OTC-27028 Numerical Modeling of Internal Waves-Rev0...2016/06/15 · OTC-27028 Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems Nishu V. Kurup,

OTC-27028

Numerical Modeling of Internal Waves and their

Influence on Deepwater Floating Systems

Nishu V. Kurup, Shan Shi, Lei Jiang, Offshore Dynamics, Inc.

Prof M. H. Kim, Texas A&M University

CONTENTS

• Introduction

• Canonical Description

• Analytical Formulation

• Internal Wave Model and Profile

• Implementation of model

• Analysis and Results • Semi

• TLP

• Spar

• Summary and Conclusion

• Acknowledgements

Slide 2

OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup


INTRODUCTION

• Reported since Viking times as deadwater and “tidal rips”

• First clearly identified by John Scott Russell in 1838 based

on observations of isolated surface solitary waves in a

Scottish canal.

• The theoretical description of the waves was presented by

Korteweg and de Vries [KdV] in 1895 as internal solitary

waves.

• Ocean internal waves have been extensively studied and

there is diverse literature on the theoretical and

experimental aspects of this phenomenon.

• In the past, internal waves have seriously disrupted offshore

exploration and drilling operations. In particular a drill pipe

was ripped from the BOP and lost during drilling operations

in the Andaman sea. Drilling riser damages were also

reported from the South China Sea among other places.

Slide 3


WORLDWIDE DISTRIBUTION OF INTERNAL WAVES

Slide 4

© Atlas of Oceanic Internal Solitary Waves


INTERNAL WAVE CANONICAL DESCRIPTION

• Counterbalance between nonlinear and dispersive effects

• Nonlinearity increases velocity of wave towards shock like condition

• Dispersive effects due to differences in velocities in Fourier components

• Built up energy dissipated through dispersive effects resulting in solitary wave

• Three phases of Internal waves

• Generation

• Propagation

• Dissipation

• Generation phase

• Influenced by tidal cycles and ocean currents

• Propagation phase

• Addition of oscillation per buoyancy cycle

• Amplitude, phase speed and wavelength decreases from front of train to trailing edge

• Dissipative phase

• Depends on topography of ocean floor

Slide 5


Internal Wave Analytical Formulation

• Full Navier Stokes Equation

• Time consuming

• Computationally intensive

• Boussinesq approximation

• Small density variations can be neglected except in buoyancy terms

• Several formulations are available in literature

• Benjamin, 1966; Benney, 1966; Joseph, 1977; Liu et al, 1985.

• Korteweg –de Vries equation

• For weakly nonlinear waves

•𝜕𝜂

𝜕𝑡+ 𝑐0

𝜕𝜂

𝜕𝑥+ 𝑐0𝛾

𝜕3𝜂

𝜕𝑥3+ 𝛼𝜂𝑐0

𝜕𝜂

𝜕𝑥= 0

• Has multiple solutions

Slide 6

INTERNAL WAVE ANALYTICAL FORMULATION



• Common Solutions

• Hyperbolic secant equation

• Cnoidal profile

• Dnoidal Profile (Apel, 2003)

𝜂 𝑥, 𝑡 = 2𝜂0 𝑑𝑛𝑠2 1

2𝑘0(𝑥 − 𝑉𝑡) − 1 + 𝑠2

𝑘0 = 2𝛼𝜂0

6𝛾

𝑉 = 𝑐0 1 +1+𝑠2

3𝛼𝜂0

• Recovery Function

Slide 7


where s is the elliptic modulus varying from 0 to 1 and

k0 is a wave number

𝑠2 =𝑒𝑟𝑓 𝛽(𝜏−𝜑) +1

2

where β and φ are parameters that govern the

distribution of wavelengths and number of oscillations

over the wave packet.

𝐼(𝑥, 𝑡) = 1 + 𝑡𝑎𝑛ℎ2𝐴(𝑥−𝑉𝑡−𝜒)

𝑥𝑎 where A, χ, and xa are parameters that control the

shape of the recovery function.



• Weight Function : The effect of the pycnocline on the internal wave is captured

by the well known Taylor Goldstein equation

• The final model with all the functions and components is presented below

𝜂 𝑥, 𝑧, 𝑡 = 𝜂0𝑊 𝑧 𝐼 𝑥, 𝑡 2𝑑𝑛𝑠21

2𝑘0 𝑥 − 𝑉𝑡 − 1 + 𝑠2

• The velocity fields can be derived by considering the boundary conditions and

the continuity equations.

• First mode considered as it is most prevalent and has highest velocity.

