directed studies-subsea pipelines
TRANSCRIPT
Subsea Pipelines
Prepared for Directed Studies CIVL 7006
Nikzad Nourpanah
Under supervision of: Dr. Farid Taheri
Winter 2008/2009
Subsea Pipelines Page 1
Scope
The scope of this document is to give a general introduction on the subject of subsea pipelines, with
reference to design codes as used by the industry. The document covers most important aspects of analysis
and design of subsea pipelines, but it should be noted that some less important topics are left out. Where
applicable, the theory and/or experimental data behind code provisions is discussed with reference to
available technical literature. The main topics are Mechanical design, on-bottom stability, free spanning and
installation of subsea pipelines.
Subsea Pipelines Page 2
Contents
1. Introduction 9
2. Material Grade Selection 11
3. Diameter Selection 12
4. Wall Thickness Selection 13
4.1. Internal Pressure Containment (Burst) 13
4.2. Collapse Due to External Pressure 19
4.3. Local Buckling Due to Bending and External Pressure 22
4.4. Buckle Propagation 27
5. On-Bottom Stability 35
5.1. Soil Friction Factor 37
5.2. Hydrodynamic Force Calculation 37
5.3. Hydrodynamic Coefficient Selection 39
5.4. Stability Criteria 44
6. Free Span (Bottom Roughness) Analysis 45
6.1. Static condition 47
6.2. VIV 50
7. Installation of Subsea Pipelines 63
7.1. J-lay 68
7.2. S-lay 72
7.3. Reel lay 73
7.4. Towed Pipelines 74
7.5. Shore Approach 75
7.6. Wet vs Dry Pipeline Installation 77
References 80
Subsea Pipelines Page 3
List of Figures
Figure 1 - US crude oil production trends (S. Chakrabarti, 2005) ................................................................9
Figure 2 - Number of ultra deepwater (>5000 ft) wells drilled in Gulf of Mexico (S. Chakrabarti, 2005) ...... 10
Figure 3 - Roles of pipelines in an offshore hydrocarbon field (Bai, 2000) ................................................. 10
Figure 4 - Free body diagram of a pipe section under internal and external pressure ................................ 13
Figure 5 – Burst pressure (Pb) according to API-RP-1111 (1999) using Equations 4 and 5 for X65 grade
steel, SY = 65 ksi, U = 77 ksi and E = 29’000 ksi .................................................................................... 15
Figure 6 – Pressure level relations (API-RP-1111, 1999) .......................................................................... 16
Figure 7 – Ductile burst sample (API-RP-1111, 1999) .............................................................................. 17
Figure 8 – Brittle burst sample (API-RP-1111, 1999) ............................................................................... 17
Figure 9 – Concept of effective axial force (Fyrileiv et al, 2005) ............................................................... 19
Figure 10 – Collapse pressures of 2900 specimen normalized with collapse pressures calculated by Equation
(15) (Murphey and Langner, 1985) ........................................................................................................ 21
Figure 11 - Collapse pressure vs. D/t per API 1111 (1999) and DNV OS-F101 (2000), (Nogueira &
Mckeehan, 2005) .................................................................................................................................. 21
Figure 12 – Mechanical behavior of pipe subjected to pure bending, (Murphey and Langner, 1985) ........... 23
Figure 13 – Moment vs. strain curves for constant diameter and yield stress but variable wall thickness
(Murphey and Langner, 1985) ............................................................................................................... 23
Figure 14 – Pipe bending tests in air – curvatures at buckling (Murphey and Langner, 1985) ..................... 24
Figure 15 – Pipe collapse due to combined bending and external pressure; comparison of experimental
results with (18) for a perfectly circular pipe (Murphey and Langner, 1985) ............................................. 25
Figure 16 - Rational model prediction of collapse pressure vs. initial ovality, compared to experimental
results for pipe with D/t = 35 (Nogueira & Mckeehan, 2005) ................................................................... 26
Figure 17 - Pressure vs. bending strain predicted by rational model and experiments (Nogueira & Mckeehan,
2005) ................................................................................................................................................... 26
Figure 18 - Pressures vs. bending strain; comparison between empirical formulations of API, DNV and the
rational model (Nogueira & Mckeehan, 2005) ......................................................................................... 27
Figure 19 – Elastic, plastic, collapse and buckle propagation pressures for an X65 grade pipeline based on
API RP 1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi ............................................... 28
Figure 20 – Hoop stress associated with elastic, plastic and collapse pressure for an X65 grade pipeline
based on API-RP-1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi ................................. 28
Figure 21 – Grouted Sleeve arrestor (Langner, 1999) .............................................................................. 29
Figure 22 – Integral Ring arrestor, which also serves as J-Lay Collar, (Langner, 1999) .............................. 30
Figure 23 - Tested sample of a pipeline with Sleeve type buckle arrestors and the numerical model .......... 30
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Figure 24 – U mode buckling of a pipeline; the collapse wave passes through a sleeve type arrestor
(Kyriakides, 2005) ................................................................................................................................. 33
Figure 25 – Comparison of integral ring buckle arrestor design formula with available test data (Langner,
1999) ................................................................................................................................................... 34
Figure 26 - Regions of applicability of different wave theories (API RP 2A, 2000) ...................................... 36
Figure 27 – Relative importance of inertia, drag and diffraction wave forces (DNV-OS-J101, 2004) ............ 38
Figure 28 – Current profile due to tides and wind (DNV-CN-30.5, 1991) ................................................... 39
Figure 29 – CD as a function of Reynolds number and roughness for a cylinder in steady current (DNV-CN-
30.5, 1991) .......................................................................................................................................... 40
Figure 30 – Added mass coefficient Ca as a function of gap ratio H/D (DNV-CN-30.5, 1991) ...................... 40
Figure 31 – CD as a function of KC and roughness (DNV-CN-30.5, 1991) .................................................. 41
Figure 32 – Influence of seabed proximity on CD for current+wave situation (DNV-CN-30.5, 1991) ............ 41
Figure 33 – Hydrodynamic force coefficients CD, CM and CL for regular waves, effect of pipe roughness (a)
and seabed roughness (b) (Bryndum, 1992) ........................................................................................... 42
Figure 34 – Hydrodynamic coefficients versus current ratio for wave plus steady current (Bryndum, 1992) 43
Figure 35 – Free body diagram of pipeline for on-bottom stability analysis (Bai, 2000) .............................. 44
Figure 36 – Free spanning pipeline on seabed ........................................................................................ 45
Figure 37 – Continental shelf and continental slope................................................................................. 45
Figure 38 – Subsea pipelines, Ormen Lange field, Norway (Source: Internet) ........................................... 46
Figure 39 - Typical free span distributions and pipeline profile (Soreide, 2001) ......................................... 46
Figure 40 – Static stresses and deformations in a free spanning pipeline (Mousselli, 1981) ........................ 48
Figure 41 – Static stress and span for pipeline passing obstruction (Mousselli, 1981) ................................ 49
Figure 42 – Vortex shedding due to steady flow at different Reynolds numbers and fluctuating pressures on
pipe resulting in oscillating lift and drag forces (Blevins, 1977) ................................................................ 50
Figure 43 – Classification of free spans (DNV-RP-F105, 2006) ................................................................. 51
Figure 44 – CFD simulation of piggyback pipeline ................................................................................... 53
Figure 45 – Effective length vs. soil stiffness (DNV-RP-F105) ................................................................... 54
Figure 46 – Illustration of the in-line VIV Response Amplitude versus VR and KS (DNV-RP-F105, 2006) ....... 57
Figure 47 – Illustration of the cross-flow VIV Response Amplitude versus VR (DNV-RP-F105) ..................... 58
Figure 48 – Typical two-slope S-N curve (DNV-RP-F105, 2006) ................................................................ 59
Figure 49 – Schematic diagram of free span pipelines with additional local stiffness and damping (Fernes
and Bertsen, 2003) ............................................................................................................................... 61
Figure 50 - Motions due to a prescribed second mode inline deflection. (C) Time series of ry/D close to an
antinode. (D) Time series of rz/D close to an antinode. (Bottom panels) Countours of time evolution of ry/D
and rz/D. (Fernes and Berntsen, 2003) ................................................................................................... 62
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Figure 51 - Combined in-line and cross flow motion of a pipeline section (Fernes and Berntsen, 2003) ...... 62
Figure 52 – Schematic of S-lay method for pipelaying (Nogueira & Mckeehan, 2005) ................................ 63
Figure 53 – Schematic of J-lay method for pipelaying (Nogueira & Mckeehan, 2005) ................................ 64
Figure 54 – Taut mooring system .......................................................................................................... 65
Figure 55 – Catenary mooring system .................................................................................................... 65
Figure 56 – Combined station-keeping method for intermediate water depths (Langner, 1973) ................. 66
Figure 57 – Location of stress concentration in sleeve connection, Top: J-lay, Bottom: S-lay (Dixon et al.
