ugm 2008 fatigue report

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UGM 2008 Fatigue Report.doc 18 December 2008

UGM 2008 – Fatigue Analysis

1. Introduction This paper presents a case study fatigue analysis. The analysis was part of the testing of the new fatigue facilities in OrcaFlex 9.2. There are quite a few objectives to cover:

‐ To compare lifetime estimates from irregular wave and regular wave fatigue analyses

‐ To identify efficient ways of using OrcaFlex for fatigue calculations ‐ To improve our understanding of the limits of both irregular and regular

wave analysis The first conclusion drawn is that the different fatigue methods produce different results for the system considered here. Regular wave analysis is found to be more conservative, and this is investigated in more detail. When working with either method, performing two fatigue analyses is recommended. The first analysis is essentially a screening of the load cases, which is intended to run as quickly as possible, and provides information that allows the second analysis to produce accurate results with the minimum of effort. This approach is based on the results from our sensitivity studies on fatigue input. This document begins with a description of the system studied, and then presents the work performed using irregular waves. An accurate value of the system’s fatigue life is introduced as soon as possible, and we use that figure as a reference for sensitivity studies and comparison to regular wave analysis.

2. Case Study System Figure 2‐1 shows the system considered for fatigue analysis; a 9 ” steel catenary riser, 1600 m long in 1000 m water depth. The riser is hung from the pontoon of a semi‐submersible platform. The environmental loads applied to the system comprise 30 storms, representing a condensed Gulf of Mexico irregular wave scatter table. We are aware that using 30 cases is quite a small set for a fatigue analysis, but condensing the storm scatter cases allowed numerous repeat analyses in a reasonable amount of time. A flexjoint is used at the connection of the riser to the platform, with a stiffness of 10 kN.m/deg. Riser touchdown is at approximately 1175 m arc length. The fatigue load cases are all applied in the far direction, which is intended to concentrate damage in the plane of the riser catenary.


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X

Z200 m

X

Z

OrcaFlex 9.3a2: SCR base case.dat (modified 15:16 on 09/10/2008 by OrcaFlex 9.3a2) (azimuth=270; elevation=0)Statics Complete

Figure 21 – Case study steel catenary riser system. The riser is attached at the outside of the

pontoon

3. Irregular Wave Analysis The first analysis performed uses standard irregular wave simulations. The 30 storm cases are each run for one hour duration. Service life is taken as 20 years, and so we aim for a minimum of 200 years fatigue life. The minimum fatigue life is obtained in the touchdown region, and is 236 years. Having found a result we believe to be reliable, we can work on ways to make this analysis more efficient. Irregular wave analysis is computationally demanding. One hour duration storm cases require quite long run times, and generate large simulation files, requiring large amounts of storage. Finally, the post‐processing of these long time histories can also be slow. The OrcaFlex fatigue module now calculates damage based only on ZZ stress ranges at the pipe’s outer stress diameter, which has made the fatigue post‐processing much faster. OrcaFlex also now makes more efficient use of computers with more than one processor, extracting fatigue results from multiple simulations simultaneously (processing as many files at once as there are available processors). These improvements to processing speed have helped to make irregular wave fatigue much faster, but we decided to look at the analysis, to try and identify if the process could be made more efficient. Storm duration has a direct impact on the time taken for irregular fatigue analysis. Individual simulations will take less time to run shorter storms, and the smaller files produced can be post‐processed more quickly. This is considered in detail in Section 3.1.


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3.1. Storm Duration Sensitivity When using irregular waves, it is important that the storm duration is long enough to generate a statistically acceptable seastate; one where the average height and period from the realisation are close to the input values. It is also important that the fatigue damage calculated from the simulations converges to a reliable value. This can be tested by repeating an analysis with a different random wave seed. Changes of seed give different wave train realisations, but the final fatigue results should not be much affected, because the storms will be statistically similar. We began by repeating the one hour fatigue analysis, using 30 different wave seeds. The results exhibited spread of ±8% around our accepted true value. This is acceptably small, and we conclude that one hour storms are long enough for accurate answers. But would shorter storms also give accurate results? To investigate the possibility, we ran further fatigue analyses using storm durations of 40, 20, 10 and 5 minutes. Each analysis was repeated 30 times, using different wave seeds. The spread of the fatigue results around our true value at the different storm durations is shown in Figure 3‐1.

