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Floating Production Systems - Houston

Petronas Deepwater SeminarSession 1BProbabilistic Analysis

John ChianisFPS Houston

Vice President, Deepwater Technology and Engineering

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Floating Production Systems - Houston

Probabilistic AnalysisAgenda:

Waves and Wave Spectra

Example Design Wave Data

Calculation of Response Spectrum

Statistical Design Values

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Floating Production Systems - Houston

Realistic Wave ConditionsABB SCF 020503 Model Test Wave Elevation - 100-yr Hurricane

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

0 500 1000 1500 2000 2500 3000

Time (sec)

Ocean waves are not regular in both form and content

Ocean waves are not unit amplitude

Actual wave conditions are referred to as a seastate

Typical Irregular Seastate Time History

A seastate is characterized by a theoretical wave

spectrum

Waves and Wave Spectra

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Floating Production Systems - Houston

Next Session . . .

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Floating Production Systems - Houston

Wave Spectrum

Wav

e En

ergy

(ft2 *

sec/

rad)

Wave Period (sec)

A wave spectrum . . . Is a mathematical

formulation

It is energy-based

Enables statistical methods

Facilitates design

Waves and Wave Spectra

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Floating Production Systems - Houston

Wave Spectral FormulationTwo-Parameter Pierson/Moskowitz

)/T/690(54

1

2sig 441e

TH5.172

)(S

=

Where :Hsig = Significant wave height (avg of highest 1/3) in feet

T1 = Mean spectral period (T1=Tp /1.296)

= Circular frequency

Waves and Wave Spectra

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Floating Production Systems - Houston

Example GoM Design Wave Data(For Illustrative Purposes Only)

Wave:HsigTp

Current:Surface

Wind:1 hr @ 33 ft

(ft)(sec)

(ft/sec)

(ft/sec)

Units

40.014.3

3.28

118.1

100-Yr

26.212.4

1.97

78.7

10-Yr

15.410.9

1.31

49.2

1 YrTypical GoM Hurricane Conditions

Example Design Wave Data

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1B

Floating Production Systems - Houston

Example GoM Design Wave Spectra(Plot of Hurricane Wave Data from Previous Slide)

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Period (sec)

Wav

e En

ergy

(ft2 *

sec/

rad)

)/T/690(54

1

2sig 441e

TH5.172

)(S

=

100-Yr

10-Yr

1 Yr

Example Design Wave Data

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Floating Production Systems - Houston

Example Design Wave Data

Worldwide Design Wave Spectra

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30Wave Period (sec)

Spec

rtal D

ensi

ty (f

t2 sec

/rad)

TLPTH

FloaterTH TP

W Africa

Malaysia

GoM

Brazil

14.8

18.7

40.0

24.9

18.8

14.3

14.315.8

14.9

11.4

15.8

12.8

Region Hsig (ft) Tp (sec)Spectral Characteristics

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Floating Production Systems - Houston

Application for Design

RAO()

RAO2

Ti

S()

Wave Spectrum

Ti

R()

Response

Ti

x =

R() = RAO2() x S()

= (RAO, Wave Spectrum)Statistical DesignValue, i.e. Response

Calculation of Response Spectrum

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Floating Production Systems - Houston

Statistical Design Values

Response Spectrum

Area

= RAO2() x S() d

0

Area under response curve

RRMS =

Rsig = 4 x RRMS

Rmax = 1.86 x RsigArea

Statistical Values:

Statistical Design Values

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Floating Production Systems - Houston

Statistical Design Values

Lets do a Quick Units Check!

ft / ft (assume heave)Units of RAO()

ft2 sec / radUnits of wave spectrum, S()

ft2 sec / radUnits of response, R()

Square-root of the area gives ft

Units of area under response curve

ft2 secrad

rad/sec = ft2

O.K. !

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Floating Production Systems - Houston

Motion Response Prediction

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 10.00 20.00 30.00Period (sec)

RA

O M

otio

n (ft

/ft)

0.0

125.0

250.0

375.0

500.0

625.0

750.0

875.0

1,000.0

Wav

e &

Res

pons

e Sp

ectra

(ft

2 *se

c/ra

d)

Motion RAO Wave Spectrum Motion Response Design Results:

Area = 209.8 ft2

HeaveRMS = 14.5 ft

Heavesig = 57.9 ft

Heavemax = 107.8 ft

Example Design Values(Plot of Example 100-Yr Hurricane Results)

Statistical Design Values

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Floating Production Systems - Houston

Summary - Application

Dry Transport: Motions of vessel-platform

system Structural design Tiedown design

Wet Tow: Motions Structural design

Installation: Motions Mooring loads Structural design

In-Place: Motions Mooring loads Structural design (strength,

buckling & fatigue)

Statistical Design Values are Used for . . .

Statistical Design Values

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