2003) ................................................................................................................................................... 67
Figure 58 – Heerema's balder in J-lay mode (Nogueira & Mckeehan, 2005) .............................................. 69
Figure 59 – Dynamics of pipelines during laying: motion, dynamic stresses and tension for different wave
periods (Clauss et al. 1991) ................................................................................................................... 70
Figure 60 – A typical S-lay Vessel (Nogueira & Mckeehan, 2005) ............................................................. 72
Figure 61 – A reel vessel (Guo et al. 2005) ............................................................................................. 73
Figure 62 – Schematic of towed pipeline (Bai, 2000) ............................................................................... 74
Figure 63 – Float and sink method used for shore approach installation ................................................... 75
Figure 64 – Bottom pull method used for pipeline shore approach ........................................................... 75
Figure 65 - Bottom pull method; launching roller track ............................................................................ 75
Figure 66 – Directional drilling method for pipeline shore approach .......................................................... 76
Figure 67 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: wall thickness as a function of
depth (Palmer, 1998) ............................................................................................................................ 78
Figure 68 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: submerged weight in laying
condition as a function of depth (Palmer, 1998) ...................................................................................... 78
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List of Tables
Table 1 - Tensile strength properties (API 5L, 2000) ............................................................................... 11
Table 2 - Crude oil sizing guidance (Nogueira & Mckeehan, 2005) ........................................................... 12
Table 3 - Diameters for selected offshore projects (Nogueira & Mckeehan, 2005) ..................................... 12
Table 4 - Temperature de-rating factor, T, for steel pipe according to ASME B31.8 (Nogueira & Mckeehan,
2005) ................................................................................................................................................... 14
Table 5 – Return period for environmental phenomena ........................................................................... 35
Table 6 – Allowable pipeline stresses (Nogueira & Mckeehan, 2005) ........................................................ 47
Table 7 – Response Behavior of free span (DNV-RP-F105, 2006) ............................................................. 52
Table 8 – Different flow regimes (DNV-RP-F105, 2006) ........................................................................... 52
Table 9 – Boundary conditions coefficients (DNV-RP-F105, 2006) ............................................................ 55
Table 10 – Advantages and disadvantages of J-lay (Nogueira & Mckeehan, 2005) .................................... 68
Table 11 – Advantages and disadvantages of S-lay (Nogueira & Mckeehan, 2005) .................................... 72
Table 12 – Advantages and disadvantages of Reel-lay (Nogueira & Mckeehan, 2005) & (Guo et al. 2005) .. 73
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Nomenclature
A = Pipeline steel cross section
0A = Pipeline outer cross section
CFA = Stress amplitude due to a unit diameter cross-flow
mode shape deflection
iA = Pipeline inner cross section
ILA = Stress amplitude due to a unit diameter in-line
mode shape deflection
YA = In-line VIV amplitude
zA = Cross-flow VIV amplitude
61 ~ CC = Boundary condition coefficients
aC = Added mass coefficient
DC = Drag coefficient
1+= am CC = Inertia coefficient
LC = Lift Coefficient
CSF=Coating Stiffness Factor
d = Water depth
D = Pipeline nominal outside diameter
fatD = Accumulated fatigue damage
E = Modulus of elasticity
E = Longitudinal joint factor
0f = Collapse factor
1f = 1st eigen-frequency of free span in still water
df = Design factor
ef = Weld joint factor
nf = nth eigen-frequency of free span in still water
pf = Buckle propagation safety factor
tf = Temperature de-rating factor for steel
ivf , = vibration frequency of pipeline due to “i”th sea
state
wf = Wave frequency
F = Construction design factor
DF = Drag force
IF = Inertia force
LF = Lift force
h= Buckle arrestor thickness
H = Wave height
I = Moment of inertia
ID= Pipeline inner diameter
k = Burst coefficient
2
4Dm
K Tes ρ
ξπ= = Stability parameter
DfU
KCw
c= = Keulegan-Carpenter number
L = Wave length
L = buckle arrestor length
mL = Length of pipeline in Miles
em = Effective (modal) mass
)(sm = mass per unit length of pipeline including
structural mass, coating mass and added mass
M = Moment
in = Number of cycles at stress range Si
iN = Number of cycles to failure at stress range Si
)(iP = Probability of occurrence for the “i”th stress cycle
(“i”th sea state)
0P = External pressure
1P = psia at start point of pipeline
2P = psia at end point of pipeline
aP = Incidental overpressure
actualP = Actual measured burst pressure
bP = Burst pressure
cP = Collapse pressure
crP = Free span critical buckling load
eP = Elastic collapse pressure
iP = Internal pressure
idP = Internal design pressure
mP = Minimum cross-over pressure
HydP −max = Maximum hyrotest pressure
pP = Buckle propagation pressure
tP = Hydrostatic test pressure
xP = Buckle arrestor cross-over pressure
yP = Plastic collapse pressure
Q = Cubic ft of gas per 24 hr
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υDU c=Re = Reynolds number
iS = Stress range due to ith seastate
uS = Soil undrained shear strength
YS = Specified minimum yield stress
aYS , = Specified minimum yield stress of buckle arrestor
actualYS , = Average measured yield strength of pipe
SF = Safety factor t = Pipeline nominal wall thickness
mint = Minimum measured wall thickness
T = Wave period
T = Temperature de-rating factor for steel
aT = True wall axial force
dT = Design life
effT =Effective axial force (true wall force including
pressure corrections)
lifeT = Fatigue life capacity
U = Steel ultimate tensile strength
actualU = average measured ultimate tensile strength
cU = Current velocity
wcm UUU +=
wU = Particle maximum horizontal velocity due to wave
wU& = Particle maximum horizontal acceleration due to
wave
windU = Current velocity due to wind
tideU = Current velocity due to tide
DfUU
Vn
wcR
+= = Reduced velocity
sW = Pipeline submerged weight
wc
c
UUU+
=α = Current flow velocity ratio
γ = Weight density
υ= Poisson’s ratio, 0.3 for steel υ= Kinematic viscosity, 1*10-6 for seawater ε = critical strain
Tξ = Damping, including structural, soil and
hydrodynamic damping ρ = Mass density
)/()( minmaxminmax DDDD +−=δ = ovality
δ = Pipeline sagging at mid span κ = Curvature η= Efficiency parameter for buckle arrestor
fatη = Fatigue safety factor
µ = Soil friction factor
θ = Seabed slope ϕ= Internal friction angle of soil
φ = mode shape
Subsea Pipelines Page 9
1. Introduction
In order to understand the importance of subsea pipelines, the importance of offshore oil and gas is first
mentioned. Figure 1 shows the US crude oil production trends from onshore and offshore resources.
Figure 1 - US crude oil production trends (S. Chakrabarti, 2005)
It is seen in Figure 1 that offshore production is increasing and onshore portion is decreasing. This is due to
the fact that most onshore hydrocarbon fields are discovered and under production and some of them are
no longer economic. Also it is seen that production from shallow waters is nearly constant while production
in deepwater (>1000 ft) is increasing. This is due to the fact that almost all resources in shallow waters are
found and being utilized, therefore exploration is active in deep and ultra deep (>5000 ft) waters. Figure 2
shows this fact: the number of wells in ultra deep waters is increasing very fast.
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Figure 2 - Number of ultra deepwater (>5000 ft) wells drilled in Gulf of Mexico (S. Chakrabarti, 2005)
In an offshore hydrocarbon production system, pipelines have a connecting role between the facilities.
Figure 3 shows a typical offshore hydro carbon field and the role of pipelines.
Figure 3 - Roles of pipelines in an offshore hydrocarbon field (Bai, 2000)
Subsea Pipelines Page 11
2. Material Grade Selection
Generally carbon steels are used for subsea pipelines. API-5L "Specification for Line Pipe" (2000) is used for
standard specifications. API-5L covers Grade B to Grade X80 steels with Outside Diameters (OD) ranging
from 4.5 to 80 inch. Table 1 shows tensile strength properties according to API-5L. Generally the most
common steel grade used for deepwater subsea pipelines is X65, regarding its cost-effectiveness and
adequate welding technology. For buried offshore pipeline in the Arctic, the more ductile X52 has been
proven the best choice for limit state design and the need for a high toughness material that could sustain
the high strain based design.
Table 1 - Tensile strength properties (API 5L, 2000)
Generally, higher grades of steel (e.g. X70, X80, Duplex) cost more per unit volume. Welding higher grades
is harder, therefore each joint requires more time so the overall operation time of the lay barge is higher.
On the other hand by using higher grade steels the required wall thickness is reduced. Therefore although
higher grades cost more per unit volume, the cost of pipeline per meter is slightly reduced. Higher grade
steels result in a lighter pipeline, therefore the required tension is lower. This factor is very important in
deep waters, where required tension can be a limiting factor.
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3. Diameter Selection
The process for selecting a pipeline diameter involves a detailed hydraulic analysis, especially for multi
phase flows. However, there exist some empirical formulas that produce reasonable accuracy. For example
Equation 1 can be used for sizing single phase gas lines and Table 2 for crude oil pipelines (Nogueira &
Mckeehan, 2005). Also, diameters of some selected offshore projects are presented in Table 3.
mLPPID
Q2
22
13500 −
=
(1)
Table 2 - Crude oil sizing guidance (Nogueira & Mckeehan, 2005)
Table 3 - Diameters for selected offshore projects (Nogueira & Mckeehan, 2005)
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4. Wall Thickness Selection
To calculate the required wall thickness for an offshore pipeline, four different failure modes must be
assessed:
1. Internal pressure containment (burst) during operation and hydro-test.
2. Collapse due to external pressure.
3. Local buckling due to bending and external pressure.
4. Buckle propagation and its arrest.
4.1. Internal Pressure Containment (Burst)
The burst pressure of the pipeline is basically calculated by the hoop stress formula for thin walled pressure
vessels. Thin wall theory is valid for D/t > 20 and t < 0.1 inner pipe radius. It assumes uniform wall stress
and gives mean circumferential stress. The burst pressure is calculated by setting the hoop stress equal to
pipeline yield stress and incorporating safety factors. Thin wall equation can be used for D/t < 20 but it
gives slightly higher estimates of stress than thick wall theory. The principal difference between the thin and
thick wall formulations is that for thick wall conditions, the variation in stress between inner and outer
surfaces becomes significant.
Figure 4 - Free body diagram of a pipe section under internal and external pressure
All the major codes (i.e. API, DNV, ASME, ABS and CSA) use the same philosophy. Here the formulation
according to US regulations (CFR, Code of Federal Regulation), which uses allowable stress design is given.
Pid is internal design pressure (CFR, 2002):
FETD
tSP Yid
2=
(2)
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F = construction design factor of 0.72 for submerged component and 0.60 for the riser component, T =
temperature de-rating factor (See Table 4), E = longitudinal joint factor (for API-5L steels E is 1.0 for
seamless, electric resistance welded, electric flash welded, submerged arc welded, and 0.6 for furnace but
welded).
Table 4 - Temperature de-rating factor, T, for steel pipe according to ASME B31.8 (Nogueira & Mckeehan, 2005)
According to 30 CFR 250 (CFR, 2002), all pipelines should be hydrostatically tested with water at a stabilized
pressure of at least 1.25 times the maximum allowable operating pressure (MAOP) for at least 8 h. Equation
(3) can be used where F, construction design factor is 0.95 for hydro test:
FETD
tSP Yhyd
2max =−
(3)
API-RP-1111 (1999) which is a limit state code and uses LRFD method uses the following logic for internal
pressure check:
A burst pressure, Pb, is defined for the pipeline:
( )tD
DLnUSP Yb 245.0
−+=
(4)
( )tD
tUSP Yb −+= 90.0
(5)
Any of the Equations (4) and (5) can be used, but API recommends use of Equation (4) for D/t<15.
Regarding geometrical properties, Equations (4) and (5) are only functions of D/t. A plot of the two
equations is given in Figure 5 and it is seen that the two equations give the same results.
Subsea Pipelines Page 15
Figure 5 – Burst pressure (Pb) according to API-RP-1111 (1999) using Equations 4 and 5 for X65 grade steel, SY = 65
ksi, U = 77 ksi and E = 29’000 ksi
The hydrostatic test pressure should satisfy the following:
btedt PfffP ≤
(6)
Where:
fd is design factor equal to 0.90 for pipelines and 0.75 for risers
fe is weld joint factor and the same as E in Equation (2), originally defined by ASME B31.4 and ASME B31.8.
API-RP-1111 only accepts pipelines with fe equal to one.
ft is temperature de-rating factor and is the same as T in Equation (2) which is given in Table 4.
