Washington Monthly 2012 National
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UC San Diego
Texas A&M
Stanford
U North Carolina
UC Berkeley
UCLA
DEVELOP CONCEPT
Water depth, well-size, fixed or floating
State-of-art Review, Experience & Imagination
FEASIBILITY STUDY
Simple mathematical model, Initial cost analysis,
Select best concept
PRELIMINARY DESIGN
Design spiral, Optimization, Stability/Performance
Verification by model test
DETAILED DESIGN
Rules (ABS, DNV, Lloyd)
Safety requirement (MMS, CG)
Environmental regulations etc (EPA)
FABRICATION
Cost & Schedule
TOWING & INSTALLATION
OPERATION & MONITORING
ROV & AUV
mx  cx  kx  F (t )
Virtual mass=
Mass + Added Mass
Mooring lines
Buoyancy
Fluid drag (Frictional or Form)
Wave
Mechanical
Wind
Material
Current
Wave-making (radiation/potential)
Ice-berg - collision
Underwater explosion
System damping from Free-Decay Test:
FPSO example; 2πζ ≈ ln(x1/x2)
100
Full Load (w . risers)
80
Full Load (w /o risers)
60
OTRC (w . risers)
40
OTRC (w /o risers)
Surge [m]
20
0
-20
-40
-60
-80
-100
-120
0
200
400
600
800
1000
Time [sec]
1200
1400
1600
1800
Production Platform: 100-yr
Design Met-Ocean Condition
Drilling Platform: 10-yr
OLD GOM 10-YR & 100-YR STORM
Revised(Post-Rita) GOM Design Condition
Wind(m/s) Hs (m)
Current
m/s
39.9
13.1
2
West-1000 49.9
16.4
2.5
WesC100
38.1
12.3
1.9
WesC1000 47.6
15.4
2.4
Cent-100
48
15.8
2.4
Cent-1000 60
19.8
3
East-100
12.2
1.9
15.3
2.4
West-100
38.4
East-1000 48
North-Sea 100-yr storm
• Much harsher than Gulf of Mexico
• Hs can be as high as 19m (62ft) (close to GOM
central 1000-yr storm)
• Site Specific!
100-yr condition for North Sea
Wave: Hs = 14.5 m ~ 15.5m, Tp = 16sec ~ 17sec
(Torset Haugen Spectrum)
Wind ~ 40 m/sec (V10, 1hr)
Surface current: 2.0m/sec ~2.5 m/sec
ISO 19901-01, API RP2-MET
West Africa
• Storm condition much milder than GOM
• Swell (persistent) from constant direction is an
important design factor
• So, spread mooring can be applied instead of
weathervaning turret mooring
100-yr condition for West Africa
Main Swell : Hs = 4m ~ 5m, Tp = 14 ~ 15s
Secondary Swell: Hs =2m ~ 3m , Tp = 11 ~ 13s
Wind Sea(Wave): Hs = 2.0 ~ 2.5 m, Tp = 8 ~ 9 s
Wind: 12.0 m/sec ~ 13.0m/sec (V10, 1hr)
Surface current : 2.0 m/sec
ISO 19901-01, API RP2-MET
Arctic
• Ice-loading should be the dominant design
condition (Including Bohai Bay China)
Seasonal Loop Current in GOM
Storm-induced shear currents
Current Profile (1000-year)
0
-500
-500
-1000
-1000
Depth(ft)
Depth(ft)
Current Profile (100-year)
0
-1500
-1500
-2000
-2000
-2500
-2500
New
Old
-3000
0
5
Speed(ft/sec)
New
Old
10
-3000
0
5
Speed(ft/sec)
10
• Loop current= GOM seasonal large-scale
density-difference-induced current : penetrate
much deeper than storm- induced current
• Surface max ~ 2m/s
Long-term wave statistics: annual scatter diagram
North Sea
Met-ocean of Offshore Western Australia
WA extreme sea states vs. GoM extreme sea states