Slide 8


N(z) is the buoyancy frequency

𝑑2𝑊(𝑧)

𝑑𝑧2+

𝑁2

𝑈−𝑐 2 −𝑈𝑧𝑧

𝑈−𝑐− 𝑘2 𝑊 𝑧 = 0

𝑁 𝑧 =−𝑔

𝜌0

𝑑𝜌

𝑑𝑧


Internal Wave Analytical Formulation Slide 9

INTERNAL WAVE MODEL


Internal Wave Analytical Formulation Slide 10

INTERNAL WAVE MODEL WITH CORRESPONDING SATELLITE PICTURE

(© ESA, April 26, 2000)

Internal Wave Input Parameters

Parameters Unit Case 1 Case 2

Internal Wave Height m 90 170

Upper Layer Depth m 200 200

Upper Layer Fluid Density kg/m3 1020 1020

Lower Layer Depth m 1019.2 1019.2

Lower Layer Fluid Density kg/m3 1028 1028

Internal Wave Pre-existing Time T0 sec 30000 10000

Recovery Function Power (A) - 4 4

Error Function β - 3.0 3.0

Error Function φ - -0.1 -0.1

Group Speed and Maximum Horizontal Velocity

Wave Height (m) Group Speed (m/s) Max. Hori. Velocity (m/s)

90 3.58 1.31

170 3.58 2.21


-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

0 2,000 4,000 6,000 8,000 10,000

Dep

th,z

(m)

Time (s)

Internal Wave Height

η,(m)

INTERNAL WAVE PROFILE WITH DEPTH (Η=90M)

Slide 11


INTERNAL WAVE VELOCITY PROFILE WITH DEPTH (Η=90M)

-1200

-1000

-800

-600

-400

-200

0

200

400

0 2,000 4,000 6,000 8,000 10,000

De

pth

,z(m

)

Time (s)

Horizontal Velocity

100*U,(m/s)

-1200

-1000

-800

-600

-400

-200

0

200

400

0 2,000 4,000 6,000 8,000 10,000

De

pth

,z(m

)

Time (s)

Vertical Velocity

100*W,(m/s)

Slide 12

reverses polarity at pycnocline

Coupled Analysis Program HARP

IMPLEMENTATION TO FULLY COUPLED ANALYSIS PROGRAM Slide 13


Internal Wave Setup for various

offshore platforms

METOCEAN CRITERIA AND INTERNAL WAVE SETUP Slide 14

Wave

Gamma

Wave Direction (deg)

Singnificant (Hs) (ft)

Spectral Peak Period (Tp) (s)

Wind

1 hour Avg. Wind (m/s)

Wind Direction (deg)

Depth Vel Depth Vel Depth Vel

(m) (m/s) (m) (m/s) (m) (m/s)

0 1.91 0 2 0 1.02

-36.88 1.4 -36.88 1.47 -50 0.77

-75 0.19 -75 0.19 -100 0.27

-1219.2 0.19 -1219.2 0.19 -1219.2 0.13

Current Direction (deg)

South china Sea

Water Depth=1219.2m

Current Profile

API API API

42.98

180

45

180

6

11.2

Normal

180

3

21.97

180

Maximum

Operating

1-year Return

Period Criteria

Jonswap

1

180

180 180

Jonswap

2.4

180

14

Normal

15.1

15.24

15.6

Normal

Jonswap

2.4

180

100-year

Hurricane

Items

1 2

Wave

Dominant

Design

Extreme

Wind

Dominant

Design

Extreme


Semi Model

ANALYSIS AND RESULTS – SEMI PRODUCTION SYSTEM

Semi Configuration

Slide 15

Semi Key Figures

Draft m 28.96

Displacement N 3.09×108

Hull Total kg 2.70×107

Column Height m 47.85

Column Side Length m 12.5

Column c/c Span m 56.39

Pontoon Width m 10.67

Pontoon Height m 6.71

Vertical C.G. from Base KG m 23.87

Vertical C.B. from Base KB m 9.92

Pitch Radii of Gyration Rxx m 32.61

Raw Radii of Gyration Ryy m 31.94

Yaw Radii of Gyration Rzz m 29.32

Semi Mooring Line Properties

Mooring Line

Properties

Diameter

(m)

EA

(KN)

Breaking Strength

(KN)

Wet Weight

(Kg/m)

Dry Weight

(Kg/m)

Length

(m)

