Paper No. 2006-JSC-356 Li 1

Extreme Response Analyses of Marlin TLP Tendon Tension during Hurricane Ivan

Guang Li EPTG, BP

Houston, TX, USA

Ronald N. Perego DWP, BP

Houston, TX, USA

David L. Garrett SES

Houston, TX, USA

ABSTRACT In order to verify design factors of Marlin TLP related to extreme tension response, a statistical study on the tension data recorded during Hurricane Ivan is conducted. We discuss the effect of the bandwidth and nonstationarity on the extreme tension estimate and conclude that the direct application of the Weibull method overestimates the extreme tension. Then, a normalization method is proposed to minimize the effect of nonstationarity. We apply this method to both stationary and nonstationary simulated data to show its robustness and effectiveness. We then apply this method to recorded tension data to calculate the observed peak factors1 (PF) during each time interval. Finally, the peak factor distributions (histograms) are calculated and compared with those of Gaussian processes. The study results are also compared with design factors. KEY WORDS: TLP; tension; peak factor; Weibull; Ivan; nonstationarity; bandwidth. INTRODUCTION The Marlin tension leg platform (TLP) was installed in the Gulf of Mexico in 1999 on Viosca Knoll Block 915. Marlin was designed for BP by ABB (1997) using an uncoupled, frequency domain numerical solution, with tendons modeled as springs, incorporating a number of empirical design factors derived from model tests. The water depth at the platform site is approximately 3,250 ft (991 m). The TLP consists of a four column hull connected by ring pontoons and is moored using two tendons per corner. The TLP has a displacement of approximately 52,000 kips (23,608 tons). Table 1 summarizes the principal hull and tendon dimensions. Figure 1 is a photo of the platform.

1 Peak factor is obtained by normalizing the difference between tension peak and mean tension against the RMS tension.

Table 1: Marlin Principal Hull and Tendon Dimensions

Column Diameter 50 ft (15.24 m) Column Centerline Spacing 160 ft (48.8 m) Column Height 140 ft (42.7 m) Pontoon Width 25 ft (7.6 m) Pontoon Height 22.5 ft (6.9 m) Draft 71 ft (21.6 m) Tendon OD 28 in (0.71 m) Tendon Wall Thickness Stepped 1.10-1.05-1.10

(0.028 0.027 0.028 m)

Fig. 1: Marlin TLP Photo A fitness study was commissioned in 2003 to evaluate the platforms payload capacity limits in light of additional development opportunities in the area. Payload capacity was found to be governed by the limit state of minimum tension failure that could lead to tendon unlatching (Li, Banon, and Perego, 2005). The acceptance criterion for this case was the requirement to maintain a positive most-probable-minimum (MPM) tension for any single hull compartment flooded case during a maximum operating storm environment. The MPM tension is calculated using the following formula

rmsMPMmeanMPM TTT = (1)

Proceedings of the Sixteenth (2006) International Offshore and Polar Engineering ConferenceSan Francisco, California, USA, May 28-June 2, 2006Copyright 2006 by The International Society of Offshore and Polar EngineersISBN 1-880653-66-4 (Set); ISSN 1098-6189 (Set)

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where MPM denotes the absolute value of the peak factor (PF) associated with exceeding probability of 62.5%, i.e., the most probable value of a Rayleigh distribution (Ochi, 1973). Understanding how a floating production system (FPS) such as Marlin responds to the environment is critical for protection of personnel, the environment and the facility, for operations, and for future expansion. It is important to verify that analytical tools and corresponding assumptions used for the design and analysis of these systems represent the true response of the floating production system. This requires real time field monitoring of the FPS. To this end, BP has extensively monitored the motions and tendon tensions of the Marlin TLP along with the wind, wave, and current environment. Extensive environment and platform response data was recorded during Hurricane Ivan in 2004. Ivan was an intense hurricane that reached Category 5 strength three times during its life. It caused extensive damage and loss of life while in the Caribbean. Ivan passed over the Viosca Knoll area late on September 15, 2004. During this time, it rapidly weakened from Category 5, and was at Category 3 at its closest approach to Marlin at approximately 18:00 CST on September 15th (Fig. 2). Sustained flight level winds at this time were 110 knots. Perego et al (2005) compared the measured platform response with the predicted values. The tension data of tendon 2, 3, 6 and 7 was recorded at 4 Hz during Hurricane Ivan by the IMMS (Integrated Marine Monitoring System).

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-90 -89 -88 -87 -86Longitude (deg)

Latit

ude

(deg

) MARLIN

NOTE: Circle indicates approximate radius to maximum winds.