Survival condition: similar
WA wave scatter diagram vs. GoM wave scatter diagram
Operational condition: quite different in major wave period
Extreme Sea States, WA vs. GoM
Parameter
Significant wave height
Wave spectral peak period
Hourly wind at 10 m
Generic WA
Units 10,000 RP 1,000 RP 100 RP
m
22.5
20.5
16.8
sec
18.1
17.1
15.3
m/s
68.5
62.0
50.0
70
Hourly wind speed (m/s)
25
Sig. wave height (m)
Central GoM
10,000 RP 1,000 RP 100 RP
22.1
19.8
15.8
18.2
17.2
15.4
67.2
60.0
48.0
20
15
10
5
0
Generic WA
60
50
40
30
20
10
0
Generic WA
10,000 RP
10,000 RP
Central GoM
1,000 RP
100 RP
Central GoM
1,000 RP
100 RP
Wave Scatter Diagrams, WA vs. GoM
Generic WA wave
scatter diagram
Generic GoM wave
scatter diagram
Generic GoM wave
scatter diagram
WA
GoM
Wave Scatter Diagrams, WA vs. GoM
30%
Generic GoM
25%
Probability
Generic WA
20%
15%
10%
a
5%
0%
0
5
10
15
20
25
Wave Peak Period Tp (s)
Probability
40%
35%
Generic GoM
30%
Generic WA
25%
20%
15%
10%
b
5%
0%
0
2
4
6
Significant Wave Height Hs (m)
8
10
FLNG
FLNG Layout
Topside Processing Units: Motion Limitations
• Static heel angle : less than 1 deg.
• Dynamic roll/pitch : less than ±8 deg.
• 8 ~ 15s more critical

Mooring Codes and Standards
API RP 2SK => Mooring/Stationkeeping System Design
API RP 2SM => Synthetic Mooring System Design
API Spec 2A => Wire Rope Specifications
API Spec 2F => Mooring Chain Specifications
DNV POSMOOR => Hydrodynamic Coeff. Of Mooring Lines
API RP 2A => Driven Pile Design, Load and Resistance Factors
API RP 2T => Driven Pile Holding Capacities Safety Factors
AISC Manual of Steel Construction => Anchor Structural Design
Mooring Design Criteria
• Dynamic Requirements:
• Intact FOS ≥ 1.67
• Damaged FOS ≥ 1.25
• Maximum Offset Capabilities
• Intact ≤ 5% h
• Damaged ≤ 7% h
• Corrosion Tolerance
• Inside Splash Zone =
increase dia 0.25 in
• Remaining Line = 0.125 in
11-8-07
TAMU Ocean Engineering
28
Modeling Dynamic System
• Linear System (superposition)
(simpler & statistically powerful)
Vs
• Nonlinear System
Gaussian
Linear
Gaussian
Input
System
Output
Gaussian
Nonlinear
Non Gaussian
Input
System
Output
SI (System Identification)
By analyzing input-output relations, find system
characteristics or defects (NDT)
NDT(Non-Destructive Testing)
NDT: Use impulse hammer or ultra-sound/MRI
Health monitoring of structures
Smart Structure: sensors : detect abnormality of
signal
Time and frequency domain of waves
Wave
spectrum
Time domain.
Random elevation
Regular
wave components.
Random phases.
How do we generalize to short-crested sea?
How energy in a wave spectrum can be distributed to individual regular
wave components: η(t)=ΣAj cos(ωjt+ej)
15.0
Number of wave
components N
s    m 2 s 
  max  min  / N
H1/3=8m,T2=10s
Wave amplitude of wave
component j:
7.5
Aj  2s  j  
max
min
0.75
  rad s 1 
1.5
Nyquist Criterion: η(t)=ΣAj cos(ωjt+ej)
• Tmax=2π /Δ ω : repeated after this!