The Maximum Operating Pressure (MOP) should not exceed 0.80 of the hydro-test pressure:
td PP 80.0≤
(7)
0 10 20 30 40 50 60 70 800
5
10
15
20
25
30
35
D/t
Bur
st P
ress
ure,
Pb (k
si)
Subsea Pipelines Page 16
Incidental overpressure (Pa) includes the situation where the pipeline is subject to surge pressure,
unintended shut-in pressure, or any temporary incidental condition. The incidental overpressure should not
exceed 90% of the hydro-test pressure. The incidental pressure may exceed MOP temporarily; but the
normal shut-in pressure condition should not be allowed to exceed MOP.
ta PP 90.0≤
(8)
The relation between maximum operating pressure, maximum incidental over pressure, hydro-test pressure
and burst pressure are shown graphically in Figure 6, with fe and ft equal to 1.
Figure 6 – Pressure level relations (API-RP-1111, 1999)
API-RP-1111 (1999) provides Appendix-A as a procedure for testing and qualification of material other than
carbon steel. This code only allows use of ductile material. Figure 7 and Figure 8 show typical failure pattern
of ductile and brittle material respectively. A ductile burst failure has a distinct bulge at the burst location. A
longitudinal fracture extends over the length of the bulge and terminates near the end of the bulge. The
end of fracture turns at roughly 45 degrees from the pipe axis at each end.
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Figure 7 – Ductile burst sample (API-RP-1111, 1999)
Figure 8 – Brittle burst sample (API-RP-1111, 1999)
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The burst coefficient, k, is defined as:
⎟⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛
−+
=
tt
tDDUS
PkactualactualY
actual
min, 2
ln)(
(9)
Having obtained the burst factor, the burst pressure, Pb, can be written as Equation (10). Note that
Equation (10) is the general form of Equation (4), in which k was set to 0.45.
( )tD
DLnUSkP Yb 2−+=
(10)
The value of k is determined from the burst test data as:
⎪⎩
⎪⎨
⎧
=45.09.0
875.0
min mink
k
kaverage
It is expected that the computed k values will all significantly exceed 0.45.
The effective tension due to static primary longitudinal loads should not exceed the allowable value:
yeff TT 60.0≤
(11)
Where
00 APAPTT iiaeff +−=
AT Aa σ=
AST yy =
Effective axial force is a concept introduced to simplify the treatment of internal and external pressures. By
arbitrarily considering a segment of pipeline as end-capped, the summation of external and internal
pressures result in buoyancy and weight of internal liquid respectively. (Fyrileiv et al, 2005). In order to
justify the end cap assumption, opposite forces are applied and summed with true axial force, Ta, (as seen
in Equation 10). If this simplifying method is not used, the external and internal pressures have to be
integrated over the outer and inner volume surface respectively, which is much more complex than the
effective axial force method. The effective axial force concept is illustrated in Figure 9.
Subsea Pipelines Page 19
Figure 9 – Concept of effective axial force (Fyrileiv et al, 2005)
Also for the combination of axial force and pressures, API-RP-1111 (1999) suggests the following interaction
equation to be satisfied:
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡≤⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛ −
loadshydrotestforloadsextremefor
loadsloperationafor
TT
PPP
y
eff
b
oi
96.096.090.022
(12)
4.2. Collapse Due to External Pressure
During installation, subsea pipelines are typically subjected to conditions where external pressure exceeds
the internal pressure. The differential pressure may cause collapse of pipe. Generally, the collapse pressure
is between the elastic and plastic collapse pressures. The elastic collapse pressure, Pe , is found by
examining the stability of a pipe section under hydrostatic load. The plastic collapse pressure, Py , is found
by equating the hoop stress to the yield stress.
3
212
⎟⎠⎞
⎜⎝⎛
−=
DtEPe υ
(13)
DtSP yy 2=
(14)
Subsea Pipelines Page 20
Each of the major codes gives a transition formula between Pe and Py for calculating the collapse pressure
Pc . DNV (2000) and ABS (2000) give a complicated third order equation. Timoshenko and Gere (1961)
propose a bi-linear transition. API-RP-1111 (1999) gives a very simple formula for Pc, which is the lower-
bound prediction for collapse pressure:
22ye
yec
PP
PPP
+=
(15)
Timoshenko and Gere (1961), propose the following design equation collapse pressure:
32 )1(1
2
⎟⎠⎞
⎜⎝⎛−
+
=
tD
ES
SP
y
yc υ
(16)
Both Equations (15) and (16) are interpolation formulas between Pe and Py. A graphical presentation of
Equations (13), (14), (15) and (16) is given in Figure 19 and the associated hoop stresses (calculated by
assuming thin-wall theory) is given in Figure 20. It is seen in Figure 20 that the collapse hoop stress of the
pipeline has the same typical pattern for column critical stress.
Equation (15) gives nearly the same results as DNV as seen in Figure 11. Equation was originally introduced
by Shell in 1975 (Murphey and Langner, 1985). Comparison of results of Equation (15) with 2900 pipe
collapse tests is shown in Figure 10, and shows that 97% of the collapse data lie above the predictions of
Equation (15).
The design equation according to API-RP-1111 (1999) for external pressure is:
ci PfPP 00 <−
(17)
Where:
0f = Collapse factor, 0.7 for seamless ERW pipe, 0.6 for cold expanded pipe, such as DSAW pipe
Subsea Pipelines Page 21
Figure 10 – Collapse pressures of 2900 specimen normalized with collapse pressures calculated by Equation (15)
(Murphey and Langner, 1985)
Figure 11 - Collapse pressure vs. D/t per API 1111 (1999) and DNV OS-F101 (2000), (Nogueira & Mckeehan, 2005)
Subsea Pipelines Page 22
4.3. Local Buckling Due to Bending and External Pressure
During installation with a lay barge, the pipeline is subject to severe bending and external pressure,
however in other situations this might happen, namely in free spans and during depressurization. Most of
the codes have addressed this failure mode and proposed relevant formulations. These formulations are
based entirely on empirical data fitting. API-RP-1111(1999) proposes Equation (18) which can be used for
D/t < 50. DNV and ABS also suggest the same formula except that the strain term is to the power of 0.8.
)()( 0 δεε g
PPP
c
i
b
≤−
+
(18)
Where:
Dt
b 2=ε =buckling strain under pure bending
1)201()( −+= δδg = collapse reduction factor which is maximum 1 for a perfectly circular pipe
The safety factor for bending strain is 2.0.
The buckling strain for a cylindrical shell under the action of uniform axial compression is 1.2 t/D. This strain
is determined by eigenvalue analysis based on the small strain elastic theory, without any account of
imperfections and residual stresses (Fatemi, 2007). The general equation is (Timoshenko and Gere, 1961):
Dt
Dt
bb 2.13.0)1(3
22
=⇒=−
= ευυ
ε
In order to understand the physical meaning of critical strain, pure bending of a pipeline is discussed here.
As bending moment is applied to the pipe, curvature is developed, which is defined as reciprocal of radius of
curvature. A convenient measure of curvature is strain of the material farthest from neutral bending plane:
2Dκε =
For small bending strains, less than the proportional limit strain, the stress at any point and the bending
moment vary linearly with bending strain. With further increase in the bending strain to just beyond the
proportional limit (Point A on the stress-strain curve in Figure 12 (a)), plastic deformation of the pipe
material begins. At this point both the stress-strain curve and the moment-curvature curve move off the
initial straight lines, and the stress distribution, Figure 12 (d), becomes nonlinear. A further increase in
strain, to point B, produces a further departure from the initial linear behavior, including residual curvature
of the pipe centerline. The plastic deformation at this degree of bending is stable, causing little ovaling or
change in cross sectional shape, as indicated in Figure 12 (c), and the pipe itself is not weakened or in any
danger of imminent failure.
Subsea Pipelines Page 23
Figure 12 – Mechanical behavior of pipe subjected to pure bending, (Murphey and Langner, 1985)
Figure 13 – Moment vs. strain curves for constant diameter and yield stress but variable wall thickness (Murphey and
Langner, 1985)
(b) Moment vs strain
(c) (d) Stress distributions
(c) Ovaling due to bending
(a) Stress-strain curve
Subsea Pipelines Page 24
As bending strain increase toward point C, ovaling increases rapidly and the slope of the bending moment
vs strain curve tends toward zero. This slope of of the moment-strain curve between points B and C is
determined by two competing effects. Moment is increased as a result of strain hardening and because an
increasing fraction of the cross section reaches yield. At the same time, ovaling of the cross section reduces
the section modulus and the hoop stresses interact with the axial stresses through the plasticity
relationships, which tends to decrease the bending moment. At point C the bending strain reaches a critical
value εb where the ovaling effect just overcomes the strain hardening characteristics of the pipe material.
The bending moment Mb is maximum at this bending strain, and after this point the pipe would buckle
(Murphey and Langner, 1985). Figure 13 shows moment-strain curves for three D/t ratios, where the
diameter is kept constant and wall thickness varies. For undamaged pipeline it has been observed that the
bending strength Mb is approximately equal to fully plastic moment, and the critical bending strain is εb =
t/2D, which is the value used in Equation (18) and is used by most major design codes (API, DNV, ABS).
Figure 14 shows how this value fits the experimental data. Figure 14 also provides some indication of the
detrimental effects of “flat” stress-strain curves and/or inhomogeneous pipe. Note that all the lowest
buckling points on this graph fall into one or both of these categories. “Flat” stress-strain is one that the
slope of the curve goes to zero or becomes negative at any point during the initial yielding process.
Premature buckling is expected for pipes with “flat” stress-strain curve.
Figure 14 – Pipe bending tests in air – curvatures at buckling (Murphey and Langner, 1985)
Subsea Pipelines Page 25
Equation (18) for a perfectly circular pipe (where the collapse reduction factor is 1) is a straight line which
intersects both axes at 1. For this case, Figure 15 shows experimental results and predictions of Equation
(18) and a good fit is observed.
Figure 15 – Pipe collapse due to combined bending and external pressure; comparison of experimental results with
(18) for a perfectly circular pipe (Murphey and Langner, 1985)
In lieu of the mentioned empirical formulation, Nogueira and Lanan (2001) have developed a rational model
from first principles, and the predictions have been shown to correlate very well with test results. In this
model it is recognized that as a pipe bends, components of the longitudinal bending stresses act into the
cross-section. This, in turn, generates a transverse moment, which ovalises the pipe cross section, or ring,
until it collapses. A pipe under bending will collapse when its cross section (or ring) loses stiffness due to
plastic hinges mechanism formation at the onset of local buckling. Therefore, when rings of the pipe lose
their stiffness, the ovalisation (initially uniform along the pipe length) will concentrate at the weakest point
along the pipe (e.g. a thinner ring) and a local buckle will form. If in addition to bending, external pressure
is applied, its effects are taken into account by noticing that it contributes to reduce the ring capacity to
resist bending. This is due to the effects of the compressive hoop stress. The resulting is an interaction
equation (between pressure and bending strain), which is too long and complicated to be presented here.
