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BY S.Nallayarasu, S.Goswami, J.S.Manral, R.M.Kotresh Presenter: S.K. Bhattacharyya Dept. of Ocean Engineering IIT Madras VALIDATION OF SPECTRAL FATIGUE ANALYSIS OF STRUCTURES IN MUMBAI HIGH FIELD

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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

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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

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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

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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

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WAVE HEIGHT (M) PERIOD (SEC) SSWWNW 0.0-1.5248.79.68.36.6 1.524 - 3.0479.210.18.77.4 3.048 – 4.5719.510.39.27.9 4.572 – 6.0959.710.49.68.4 6.096 – 7.6199.910.510.08.9 7.620 - 9.14310.610.3-- 9.144 – 10.66710.810.6-- 10.668 – 12.19211.010.9-- WAVE SCATTER DATA – Deterministic Table - 1

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Wave Height (m) Number of Waves Exceeding Specified Height In One Year S DIRSW DIRW DIRNW DIRCUMULATIV E 01276045770535101571312205114282804 1.5246170421934722098569788571824 3.04831323792931902376476727 4.5721675878407317710295 6.0961186949381381 7.6200126590185 9.144-187-25 10.668-21-3 12.192-00-0 WAVE SCATTER DATA – Deterministic Table - 2

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Wave Height (m) WSWSNW 0.381541944359421995444928660 1.143252784191767218897222063 1.9051370221281354780253581 2.66752061532831077012443 3.429205032299824092948 4.19173269053556639 4.95326563618124139 5.71592413913230 6.447322538118 7.23911220500 8.001397800 8.763133000 WAVE SCATTER DATA – Deterministic Table - 3

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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) 3-44-55-66-77-88-99-1010-11Total 0.0 - 0.5 0.38 0.77 0.00 1.15 0.5 - 1.0 0.00 5.00 17.31 18.85 11.54 1.15 0.00 53.85 1.0 - 1.5 0.00 2.69 10.77 15.00 1.92 2.31 0.00 32.69 1.5 - 2.0 0.00 2.31 3.85 0.77 12.31 Total 0.38 8.46 30.38 36.15 15.77 7.31 0.77 100.00 WAVE SCATTER DATA – Spectral

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Hs (m) Mean wave period (s) 3-44-55-66-77-88-99-1010-11Total 0.0 - 0.5 0.00 0.5 - 1.0 0.21 2.92 5.22 1.67 0.84 0.00 10.86 1.0 - 1.5 0.00 0.84 11.90 9.81 2.71 0.21 0.00 25.47 1.5 - 2.0 0.00 4.59 16.08 9.60 2.09 0.00 32.36 2.0 - 2.5 0.00 3.97 5.22 2.30 0.00 11.48 2.5 - 3.0 0.00 3.55 2.51 0.42 0.00 6.47 3.0 - 3.5 0.00 1.88 2.51 0.00 4.38 3.5 - 4.0 0.00 0.63 3.34 0.00 3.97 4.0 - 4.5 0.00 0.42 0.00 0.42 4.5 - 5.0 0.00 1.25 0.84 0.00 2.09 5.0 - 5.5 0.00 0.63 1.67 0.00 2.30 5.5 - 6.0 0.00 0.21 0.00 0.21 Total 0.21 3.76 21.71 37.58 29.02 7.72 0.00 100.00 WAVE SCATTER DATA – Spectral

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Hs (m) Mean wave period (s) 3-44-55-66-77-88-99-1010-11Total 0.0 - 0.5 0.00 0.5 - 1.0 0.28 1.83 0.00 3.94 1.0 - 1.5 0.00 1.69 4.22 0.70 0.00 6.61 1.5 - 2.0 0.00 0.42 9.00 2.81 0.00 12.24 2.0 - 2.5 0.00 6.05 5.63 0.56 0.00 12.24 2.5 - 3.0 0.00 2.39 12.80 0.84 0.14 0.00 16.17 3.0 - 3.5 0.00 0.14 9.00 3.66 0.00 12.80 3.5 - 4.0 0.00 3.52 6.33 0.14 0.00 9.99 4.0 - 4.5 0.00 0.14 9.85 0.00 9.99 4.5 - 5.0 0.00 6.61 1.69 0.00 8.30 5.0 - 5.5 0.00 2.53 3.38 0.00 5.91 5.5 - 6.0 0.00 0.14 1.27 0.00 1.41 6.0 - 6.5 0.00 0.42 0.00 0.42 Total 0.28 3.94 23.63 34.60 30.52 7.03 0.00 100.00 WAVE SCATTER DATA – Spectral

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Hs (m) Mean wave period (s) 3-44-55-66-77-88-99-1010-11Total 0.0 - 0.5 0.00 0.5 - 1.0 4.35 34.78 19.57 0.00 58.70 1.0 - 1.5 0.00 17.39 19.57 2.17 0.00 2.17 41.30 Total 4.35 52.17 39.13 2.17 0.00 2.17100.00 WAVE SCATTER DATA – Spectral

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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

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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

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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 T n 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. DETERMINISTIC ANALYSIS

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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. SPECTRAL ANALYSIS

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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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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. ESTIMATION OF FATIGUE DAMAGE – (Contd.)