Solution: use irregular Δ ω or perturb central component frequency ωj
• Δt < π / ωmax
• Discrete spectrum to Continuous spectrum:
By using FFT, we get Aj. Then, S(ω) = Aj²/2Δω
Continuous Random Variables
Example: Record of ocean surface
W ave elevation time history
Response spectrum
5
6
Generated wave spectrum
Theoretical wave spectrum
4
5
3
Wave elevation (m2  sec)
Wave elevation (m)
2
1
0
-1
-2
-3
4
3
2
1
-4
-5
0
2000
4000
Time (sec)
6000
0
8000
0
0.5
1
1.5
2
 (rad/sec)
W ind s peed time his tory
Res pons e s pec trum
20
40
Generated wind s pec trum
Theoretic al winds pec trum
35
18
Wave elevation (m2  sec)
Wind Speed (m/s)
30
16
14
12
25
20
15
10
10
5
8
0
2000
4000
6000
Time (s ec )
8000
0
0
0.5
1
 (rad/s ec )
1.5
2
Surface & Wave-height Distribution
• Ocean Surface: zero-mean Gaussian (Central
limit theorem)
Distribution (symmetric)
• Wave Height: Rayleigh Distribution (H>0, nonsymmetric)
Assume: Gaussian + narrow banded
Short-term statistics
• Given significant wave height and mean/peak
wave period
• Assume long-crested sea
• A linear system allows us to add the response in
each regular wave component
Variance of the response

   s( ) H ( ) d 
2
2
0
Wave spectrum
Square of RAO (ratio between response
and incident wave amplitude
Haskind-Newman Relation: relation
bet. wave exciting force and radiation
damping
bii 
Fi
2
2 gC g A
2D sym
2
k
bii 
2
8gCg A
2
 F ( )
i
0
3D
2
d
2.3 AIR SPRING-MASS VIBRATION ABSORBER
(VAB)
Use this area for your image
Air Spring-Mass Vibration Absorber (VAB) within a TLP column (Courtesy of SBM
Atlantia Inc.)
A conventional TLP hull (under waterline) with VAB (Courtesy of SBM Atlantia Inc.)
TLP model test in OTRC wave basin (Courtesy of SBM Atlantia Inc.)
An artist's rendition of application in field (Courtesy of SBM Atlantia Inc.)
Spar concept & installation
• http://www.youtube.com/watch?v=DvBnlk4A
U-g
• http://www.youtube.com/watch?v=JpfJJ2mh8
yo&feature=related
• http://www.youtube.com/watch?v=YB_Gv6up
Zd0&feature=relmfu
BIEM after applying Green theorem:
Fredholm 2nd-kind Integral Eq.
G=lnr (2D): α = 0(outside), -π (on
body), -2π
G=1/r (3D): α = 0(outside), 2π (on
body), 4π
G (x; )
 ()
 (x)    ()
dS  
G (x; )dS
S
S n
n
Alternative Source Formulation
 (x)    ()G(x; )dS
S
G (x; )
 (x)
 (x)    ()
dS 
S
n
n
BEM: Source distribution method
1. Approximate the body surface by N segments
2. Assume source density constant over each element
3. Satisfy the BBC at the collocation (mid) points
Aij qj = Bi
Apply symmetry if possible!!
4. Solve the resulting matrix equation for source-strength or
velocity potential
5. Obtain pressure and hydrodynamic coefficients
NxN FULL MATRIX SOLVER
• Gauss Elimination: N³
• Iterative Method: N² x m
Boundary Element Method with zero speed: smaller panels
near the FS and corners
One quadrant
of a TLP.
Totally
12608 elements
Paneling of the hull surface
• Plane quadrilateral panels
• BC satisfied at the element center
• May have leaks at the edge
• Smaller elements for higher variation
Ex. Near the edge, free surface
• Mid-points are not to be very close to the
edges of another elements (induced
velocities singular at the edge)
• At least 8 elements per wavelength
When calculating velocities close to
body boundary
• Source formulation is preferred!
• In 2nd-order drift-force calculation by nearfield method, source formulation is preferred!
Irregular Frequencies
• Purely mathematical, nonphysical
• Eigenvalues for Inner Dirichlet (Ф=0)
problem with free surface
• Exist when kD > 1 (proved by Fritz John)
• How to remove?
• Multi-body: physical resonance peaks
• B-M Cylinder lowest IF
L=0.82D (surge), L=1.31D (heave)
• J0(kR)=0 : kR=2.4 ; L/D=0.82
• J1(kR)=0 : kR=3.83 ; L/D=0.82