Figure 16 shows comparison of collapse pressure predicted by model with those by the experiments which
are in good agreement.
Subsea Pipelines Page 26
Figure 16 - Rational model prediction of collapse pressure vs. initial ovality, compared to experimental results for pipe
with D/t = 35 (Nogueira & Mckeehan, 2005)
Figure 17 shows the collapse pressure vs. bending strain predicted by the rational model and experiments.
A good match is observed.
Figure 17 - Pressure vs. bending strain predicted by rational model and experiments (Nogueira & Mckeehan, 2005)
Subsea Pipelines Page 27
Finally the results from empirical formulations of codes (API and DNV) are compared with results of the
rational model in Figure 18.
Figure 18 - Pressures vs. bending strain; comparison between empirical formulations of API, DNV and the rational
model (Nogueira & Mckeehan, 2005)
4.4. Buckle Propagation
If a local buckle is present in a section of a pipeline, for example resulting from excessive bending, the
external pressure may cause the buckle to propagate (travel) along the pipeline. As long as the external
pressure is less than the propagation pressure threshold, the buckle cannot propagate. Codes present
different empirical formulations for buckle propagation pressure which mainly depend on diameter, wall
thickness and steel grade. The equation given by API-RP-1111 (1999) is presented.
4.2
24 ⎟⎠⎞
⎜⎝⎛=
DtSP yp
(19)
It is noted that propagation pressure Pp is smaller than collapse pressure Pc (collapse pressure is the
pressure required to buckle a pipeline section). Figure 19 is a plot of Pe, Py, Pc, Pp for an X65 pipeline. Figure
20 shows the hoop stress associated with the mentioned levels.
Subsea Pipelines Page 28
Figure 19 – Elastic, plastic, collapse and buckle propagation pressures for an X65 grade pipeline based on API RP 1111
(1999) and Timoshenko (1961) formulations, E = 29’000 ksi
Figure 20 – Hoop stress associated with elastic, plastic and collapse pressure for an X65 grade pipeline based on API-
RP-1111 (1999) and Timoshenko (1961) formulations, E = 29’000 ksi
0 10 20 30 40 50 60 70 800
1
2
3
4
5
6
7
8
9
10
D/t
Pres
sure
(ksi
)
PlasticCollapsePressure,Py
ElasticCollapsePressure,Pe
APICollapsePressure,Pc
TimoshenkoCollapsePressure,Pc
BucklePropagationPressure,Pp
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
D/t
Stre
ss (k
si)
PlasticCollapseHoopStress
ElasticCollapseHoopStress
APICollapseHoopStress
TimoshenkoCollapseHoopStress
Subsea Pipelines Page 29
In order to avoid buckle propagation, the following equation with safety factor fp = 0.8 should be satisfied:
ppi PfPP ⋅≤−0
(20)
In order to satisfy Equation (20) in deep waters, very large thickness is required which is not economical.
Buckle arrestors can be used to mitigate the risk of buckle propagation. In general, the distance between
buckle arrestors should be selected to enable repair of the flattened section of pipeline between two
adjacent arrestors, at “reasonable” cost. For pipelines installed by J-Lay, the buckle arrestors also serve as
pipe support collars. In this case the distance between arrestors is simply the length of each J-Lay joint.
Three types of buckle arrestors are in common use, namely Grouted Sleeve arrestors, Integral Ring
arrestors, and Thick Wall Pipe Joints (Langner, 1999).
Grouted Sleeve arrestors are steel sleeves that are slid over the ends of selected pipe joints and are
grouted in place, as shown in Figure 21, before being installed offshore. Grouted Sleeve arrestors are
preferred, where feasible, because of their low cost. However, this type of arrestor has limited usefulness in
deep water because, as external pressure increases, a collapsed pipe will transform from its normal flat
“dogbone” cross section into a C-shaped cross section which then passes through the arrestor. Hence, for
sufficiently deep water, even an infinitely rigid Grouted Sleeve arrestor is ineffective.
Figure 21 – Grouted Sleeve arrestor (Langner, 1999)
Integral Ring arrestors are thick-wall rings that are welded into selected pipe joints, as illustrated in Figure
22, before being installed offshore. Integral Ring arrestors are used for pipelines in which the strength of
sleeve type arrestors is not adequate, and for J-Lay applications that require a support collar on each pipe
joint. These arrestors are very efficient in terms of strength for a given amount of steel, but are more
expensive than sleeve arrestors because of the additional welding required. Thick Wall Pipe Joint arrestors
Subsea Pipelines Page 30
are special pipe sections (each designed to prevent collapse propagation), that are welded into a pipeline at
intervals. A Thick Wall Pipe Joint is essentially a very long integral ring arrestor, but is much less efficient in
the amount of steel used.
Figure 22 – Integral Ring arrestor, which also serves as J-Lay Collar, (Langner, 1999)
Figure 23 - Tested sample of a pipeline with Sleeve type buckle arrestors and the numerical model
Due to the complexities of the buckle propagation phenomenon, design relationships are empirical.
The strength of a buckle arrestor is expressed by its crossover pressure, Px, which is the minimum pressure
that can force a buckled section of pipe to “cross over” the arrestor and start buckling the undamaged pipe
on the other side. Obviously, the minimum crossover pressure for a “weak” arrestor is the propagation
pressure Pp (Equation (19)) and the maximum crossover pressure for a “strong” pipe is the collapse
pressure Pc (Equation (15)). An efficiency parameter that varies between 0 and 1 is defined which depends
on the arrestor strength:
Subsea Pipelines Page 31
pc
px
PPPP
−
−=η
(21)
Providing a safety factor of 1.35 for any buckle arrestor the minimum crossover pressure Pm is defined as:
max35.1 dPm γ=
(22)
Design formulas for each of the three mentioned types of buckle arrestors are given here from Langner
(1999) which is the reference as stated by API-RP-1111 (1999).
Thick Wall Pipe Joint. Thick Wall Pipe Joints have been used as buckle arrestors in situations where
suitable thick-wall joints are readily available and where the weight of the suspended pipeline during laying
is not a critical issue. The design of a thick wall pipe joint arrestor is obtained by equating the minimum
crossover pressure Pm with the design crossover pressure Px which is the same as the propagation pressure
Pp, and solving for the thickness of the Thick Wall Pipe Joint:
4167.0
24 ⎟⎟⎠
⎞⎜⎜⎝
⎛=
Y
m
SP
Dt
(23)
Integral Ring Arrestors. Integral Ring arrestors are forged and/or machined weld-neck rings that are
butt-welded into a pipe joint. A less expensive version slides over the pipe and is fillet welded both sides
onto the outside of the pipe joint. For this technique stress concentration issues must be accounted for.
Integral arrestors are categorized into two types, based on their geometry. Narrow arrestors, in which the
length-to thickness ratio varies between L/h = 0.5 – 2.0, are used primarily for pipelines installed by J-Lay;
here the arrestor doubles as a collar for supporting the suspended pipe span. Wide integral arrestors, where
L/h > 2, are used primarily for pipelines installed by S-Lay, because of the easier passage of this type of
arrestor through the tensioners and over the stinger rollers. The efficiency parameter of the arrestor is
given by:
Subsea Pipelines Page 32
1≤≥ ηλη andk
(24)
Where:
⎩⎨⎧
><<
=)(2/8
)(2/5.05widehLfornarrowhLfor
k
)( factorstrengtharrestorDPLP
p
a=λ
4.2
,24 ⎟⎠⎞
⎜⎝⎛=
DhSP aYa
The buckle arrestor should be dimensioned such that the crossover pressure Px which is calculated from
Equation (21) is greater than minimum crossover pressure Pm (Equation (22)). As an example, the following
case is examined:
mHmNXMPaYMPaE
mmtmmD
500/10104)65(448199938
9.15457
3 ==
====
γ
Using the given formulas we have:
requiredarearrestorsBucklePP
MPaHPMPaP
MPaPMPaPMpaP
p
p
cye
⇒≤
===
=⇒==
80.0
05.540.3
93.1517.3153.18
0
0 γ
The integral ring buckle arrestor design is as follows:
adequateisarrestorBucklePPMPaP
MPaPkarrestorbucklenarrowhL
MPaYmmhmmLMPaP
mx
x
a
a
m
⇒>=⇒=
===⇒<
====
16.730.05.109.31
5,2/
448407597.6
ηλ
Subsea Pipelines Page 33
Grouted Sleeve Arrestor. Grouted Sleeve arrestors are forged or fabricated steel cylinders, typically with
dimensions of L/D = 0.5 – 2.0, that are slid over the end of a pipe joint, and grouted in place near the
middle of the joint. Typical grout materials that have been used are portland cement, sand-filled epoxy, and
two-part polyurethane. Sleeve arrestors generally are the lowest cost type of buckle arrestor, but may not
be suitable in deep water due to their limited arrestor strength. At the crossover limit, the cross section of a
buckled pipeline can change from the “dogbone” shape typical of free buckle propagation, to a U mode that
enables the collapse wave to pass through a sleeve-type arrestor, as seen in Figure 24
Figure 24 – U mode buckling of a pipeline; the collapse wave passes through a sleeve type arrestor (Kyriakides, 2005)
Design formulas for rigid sleeve type arrestors are as follows:
),min(5.0/3
21 PPPDLand
x ≥≥≥λ
Where
3,4.2 21
pcpp
PPPPPP
−+==
Choosing the spacing between buckle arrestors is an optimization problem. An approach is given in Bai
(2001).
Figure 25 shows the fitting of design formulas for integral ring buckle arrestors with test data.
Subsea Pipelines Page 34
Figure 25 – Comparison of integral ring buckle arrestor design formula with available test data (Langner, 1999)
Subsea Pipelines Page 35
5. On-Bottom Stability
A pipeline laid on seabed is subject to current and/or wave forces. The pipeline withstands these forces by
friction; which is relative to submerged weight of pipeline. It should be noted that in a complete 3D
analysis, the strain energy of the pipeline is also taken into account. The goal of this analysis is to
determine required submerged weight of pipe. If pipeline self-weight is insufficient, additional concrete
coating would be required. Pipeline stability is checked for both operation and installation (pipeline empty)
cases. Return period of environmental phenomena for on-bottom stability analysis is given in Table 5.
Table 5 – Return period for environmental phenomena
Condition Installation*
(Less than 3 days)
Installation*
(Longer than 3 days) Operation**
Return Period Based on weather
forecast
1 year (no threat to human lives)
100 year (threat to human lives)
100 year wave + 10 year
current
10 year wave + 100 year
current
*The installation time is usually short in comparison with operational lifetime of the pipeline. During installation the pipeline might be empty. Regarding the rather short period, less severe design environmental phenomenon are selected (shorter return periods). **Operation lifetime of pipeline might be several decades. The pipeline is usually filled during operation lifetime. Therefore more severe design environmental phenomenon are selected (longer return periods).
