2 Theory Related to Subsea Lifting Operations
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Transcript of 2 Theory Related to Subsea Lifting Operations
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1MARINTEK
Subsea lifting operationsStavanger November 27-28 2007
Peter Chr. SandvikMARINTEK
Theory related to subsea lifting operations
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Content
Introduction, main critera for safe liftingLifting dynamics, simple equation of motion
Static and dynamic forces, wave forces on small objects Mass, stiffness and dampingResponse (motion) calculation, resonance
Large structures, 6 degrees of freedomWave forces on long structures (e.g. pipes)RAO calculation for ships, inherent limitations
Snatch and impact loadsStability
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The installation often gives the highest life-time forces on subsea equipment (1)
General
Templates, trawl protection
Suction anchor
Snatch at lift-off or after slackImpact after uncontrolled pendulous motionLocal loads from wave impact
Wave forces in the splash zone
Wave forces in the splash zoneSoil penetration forces
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The installation often gives the highest life-time forces on subsea equipment (2)
Jackups
ROV
Tools (ROT)
Spool pieces
Side forces at landing on seabed structure or the sea bed
Impact during launch and recoveryImpact at entry into the TMS
Landing impact
Forces during lift in airWave forces at /near the surface
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The installation often gives the highest life-time forces on subsea equipment (3)
Steel pipe
Cables
Flexible pipes
Bending stresses over stinger or at the sea bed, and during tie-in
"Kink" at pay-out after landing (due to rotation)
Curvature just above the sea bed
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Lift in general
Is the structure designed for the loads occurring during lifting and deployment?
Hydrodynamic forces
Limited lifting height may give large compressive forces from the slings
Measures:
Lifting frame
Spreader beam
Reinforcement(compression bar)
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Operation criterion:Ensure safe operation
Avoid:Excessive pendulum motion in air
Slack wire (when not intended)
Overload (in any lifting equipment)
Too hard landing
Do:Ensure acceptable stability
Have ability to handle unexpected changes
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Simple equation of motion
)()()()( tFxkxcxM =++ ωωω &&&
)()()()( 0 txkxkxcxM =++ ωωω &&&
Force excitation
Motion excitationF(t)
x0(t)
Force excitation Motion excitation
x
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Forces on the lifted object (Newtons, or kN)
Static forcesWeight (in air)BuoyancySubmerged weight
Dynamic forcesDampingInertia, moving objectInertia, wave force
Slamming force
cs = slamming coefficientx = body motionζ = wave particle motion
rrrd vvBvBF 21 +=
( ) ( ) xcVmxmmF aa &&&& ρ+=+=
( ) ( )ζρζρ &&&&aa cVmVF +=+= 1
2221
ra
rss vdhdcVvAcF ρρ ==
W = mgB = ρgVWs = mg - ρgV
Uncertaintyduring launchand recovery
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H-frame being taken on boardDrainage
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Wreck recovery
Unknown weight,weight distributionand stability
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Wave forces in the splash zoneExample: Template (1- 2)
1
218 x 18 x 7 m, 180 tonnes
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Wave forces in the splash zoneExample: Template (3- 8)
Large dynamic forces (± 150 T)
3 4 5
6 7 8
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Wire tension when lowering a body throughthe splash zoneExample
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
0 500 1000 1500 2000 2500
Tension (kN)
Vert
ical
pos
ition
(m)
} Splash zone dynamics
Reducing
Weight in airWeight in water
!
!
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Wave kinematics (1)
Profile of regular waves propagating in x direction
Wave number (deep water)
Wave length
Propagation speed
Max. wave slope
kx)t( = −ωζζ sin0
gk
22 ωλπ==
256.12 Tk
==πλ
TT
vw 56.1==λ
0max
ζζ kdxd
=⎭⎬⎫
⎩⎨⎧
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Wave kinematics (2)
Wave particle velocity and acceleration
( ) ( )( ) ( )xktexkte
xktexktezk
zzk
x
zkz
zkx
−−=−=−=−=ωζωζωζωζ
ωζωζωζωζsincos
cossin0
20
200
&&&&
&&
Reduction factor with depth⎟⎠⎞
⎜⎝⎛
== λπ z
kz eeR2
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Wave kinematicsReduction with depth
Reduction of wave kinematics with depth
-100-90-80-70-60-50-40-30-20-10
0
0 0.2 0.4 0.6 0.8 1Depth reduction
Z (m
)
T = 4sT = 6sT = 10sT = 14sT = 20s
⎟⎠⎞
⎜⎝⎛
== λπ z
kz eeR2
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Wave kinematics in the VMO-rules
Parameter General expression(deep water)
Expression (VMO) Based on λ / Hs = 20
Extreme wave amplitude (m)
~Hs Hs
Wave particle velocity (m/s)Wave particle acceleration (m/s2)
3.1
Wave number (1/m)
Reduction with depth (-)
Hs⋅1.3
0.32 / Hs
ω2*Hs
k = ω2/g
)exp( kd− )/32.0exp( Hsd−
ω*Hs = 2π/T*Hs
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Wave force on a long member(heave force and pitch moment)
Wave force on an element dx
Total force, wave in worst position
dxcAf a ζωρ 2)1( +=
lengthwaveLLF
F == λλπ
πλ sin
0
02
0 )1( ζωρ acLAF +=
Harmonic wave:amplitude ζ
frequency ω
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3L / Wavelength
F / F
0,
M /
F0 L
ForceMoment
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Shielding-effect from the crane vesselExample of analysis results
1500
1750
2000
2250
2500
2750
3000
6 7 8 9 10 11 12Tp (s)
Max
liftw
ire fo
rce
(kN
)
Wavedir. 180 deg.Wavedir. 165 deg.Wavedir. 150 deg.