Variation of Fatigue Life with Storm Duration

050

100150200250300350400450

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Storm Duration (mins)

Fatigue

Life

(years)

Figure 31 – Variation in fatigue results due to changing wave seed for given storm durations

Each point above represents a full fatigue analysis. Our true value (the mean of the analyses using one hour storms) is shown as a green line.


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The standard deviation of the results about this true value varies with the square root of storm duration, √T. This means that halving the storm duration does not double the deviation of the points above. The increase in spread is less severe. Using 20 minute storm durations, the spread was ±14% for this system. We believe that in many cases this level of variation may provide an acceptable accuracy for an initial assessment of fatigue performance – depending how close the results are to acceptable values. To clarify this point, if a system requires a minimum 200 year fatigue life and an initial assessment using 20 minute storm durations predicts a 300 year fatigue life, then even assuming a spread of 30% about the true value, the results are acceptable. This kind of assessment will be useful early in the design process, where a rapid evaluation of performance is needed. Further, when a more accurate fatigue analysis is required, this preliminary work will allow a more efficient approach to the repeated calculations. Fatigue damage is rarely evenly distributed over the set of fatigue load cases. Some of the storms run will contribute very little to the total damage, while others will take up a large proportion of the fatigue life. Clearly a good quality seastate (a long duration) is required for the cases that provide most of the damage, but the less critical cases will tolerate a shorter storm duration. To illustrate this point, Table 3‐1 shows the percentage damage contribution from each of our 30 irregular load cases, laid out on a scatter table just as environmental data is presented. The data were taken from one of the fatigue analyses performed using one hour duration storms. Increasing contributions of damage are highlighted, with red seastates consuming the most fatigue life.


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Hs / Tp 1 3 5 7 9 11 13 15

0.3 0.00% 0.8 0.00% 0.9 0.00% 0.00% 1.5 0.00% 0.9 0.00% 0.00%

2 1.29% 0.56% 2.7 1.29%

2 1.29% 0.56% 3.2 35.35% 4.6 7.03% 6.4 0.26% 1.8 0.06% 3.7 2.74% 5.1 27.88% 6.8 15.40% 8.7 5.12%

10.6 0.26% 1.9 0.00% 3.5 0.29% 5.2 0.63%

Table 31 – Total Damage contributed from each of the irregular load cases considered

This information – which cases contribute the majority of fatigue damage – is provided by the initial analysis even when short storms are used. The second analysis can take advantage of this knowledge by using long storm durations for critical cases, and shorter storms for less important load cases. The 20 minute runs could be re‐used for cases contributing little damage.

4. Regular Wave Analysis Regular wave analysis provides a simpler approach to fatigue calculations. Irregular waves provide a realistic history of load, which is analysed by rainflow counting to calculate damage over a given exposure. Regular waves are assumed to generate the same stress range each cycle, and this loading is applied to the system for the number of wave cycles in the total exposure. To use this simple assumption, irregular wave seastates are expanded into their individual waves. These single waves are allocated to ‘bins’ of given height and period, and therefore each bin accumulates a number of cycles for a chosen exposure. Each bin is represented by a single regular wave simulation of appropriate height and period. These simulations are of short duration, and consequently run quickly.