Additionally, a minimum pipeline specific gravity of 1.20 during installation is desired.
The on-bottom stability analysis is performed by the following steps:
1. Definition of environmental condition for different return periods, including:
• Water depth (d)
• Significant wave height (H), wave period (T) and angle of attack
• Steady current velocity (Uc) and angle of attack
• Wave only particle velocity (Uw), maximum water particle velocity due to wave and current
(Um) and steady current ratio (UR = Uc/Um)
• Soil submerged weight (γ ), soil friction factor or undrained shear strength (Su)
• Seabed slope (θ ) measured positive in downward loading
2. Determination of hydrodynamic coefficients: drag (CD), lift (CL), Inertia (Cm). These coefficients
should be adjusted for Reynolds number, Keulegan-Carpenter Number, ratio of wave to steady
current and embedment depth of pipeline.
3. Calculation of hydrodynamic forces drag (FD), lift (FL) , inertia (FI)
Subsea Pipelines Page 36
4. The last step is to perform a static force balance; the hydrodynamic loads are opposed by friction of
pipe over seabed.
Hydrodynamic forces on the pipeline (wave and current) are related to velocity and acceleration of flow at
the pipeline level. Current velocity (Uc) is steady while particle velocity due to a passing wave (Uw) is
oscillatory. Uw is dependent upon wave height, period and water depth. By knowing these parameters a
suitable wave theory can be used to calculate Uw. For most situations linear theory is adequate, because the
particle velocities and accelerations do not vary significantly between theories. As wave height to water
depth ratio increases, Stoke's fifth order theory becomes more appropriate. For shallow water or very high
wave heights, solitary theory is best suited. For breaking waves, a large diameter might affect the flow
regime and other methods may be appropriate, but in general pipelines should be trenched within the
breaking wave (surf) zone. Figure 26 shows the validity of different wave theories for different wave and
depth characteristics.
Figure 26 - Regions of applicability of different wave theories (API RP 2A, 2000)
Subsea Pipelines Page 37
5.1. Soil Friction Factor
Friction factor is defined as the ratio between the force required to move a section of pipe and the vertical
contact force applied by the pipe on the seabed. The friction factor is dependent upon soil type, pipe
roughness, seabed slope and burial depth. In the absence of site specific data, the following can be used:
• Loose sand: o30,tan == ϕϕµ
• Compact sand: o35,tan == ϕϕµ
• Soft clay: 7.0=µ
• Stiff clay: 4.0=µ
• Rock and gravel: 7.0=µ
The starting friction factor in sand is about 30% less than the maximum value, which occurs after a very
small displacement of the pipe builds a wedge of soil.
5.2. Hydrodynamic Force Calculation
The drag, lift and inertia force can be calculated by the Morrison equation. The general assumption for
Morrison's equation is that the body (pipeline) is small enough not to disturb the flow pattern caused by the
wave. The condition in which Morrison's equation is valid is when the ratio of wave length to pipeline
diameter is greater than 5, and therefore the pipeline is considered as slender. If the ratio is less than 5, the
body diffracts the waves and a diffraction theory should be used. For typical ocean waves and subsea
pipelines the slender body assumption is true. The Morrison equation states that wave loading is summation
of drag and inertia forces. The backbone of the equation can be derived using the momentum conservation
for a control volume containing the pipeline:
22. 1.
)()()( VelocityAreaConAcceleratiVolumeCAdvvdVvtdt
vmdFscvc
⋅⋅+⋅⋅=⋅+∂∂
== ∫∫∑ ρρρρrrrr
rr
(25)
C1 and C2 are constants for inertia and drag, dV is volume element, dA is area element and v is velocity. The
first integration is over a control volume and the second one is over a control surface. Morrison's formula is
usually written as:
Subsea Pipelines Page 38
mmDD UDUCF ρ21
=
2
21
mLL DUCF ρ=
mMI UDCF &⎟⎟⎠
⎞⎜⎜⎝
⎛=
421 2πρ
(26)
Only velocity and acceleration perpendicular to pipeline axis is considered in Morrison's equation. Figure 27
shows relative importance of inertia, drag and diffraction wave forces. It is seen that as slenderness (L/D)
increases, drag forces are dominant. Although Figure 27 is for a vertical pile, it can be used for a subsea
pipeline if the water depth is not more than half the wave length.
Figure 27 – Relative importance of inertia, drag and diffraction wave forces (DNV-OS-J101, 2004)
The magnitude of particle horizontal velocity and acceleration due to waves according to linear (Airy) theory
are as follows (L is wave length and z origin is at water surface and negative downward):
]/2cosh[]/)(2cosh[
2 LdLdz
LgTHU w π
π += (Horizontal particle velocity at elevation z)
]/2cosh[]/)(2cosh[
LdLdz
LHgU w π
ππ +=& (Horizontal particle acceleration at elevation z)
)2tanh(2
2
LdgTL π
π=
(27)
Subsea Pipelines Page 39
Currents have different sources but the most important ones are due to tides and wind. Tidal currents have
a 1/7 power law profile in depth. Wind driven currents have a linear profile and affect a limited depth (50
m). The combined current profile is shown in Figure 28. In the absence of site specific data the profile given
below can be used (z is distance from free surface and positive downwards):
⎟⎠⎞
⎜⎝⎛ −
+⎟⎠⎞
⎜⎝⎛ −
=50
507/1 zUd
zdUU WindTidec
(28)
UWind is wind-driven current velocity at surface and can be approximated as 0.015 x wind velocity at 10 m
elevation. Velocities of tidal currents depend strongly on the location and no approximate formulas are
established.
Figure 28 – Current profile due to tides and wind (DNV-CN-30.5, 1991)
5.3. Hydrodynamic Coefficient Selection
CD, CL and CI are dependent on one of the following situations:
Steady current only
Steady current and waves
For steady current conditions acting on a pipeline resting on seabed, CD ~ 0.7 and CL ~ 0.9. CD is generally
dependent upon Reynolds number (Re) and roughness, but for post critical state it is constant. Figure 29
can be used to evaluate these effects on CD for steady current.
Subsea Pipelines Page 40
Figure 29 – CD as a function of Reynolds number and roughness for a cylinder in steady current (DNV-CN-30.5, 1991)
In the case of steady current and waves, the coefficients are dependent on Keulegan-Carpenter KC number,
roughness and steady current ratio. The added mass coefficient (Ca = Cm-1) is given in Figure 30 as a
function of gap ratio. Physically KC is the amplitude of fluid particle displacement in each period normalized
by pipeline diameter, and is interpreted as measure of drag to inertia ratio.
Figure 30 – Added mass coefficient Ca as a function of gap ratio H/D (DNV-CN-30.5, 1991)
D
Ca
CD
Subsea Pipelines Page 41
If Uc is large with respect to Uw, the situation is similar to steady current alone (If Uc/Uw is greater than 0.4
this is true). For situation where the ratio is << 0.4, Figure 32 can be used for CD. The influence of seabed
proximity can be seen by using correction factors obtained from Figure 35.
Figure 31 – CD as a function of KC and roughness (DNV-CN-30.5, 1991)
Figure 32 – Influence of seabed proximity on CD for current+wave situation (DNV-CN-30.5, 1991)
Extensive experimental studies by Bryndum et al. (1983 and 1992) have led to hydrodynamic coefficients
graphs, as seen in Figure 33 and Figure 34.These experiments cover a wide range of flow conditions. Tests
for wave only have been done for 0<KC<160. Also effect of superposition of a steady current on the waves
is investigated for current ratios of 0<Uc/Uw<2. They have also concluded that increasing the current ratio
decreases all hydrodynamic coefficients, as seen in Figure 34. These studies are used in the comprehensive
on-bottom stability program by American Gas Association (AGA 1993).
Subsea Pipe
Figure 33 –
elines
Hydrodynamiic force coefficients CD, CM
roughne
and CL for re
ess (b) (Brynd
egular waves,
dum, 1992)
effect of pipee roughness (
Page
(a) and seabe
42
ed
Subsea Pipe
Figure 34
elines
– Hydrodynamic coefficiennts CD, CM andd CL versus cu
1992)
urrent ratio foor wave plus ssteady curren
Page
nt (Bryndum,
43
Subsea Pipelines Page 44
5.4. Stability Criteria
The last step of the simplified on-bottom stability analysis consists in assessing stability using a simple
lateral force equilibrium equation. Figure 35 shows a free body diagram of the problem.
Figure 35 – Free body diagram of pipeline for on-bottom stability analysis (Bai, 2000)
The following formula assumes a coulomb friction model and is over-conservative if the pipe is embedded. A
safety factor (SF) is included to account for actual values of soil friction, environmental data, particle
velocity and acceleration and hydrodynamic coefficients. Recommended SF is 1.05 and 1.1 for installation
and operation conditions respectively. The rather low safety factors are due to the very conservative nature
of this simplified 2D method. Ws is pipeline submerged weight.
)sin()cos( θθµ SMDs WFFSFFW ++≥−
(29)
Subsea Pipelines Page 45
6. Free Span (Bottom Roughness) Analysis
The goal of this analysis is to identify possible free spans that exceed the maximum allowable span length.
Figure 36 shows a schematic of a pipeline laid on a rough seabed in which free spans are possible.
Figure 36 – Free spanning pipeline on seabed
The irregular seabed profile is seen on the continental slope; a steep slope where the mild slope continental
shelf reaches ultra deep waters as seen in Figure 37. Figure 38 shows visualizations of a rough seabed
topography and subsea pipelines of the Ormen Lange field (Norway) passing a rough seabed.
Figure 37 – Continental shelf and continental slope
Subsea Pipelines Page 46
Figure 38 – Subsea pipelines, Ormen Lange field, Norway (Source: Internet)
The length and height of the span have a random distribution and lengths as long as 300-400 m is possible.
A typical distribution of free span length vs height and also the resulting profile of the pipeline is shown in
Figure 39.
Figure 39 - Typical free span distributions and pipeline profile (Soreide, 2001)
Subsea Pipelines Page 47
6.1. Static condition
The pipe span is checked for stresses under static conditions. Both Von-Mises and longitudinal stresses
should be checked and limited to the values given in Table 6.
Table 6 – Allowable pipeline stresses (Nogueira & Mckeehan, 2005)
A typical pipeline span free body diagram is shown in Figure 40, along with dimensionless diagrams for
calculation of stress at mid-span and span shoulders, and also mid-span deflection and induced pipe span.
The stresses depend on span length and pipeline tension.
Subsea Pipelines Page 48
Figure 40 – Static stresses and deformations in a free spanning pipeline (Mousselli, 1981)
w is submerged weight of pipeline per unit length
Subsea Pipelines Page 49
Another scenario is that the pipeline passes over an obstruction. A schematic of the pipeline is given in
Figure 41, along with dimensionless diagrams for pipeline span and maximum stress at mid-span. For this
situation the span is a function of obstruction height and pipeline tension, while mid-span stresses do not
depend on tension.
