DNV GL © 2015 30 August 2017 SAFER, SMARTER, GREENERDNV GL © 2015

30 August 2017Arne Nestegård

OIL & GAS

Retningslinjer for lavfrekvent respons av flytere

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Konstruksjonsdagen, Ptil

DNV GL © 2015 30 August 2017

Background

Several line breakages on MODUs and floating production units may be attributed to overload during heavy weather.

Need to improve methods, procedures and standard industry practice in mooring line design predictions of nonlinear wave loads in large sea states.

In particular, the significant effect of low-frequency floater motions on extreme mooring loads needs attention.

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DNV GL © 2015 30 August 2017

Exwave JIP – Wave Forces on Floating Units in Extreme Seas

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MARINTEKNorwegian Marine Technology Research Institute

DNV GL © 2015 30 August 2017

Exwave JIP objectives

Identify, explore and describe technology gaps that can explain the occurrence of extreme wave-induced forces higher than expected, which may result in overload and line breakages in extreme seas.

Emphasis shall be on low-frequency (slowly varying) wave forces leading to slow drift vessel motions and deviations from classical 2nd order wave drift forces

Recommend improvements with guidelines in industry practice, taking into account proper modeling of low-frequency wave forces

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DNV GL © 2015 30 August 2017

Exwave - Handbook on low-frequency wave forces and response

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Contents• Introduction

• Main characteristics of moored floaters

• Wave and current loads

• Hydrostatic loads

• Steady current loads

• Wave frequency loads

• Slowly varying wave loads

• Simplified formulas

• Damping of low frequency motion

• Modelling alternatives

• Computational Fluid Dynamics

• De-coupled and coupled response analysis

• Validation and calibration of slowly varying forces and response

• General guidance on model testing

• Main findings in Exwave JIP

DNV GL © 2015 30 August 2017

Design equation and safety factors (DNVGL-OS-E301)

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The design equation for the ULS may be given by characteristic mean and dynamic tension and partial safety factors

TC-mean = characteristic mean line tension from mean environmental loads TC-dyn = characteristic dynamic line tension from LF and WF motions SC = characteristic mooring line capacity γ = partial safety factor

Class 1: Where mooring line failure is unlikely to lead to unacceptable consequences (loss of life, collision with adjacent platform, uncontrolled outflow of oil or gas, capsize or sinking)

Class 2: Where mooring line failure may well lead to unacceptable consequences of these types

0≥⋅−⋅− −− dyndynCmeanmeanCC TTS γγ

DNV GL © 2015 30 August 2017

Forces from waves, wind and currrent

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WF Mean LF

Waves 1st order wave frequency force

• 2nd order meanwave drift force

• 2nd order low frequency (slowly varying) force

• Wave drift damping

Wind • Mean wind force • LF force due to LF wind gusts

Current • Mean current force• Modifies mean wave

drift force

• Damping of LF motion• Modifies LF wave loads

DNV GL © 2015 30 August 2017

Floater excitation forces

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risermoorextWAWACUWIt qqqqqqqxx,q ++++++= )2()1(),(

Mean andLF windforce Mean

currentforce

WFwaveforce Mean and

LF wave force

Mooringforce

Riserforce

Other external force

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The challenge of mooring line tension predictions

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After calibrationModel test

Before calibrationModel test

Aksnes, V.Ø. (2014), "Correct" response in positioning analyses", Tekna Conference on DP and Mooring of Floating Structures Offshore, Trondheim, Norway, 12-13 February 2014

DNV GL © 2015 30 August 2017

Effect of sea state on wave drift force coefficient

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Comparing potential flow drift coefficient (WAMIT) with measured coefficient in 4 different sea states.

Verideep JIP – MARINTEK

Semi-submersible VISUND

Reported by Stansberg (ISOPE, 2001)

DNV GL © 2015 30 August 2017

DNVGL-OS-E301 Position mooring

3.4.2 The wave drift force coefficients calculated by standard wave diffraction analysis (potential theory) do not include viscous effects or current interaction effects. Current interaction effects on wave drift force shall be included together with viscous effects as relevant.

Viscous effects may be determined from experiments.

Current interaction effects can be extracted from model basin test with waves and current, or it can be calculated by an extended wave diffraction analysis. Such analysis shall be calibrated towards model basin results.

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DNV GL © 2015 30 August 2017

Simplified formula for current and viscous effects

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)()(~)( ωωω pdkB sum ⋅⋅=

))(95.0exp()( 30kDp −=ω

2)(1

)(~−+

=kLkk ω

OTC (2015)

( )

+−⋅⋅+⋅+=

ββ

αβωωβωsincos

)cos()()()cos1(),,( )(,, scepotidwccpscid HUGBfUCHUf

πNA

Nd WPsum

4=

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Validation of simplified formula

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Hs=11.5m – Tp = 12.5s – Uc = 0 m/s Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – CollinearHs=11.5m – Tp = 12.5s – Uc = 0 m/s Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Non-collinear

Yang, Falkenberg, Nestegård & Birknes-Berg (2017) “Viscous Drift Force and Motion Analysis of Semi-Submersible in Storm Seastates compared with Model Tests” OMAE2017-62319

DNV GL © 2015 30 August 2017

Validation of response by simplified formula

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4040: Hs=11.5m – Tp = 12.5s – Uc = 0 m/s 4240: Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Collinear4320: Hs=11.5m – Tp = 12.5s – Uc = 0 m/s4350: Hs=11.5m – Tp = 12.5s – Uc = 1.58 m/s – Non-collinear

Mean

Std

Extreme

DNV GL © 2015 30 August 2017

Wave current interaction

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0

50

100

150

200

250

300

0.3 0.4 0.5 0.6 0.7 0.8 0.9

F 1(k

N/m

2 )

ω (rad/s)

U=0 m/s

U=0.4 m/s

U=0.8 m/s

DNV GL © 2015 30 August 2017

Wave current interaction

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Exwave semi-submersible. Collinear current Uc = 0.82 m/s.