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4.1. OrcaFlex Wave Scatter Conversion The conversion of irregular wave load cases to a set of regular waves with associated numbers of cycles can be done using OrcaFlex. The Wave Scatter Conversion tool takes a set of irregular wave load cases as input, and will produce regular wave cases with a matching total time of exposure. The cycles of each regular wave are calculated using the joint probability method of Longuet‐Higgins, referenced in the OrcaFlex help. Once the irregular wave load cases are entered into the conversion module, OrcaFlex will output a table of regular wave occurrences, and then can convert this table into an OrcaFlex batch script, and a corresponding fatigue analysis file, with the data on simulation file names and associated cycles entered automatically. This functionality is also available if a set of regular wave load cases is supplied to the wave scatter conversion tool – no conversion is performed, but the automation can still be used. This facility makes setting up a regular wave fatigue analysis very easy. Regular wave analysis is also less computationally demanding than irregular wave calculations. The simulation files are smaller, run more quickly, typically include only 5 wave periods duration, and no rainflow counting is required on the output. The stress range (from maximum and minimum values) is taken over the last wave cycle of simulation. The conversion of irregular seastates into regular waves involves a discretisation of a continuous spectrum into bins. This means that using a large number of small bins over a fixed range of height and period will give a more accurate representation of real conditions. A coarse discretisation, using fewer bins over the same height and period range, will be further from real conditions. For any discretisation, it is believed that the process of conversion from irregular storm cases to regular wave occurrences is likely to increase the number of large waves applied to the system. When each irregular storm is considered by the conversion process, it is assumed that the storm persists for a duration equal to its stated exposure. For example, the irregular wave case using Hs = 5.1 m and Tp = 11 s has an exposure of 628 hours, a little over 26 days. This is far longer than a single seastate is typically assumed to prevail, but we consider a seastate of these properties for this duration. Clearly this allows plenty of time for large less‐likely waves from that seastate to arise and be counted in the regular wave occurrence data. For this reason, the occurrences of large‐height and long‐period waves are potentially larger than limited duration seastates will produce, because a long seastate duration is considered during the conversion process. These large less‐likely waves may then cause an increase in the fatigue damage predicted by regular wave analysis.


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4.2. Regular Wave Results The first attempt made at regular wave fatigue for this system used regular waves ranging from 1 s to 20 s in period, combined with 1 m to 20 m in height. Over this range the discretisation used 1 m steps in height and 1 s steps in period. There are therefore 400 bins available to the wave scatter conversion module but many of them are empty. The 20 m, 20 s ranges were used because the majority of fatigue waves should fall within these limits. The 1 m, 1 s spacing for the initial study was chosen simply because the numbers involved were easy to work with. As before with irregular wave analysis, this first pass will provide an initial damage value, information on critical load cases and a suggested efficient discretisation for accurate results. The regular wave occurrence table generated is included here in the appendices. To represent the 30 storm scatter cases, 311 regular wave load cases were required. The scatter table has the expected overall shape, with a roughly bell‐shaped distribution of wave cycles. The value of ‘total probability covered’ is close to 1.0, showing that the majority of waves believed to appear over our chosen 20 year exposure are represented in the table. The lifetime estimate from our 1 m, 1 s regular wave analysis was 182 years, somewhat lower than the accurate value of 236 years. When we look at the other information available from this analysis, we can form an opinion regarding the reliability of this result. In a similar manner to the damage scatter table produced for Table 3‐1, we can view the contribution of each regular wave case to the total damage suffered by the system. For the regular wave cases, rather than show a scatter table, we sum the damage over wave height, and show the variation of damage with wave period.

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Wave Period Bins

%-a

ge o

f Tot

al D

amag

e

Figure 41 – Damage contributions from regular waves show dependence on wave period


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It is clear that most of the damage is contributed by load cases having a wave period of 9 s. There is in fact a period range from 7 s to 12 s where the majority of damage is generated. As mentioned previously, using numerous small wave bins will yield a more accurate representation of real conditions. When resolving a simple graph of results, we typically consider that 10 points will provide a reasonable looking curve. As we have a critical period range of 5 s width (from 7 s to 12 s) our minimum resolution over this range would usually include 10 bins, each of 0.5 s width. At this point, the fatigue analysis could be repeated, depending on the results as mentioned at the end of Section 3.1. In our case, this regular wave analysis does not give an acceptable fatigue life estimate, and so we refine the bins used to discretise wave period, hoping for answers closer to the irregular wave result. Whereas the irregular wave analysis proposed that the second attempt at fatigue analysis could re‐use previous calculations for non‐critical cases, with regular wave analysis, this is less important. It would be possible to do so, but the regular wave calculations are so quick that it is probably easier to repeat the whole analysis with a finer bin discretisation, than to perform a specific second pass over a small period range, and then add back in some of the results from the first attempt. Our second regular wave analysis used 1 m bin discretisation for height, and 0.5 s bin discretisation for period, over the 20 m, 20 s ranges used previously. Damage was found to be less sensitive to discretisation over the range of wave heights, and so our approach there was not changed. The revised fatigue life estimate from this second regular wave analysis was 190 years. In search of a converged regular wave result, a final set of cases was generated using 1 m, 0.25 s bin discretisation over the 20 m, 20 s ranges. This most detailed analysis yielded a fatigue life of 191 years. The converged regular wave fatigue life shows a scatter of 19% away from our true value. This distance from the accepted true value is similar to the scatter in results obtained by running 20 minute duration irregular storm cases. As such, regular wave fatigue analysis provides an alternative to running short storm durations for the first load case screening fatigue analysis. Finally we note that the converged regular wave fatigue life is shorter than the irregular wave predictions, and that this conforms to our earlier comments. The conversion of irregular storms into regular wave cases can lead to a more conservative analysis.