Figure 41 – Static stress and span for pipeline passing obstruction (Mousselli, 1981)
T
f
W
w
V
f
Subsea Pipe
6.2. VIV
The free spa
cross-low VI
fatigue dam
When free s
water) may
oscillate due
are caused
VIV and lift
oscillation n
frequency of
Figure 42
elines
an should al
IV do not o
age has to b
spans occur
y cause dyn
e to vortex s
by symmetr
t forces cau
normal to th
f inline VIV
– Vortex she
so be assess
occur. Recen
be assessed
due to seab
namic effects
shedding. Tw
ric and asym
se cross-flo
he flow, tw
is approxima
edding due to
resulting
sed for VIV.
ntly codes ha
and shown
bed irregula
s. The fluid
wo forms of
mmetric vort
ow VIV. As
wo cycles of
ately twice c
steady flow a
g in oscillating
Regarding V
ave added a
to be allowa
arities the pr
d interaction
f oscillation a
ex shedding
can be seen
f pressure o
cross-flow VI
at different R
g lift and drag
VIV, the free
an option w
able.
resence of b
n with the p
are observed
g, as seen in
n in Figure
oscillation p
IV.
Reynolds numb
g forces (Blev
e spans mus
which VIV is
bottom curre
pipeline can
d namely in-
n Figure 42.
42, for eve
parallel to th
bers and fluct
vins, 1977)
st be such th
allowed to
ent (and wav
n cause the
-line and cro
Drag forces
ery one cycl
he flow occ
tuating pressu
Page
hat in-line a
occur but t
ves in shallo
free span
oss-flow whi
s cause in-li
le of pressu
cur. Therefo
ures on pipe
50
nd
the
ow
to
ich
ne
ure
ore
Subsea Pipelines Page 51
Generally the following tasks have to be performed in the assessment of free spans for VIV:
• Structural modeling
• Load modeling
• A static analysis to obtain the static configuration of the pipeline
• An eigen-value analysis which provides natural frequencies and corresponding modal shapes for in-
line and cross-flow vibrations
• A response analysis using a response model or force model in order to obtain the stress ranges from
environmental actions
It is necessary to predict if a free span is isolated or affected from adjacent spans. Generally if the shoulder
length between two spans are relatively short, and also length of two adjacent spans are comparable, the
two spans interact, as seen in Figure 43.
Figure 43 – Classification of free spans (DNV-RP-F105, 2006)
A pipe over a short span behave like a beam (bending mode is dominant), while a pipe over a long span
behaves like a cable (axial mode is dominant). Table 7 shows this classification, where L is free span length
and D is pipeline diameter.
Subsea Pipelines Page 52
Table 7 – Response behavior of free span (DNV-RP-F105, 2006)
Another important parameter is the current flow velocity ratio which distinguishes between current and
wave dominated flow regimes and is defined by Equation (30). Table 8 shows different regimes.
wc
c
UUU+
=α
(30)
Table 8 – Different flow regimes (DNV-RP-F105, 2006)
Subsea Pipelines Page 53
The state of the art code for free spanning pipelines is DNV-RP-F105. This code recognizes three methods
for VIV assessment, and the first one is the most commonly used:
1. “Response Models” approach to predict the vibration amplitudes due to vortex shedding. These
response models are empirical relations between “reduced velocity” response amplitudes. Hence the
stress response is derived from an assumed vibration mode with an empirical amplitude response.
“Reduced velocity” is a function of still-water natural frequency and flow velocity.
2. Semi-empirical lift coefficients, or generally “Force Model” (Larsen, 2002). If the loading is defined,
the response can be achieved from solution of governing equations. The main disadvantage is that
appropriate formulations for loading –especially for cross-flow VIV- do not exist.
3. As a third option, Computational Fluid Dynamics (CFD) simulation of the turbulent fluid flow around
one or several pipes can in principle be applied for VIV assessment to overcome the inherent
limitations of the state-of-practice engineering approach. The application of CFD for VIV assessment
is at present severely limited by the computational effort required. In addition, documented work is
lacking which shows that the estimated fatigue damage based on CFD for realistic free span
scenarios gives better and satisfactory response than the methods described above. Figure 44 shows
results of a CFD simulation for the case of a pipeline with a piggyback pipe.
Figure 44 – CFD simulation of piggyback pipeline
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Natural Frequency
Natural frequencies of the span can be found using FEM including pipe-soil interaction effects, geometric
non-linearities and static equilibrium conditions. Also approximate formulations are available (DNV-RP-
F105). The formulas are valid for single span on relatively flat seabed (almost horizontal spans), L/D is less
than 140 and sagging deflection/D is less than 2.5. Also compressive axial force should be less than half the
buckling load. The static deflection can be estimated as:
cr
eff
eff
PTCSFEI
qLC
++⋅
=1
1)1(
4
6δ
(31)
C6 is boundary condition coefficient and is given in Table 9, and CSF is a factor accounting for stiffness of
coating. Teff is effective axial force (true axial force with consideration of in external and internal pressure
effects) and Pcr is the critical buckling load. The formulations are based on fixed-fixed boundary conditions
and Leff account for this. Boundary conditions are a function of shoulder soil stiffness. As this stiffness
increases the conditions are more like fixed, as seen in Figure 45 (β represents soil stiffness).
Figure 45 – Effective length vs. soil stiffness (DNV-RP-F105)
Subsea Pipelines Page 55
The first eigen-frequency can be approximated by (32). For a (geometrically) linear structure, natural
frequencies are a function of stiffness and mass only. For a geometrically nonlinear structure natural
frequencies are dependent also upon deflection (sagging of pipe span), as can be seen in Equation (32).
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛+++⋅≈
2
3411 11D
CPT
LmEICSFCf
cr
eff
effe
δ
(32)
Where C1 – C3 are boundary condition coefficients given in Table 9, E is Young’s modulus, I is moment of
inertia and me is effective (modal) mass. Effective modal mass is defined as:
∫
∫=
L
Le dss
dsssmm
)(
)()(
2
2
φ
φ
(33)
Where m(s) is mass per unit length of pipeline including steel and concrete coating mass, content mass and
added mass, and Φ is assumed mode shape (i.e. half wave cosine for first mode).
Equation (32) predicts the eigen-frequency with ±30% accuracy (DNV-G14, 1998). In this Equation, the
three terms in the parentheses represent bending, axial and sagging effects respectively (Bruschi & Vitali,
1991).
Table 9 – Boundary conditions coefficients (DNV-RP-F105, 2006)
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Important Parameters for VIV
VIV response depends on these parameters (Blevins, 1977):
• Reduced velocity: as a structure vibrates in a flow, it traces out a path. For steady vibrations the path
length normalized by diameter is termed reduced velocity:
DfUUV
n
wcR
+=
(34)
• Reynolds number:
υDUc=Re
(35)
Kinematic viscosity (ν) is defined as ratio of viscosity to density.
• Keulegan-Carpenter Number:
DfU
KCw
w=
(36)
• Damping factor: dependant on ratio of energy dissipated by the structure per cycle over total energy of
structure. A non-dimensional parameter named reduced damping or stability parameter is used instead:
2
4Dm
K Tes ρ
ξπ=
(37)
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Response Models
Amplitude response models are empirical models providing the maximum steady state VIV amplitude
response as a function of basic hydrodynamic and structural parameters mentioned above. The response
models are based on experimental laboratory test data and full-scale tests. Figure 46 shows a curve relating
reduced velocity (Equation 19) to maximum in-line VIV amplitude. As with an SDOF system, increasing the
damping (which increases stability parameter Ks (Equation 22)) reduces the vibration amplitude.
Figure 46 – Illustration of the in-line VIV Response Amplitude versus VR and KS (DNV-RP-F105, 2006)
The effect of flow regime (Table 8) is included with a correction factor applied to stress range. In-line VIV
stress range is calculated as:
ILY
ILIL DA
AS ,2 αψ⎟⎠
⎞⎜⎝
⎛=
(38)
Where the correction factor for current flow ratio is defined as:
8.08.00.15.03.0/)5.0(5.00.0
, <<⎪⎩
⎪⎨
⎧
>−
<= α
αα
αψα
forforfor
IL
(39)
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Equation (39) shows that for wave dominant flow regimes (according to Table 8), in-line VIV is negligible or
does not occur.
For cross-flow VIV, Figure 47 can be used to relate reduced velocity VR to maximum vibration amplitude.
Figure 47 – Illustration of the cross-flow VIV Response Amplitude versus VR (DNV-RP-F105)
Cross-flow VIV stress range can be calculated as:
kZ
CFCF RDAAS ⎟
⎠⎞
⎜⎝⎛= 2
(40)
The effect of damping is included via the amplitude reduction factor Rk:
⎩⎨⎧
>
≤−=
− 42.3
415.015.1
ss
ssk KK
KKR
(41)
Fatigue Criteria
Having calculated the stress for each sea state (for example by using the above mentioned Response
model), the fatigue damage can be calculated by using S-N curves. An S-N curve gives the number of cycles
required for failure of a structure (N) for a given stress range (S). Three methods are available for
generating an S-N curve:
1. Dedicated laboratory test data
2. Accepted fracture mechanics theory
3. Use of codes
Subsea Pipelines Page 59
DNV-RP-F105 (2006) gives the following formulation for S-N curves:
⎪⎩
⎪⎨⎧
≤⋅
>⋅=
−
−
SWm
SWm
SSSa
SSSaN
2
1
2
1
(42)
a1 and a2 are characteristic fatigue strength constant defined as the mean minus two standard deviation
curve. SSW is stress at intersection of the two S-N curves, defined by:
⎟⎟⎠
⎞⎜⎜⎝
⎛ −
= 1
1 loglog
10 mNa
SW
SW
S
Where NSW is the number of cycles for which change in slope appear. Log NSW is typically 6-7.
By plotting Equation (42) in a logarithmic plane, a bi-linear curve is obtained in which m1 and m2 are the
slopes of each segment. Figure 48 shows a typical two-slope S-N curve. Log NSW is typically 6-7.
Figure 48 – Typical two-slope S-N curve (DNV-RP-F105, 2006)
For a given sea state number i, the stress range, number of cycles (ni) and number of cycles to failure (Ni,
from S-N curve) are known. The accumulated fatigue damage of different sea states during the pipelines
life can be evaluated using the Palmgren-Miner law (DNV-RP-F105, 2006) with Equation (43), which states
that fatigue damage due to each individual stress range can be summed up to give the total damage D. the
value D = 1 is equivalent to fatigue failure:
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∑=i
ifat N
nD
(43)
Where:
ivlifeii fTPn ,××=
mii aSN −=
By equating Equation (43) equal to unity, the fatigue life capacity, Tlife, is formally expressed as (DNV-RP-
F105):
∑⋅⋅
=
aiPSf
T miiv
life )(1
,
(44)
The fatigue life is the minimum of the in-line and cross-flow fatigue lives.