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FACTOR OF SAFETY FAILURE CRITICAL API RP 2A ONGC INSPECTABLENON-INSPECTABLE NO252 YES5104 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 4 th and 5 th 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) DETERMINISTICSPECTRAL 203L74.7117.8456.87 217L31.1731.790 283L968.58473.76494 297L*627.151400 201X**0 303L224.983.01142 317L1039.15215.84824 383L*245.01750 397L456.34187.75269 301X**0 302X287.44172.09115 303X416.70241.13175 303**0 304**0 305**0 403L307.89844.62- 417L1287.7*0 483L369.6290.76278.86 497L118.8732.1486.73 401X23.185.3217.86 402X4.110.873.24

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JOINT NO. FATIGUE LIFE DIFFERENCE (D-S) DETERMINISTICSPECTRAL 403X**0 404X**0 503L255.38252.722.66 517L541.82432.30109.52 583L78.5614.5863.98 597L67.8225.8042.02 501X49.133.8645.27 502X18.421.9116.51 503X*655.58345 504X**0 603L145.32141.13131.19 617L273.3512.08261.27 683L160.9919.34141.65 697L28.887.2121.67 601X*399.95600 602X*398.85600 603X*23.92976 604X*24.27976 703L1344.4636.60994 717L*6.055994 783L*6.099994 797L*5.54994 Table 8. Continued

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JOINT NO. FATIGUE LIFE DIFFERENCE (D-S) DETERMINISTICSPECTRAL 404X**0 503L255.38252.722.66 517L541.82432.30109.52 583L78.5614.5863.98 597L67.8225.8042.02 501X49.133.8645.27 502X18.421.9116.51 503X*655.58345 504X**0 603L145.32141.13131.19 617L273.3512.08261.27 683L160.9919.34141.65 697L28.887.2121.67 601X*399.95600 602X*398.85600 603X*23.92976 604X*24.27976 703L1344.4636.60994 717L*6.055994 783L*6.099994 797L*5.54994 Table 8. Continued

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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) DETERMINISTICSPECTRAL 203L52.41108.38-56 207L9.4734.14-24 213L9.2621.43-12 217L78.80127.34-49 283L52.93129.05-77 287L11.5581.14-70 293L11.1469.06-58 297L43.6588.38-45 204X**0 205X**0 206X**0 207X**0 208X**0 209X**0 210X**0 211X**0 212X**0 213X**0 203L52.41108.38-56 207L9.4734.14-24 213L9.2621.43-12 217L78.80127.34-49

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JOINT NO. FATIGUE LIFE DIFFERENCE (D-S) DETERMINISTICSPECTRAL 303L20.89202.21-182 307L70.45508.03-438 313L69.36806.51-737 317L18.49302.99-284 383L19.56267.49-248 387L197.60485.68-288 393L253.92783.73-530 397L18.97358.24-339 304X** 305X** 306X** 307X** 308X** 309X** 310X** 311X** 312X** 313X** 403L149.07*-851 407L20.62200.44-180 Table 9. Continued

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JOINT NO. DIFFERENCE (D-S) DETERMINISTICSPECTRAL 417L156.0972.3284 483L185.24163.2322 487L168.31147.3721 493L140.70132.468 497L135.05118.9716 404X** 405X** 406X** 407X** 408X** 409X** 410X*96.67903 411X*513.86486 412X*125.03875 413X429.9521.49409 503L104.710.88104 507L24.170.0624 513L23.691.0722 517L153.880.85153 583L301.030.87300 Table 9. Continued

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JOINT NO. DIFFERENCE (D-S) DETERMINISTICSPECTRAL 587L73.390.8972 593L156.721.01155 597L181.490.69180 501X*127.26873 502X*136.83864 503X*234.38760 504X*115.94884 505X*108.49892 506X*233.61767 507X*1.42999 508X*1.57999 509X*1.42999 510X*0.21999 603L151.580.57151 607L99.521.1898 613L184.741.21183 617L370.080.56369 683L206.420.70205 687L105.741.20104 693L180.441.13179 Table 9. Continued

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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

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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

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