5. Conclusions Irregular wave analysis is generally accepted as being a more realistic treatment than regular waves, and as such should include less conservatism. This has been confirmed by our results. However, we have shown that the results of irregular wave analysis are affected by the duration of the storm cases used. The degree of scatter that appears in repeated irregular wave analyses indicates that a storm duration of one hour gives a close grouping of fatigue life estimates.

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Because fatigue analysis is computationally demanding, we were looking for ways to optimise the process. For regular and irregular wave methods, the concentration of damage over a specific wave period range, or in key storm cases, was valuable information. To discover which part of the input is generating the majority of the damage, a screening analysis is recommended. The screening analysis can be performed with regular waves; taking advantage of the automation features within the scatter conversion module, or with irregular storms of short duration. Both approaches are accurate enough to provide useful initial information on the sensitivity of the system’s fatigue life to the various input cases. The second analysis can then concentrate on achieving accurate results where they will have the most influence on the final fatigue life. This analysis will therefore usually be slower than the initial screening. The powerpoint presentation that accompanies this report has more information on the faster performance of OrcaFlex 9.2 compared to version 9.1. In OrcaFlex 9.2, we believe that the fatigue facilities are now fast enough and sophisticated enough to provide an excellent tool for service life assessment. We have tried to consider the whole process of setting up a fatigue analysis, in order to provide advice on how to get the best out of the program. If you have any comments or questions regarding the fatigue module in OrcaFlex, then please do get in touch.

Colin Lewis 18 December 2008


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6. Appendix: Regular Wave Scatter Table

Number of Occurrences Height (m)

20 5.8E‐01 1.8E+00 3.0E+00 3.0E+00 2.1E+00 1.2E+00 5.6E‐01 2.5E‐01 1.1E‐01

19 1.8E‐01 1.2E+00 3.3E+00 4.9E+00 4.7E+00 3.2E+00 1.8E+00 9.1E‐01 4.2E‐01 1.9E‐01

18 4.5E‐01 2.6E+00 5.9E+00 7.9E+00 7.2E+00 4.9E+00 2.8E+00 1.4E+00 7.0E‐01 3.3E‐01 1.6E‐01

17 1.1E+00 5.3E+00 1.0E+01 1.3E+01 1.1E+01 7.3E+00 4.2E+00 2.2E+00 1.1E+00 5.6E‐01 2.8E‐01 1.4E‐01

16 1.2E‐01 2.6E+00 1.1E+01 1.8E+01 2.0E+01 1.6E+01 1.1E+01 6.2E+00 3.4E+00 1.8E+00 9.2E‐01 4.8E‐01 2.5E‐01 1.4E‐01

15 3.5E‐01 6.1E+00 2.1E+01 3.1E+01 3.1E+01 2.4E+01 1.6E+01 9.1E+00 5.1E+00 2.7E+00 1.5E+00 8.0E‐01 4.5E‐01 2.5E‐01 1.5E‐01

14 1.0E+00 1.4E+01 4.0E+01 5.3E+01 4.8E+01 3.5E+01 2.2E+01 1.3E+01 7.4E+00 4.1E+00 2.3E+00 1.3E+00 7.6E‐01 4.5E‐01 2.7E‐01