Chain 0.1302 1.96×106

15118 292.87 336.77 106.7

Polyester 0.22 4.10×105

14168 8.53 32.72 1676.4

Chain 0.1302 1.96×106

15118 292.87 366.77 250



Example – Semi Production System

Slide 16

ANALYSIS AND RESULTS – SEMI PRODUCTION SYSTEM

0 2000 4000 6000 8000 10000-30

-20

-10

0

10

20SEMI Surge Motion

Off

se

t (m

)

Time (s)

With Internal Wave

Without Internal Wave

0 2000 4000 6000 8000 10000-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0SEMI Heave Motion

Off

se

t (m

)

Time (s)

With Internal Wave


0 2000 4000 6000 8000 10000-6

-4

-2

0

2

4

With Internal Wave


SEMI Pitch Motion

An

gle

(d

eg

)

Time (s)

0 2000 4000 6000 8000 100001000

1500

2000

2500

3000

3500

With Internal Wave


Mooring Line Top Tension

Tens

ion

(KN

)

Time (s)

Semi Motion Statistics

Condition Operation

Survival

Wave Dominant

Wind Dominant

Internal Wave Height N/A 90m 170m N/A N/A

Offset

MAX m 0.45 0.39 0.28 -0.81 -0.80

MIN m -7.43 -12.85 -25.16 -33.37 -32.25

MEAN m -3.32 -3.65 -3.80 -18.34 -18.38

Heave

MAX m 1.14 1.19 1.28 5.80 5.11

MIN m -1.24 -1.19 -1.29 -6.09 -5.39

MEAN m -0.03 -0.02 -0.03 -0.17 -0.18

Pitch

MAX deg 0.60 2.02 3.72 5.93 5.58

MIN deg -2.68 -2.73 -2.38 -1.32 -1.32

MEAN deg -0.97 -0.88 -0.82 1.88 1.77

Semi Mooring Line #3 Max Tension and Utilization Ratio

Condition Operation

Survival

Wave Dominant

Wind Dominant


Line Max Tension KN 2.40E+03 2.65E+03 3.39E+04 4.30E+03 4.18E+03

Utilization Ratio - 0.17 0.19 0.24 0.30 0.29

TLP Model

TLP Configuration

Slide 17

ANALYSIS AND RESULTS – TLP PRODUCTION SYSTEM

TLP Key Figures

Draft m 31.09

Displacement N 7.05×108

Total Weight kg 2.70×107

Column Height m 57.91

Column Diameter m 22.86

Column c/c Span m 67.06

Pontoon Width m 11.43

Pontoon Height m 9.00




Roll Radii of Gyration Ryy m 41.39


TLP Tendon Properties

Tendon

Properties

Diameter

(m)

EA

(KN)

EI

(KN·m^2)

Wet Weight

(Kg/m)

Dry Wight

(Kg/m)

Length

(m)Material

Segment 1 0.711 2.30×107

1.24×106

586.01 993.27 6.71 X75

Segment 2 1.07 2.26×107

3.02×106

61.17 977.51 294.44 X70

Segment 3 1.07 2.28×107

3.04×106

68.04 984.38 236.52 X70

Segment 4 0.914 2.10×107

2.02×106

232.37 905.6 371.86 X70

Segment 5 0.914 2.21×107

2.12×106

281.33 954.56 274.32 X70



Example – TLP Production System

Slide 18

ANALYSIS AND RESULTS – TLP PRODUCTION SYSTEM

0 2000 4000 6000 8000 10000-120

-80

-40

0

40

TLP Surge Motion

Off

se

t (m

)

Time (s)

With Internal Wave


0 2000 4000 6000 8000 10000-6

-4

-2

0

2

4TLP Heave Motion

Off

set

(m)

Time (s)

With Internal Wave


0 2000 4000 6000 8000 10000-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

With Internal Wave


TLP Pitch Motion

An

gle

(d

eg

)

Time (s)0 2000 4000 6000 8000 10000

0

4000

8000

12000

16000

20000

With Internal Wave


Tendon Top Tension

Te

ns

ion

(K

N)

Time (s)

