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ICSE-6 2012, Paris
Subsea Pipeline Stability Design
Development of a Novel 2D Pipe-Soil-Fluid Interaction Model
Terry J. Griffiths, Mengmeng XU, Wenwen SHEN, Marvin RAMSAWMY, Amar SHAH
J P Kenny
Perth, Australia
ICSE-6 2012, Paris
ICSE-6 2012, Paris
Background – status quo
With… present code and design models:
• ‘Coulomb’ friction pipe-soil model:
– Ignores passive resistance
– Ignores fluid effects on soil
• Verley passive resistance pipe-soil model:
– Ignores fluid effects
– e.g. scour
– e.g. piping
– e.g. liquefaction
Fx
x
Fx = m.Rz
Fx
x
Fx = m.Rz
ICSE-6 2012, Paris
Background – the problem
Stable pipelines on a mobile seabed?
• Sand unstable
• Pipe embeds
• Pipe stable
The problem?
“…it must follow that the seabed must become grossly unstable long before the
extreme design conditions. The traditional model is irrelevant: it makes no sense
to consider the stability of a stationary pipeline on a stationary seabed…”
A. Palmer (1996)
(Image courtesy Li & Cheng 2001)
ICSE-6 2012, Paris
We need a model which can bridge the gap between:
The (too simple) hysteresis friction models and
The (too expensive) continuum FEA / CFD models
JPK PSF Model
CO
MP
LE
XIT
Y
ACCURACY
?
Pipe-Soil-Fluid Interaction (PSF) Model
Fx
x
Fx =
m.Rz
ICSE-6 2012, Paris
Pipe-Soil-Fluid Interaction
• Pipe-Soil Interaction
– Vertical Reaction Force
– Soil Resistance
– Soil deformation due to pipe movement
• Pipe-Fluid Interaction
– Pipeline hydrodynamics
• Soil-Fluid Interaction
– Suspended sediment transport
What is the PSF Model?
Pipe Fluid
Soil
PF
PS FS PSF
Pipe Fluid
Soil
Rigid Pipeline on Sea Floor
ICSE-6 2012, Paris
Seabed
• Set of nodes at user defined, symmetric spacing, either side of the pipe
• Node parameters:
– Seabed elevation
– Suspended sediment concentration
Pipe
• Set of nodes (up/dn) with the same spacing as the seabed nodes
The PSF Model – Pipe/Soil P F
S
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-3 -2 -1 0 1 2 3
Sbed
upPnod
dnPnod
ICSE-6 2012, Paris
• RULE 1: Conservation of soil
• RULE 2: Soil can’t exist inside pipe
The PSF Model – Pipe/Soil Step 2 Update soil profile to account for pipe motion
P F
S
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-1.5 -1 -0.5 0 0.5 1 1.5
Ve
rtic
al P
osi
tio
n /
Pip
e D
iam
Lateral Position / Pipe Diam
Old Pipe Position
New Pipe Upper Nodes
New Pipe Lower Nodes
Old Seabed
Seabed Post Sweep
Swept area
ICSE-6 2012, Paris
• RULE 3: Soil cannot exceed its internal angle of repose
– “Slumps” down until the soil complies with this requirement
– Conservation of soil volume
The PSF Model – Pipe/Soil Step 3 Account for slope failure (Slumping)
P F
S
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1.5 -1 -0.5 0 0.5 1 1.5
Ve
rtic
al P
osi
tio
n /
Pip
e D
iam
Lateral Position / Pipe Diam
Old Pipe Position
New Pipe Position
Plough Seabed
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Ve
rtic
al P
osi
tio
n /
Pip
e D
iam
Lateral Position / Pipe Diam
Old Pipe Position
New Pipe Position
Plough Seabed
Slumped Seabed
ICSE-6 2012, Paris
Algorithmic model
• Representation of seabed shear stress as local velocity
• Parametric based on CFD results
PSF Model: Sediment Transport P F