Buoy 42040

Closest Model Grid Point

9/16 00Z

9/15 18Z

9/15 12Z

9/16 06Z

Fig. 2: Track of Hurricane Ivan DATA PROPERTIES Tendon Tension Monitoring System (TTMS) status channels indicated that some of the individual sensors were out of tolerance after 12:00 CST (date/time of 15.5 in the plots) on September 15th. Therefore, only data between 0:00 CST on September 14th and 12:00 CST on September 15th is used in our analysis. A one-second moving average was applied to the raw data to remove the local noise.

Nonstationarity Design tensions are typically based on the assumption of stationary seastate. Hence, the tension response is also assumed to be stationary. As the necessary conditions, the mean and RMS tensions are assumed to be independent of time. Figs. 3 and 4 show the mean and RMS tensions calculated at 1800-second non-overlapping intervals during Hurricane Ivan. Their trends with respect to time clearly illustrate the nonstationarity of the recorded data. The trend of mean tension can be removed by subtracting the linear fit to the tension trace. However, the trend of RMS tension requires careful treatment when the extreme tension response is studied. We will discuss our treatment in detail in the next section.

Fig. 3: Mean Tensions during Hurricane Ivan

Fig. 4: RMS Tensions during Hurricane Ivan

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Bandwidth Bandwidth of a tension history indicates the distribution range of its periodic components in the frequency domain. A narrowband process has a single dominant frequency component while a broadband process has its components more uniformly distributed. Increase of the bandwidth of a random process will increase its mean-crossing rate and decrease the ratio between the number of mean-crossings and the number of peaks (defined as ). The peak distribution of a random Gaussian process asymptotically approaches a Weibull distribution as the bandwidth of this process approaches zero ( approaches unity). As shown in Fig. 5, the values of tension histories are generally between 0.6 and 0.9; their bandwidths increase during Hurricane Ivan. In the subsequent section, we will examine the impact of bandwidth on PF determination.

Fig. 5: Values during Hurricane Ivan PEAK FACTOR CALCULATION Weibull Method As an approach commonly used in model tests (Mercier et al, 1997), a Weibull distribution can be fitted to a subset of observed peaks (maxima or minima) from a time series of limited duration (e.g. 20 minutes). Then the distribution can be extrapolated to target probability level to determine the corresponding PF. Fig. 6 illustrates this method, where + symbols denote the PF observed in a 30-minute interval of tension history. The upper and the lower plots show Weibull fits to the maxima and the minima, respectively. However, only the peaks of a narrowband Gaussian process follow the Rayleigh distribution (a special case of Weibull). Fig. 7 shows the shapes of the conditional distributions of positive peaks for Gaussian processes with different bandwidth. Because actual peak probability distribution is something between a Gaussian ( 0= ) and a Rayleigh ( 1= ) distribution (Bendat and Piersol, 2000), the Weibull fit method often overestimates the MPM PF The larger the subset of data is used for the Weibull fit, the more overestimation the Weibull method creates. Because the tension data from model tests is not necessarily narrowband, the PFs predicted based on model test results are often conservative.

Fig. 6: Weibull Fit to Observed Peak Factors

Fig. 7: Peak Distributions of Gaussian Processes with Different Bandwidth Additionally, nonstationarity in the recorded data can also cause this method to overestimate the MPM PF. As an illustration, we simulated a 40-minute zero-meaned tension history based on a power spectrum calculated from recorded tension data. Then, we normalized the tension history against its RMS value and multiplied the simulated data by a linear trend so that it becomes nonstationary. The slope of the trend was chosen to increase the RMS tension by 50% over the 40-minute interval. Finally, we plotted the PF (z) distributions for both processes, as shown in Fig. 8. The nonstationarity elevates the tail of the peak distribution as compared to the underlying stationary process; as a result, a Weibull fit to the peaks of a nonstationary process will overestimate the MPM PF. As shown in the last section, neither the seastates during a hurricane nor the corresponding platform responses are stationary. In addition, the tension responses are not exactly narrowband. Hence, a direct application of the Weibull method to the data should be avoided.

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0.0010

0.0100

0.1000

1.0000

-2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

z

Prob

>

NonStationaryStationary

Fig. 8: Peak Distributions of Stationary and Nonstationary Processes Normalization Method In order to remove the trend in the mean and RMS tension, we propose a normalization method based on the following formula ( )

)()()()( t

tmtTtuT

T = (2) where )(tmT and )(tT are the average and STD of tension T over a 10-minute moving window centered at time t, respectively. The normalized process u has zero mean and unit STD, approximately. We applied this normalization method to the nonstationary process we created in the last subsection and obtained a normalized process. Fig. 9 compares the peak distributions of these two processes and reveals that our normalization method can lower the tail of peak distribution of the nonstationary process. Because the nonstationarity elevates the tail of the peak distribution as compared to the underlying stationary process (as shown in Fig. 8), we conclude that our normalization method can reduce the nonstationarity effect on peak distributions.