TLP Motion Statistics

Condition Operation

Survival

Wave Dominant

Wind Dominant


Offset

MAX m -18.60 -18.81 -18.84 -48.04 -52.14

MIN m -34.39 -78.27 -111.44 -82.00 -82.64

MEAN m -26.36 -29.39 -30.31 -63.17 -65.66

Heave

MAX m -0.08 -0.09 -0.08 -0.53 0.79

MIN m -0.50 -2.42 -4.90 -2.57 -2.62

MEAN m -0.27 -0.37 -0.44 -1.51 -1.65

Pitch

MAX deg 0.12 0.12 0.10 0.20 0.19

MIN deg -0.13 -0.13 -0.14 -0.29 -0.28

MEAN deg -0.01 -0.02 -0.02 -0.03 -0.03

TLP Tendon #10 Max Tension and Utilization Ratio

Condition Operation

Survival

Wave Dominant

Wind Dominant



Utilization Ratio - 0.49 0.55 0.68 0.91 0.85

Spar Model

Spar Configuration

Slide 19

ANALYSIS AND RESULTS – SPAR PRODUCTION SYSTEM Previously published in OSE 2016, shown for

comparison

Spar Key Figures

Draft m 164.59

Displacement (including entrapped water) N 8.69×108

Total Weight (including entrapped water) N 7.73×108

Hard Tank Diameter m 37.19

Hard Tank Height above MWL m 16.76

Hard Tank Height below MWL m 63.09

Center Well Dimension m 10.97×10.97

Main Truss Member Length m 97.49

Heave Plate Dimension m 37.19×37.19

Heave Plate Height m 1.0

Number of Heave Plates - 3

Soft Tank Dimension m 37.19×37.19

Soft Tank Height m 6.1




Roll Radii of Gyration Ryy m 77.27




Example – Spar Production System

Slide 20

ANALYSIS AND RESULTS – SPAR PRODUCTION SYSTEM

0 2000 4000 6000 8000 10000-40

-30

-20

-10

0

10

20SPAR Surge Motion

Off

se

t (m

)

Time (s)

With Internal Wave


0 2000 4000 6000 8000 10000-1.5

-1.0

-0.5

0.0

0.5

1.0

With Internal Wave


SPAR Heave Motion

Off

se

t (m

)

Time (s)

0 2000 4000 6000 8000 10000-8

-6

-4

-2

0

2

4

6

With Internal Wave


SPAR Pitch Motion

An

gle

(d

eg

)

Time (s)

Spar Motion Statistics

Condition Operation

Survival

Wave

Dominant Wind Dominant


Offset

MAX m -2.42 -2.48 -1.77 -5.59 -7.11

MIN m -9.13 -21.29 -39.05 -29.32 -29.69

MEAN m -5.38 -6.17 -6.56 -15.33 -16.36

Heave

MAX m 0.03 0.03 0.01 1.88 1.46

MIN m -0.23 -0.51 -1.18 -2.23 -1.90

MEAN m -0.11 -0.12 -0.14 -0.21 -0.23

Pitch

MAX deg 0.63 2.24 4.38 1.04 0.91

MIN deg -2.46 -2.46 -2.20 -6.86 -6.92

MEAN deg 0.36 -0.73 -0.65 -2.48 -2.68

Spar Mooring Line #5 Max Tension and Utilization Ratio

Condition Operation Survival

Wave Dominant Wind Dominant



Utilization Ratio (Max

Tension/Min Breaking

Tension)

- 0.28 0.45 0.71 0.53 0.53

SUMMARY AND CONCLUSION

• Dnoidal model implemented within coupled

analysis framework

• Due to long period nature of IW can be

superimposed on wind and wave analysis

• Provides relatively realistic representation of

internal waves including temporal effects

associated with solitary wave trains

• Can be used in a real time monitoring

framework to gage the wave forces on the

platform.

• Impact on Semi • Mainly impacts offset and pitch motions

• Does not control if designed for 100 yr survival

• Impact on TLP • Large platform offset compared to survival event

• Internal wave could be controlling case if

amplitudes are high enough

• Impact on Spar • Significant impact on heave, pitch and offset

• Internal wave case could be highly critical and

should be analyzed

• Future Work • Comparison with other IW models

• Effect of relaxing assumptions

• Effect of nonlinearity

Slide 21


Acknowledgements / Thank You / Questions

Slide 22

Name Company

James Pappas (President) RPSEA

Bill Head (Technical Coordinator) RPSEA

Gary Covatch (Project Manager) NETL

Anil Sablok (Project Champion) Technip

Bonjun Koo Technip

Xiaoqing Teng Hess

Peimin Cao SBM Offshore

Robert Fredericks Houston Offshore Engineering

Heonyong Kang Texas A&M University

HaKun Jang Texas A&M University

RPSEA / NETL Team

Working Project Group

Other Project Participants

Documents

OTC-27028 Numerical Modeling of Internal Waves-Rev0...2016/06/15 · OTC-27028 Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems Nishu V. Kurup,