S
ICSE-6 2012, Paris
CFD by UWA CEED Students (Mengmeng Xu, Wenwen Shen)
• Parametric
• 2D initially
• Over 100 cases
– Geometries
– Wave and Currents
PSF Model: Sediment Transport P F
S
ICSE-6 2012, Paris
Study scaling factors
• Vary steady current Uc (up to 1.5m/s)
• Vary pipe diam. D (0.2m to 1.2m)
• Unscaled
results:
PSF Model: Sediment Transport P F
S
-1.5
-1
-0.5
0
0.5
1
1.5
2
-40 -30 -20 -10 0 10 20 30 40
Loca
l Ve
loci
ty (m
/s)
Lateral Position (m)
1
2
3
79
81
83
85
ICSE-6 2012, Paris
Study scaling factors
• Vary steady current Uc & Pipe Diam D (pipe on-bottom)
• Scale results by:
– Uc
– D
PSF Model: Sediment Transport P F
S
-1.5
-1
-0.5
0
0.5
1
1.5
-10 -5 0 5 10 15 20
Loca
l Ve
loci
ty /
Re
fere
nce
Ve
loci
ty
Lateral Position / Pipe Diam
1
2
3
79
81
83
85
ICSE-6 2012, Paris
Model Algorithm Equation:
• Vary Uw, T, D
• Scaled results:
PSF Model: Sediment Transport P F
S
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Soil
Pipe x
Case = 2
-1.5
-1
-0.5
0
0.5
1
1.5
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Compare at a given time
CaseCFD
CaseERR
TOTerr
CaseMOD
Pipe On-Bottom
ICSE-6 2012, Paris
• RED pipe =
– PSF Model but with Sediment Transport switched off
– Equivalent to & calibrated against Verley Model
• GREEN pipe =
– PSF model, with Sed. Trans. (looks more like reality?)
PSF Model: Random Wave Series P F
S
ICSE-6 2012, Paris
Thank you
Acknowledgements
Any Questions?
ICSE-6 2012, Paris
• The pipe acts as the moving reference frame for the soil nodes
• Soil nodes shift with the pipe in the horizontal axis
• Allows for a fine node mesh under the pipe and a coarse mesh for the
seabed extremities
The PSF Model – Pipe/Soil Step 1 Interpolate new profile from old profile
P F
S
ICSE-6 2012, Paris
Options:
• Iteratively find equilibrium pipe position at each timestep
• Fix horizontal, vertical or both axes for prescribed displacement
Pipe-Soil-Fluid Interaction Model Flowchart
No
Calculate new pipe based on:
• Hydrodynamic loads
• Soil reaction loads
• Accounting for embedment, trench
profile, and pipe velocity
Wave /
current
velocity
timeseries
Previous time
step / Initial
Condition
Estimate new pipe
acceleration,
velocity and
position based on
loads
Interpolate
new soil
profile from
old profile
Update new
soil profile to
account for
pipe motion
(sweep, suck, slump)
Update
new soil
profile to
account for
scour
Converged? Next time step
Yes
ICSE-6 2012, Paris
Soil Reaction Forces:
• Vertical force based on RP-F109
• Embedment vs penetration
• Contact angle
The PSF Model – Pipe/Soil P F
S
Em
be
dm
en
t (u
se
d in
PS
F)
Pe
ne
tra
tion
(u
se
d in
Ve
rle
y, F
10
9)
Contact angle (L&R)
ICSE-6 2012, Paris
Pipe-Soil Reaction Forces: Benchmark Against Published Model
• Pz vs Py graph
• Imposed lateral displacement
• Compare to Verley (Brennodden et al 1989)
The PSF Model – Pipe/Soil P F
S
-0.15
-0.13
-0.11
-0.09
-0.07
-0.05
-0.03
-0.01
0.01
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
Pz vs Py (4 cycles)
NewPz
ICSE-6 2012, Paris
Flow Flow separation
High
pressure
Low
pressure
A typical scour process below a pipeline (Cheng et al.2009)
Water particles
PSF Model: Scour Mechanisms P F
S
• Onset of piping based on F109
