10.668 2 1 3 12.192

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**WAVE SCATTER DATA – Deterministic Table - 3**

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 8.001 39 78 8.763 13

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**WAVE SCATTER DATA – Spectral**

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 0.38 0.77 0.00 1.15 5.00 17.31 18.85 11.54 53.85 2.69 10.77 15.00 1.92 2.31 32.69 3.85 12.31 8.46 30.38 36.15 15.77 7.31 100.00

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**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 0.00 0.21 2.92 5.22 1.67 0.84 10.86 11.90 9.81 2.71 25.47 4.59 16.08 9.60 2.09 32.36 3.97 2.30 11.48 3.55 2.51 0.42 6.47 1.88 4.38 0.63 3.34 1.25 3.76 21.71 37.58 29.02 7.72 100.00

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**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 0.00 0.28 1.83 3.94 1.69 4.22 0.70 6.61 0.42 9.00 2.81 12.24 6.05 5.63 0.56 2.39 12.80 0.84 0.14 16.17 3.66 3.52 6.33 9.99 9.85 8.30 2.53 3.38 5.91 1.27 1.41 23.63 34.60 30.52 7.03 100.00

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**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 0.00 4.35 34.78 19.57 58.70 17.39 2.17 41.30 52.17 39.13 100.00

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**RS-14 WELLHEAD PLATFORM SELECTED STRUCTURES**

4 LEGGED PRODUCTION CUM DRILLING PLATFORM WATER DEPTH M 0 MAIN & 8 SKIRT PILES 16 WELL SLOTS & CONDUCTORS MODULAR DRILLING RIG HAVING RIG MAST, RIG SUPPORT & LQ MODULE TOPSIDE WEIGHT MT JACKET WEIGHT-3300 MT (GROSS)

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**SELECTED STRUCTURE 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 MT 3 PROCESS GAS COMPRESSORS, 1 BOOSTER GAS COMPRESSOR. SUBSTRUCTURE SUPPORTS FOR 3 BRIDGES

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**DETERMINISTIC ANALYSIS**

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.

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SPECTRAL 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.

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**Where X” is the Eigen frequencies and X is the displacements**

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

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**SPECTRAL ANALYSIS FIG-1**

TRANSFER FUNCTION FOR BASE SHEAR

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**SPECTRAL ANALYSIS FIG-2**

TRANSFER FUNCTION FOR OVERTUNING MOMENT

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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.

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**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)

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**ESTIMATION OF FATIGUE DAMAGE – (Contd.)**

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.

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**FACTOR OF SAFETY FAILURE CRITICAL API RP 2A ONGC INSPECTABLE**

NON-INSPECTABLE NO 2 5 YES 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

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**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.

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Table 8. RS-14 Well platform Comparison of results of deterministic & spectral fatigue on selected joints JOINT NO. FATIGUE LIFE DIFFERENCE (D-S) DETERMINISTIC SPECTRAL 203L 74.71 17.84 56.87 217L 31.17 31.79 283L 968.58 473.76 494 297L * 400 201X 303L 224.9 83.01 142 317L 215.84 824 383L 245.01 750 397L 456.34 187.75 269 301X 302X 287.44 172.09 115 303X 416.70 241.13 175 303 304 305 403L 307.89 844.62 - 417L 1287.7 483L 369.62 90.76 278.86 497L 118.87 32.14 86.73 401X 23.18 5.32 17.86 402X 4.11 0.87 3.24

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**Table 8. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)**

DETERMINISTIC SPECTRAL 403X * 404X 503L 255.38 252.72 2.66 517L 541.82 432.30 109.52 583L 78.56 14.58 63.98 597L 67.82 25.80 42.02 501X 49.13 3.86 45.27 502X 18.42 1.91 16.51 503X 655.58 345 504X 603L 145.32 141.13 131.19 617L 273.35 12.08 261.27 683L 160.99 19.34 141.65 697L 28.88 7.21 21.67 601X 399.95 600 602X 398.85 603X 23.92 976 604X 24.27 703L 6.60 994 717L 6.055 783L 6.099 797L 5.54

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**Table 8. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)**

DETERMINISTIC SPECTRAL 404X * 503L 255.38 252.72 2.66 517L 541.82 432.30 109.52 583L 78.56 14.58 63.98 597L 67.82 25.80 42.02 501X 49.13 3.86 45.27 502X 18.42 1.91 16.51 503X 655.58 345 504X 603L 145.32 141.13 131.19 617L 273.35 12.08 261.27 683L 160.99 19.34 141.65 697L 28.88 7.21 21.67 601X 399.95 600 602X 398.85 603X 23.92 976 604X 24.27 703L 6.60 994 717L 6.055 783L 6.099 797L 5.54

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Table 9. MNP Process platform Comparison of results of deterministic & spectral fatigue on selected joints JOINT NO. FATIGUE LIFE DIFFERENCE (D-S) DETERMINISTIC SPECTRAL 203L 52.41 108.38 -56 207L 9.47 34.14 -24 213L 9.26 21.43 -12 217L 78.80 127.34 -49 283L 52.93 129.05 -77 287L 11.55 81.14 -70 293L 11.14 69.06 -58 297L 43.65 88.38 -45 204X * 205X 206X 207X 208X 209X 210X 211X 212X 213X

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**Table 9. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)**

DETERMINISTIC SPECTRAL 303L 20.89 202.21 -182 307L 70.45 508.03 -438 313L 69.36 806.51 -737 317L 18.49 302.99 -284 383L 19.56 267.49 -248 387L 197.60 485.68 -288 393L 253.92 783.73 -530 397L 18.97 358.24 -339 304X * 305X 306X 307X 308X 309X 310X 311X 312X 313X 403L 149.07 -851 407L 20.62 200.44 -180

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**Table 9. Continued JOINT NO. DIFFERENCE (D-S) DETERMINISTIC SPECTRAL**

156.09 72.32 84 483L 185.24 163.23 22 487L 168.31 147.37 21 493L 140.70 132.46 8 497L 135.05 118.97 16 404X * 405X 406X 407X 408X 409X 410X 96.67 903 411X 513.86 486 412X 125.03 875 413X 429.95 21.49 409 503L 104.71 0.88 104 507L 24.17 0.06 24 513L 23.69 1.07 517L 153.88 0.85 153 583L 301.03 0.87 300

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**Table 9. Continued JOINT NO. DIFFERENCE (D-S) DETERMINISTIC SPECTRAL**

73.39 0.89 72 593L 156.72 1.01 155 597L 181.49 0.69 180 501X * 127.26 873 502X 136.83 864 503X 234.38 760 504X 115.94 884 505X 108.49 892 506X 233.61 767 507X 1.42 999 508X 1.57 509X 510X 0.21 603L 151.58 0.57 151 607L 99.52 1.18 98 613L 184.74 1.21 183 617L 370.08 0.56 369 683L 206.42 0.70 205 687L 105.74 1.20 104 693L 180.44 1.13 179

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CONCLUSIONS 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.

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References 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.

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