0.0010

0.0100

0.1000

1.0000

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

z

Prob

>

NonStationaryNormalized

Fig. 9: Peak Distributions of Nonstationary and Normalized Processes To show the robustness of this method, we applied it to a stationary process. Fig. 10 shows the peak distributions of the stationary and the normalized processes. The normalization method had little effect on the peak distribution of a stationary process.

0.0010

0.0100

0.1000

1.0000

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00

z

Prob

>

NormalizedStationary

Fig. 10: Stationary Peak Distributions Before and After Normalization To show the effectiveness of this method, we applied it to a nonstationary process with 50% increase of its RMS tension over 40 minutes. Figure 11 shows the peak distribution of the normalized process against the stationary process that underlies the nonstationary process. The normalization method effectively recovers the peak distribution of the underlying stationary process. Therefore, unless noted otherwise, all PFs in the subsequent text refer to ones obtained from normalized processes.

0.0010

0.0100

0.1000

1.0000

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00

z

Prob

>NormalizedStationary

Fig. 11: Peak Distributions of Stationary and Normalized Processes In order to avoid the error in MPM PF calculation due to broadbandness, we calculate the maxim and minim observed PFs in each half-hour interval during Hurricane Ivan (one maximum and one minimum from each tendon in each interval.) All tension data is normalized using the aforementioned method. We further average the four maxima and four minima in each interval and plot the averaged values in Fig. 12.

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Fig. 12: Tendon-Averaged Observed Peak Factors during Ivan The mean values of the observed maxim or minim PFs exhibit little correlation to storm intensity; therefore, we make the assumption that the normalized tension process is stationary throughout the storms. (We will discuss the accuracy of this assumption in the next subsection.) Hence, we average these observed PFs over the analysis period and find that the maxim PFs are slightly larger (3.64 vs. 3.48) than the absolute values of the minim PFs. Histogram Method As discussed in the Introduction, minimum tension is the governing condition for the platform. Therefore, we can conservatively combine the observed maxim and minim PFs (absolute values) from all four tendons during Hurricane Ivan and treat them as realizations of a single random variable (denoted generally as PF). All tension data is normalized using the aforementioned method. The histogram of 30-minute observed PFs is shown in Fig. 13. The PDF (probability density function) of Gaussian peaks is also plotted. The observed peak distribution for Ivan compares very well with that of a Gaussian process. The peak of the observed histogram also agrees well with that of a Gaussian process.

Fig. 13: Peak Factor Distribution for Ivan. The MPM PF of a Gaussian process can be calculated using the following equation (Ochi, 1981)

)ln(2 nMPM = (3)

where n is the number of zero up-crossings of the normalized process. A similar formula has been adopted in API RP 2T (American Petroleum Institute, 1997). We also calculate the PF corresponding to 62.5% exceeding probability based on the observed histograms, denoted as observed MPM PF. The Ochi Factor approximates the observed MPM PF closely. We further apply Eq. 3 to every 3-hour non-overlapping time interval for each tendon during Ivan and calculate the Ochi Factor, shown in Fig. 14. The predicted MPM FPs vary little throughout the storm, consistent with our assumption made earlier that the normalized tension process is stationary throughout the storm.

2.0

2.2

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2.6

2.8

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3.8

4.0

14.0 14.5 15.0 15.5 16.0

2004 Sep Date (day)O

chi P

eak

Fact

or

T2T3T6T7

Fig. 14: Ochi Peak Factor during Ivan In order to study PF variation across storms, we compare observed PF distributions for other storms together with that of an equivalent (in terms of bandwidth) Gaussian process (not shown here). Again, the peak distribution of a Gaussian process agrees well with observed distributions. Also, the Ochi Factor range predicts well the observed MPM values. Our histogram method can also be applied to 3-hour (vs. half-hour) intervals, commonly used for design, as the effect of nonstationarity is removed through the normalization process. Fig. 15 shows the observed 3-hour PF distribution, together with that of a Gaussian process. The design ranges (ABB, 1997) and the Ochi MPM range are also shown for reference. The design ranges are obtained based on Weibull fit to model test results.