• (drag force approximate to dp across soil)
(Diagram courtesy Shen 2011)
ICSE-6 2012, Paris
Study scaling factors
• Vary Zp & Zs
• Unscaled results:
(a.Zp^2+b.Zp+c).(d.Zs^2+e.Zs+f)
PSF Model: Sediment Transport P F
S
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-10 -5 0 5 10 15 20
0h 2
28 29
30 35
37 38
39 48
50 51
75 87
89 91
93 95
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-2 -1.5 -1 -0.5 0
Zso
il (m
)
Zpipe (m)
Zsoil (m)
ICSE-6 2012, Paris
Study scaling factors
• Vary Uw, T, D
• Unscaled results:
PSF Model: Sediment Transport P F
S
-2
-1
0
1
2
3
-10 -5 0 5 10
Unscaled axes 994586678097988284
ICSE-6 2012, Paris
Study scaling factors
• Vary Uw, T, D
• Scaled results:
PSF Model: Sediment Transport P F
S
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-1 -0.5 0 0.5 1
x axis scaled by D*KC, y axis scaled by Uw.(g.T^2/L)^0.59945866780979882
ICSE-6 2012, Paris
Model Algorithm Equation:
• Vary Uw, T, D
• Scaled results:
PSF Model: Sediment Transport P F
S
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Soil
Pipe x
Case = 35
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Compare at a given time
CaseCFD
CaseERR
TOTerr
CaseMOD
0.25D Trench
ICSE-6 2012, Paris
Model Algorithm Equation:
• Vary Uw, T, D
• Scaled results:
PSF Model: Sediment Transport P F
S
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Soil
Pipe x
Case = 48
-1.5
-1
-0.5
0
0.5
1
1.5
2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Compare at a given time
CaseCFD
CaseERR
TOTerr
CaseMOD
0.5D Trench
ICSE-6 2012, Paris
• WAVE CASE
PSF Model: Sediment Transport P F
S
Series1
Series14
Series27
Series40
Series53
Series66
Series79
Series92
-2.6-2.4-2.2-2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40.60.811.21.41.61.822.22.42.6
1 14
27
40
53
66
79
92
10
5
11
8
13
1
14
4
15
7
17
0
18
3
19
6
20
9
22
2
23
5
24
8
26
1
27
4
28
7
30
0
31
3
32
6
33
9
35
2
36
5
37
8
39
1
40
4
41
7
43
0
44
3
45
6
46
9
48
2
49
5
CaseCFD (m/s)
Series1
Series13
Series25
Series37
Series49
Series61
Series73
Series85
Series97
-2.8-2.6-2.4-2.2-2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40.60.811.21.41.61.822.22.42.62.8
1 12
23
34
45
56
67
78
89
10
0
11
1
12
2
13
3
14
4
15
5
16
6
17
7
18
8
19
9
21
0
22
1
23
2
24
3
25
4
26
5
27
6
28
7
29
8
30
9
32
0
33
1
34
2
35
3
36
4
37
5
38
6
39
7
40
8
41
9
43
0
44
1
45
2
46
3
47
4
48
5
49
6
CaseMOD (m/s)
Upstream Downstream
Wave P
hase
ICSE-6 2012, Paris
Model Algorithm Equation:
• Parameter = F(Geom) * F(Flow)
• F(Geom) = (l*Zp^2 + m*Zp+ n) * (o*Zs^2 + p*Zs+ q) * (r*Lb^2 + s*Lb + t)
* (u*Zb^2 + v*Zb + w)
• F(Flow) = (a*Uc + b + (c*Uw +d) * (e + f*(g*T^2/L)^0.5) * (g*KC + h)
* (i*Alpha^2 + j*Alpha + k))
• Parameters are:
– WPASP Wave phase start
– CLM Phase length multiple
– LSP Position start
– LSW Position length
– Amp Amplitude
PSF Model: Sediment Transport P F
S
ICSE-6 2012, Paris
Pipe Hydrodynamic Forces:
• Near-bed velocity timeseries from JPK WaveForce
• Hydrodynamic force-time history from JPK WaveForce
(On-bottom stationary pipe)
• Force correction on-the-fly as per SIMULATOR
– Pipe horizontal velocity
– Shielding due to trench
– Shielding due to embedment
– Lift force reduction due to spanning
The PSF Model – Pipe/Fluid P F
S