x
y21
3
45
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The mass: Structure mass (in kg or tonnes)
⎥⎦
⎤⎢⎣
⎡=
Im
M0
0
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
mm
m
000000
m
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
II-I-
I-II-
I-I-I
= Iczz
cyz
cxz
cyz
cyy
cxy
cxz
cxy
cxx
c
Coupling terms = 0if symmetry
and origo in COG
Coupling terms = 0if origo in COG
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Hydrodynamic (added) mass, ma6 values - (for motion in 3 directions and rotation about 3 axis)
Plate
BoxSuction anchor
Added mass coefficient: Ca = ma / ρVρ = water density
V = reference volume
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Added mass - simple structures - 1
ca Vm ρα=
b4aV
2c
π=
a
b
Cylinder volume:
Geometry Formula b/a α
1.0 0.5791.2 0.6301.25 0.6421.33 0.6601.5 0.6912.0 0.7572.5 0.8013.0 0.8304.0 0.8715.0 0.8978.0 0.93410.0 0.947
Rectan-gular
a = shortest edge
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Geometry Formula b/a α β0 - 1.00
0.1 5.139 1.130.3 2.016 1.33
0.50 1.310 1.440.75 0.916 1.511.00 0.705 1.551.25 0.575 1.581.60 0.458 1.612.00 0.373 1.642.40 0.316 1.672.80 0.274 1.693.60 0.217 1.72
Rectangular block with rectangular base
α and Vc from rectangular plate, (1), Table 1
β from (1), this table
Rectangularblock withquadraticbase
a = base edge
Added mass - simple structures - 2
p
aVVm
ρβρα
==
4a579.0V
3p
π⋅=
ca Vm ρβα=
b4aV
2c
π=
aa
b
V = a2 b
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Added mass - simple structures - 3
p
saVVm
ρβρα
==
6a637.0V
a6
V
3p
3s
π
π
⋅=
=
ca Vm ρα=
b4aV
2c
π=
a
b
a
b
Geometry Formula b/a α β
0.8 to2,4 1.0 π/2 =
1.57
Same as for rectangular plate
Circular cylinder
Exclusive water inside the object.
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Added mass of ventilated structures
Added mass
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2
z(1-p)/(2Dp^2)
a/a0 Hatch 20, p=0.15
Hatch 18, p=0.25Roof #1, p=0.267Roof #2, p=0.47Roof #3, p=0.375
p = perforation ratio = open area / total area
Example
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Hydrodynamic mass for suction anchorsNumerical assessment compared to test results
D
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 10 100 1000 10000
Amplitude / D * (1-p)/p^2
a / a
0
Calculated p=1%Measured p=1%Calculated p=3%Measured p=3%Calculated p=11%Measured p=11%
p = perforation ratio
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StiffnessGeneral
Axial wire stiffnessE = modulus of elasticityA = section areaL = length
Transverse stiffness
Hydrostatic stiffness
Rotation stiffness(spring k, distance a from
rotation center)Parallel springs
Springs in series
dxFkx∂
=
∑∑ =∆
= ii
tot kF
k
∑∑ ⎟⎟⎠
⎞⎜⎜⎝
⎛=⇒⎟⎟
⎠
⎞⎜⎜⎝
⎛==∆
itotitot kkkF
kF 11
LEAk =
LFF
kL
FFy
yy
yy =
∆=⇒
∆⋅=
WPAgk ρ=
2akK ⋅=
[Compression: k = 0]
[AWP = waterplane area]
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Guidewires - transverse force and stiffness
h
XFx
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Damping
Coulomb dampingFriction, hysteresis loss, ....
Linear dampingWave potential damping, material damping, oscillation damping in wind, ....