The design life, Td, should be less than Fatigue life. Various codes give safety factors. The general equation
is as follows:
lifefatd TT ⋅≤ η
(45)
DNV-RP-F105 (2006) defines the safety factor fatη as 1.0, 0.5 and 0.25 for “Low”, “Normal” and “High”
safety classes respectively. On the other hand API-RP-1111 (1999) defines the safety factor as 0.1. The
difference between the numbers is because DNV uses partial safety factors for VIV.
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On-going Research
Recently, it has been shown that in-line and cross-flow vibrations are not independent (Fernes and
Berntsen, 2003). Excitation in a cross flow mode shape might lead to in line excitations and vice versa.
Fernes and Berntsen (2003) have approached by a “Force Model” technique. A general geometrically-
nonlinear beam-cable with additional local damping and stiffness (which can be used to model shoulder soil)
is formulated, as seen in Figure 49. The governing equation of motion is given in Equation (46)
Figure 49 – Schematic diagram of free span pipelines with additional local stiffness and damping (Fernes and Berntsen,
2003)
)()(24
4
1 axkraxtrRGiF
xrT
xxrEI
trR
trM
t−−−
∂∂
−+=⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
−∂∂
+∂∂
+⎟⎠⎞
⎜⎝⎛
∂∂
∂∂ δδ
(46)
Where:
M is mass, r is deflection vector (y and z components, r = ry + irz), T is tension, F is hydrodynamic forces
calculated by Morrison’s equation, G is submerged weight per unit length, i is imaginary unit, R1 and R2 are
global and local damping respectively, k is local stiffness and δ is Kronecker delta function. The above
partial differential equation has two sources of non-linearity: time dependency of tension and hydrodynamic
forces. At any instant, tension can be calculated as:
LLSEATT −
+= 0
Where:
T0 is the residual lay tension, L is initial length and S is elongated length, calculated from:
2
1 ⎟⎠⎞
⎜⎝⎛+=
dxdr
dxds
Equation (46) is solved using the Fourier Sine Transform technique (Fernes and Berntsen, 2003), (Kreyszig,
1993). Coupling of cross-flow and in-line mode shapes can be investigated using this model. As an example,
Subsea Pipelines Page 62
a unit diameter in-line second mode shape is imposed as initial condition (ry). The coupling of cross-flow
mode shape (rz) is observed, as seen in Figure 50.
Figure 50 - Motions due to a prescribed second mode inline deflection. (C) Time series of ry/D close to an antinode. (D)
Time series of rz/D close to an antinode. (Bottom panels) Countours of time evolution of ry/D and rz/D. (Fernes and Berntsen, 2003)
An example trajectory of a point on a pipeline free span is generally 8 shaped; as seen in Figure 51.
Figure 51 - Combined in-line and cross flow motion of a pipeline section (Fernes and Berntsen, 2003)
Subsea Pipelines Page 63
7. Installation of Subsea Pipelines
There are four methods for installing pipelines on the seabed, namely S-lay, J-lay, Reel-lay and Tow. J-lay
and S-lay methods are schematically shown in Figure 52 and Figure 53 respectively. The shape of the
suspended pipeline from lay barge to seabed justifies the corresponding name. In the reel-lay method, the
pipeline is spooled around one or more spools and un-spooled during offshore works. The unspoiled pipeline
departs the vessel in an S-lay or J-lay shape depending on the vessel method employed. In the J-lay
method the pipeline departure angle is large. This geometrical condition results in a single curvature for the
pipeline, or J-shape. On the other hand, the departure angle in the S-lay method is smaller and therefore
the pipeline has a double curvature, or S-shape.
Figure 52 – Schematic of S-lay method for pipelaying (Nogueira & Mckeehan, 2005)
Subsea Pipelines Page 64
Figure 53 – Schematic of J-lay method for pipelaying (Nogueira & Mckeehan, 2005)
Apart from the tow method, the three other ones require a lay-barge that can store line-pipe onboard, and
also additional supply barges as required. The lay-barge needs to be positioned in a specific position for
some time during the laying operation. Generally two methods exist for station-keeping:
• Mooring and anchoring
• Dynamic Positioning System (DPS)
There are two mooring types, namely taut and catenary which are shown in Figure 54 and Figure 55
respectively. The taut system withstands the environmental forces acting on lay-barge with its axial
stiffness. Taut mooring can be made of steel cables or nylon ropes. Taut mooring is suitable for shallow
waters. The catenary mooring withstands forces by its weight. Catenary moorings can be made of chains,
and are mainly used in deep waters but by using intermediate buoys they can be used in shallow waters
too. Moorings are not effective regarding angular motions of the vessel, namely roll, pitch and heave.
Subsea Pipelines Page 65
Figure 54 – Taut mooring system
Figure 55 – Catenary mooring system
A DPS vessel has thrusters in every direction. It has sensors which sense the environmental forces acting on
the vessel. Based upon the magnitude of environmental forces sensed, the thrusters are activated and exert
a force opposite that of environmental ones, and thus the vessel achieves relative positioning. It should be
noted that accuracy of DPS is generally less than mooring, but for ultra deep waters, DPS is the only option.
Subsea Pipelines Page 66
Any unexpected movement away from the planned laying route may severely bend the pipeline either in a
sag-bend or in an over-bend and the pipe may buckle or kink, therefore station-keeping is very important
during pipelaying.
A DPS lay-barge has substantial advantages in deepwater (e.g. 100 ft and deeper). At shallower depths, a
DPS lay-barge has disadvantages which are uncompensated. In shallow water any motion of the vessel
other than the prescribed forward motion, if unrestrained, can damage the pipe. It is apparent that engines
of substantial size are required to limit the control vessel motions with this high accuracy. At greater depths
the pipe assumes a nearly vertical attitude as it sags to bottom. Consequently, the lay-barge has greater
freedom of movement before the pipe is endangered. A combined station-keeping method was patented in
1973 (Langner, 1973) which utilizes both DPS and anchoring: lateral positioning is done via moorings and
longitudinal positioning is achieved via thrusters, as seen in Figure 56.
Figure 56 – Combined station-keeping method for intermediate water depths (Langner, 1973)
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Regarding the new strain based design method of pipelines, strain and stress concentrations during offshore
installations have to be carefully considered. For example a new (and faster) installation method for pipe-in-
pipe welding is as follows: Typically two offshore welds are required for connecting two pipe-in-pipe joints
together (i.e. one for inner and one for outer pipe). In the new technique the outer pipe is swaged and fillet
welded to inner pipe onshore, and only one offshore weld is required for welding two inner pipes together. A
sleeve is slided over the connection area. These types of innovative techniques have to be carefully
examined regarding stress and strain concentrations. Dixon et al. (2003) performed a FEM analysis of the
mentioned connections. They have found different locations of stress concentration for J-lay and S-lay, as
seen in Figure 57.
Figure 57 – Location of stress concentration in sleeve connection, Top: J-lay, Bottom: S-lay (Dixon et al. 2003)
Subsea Pipelines Page 68
7.1. J-lay
The J-lay installation method is a relatively new type of installation method specifically aimed at deepwater
and ultra-deepwater projects. This method is characterized by a steep ramp, typically 65 deg or higher
departure angle, therefore the pipeline has a suspended J-shape. Figure 58 shows a J-lay vessel laying pipe
with the aid of a side tower. During J-lay, the stresses and strains close to the top and the horizontal
tension component and also the horizontal tension at the seabed are minimized. The advantages and
disadvantages of the J-lay method are described in Table 10.
Table 10 – Advantages and disadvantages of J-lay (Nogueira & Mckeehan, 2005)
Adv. Best suited for ultra deepwater pipeline installation.
Adv. Suited for all diameters.
Adv. Smallest bottom tension of all methods, which leads to the smallest route radius, and allows
more flexibility for route layout. This may be important in congested areas.
Adv. Touchdown point is relatively closer to vessel, thus easier to monitor and position.
Adv. Can typically handle in-line appurtenances with relative ease, with respect to landing on the
seabed, but within the constraints of the J-lay tower.
Disadv. Regarding the near vertical ramp, fewer welding stations are available, typically one or two.
Therefore the laying rate is generally less than S-lay.
Disadv. Some vessels require the use of J-lay collars to hold the pipe (as mentioned in section 4.4.
Buckle Propagation, these collars may be used as buckle arrestors too).
Disadv. If shallower water pipeline installation is required in the same route, the J-lay must be
lowered to a less steep angle. Even then, depending on the water depth, it may be not
feasible to J-lay the shallow end with a particular vessel and a dual (J-lay/S-lay) installation
may be required.
Subsea Pipelines Page 69
Figure 58 – Heerema's balder in J-lay mode (Nogueira & Mckeehan, 2005)
In order to assess the pipeline structural integrity during any installation method where the pipeline is
suspended from the vessel to the seabed, a structural analysis by FEM method has to be performed. A FEM
package has to be used. Depending on the degree of accuracy required, several aspects have to be
modeled namely:
• Geometrical nonlinearity
• Material nonlinearity: the pipeline in the sagbend and overbend usually undergoes plastic
deformations
• Material anisotropy: the new higher grade carbon steels which are being developed (e.g. X80 and
above and Duplex) are anisotropic; the yield stress and modulus of elasticity may be different in
hoop and longitudinal directions
• Seabed soil: the seabed soil serves as an elastic foundation for the pipeline. Also the seabed resists
horizontal and longitudinal pipeline movement with friction. The seabed also damps the vibrations of
the suspended span
• Effect of wave and current forces on the suspended pipeline
• Effect of wave, current and wind forces on lay-barge which induce movement of top of suspended
pipeline. Some researchers in the early 90’s have addressed this topic namely Vlahpoulos et al.
(1990), Clauss et al. (1991) and Clauss et al. (1992). All these researches neglect the Material
nonlinearity and material anisotropy. It should be noted that these researches are basically two
uncoupled analyses:
Subsea Pipelines Page 70
First, analysis of the vessel motions from a seaway neglecting effect of pipeline on vessel motions
which can be done using standard packages (e.g. WAMIT, ANSYS AQUA, MOSES, etc). Result is the
time history of stinger motions, which is used as input boundary condition for the second analysis.
Second, analysis of a geometrically non-linear beam-column moving in fluid (which is subjected to
boundary condition derived from first analysis
The results of an analysis of this kind, including motions of the suspended pipeline, dynamic stresses
and dynamic tension range are shown in Figure 59.