13 3.0E+00 3.1E+01 7.8E+01 9.0E+01 7.4E+01 5.1E+01 3.2E+01 1.9E+01 1.1E+01 6.2E+00 3.6E+00 2.1E+00 1.3E+00 7.7E‐01 4.8E‐01

12 1.4E‐01 8.4E+00 6.7E+01 1.5E+02 1.5E+02 1.2E+02 7.6E+01 4.7E+01 2.8E+01 1.6E+01 9.2E+00 5.4E+00 3.3E+00 2.0E+00 1.3E+00 8.3E‐01

11 6.0E‐01 2.4E+01 1.5E+02 2.9E+02 2.7E+02 1.9E+02 1.2E+02 6.9E+01 4.0E+01 2.3E+01 1.4E+01 8.3E+00 5.1E+00 3.2E+00 2.1E+00 1.4E+00

10 2.5E+00 6.7E+01 3.2E+02 5.6E+02 4.8E+02 3.1E+02 1.8E+02 1.1E+02 6.1E+01 3.5E+01 2.1E+01 1.3E+01 8.0E+00 5.2E+00 3.4E+00 2.3E+00

9 1.1E+01 2.0E+02 7.4E+02 1.1E+03 8.9E+02 5.3E+02 3.0E+02 1.7E+02 9.6E+01 5.5E+01 3.3E+01 2.0E+01 1.3E+01 8.4E+00 5.7E+00 3.9E+00

8 3.4E‐01 4.8E+01 6.2E+02 1.8E+03 2.3E+03 1.7E+03 9.8E+02 5.2E+02 2.8E+02 1.6E+02 9.1E+01 5.5E+01 3.4E+01 2.2E+01 1.4E+01 9.7E+00 6.8E+00

7 3.0E+00 2.4E+02 2.1E+03 4.5E+03 4.6E+03 3.2E+03 1.8E+03 9.7E+02 5.1E+02 2.8E+02 1.6E+02 9.7E+01 6.0E+01 3.9E+01 2.6E+01 1.8E+01 1.3E+01

6 4.9E+01 1.6E+03 8.3E+03 1.3E+04 1.0E+04 6.2E+03 3.4E+03 1.8E+03 9.8E+02 5.5E+02 3.2E+02 1.9E+02 1.2E+02 7.7E+01 5.2E+01 3.6E+01 2.6E+01

5 9.1E‐01 1.1E+03 1.4E+04 3.9E+04 4.4E+04 2.7E+04 1.3E+04 6.7E+03 3.5E+03 1.9E+03 1.1E+03 6.5E+02 4.0E+02 2.6E+02 1.7E+02 1.2E+02 8.3E+01 6.0E+01

4 1.5E+02 1.9E+04 1.2E+05 1.7E+05 1.3E+05 7.4E+04 3.5E+04 1.6E+04 8.2E+03 4.4E+03 2.5E+03 1.5E+03 9.4E+02 6.2E+02 4.2E+02 3.0E+02 2.1E+02 1.6E+02

3 2.6E+00 3.4E+04 3.1E+05 7.5E+05 6.4E+05 3.6E+05 1.8E+05 8.9E+04 4.5E+04 2.4E+04 1.3E+04 7.9E+03 4.9E+03 3.2E+03 2.1E+03 1.5E+03 1.0E+03 7.6E+02 5.6E+02

2 1.7E‐01 6.2E+04 1.7E+06 3.8E+06 3.1E+06 1.8E+06 8.9E+05 4.4E+05 2.2E+05 1.2E+05 7.1E+04 4.4E+04 2.8E+04 1.9E+04 1.3E+04 9.3E+03 6.9E+03 5.1E+03 3.9E+03 3.1E+03

1 6.0E+07 5.0E+07 4.1E+07 2.6E+07 1.1E+07 5.1E+06 2.6E+06 1.4E+06 8.6E+05 5.5E+05 3.7E+05 2.6E+05 1.9E+05 1.4E+05 1.1E+05 8.6E+04 6.9E+04 5.6E+04 4.6E+04 3.8E+04 Period (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ugm 2008 fatigue report

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