Quadratic damping
Hydrodynamic dragMorison's formulaNotice:cd for oscillating objects is larger
than cd for steady flow !
vvcF ⋅= 00
vcF ⋅= 11
vvcF ⋅= 22
rrdd vvAcF ρ21=
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Hydrodynamic damping of oscillations
The damping, expressed by the quadratic Morison formula, will have amplitude-dependent drag coefficientExample: cube
0.5
1
1.5
2
2.5
0 5 10 15 20
KC = 2 pi X / D
Dra
g co
effic
ient
, Cd
Only possible to calculate damping in harmonic oscillation
Solution:Adding a linear dragterm makes it possible to use constant coefficients
Cd for oscillating objects larger than in steady flow(factor ~2)
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Oscillation damping in wind
( )( )22
21
221
2 xvxvAcxvAcF
wwda
wdaw
&&
&
++=
+=
ρρ
Constant wind forceLinear wind damping
(Small)
x = body oscillation (inline with wind)vw = wind speed
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Damping linearization
Objective : To calculate dynamic behaviour by use of linear equations of motion. Method: Find linear damping that dissipates the same energy as the non-linear damping during one motion cycle
Linearized friction:
Linearized drag:
Total linearized damping:
0
00 x
c 4 = c*1 ωπ
c x 38 = c*
1 22 ωπ
vcccF e )( 1*12
*101 ++=
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Response of simple oscillating system
mc
mk2c =
kmT
mk
T =
4 + - 1
1 = F
k X = )H(
0
2
0
2
0
2 20
0
00
2
22
ωη
ππω
ηωω
ωω
ω
=
==
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
F(t)=x k + x c + x &&&m
ηωω 21
00
==X
XResponse at resonance:
F
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Response curve (RAO) of simple oscillating system
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Resonance periods - examples
Vertical oscillation in air:
∆≈∆=
∆
== 22220 gmgm
EAmLT πππ
∆ = elongation of wire due to weight mg
Vertical oscillation in water (long wire, wire mass mwincluded):
( )L
EAmam
T w31
330 2
++= π
LLgmg
mLF
mLT 22220 ≈===πππ
Pendulum oscillation in air:
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Snatch loads in the liftwire
MkVFF relstatic+=max
The snatch load is highest for:- Short lift wire (high stiffness)- Large hydrodynamic mass- Large relative velocity between
crane and load at snatch instant
The probably largest relative velocity at snatching should be used
Impact between objects or at landing can be assessed similarly.
k = wire stiffnessM = mass (incl. added mass)Vrel = relative velocity
Assumed:Short duration of impulsive load compared to motionperiod.
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Snatch-load: Lift-off from the sea bed
Assume a winch that can shift from constant tensionmode to lift mode when the crane passes its lowerpoint (i.e. when the winch stops taking in wire).
The lower end tension (F0) is below the object weight (W) at shift to lifting mode.
The lifting starts (the load moves) when F0 reaches W
The peak snatch load is reduced by selecting F0 closelybelow W
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Snatch load at lift-off from sea bedExample: Favourable lift-off time
1.00
1.251.50
1.75
2.00
2.252.50
2.75
3.00
100 200 300 400 500Water depth (m)
Fmax
/ W F0 / W = 0
F0 / W = 1 VMO formula
Module mass 12.6 tTotal dyn. mass 15.6 tSubmerged weight 107 kNWire diameter 38 mmCrane amplitude2.5 m
period 8.8 sspeed 1.8 m/s
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Calculation of RAO data for a ship
) F(=x k + x ))c(( + x ))(( 1 ωωω &&& ++ cmm a
6 coupled, linear equations of motion
Wave forces(only)
Frequency dependent added mass and damping
Mass matrix
Stiffness(heave, roll and pitch only)
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Frequency domain vs. time domain analysis ofcrane operations
Equations of motion can be solved directly if all coefficients areconstant (or function of frequency only)
However:Water entry/exit, slamming: M, c, k and F position dependentImpact, slack/snatch, winch operation: k variesDamping: quadratic drag, contact frictionNumerical analysis by time stepping is required (typical model):
Time domain analysis:Calculate and add all forces at t=tiEstimate accelerationIntegrate to find velocity and position at next time step, t=ti+dt
) F(=x k + x ))c(( + x ))(( 1 ωωω &&& ++ cmm a
(t)F + (t)F + (t)F = x k + |x|xB + xBxxB +
t)x(M
exlinesenvrr2r &&&&
&&10 +
∂∂
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Assume:Centre of buoyancy, CB, off centre of gravity, CG. The force centre, CF,
will be vertically below the hookheel angle
If center of vertical added mass is not inline with F:vertical excitation tilting oscillations
Lifting at points below CG should be analysed with care
Stability, tilt angle and angular oscillations
B
CF CG CB
F = mg-B
mg
BmgCGmgCBBCF
−⋅−⋅
=
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Underwater lifting operation(Not intended)
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Safe Job Analysis
Can anything go wrong ?
Shhh, Zog! ....Here come one now!