Figure 59 – Dynamics of pipelines during laying: motion, dynamic stresses and tension for different wave periods
(Clauss et al. 1991)
Subsea Pipelines Page 71
General FEM packages such as ABAQUS and ANSYS can be used for this means. Other packages are also
available which are specifically aimed at subsea pipelines, the oldest and most common one being OFFPIPE
(www.offpipe.com). The goal of the installation analysis is to check the wall thickness of the pipeline, the
top tension required during installation and seabed tension. The top tension has to be checked with capacity
of lay-barge tensioners. The tensioner force is equal to the submerged weight of the suspended span minus
seabed tension. Some modeling features of OFFPIPE are as follows:
Dynamic analysis capability, lay-barge RAO’s (Response Amplitude Operators) and regular wave or wave
spectrum can be specified, the resulting vessel motions are incorporated in the analysis.
• The finite element method considers both geometric (large displacement) and material (nonlinear
stress-strain curve) non-linearities.
• Provides a detailed model of the lay-barge and a simplified structural model of the stinger which
includes the effects of the ballast schedule and hinges between stinger sections.
• Includes detailed pipe support models, which can include angled horizontal and vertical rollers,
overhead restraints and finite length roller beds.
• The seabed is modeled as a continuous elastic-plastic foundation (not a series of point supports).
The lateral soil resistance is bilinear, elastic for small horizontal displacements and frictional for large
displacements.
OFFPIPE uses the Ramberg-Osgood material model, expressed as: B
yyy MMA
MM
K ⎟⎟⎠
⎞⎜⎜⎝
⎛+=
κ
Where:
EDS
K yy
2=
DIS
M yy
2=
A = Ramberg-Osgood equation coefficient
B = Ramberg-Osgood equation exponent
In lieu of the detailed analysis mentioned above –which is required for the detail design stage of a project-
preliminary analysis using the stiffened catenary equations can be used. The original catenary equations
consider only tension in the line. By modifying the original catenary equations to include the effect of
bending stiffness, the stiffened catenary equations result. These equations yield very accurate for the J-lay
configuration (Langner, 1984) and the output is top and bottom tension and pipeline stresses and strains,
therefore a preliminary check of wall thickness and vessel tensioner can be done.
Subsea Pipelines Page 72
7.2. S-lay
The majority of offshore pipelines are installed using S-lay. For shallow waters the stinger and departure
angle are near horizontal. Recently S-lay vessels configuration is modified such that the stinger can reach
very steep angles of departure, which enables it to operate in deeper waters. This method is termed steep
S-lay. An S-lay vessel is seen in Figure 60.
Figure 60 – A typical S-lay Vessel (Nogueira & Mckeehan, 2005)
All offshore welding is done with the pipe in a horizontal position; therefore S-lay is very efficient compared
to J-lay. The main advantages and disadvantages of S-lay are given in Table 11.
Table 11 – Advantages and disadvantages of S-lay (Nogueira & Mckeehan, 2005)
Adv. All welds are done in horizontal position, making for efficient productivity of multiple welding
stations (typically 5-6).
Adv. Suited for all diameters.
Adv/Disadv. Can typically handle smaller, more compact in-line appurtenances with ease, but larger in-
line structures may be too large to go through the stinger.
Disadv. Buckle arrestors will induce concentrated higher strains in their vicinity within the stinger
Disadv. Typically, pipeline will twist (rotate axially) during installation. Bai (2000) describe this
phenomenon as a result of plastic strains.
Disadv. Requires a very high component of horizontal tension.
Subsea Pipelines Page 73
7.3. Reel lay
Reel-lay is a method of installing pipelines from a giant reel mounted on the lay-barge. Pipelines are
assembled at an offshore spool-base facility and spooled onto a reel which is mounted on the deck of a lay-
barge, as seen in Figure 61. Reel-lay was first patented in USA in 1968.
Figure 61 – A reel vessel (Guo et al. 2005)
Reeled pipelines can be installed up to 10 times faster than conventional pipelay. The greater speed allows
pipelines to be laid during shorter weather windows. Reel-lay can be used for pipelines up to 18 inches in
diameter. The reel can be either horizontal or vertical. Horizontal reel vessels lay pipelines in shallow to
intermediate water depths using a stinger and S-lay. The vertical reel-lay vessel is used for intermediate to
deep waters. The main advantages and disadvantages of real-lay are given in Table 12.
Table 12 – Advantages and disadvantages of Reel-lay (Nogueira & Mckeehan, 2005) & (Guo et al. 2005)
Adv. Almost all welds are done onshore, minimizing offshore welding.
Adv/Disadv. Well suited for smaller diameter lines and smaller D/t ratios. Maximum diameter is 18 inches.
Adv. If all pipeline can be stored on-board, a very fast installation campaign is achieved, making
this method very cost effective.
Disadv. If the route is too long or the diameter is too large, all the pipes may not be able to be
stored on-board and a number of recharging trips to the spooling base may be necessary to
reload, thus offsetting the high lay rate.
Disadv. Very high pipeline strains (3-5%) are applied to the pipeline. also the pipeline is plastically
deformed and then straightened. Some thinning of the wall and loss of yield strength of the
material in localized areas can occur (Bauschinger effect)
Disadv. Due to high strains, welding methods and acceptance criteria are more stringent.
Disadv. Pipeline will rotate during installation and may coil on the seafloor
Disadv. Inline structures are typically more difficult to handle and install.
Disadv. Concrete coated pipelines cannot be reeled.
Disadv. Only specifically designed pipe-in-pipe pipelines can be reealed.
Subsea Pipelines Page 74
7.4. Towed Pipelines
In this installation method, the pipeline is constructed onshore and towed into place, as illustrated in Figure
62. There are different ways to tow the pipeline string to site: surface tow, mid-depth tow or bottom tow.
In the surface tow the pipe is positively buoyant, towed to location on the surface, and sunk in position by
flooding. Wave action is a factor; therefore this method is used typically where rough seas are not likely. In
the mid-depth tow typically the pipe or pipe bundle is negatively buoyant, suspended above the seabed and
towed by a lead tug with a tail tug at the end of the pipe string. If the pipe is positively buoyant, mid-depth
tow may be achieved by incorporating the use of drag chains at specified intervals along the pipe string, so
that the pipe string assumes an equilibrium position above the seabed. For the bottom tow method, the
pipeline rests on the seabed, and a tug pulls it.
Figure 62 – Schematic of towed pipeline (Bai, 2000)
The length of the towed string is limited to about ten miles in the most favorable conditions.
The tow methods are challenging due to the effects of the environment such as waves action, oscillations
during pull or abrasive effects of the seabed during bottom tow. However, the onshore construction may
significantly reduce cost when compared to the installation methods described in the previous sections.
Several failures of pipe bundles during tow attest to the precautions that the offshore pipeline engineer
must take when using the tow method of installation.
Subsea Pipelines Page 75
7.5. Shore Approach
The methods mentioned above may not be able to install the subsea pipeline as it approaches very shallow
waters and the shore. Three methods exist:
• Float and sink, illustrated in Figure 63:
Figure 63 – Float and sink method used for shore approach installation
• Bottom pull method: the pipeline is pulled from shore to sea, illustrated in Figure 64. The required
roller tracks installed onshore are seen in Figure 65:
Figure 64 – Bottom pull method used for pipeline shore approach
Figure 65 - Bottom pull method; launching roller track
Subsea Pipelines Page 76
• Directional drilling method: the pipeline is drilled from shore under the seabed to a point where
water depth is sufficient, as illustrated in Figure 66:
Figure 66 – Directional drilling method for pipeline shore approach
Subsea Pipelines Page 77
7.6. Wet vs Dry Pipeline Installation
Conventional design in deep water requires the pipeline to withstand hydrostatic pressure of the sea,
because the pipeline is normally installed air-filled (dry). Collapse under external pressure usually governs
the establishment of wall thickness, and the calculated wall thickness is very large. In the design studies of
Oman-to-India pipeline in maximum depths of 3000 m, for example, experimental and analytical studies
indicate that the required minimum wall thickness is well over 30 mm even for modest diameters of 20 and
26 inches (Palmer, 1998). These wall thicknesses burden the economic feasibility of projects attractive on
other grounds.
Once the pipeline is in service, the internal pressure during operation is almost invariably higher than the
external pressure. 2000 m of seawater corresponds to 20 MPa: most flowlines operate at higher pressure
than this, because if the internal pressure were less than the external hydrostatic pressure the produced
fluid would normally go back down the hole. The conclusion is that:
Most of the wall thickness of a conventionally designed pipeline is only required while the pipe is being laid.
In a real sense, the additional steel required to resist external pressure during laying is wasted.
Generally, two methods are available for installing the pipeline:
• Air filled (dry)
• Liquid filled (wet)
The advantage of air-filled installation is reduced submerged weight which results in lower force required by
vessel tensioner, and as mentioned above the biggest disadvantage is large wall thickness required to
withstand external pressure. On the other hand in the liquid filled technique, the submerged weight is
higher, but internal and external pressure counter act and wall required thickness is not governed by
external pressure. In shallow water this is true. In ultra deep water it is no longer true, if we take
advantage of the reduced wall thickness that wet installation grants. Also wet laying enhances on-bottom
stability immediately after installation.
Alternative liquids might have advantages for wet installation. A lighter liquid fill reduces the submerged
weight. Pentane (626.2 kg/cu.m), Methanol (791 kg/cu.m), Gasoline and water have been used for
installation. If the pipeline is filled with lighter liquids the external and internal pressures don’t counter act
completely, and the pipeline has to be designed for the pressure difference. The advantage of wet
installation in ultra deep waters is illustrated in the following example:
An X65 steel pipeline with D = 660.4 (26 inch) is designed for the worst of the following two cases:
The pipeline must withstand an operating gauge pressure of 20 MPa
The pipeline must withstand the difference between external and internal pressure
The required wall thickness for different depths is shown in Figure 67. It is seen that liquid filling reduces
the required wall thickness substantially.
Subsea Pipelines Page 78
Figure 67 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: wall thickness as a function of depth
(Palmer, 1998)
The pipeline submerged weight (which has to be in the range of vessels tensioner capacity) is shown in
Figure 68. In water depths up to about 1000 m, the pipeline designed and constructed air filled is lighter
during construction than the liquid filled one, as would be expected. However if the depth exceeds 2700 m,
the pentane filled procedure gives a submerged weight during construction smaller than air filled. At these
ultra deep waters, a liquid filled installation allows large reductions in wall thickness without any penalty in
submerged weight.
Figure 68 – Comparison of design strategies for 660.4 mm (26 inch) pipeline: submerged weight in laying condition as
a function of depth (Palmer, 1998)
The liquid filled strategy clearly allows huge reductions in the cost of steel. In the above example and a
maximum depth of 3000 m, air filled installation has a steel weight of 566 kg/m, whereas pentane filled
requires 367 kg/m and water filled requires 216 kg/m. for a 1000 km pipeline the reduction in tonnage of
steel with Pentane fill is therefore 200’000 tonnes, which at a round figure of $1000/tonne corresponds to a
saving of 200 M$.
Subsea Pipelines Page 79
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