DNV GL © 2015 30 August 2017

Aranha’s formula

)0,,(cos41),,,( redcwccd U

gU βωβωαβω FF

+=

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+= cwce U

gβωωω cos1

cw

cr g

Uβ

ωββ sin

2−=

= frequency of encounter

= frequency of encounter

αββ −=cw

DNV GL © 2015 30 August 2017

Slowly varying (LF) wave force - QTFs

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𝐹𝐹𝐿𝐿𝐹𝐹(𝑡𝑡) = 𝑅𝑅𝑅𝑅�𝑎𝑎𝑖𝑖𝑎𝑎𝑗𝑗𝐻𝐻(2)(𝜔𝜔𝑖𝑖 ,𝜔𝜔𝑗𝑗 )𝑅𝑅𝑖𝑖(𝜔𝜔𝑖𝑖−𝜔𝜔𝑗𝑗 )𝑡𝑡𝑁𝑁

𝑖𝑖 ,𝑗𝑗

Numerical prediction of QTFs

– Complete / simplified

Extracting QTFs from model tests

– Cross bi-spectral analysis

Newman’s approximation

Validity of Newman’s approximation

– Semis/FPSOs– Shallow/deep water

Unresolved: Effect of current and viscous effects on QTF.

DNV GL © 2015 30 August 2017

Damping of low frequency motion

Viscous hull damping

Wave drift damping

Mooring line damping

Thruster damping

Wind induced damping

Sea floor friction damping

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DNV GL © 2015 30 August 2017

Wave drift damping

Wave drift damping = rate of change of wave drift force wrt low frequency velocity of floater

Equivalence to wave current condition

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)()()0,(),( 2xOxBFxF dd +−= ωωω

0|)(

=∂∂

−=xx

FB d

ω

0

)(=

∂∂

=cUc

d

UF

B ω

𝐵𝐵 𝜔𝜔 ≈𝐹𝐹𝑑𝑑 𝜔𝜔,∆𝑈𝑈𝑐𝑐 − 𝐹𝐹𝑑𝑑 𝜔𝜔,−∆𝑈𝑈𝑐𝑐

2∆𝑈𝑈𝑐𝑐 0

50

100

150

200

250

300

0.3 0.4 0.5 0.6 0.7 0.8 0.9

F1

(kN

/m2)

ω (rad/s)

U=0 m/s

U=0.4 m/s

U=0.8 m/s

DNV GL © 2015 30 August 2017

Wave drift damping from Aranha’s formula

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dd F

gF

gB ω

ωωω 4)(

2

+∂∂

=

0

50

100

150

200

250

300

0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

F 1(k

N/m

2 )

ω (rad/s)

-200

-100

0

100

200

300

400

0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

B 11

(kN·

s/m

3 )

ω (rad/s )

Fd(ω)B(ω)

DNV GL © 2015 30 August 2017

Accuracy of Aranha’s formula

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DNV GL © 2015 30 August 2017

Modelling alternatives for LF wave excitation and damping

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DNV GL © 2015 30 August 2017

Morison modeling of viscous loads

Viscous drag excitation and damping from waves and current on hull is represented by the Morison drag model;

Relative velocity between floater and fluid particles is applied;

For the columns above the still water level (SWL), drag forces are integrated up to the actual free surface;

Both horizontal and vertical loads are accounted for.

Recommended drag coefficients from DNV-RP-C205.

Use asymmetry factor above SWL to account for enhanced wave kinematics relative to linear theory Yang et.al. (Exwave) OMAE2017-62319

DNV GL © 2015 30 August 2017

Statistics of surge motion comparison

DNV GL © 2015 30 August 2017

Computational Fluid Dynamics for wave drift force

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Modeling issues

– Vessel motions: Moving rigid mesh following the vessel motion

– Boundary condtions: Euler Overlay Method. Mass and momentum sources force CFD solution into undisturbed wave solution near boundaries

– Grid resolution

– Physical modelling: Euler solution vs NavierStokes

Drift force extracted from mooring line force

H=25.5 m, T=12.7 s

DNV GL © 2015 30 August 2017

Validation and calibration of slowly varying forces and response

Background and need for model testing

– Wave-current interaction

– Viscous effect on drift force

– Full second order modelling of LF wave force (QTFs)

– Higher order effects on wave drift force in high seastates

Types of tests

– Global design verification of complete floating system

– Taylor made model tests for estimation of wave forces on floater hull

Planning and execution of tests

Data processing, interpretation and documentation

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DNV GL © 2015 30 August 2017

Acknowledgements

Exwave JIP participants

Dr. Carl Trygve Stansberg, Advisor SINTEF Ocean

Dr. Nuno Fonseca, SINTEF Ocean

Dr. Jørn Birknes-Berg, DNV GL

Dr. Limin Yang, DNV GL

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DNV GL © 2015 30 August 2017

SAFER, SMARTER, GREENER

www.dnvgl.com

Thank you

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Arne Nestegårdarne.nestegard@dnvgl.com+47 41419215