0%

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3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2

Peak Factor

% in

bin

Observed (10-Min Moving)Gaussian

MarlinDesignRange

for WinterStorms

MarlinDesignRange

for 100-Yrto 1000-YrHurricanes

OchiMPM

Range

Fig. 15: 3-Hour Peak Factor Distribution To illustrate the bandwidth effect, we plot the observed 3-hour PF distribution and those obtained using various Weibull fits to half-hour

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data samples in Fig. 16. The curves labeled Weibull-95% or 50% Peaks are calculated based on Weibull fit to the subsets of 95% and 50% data, respectively. Additionally, we plot the observed distributions with and without normalization (denoted as 10-Min Moving and 3-Hour Fixed, respectively) in Fig. 17 to illustrate the nonstationarity effect.

0%

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10%

15%

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25%

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3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2

Peak Factor

% in

bin

Weibull-95% PeaksWeibull-50% PeaksObserved (10-Min Moving)

MarlinDesignRange

for WinterStorms

MarlinDesignRange

for 100-Yrto 1000-YrHurricanes

OchiMPM

Range

Fig. 16: Bandwidth Effect on 3-Hour Peak Factor Distribution

0%

5%

10%

15%

20%

25%

30%

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2

Peak Factor

% in

bin

3-Hour Fixed10-Min Moving

MarlinDesignRange

for WinterStorms

MarlinDesignRange

for 100-Yrto 1000-YrHurricanes

OchiMPM

Range

Fig. 17: Nonstationarity Effect on 3-Hour Peak Factor Distribution As seen in Fig. 13, the observed 3-hour PF distribution approximates that of a Gaussian process. Also, the Ochi PF range predicts the observed MPM value well. The Weibull fit method and the methods without normalization each shift the observed PF distribution to the right. The conservatism seen in the design ranges may result from application of these methods to model test data. CONCLUSIONS Full scale tension data was collected for the Marlin TLP during Hurricane Ivan. Data noise was discussed and treated by a moving-average technique. The tension data are clearly nonstationary and broadband. The resulting effects on tension PF distribution are discussed. We proposed a normalization method to minimize the nonstationarity effect. We also applied a histogram method to the normalized process to calculate the observed PF distributions.

The conclusions from our study are

1. Weibull fit method, as commonly applied to model test data, overestimates the MPM PF of a broadband process;

2. Application of conventional stationary analysis techniques to nonstationary data also results in overestimation of the MPM PF;

3. Our normalization method effectively minimizes the nonstationarity effect and has little effect on a stationary process;

4. The Gaussian PF distribution approximates the observed distributions very well;

5. The Ochi peak factor serves as an excellent predictor of observed MPM PF;

6. Conservatism in the design range of the MPM PF may result from application of the Weibull fit method to broadband and/or nonstationary data from model test.

Although our study was focused on Marlin, our conclusions are applicable to other TLPs because the same methodologies (model tests, data analysis, etc.) are commonly used in their designs. ACKNOWLEDGEMENTS We wish to thank the BP Gulf of Mexico Deepwater Production Business Unit for funding this work. BMT Scientific Marine Services provided Marlins Integrated Marine Monitoring System (IMMS). BBN Technologies provided Marlins Tendon Tension Monitoring System (TTMS). REFERENCES ABB (1997). AMOCO Marlin TLP Phase II, Global Performance

Analysis, Prepared for Amoco, Report No. OH685-09252. American Petroleum Institute (1997). Recommended Practice for

Planning, Designing, and Constructing Tension Leg Platforms, API RP 2T, second edition, API.

Bendat, JS and Piersol, AG (2000). Random Data Analysis and Measurement Procedures, third edition, John Wiley & Sons, New York, USA.

Li, G, Banon, H, and Perego, RN (2005). TLP Reliability Study Based on the Limit State of Tendon Unlatching, Proc Offshore Mechanics and Arctic Engineering Conference, OMAE 2005-67083, Halkidiki, Greece.

Mercier, RS, et al (1997). Mars Tension Leg Platform Use of Scale Model Testing in the Global Design, Proc Offshore Technology Conference, OTC 8354, Houston, USA.

Ochi, MK (1973). On the Prediction of Extreme Values, Journal of Ship Research, March 1973, pp. 29-37

Ochi, MK (1981). Principles of Extreme Value Statistics and their Application, Proc Extreme Loads Response Symposium, Arlington, VA, USA.

Perego, RN, et al (2005). Marlin TLP: Measured and Predicted Responses during Hurricane Ivan, Proc Offshore Technology Conference, OTC 17335, Houston, USA.

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