OTC-27028 Numerical Modeling of Internal Waves-Rev0...2016/06/15 · OTC-27028 Numerical Modeling...
Transcript of OTC-27028 Numerical Modeling of Internal Waves-Rev0...2016/06/15 · OTC-27028 Numerical Modeling...
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
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
WORLDWIDE DISTRIBUTION OF INTERNAL WAVES
Slide 4
© Atlas of Oceanic Internal Solitary Waves
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
INTERNAL WAVE ANALYTICAL FORMULATION
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.
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
Internal Wave Analytical Formulation
• 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
INTERNAL WAVE ANALYTICAL FORMULATION
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
Internal Wave Analytical Formulation Slide 9
INTERNAL WAVE MODEL
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
-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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
Without Internal Wave
0 2000 4000 6000 8000 10000-6
-4
-2
0
2
4
With Internal Wave
Without 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
Without 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
Internal Wave Height N/A 90m 170m N/A N/A
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
Vertical C.G. from Base KG m 45.11
Vertical C.B. from Base KB m 12.53
Pitch Radii of Gyration Rxx m 41.58
Roll Radii of Gyration Ryy m 41.39
Yaw Radii of Gyration Rzz m 42.09
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
Without Internal Wave
0 2000 4000 6000 8000 10000-6
-4
-2
0
2
4TLP Heave Motion
Off
set
(m)
Time (s)
With Internal Wave
Without 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
Without 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
Without Internal Wave
Tendon Top Tension
Te
ns
ion
(K
N)
Time (s)
TLP Motion Statistics
Condition Operation
Survival
Wave Dominant
Wind Dominant
Internal Wave Height N/A 90m 170m N/A N/A
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
Internal Wave Height N/A 90m 170m N/A N/A
Line Max Tension KN 1.35E+04 1.51E+04 1.89E+04 2.51E+04 2.35E+04
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
Vertical C.G. from Base KG m 98.66
Vertical C.B. from Base KB m 109.0
Pitch Radii of Gyration Rxx m 77.12
Roll Radii of Gyration Ryy m 77.27
Yaw Radii of Gyration Rzz m 14.63
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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
Without Internal Wave
0 2000 4000 6000 8000 10000-1.5
-1.0
-0.5
0.0
0.5
1.0
With Internal Wave
Without 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
Without Internal Wave
SPAR Pitch Motion
An
gle
(d
eg
)
Time (s)
Spar Motion Statistics
Condition Operation
Survival
Wave
Dominant Wind Dominant
Internal Wave Height N/A 90m 170m N/A N/A
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
Internal Wave Height N/A 90m 170m N/A N/A
Line Max Tension KN 4.00E+03 6.37E+03 1.01E+04 7.51E+03 7.52E+03
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
OTC-27028 • Numerical Modeling of Internal Waves and their Influence on Deepwater Floating Systems • Nishu Kurup
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