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of the pipeline into spans and gives a better estimate of

pipeline end movements. The number and location of free

spans together with support conditions and stresses are

extracted for pipe verification and span correction definition.

Effects of pipeline walking are then determined using the

same method.

Lateral buckling study is performed in parallel or as a final

check. This is based on an analytical method derived fromaxial loads found in the lateral stability analysis. The aim is to

define the propensity to buckle and define any mitigation

measures such as snake lay that would need to be incorporated

into the final routing.

The routing defined by the preceding simplified analyses is

then validated using more accurate Finite Element analyses.

Route definition

Lateral Stability

Free Spans

Pipe Walking

Lateral buckling

Mitigation if required

Validation of layout by FEA

Figure 1: Analysis Flowchart

Lateral stabilityTo keep the pipeline laying curve shape during operational

life, the pipeline must have sufficient curve capacity to sustain

high buildup tension load without large movements or lateral

buckling initiation. If the line is not laterally stable, a change

of layout or pipeline design is required. It has been widely

accepted that it is imperative to anticipate lateral stability

susceptibility of proposed layouts prior to any further detail

work.

The complexity of the lateral stability prediction involves

the laying curve profile, pipeline design options (single

pipe/PIP), possible tension load from risers, constant pressure

loads, cyclic thermal loads and anchoring, etc. It is difficult to

consider every condition in one toolkit without using finite

element methods. However, the current available FEA

programs are time-consuming whereas a short answer is

preferred. This is especially necessary when the layout or

pipeline design is not yet optimized. Usually, a 2D FEA model

is used to simulate lateral stability behavior. This can be

simplified for efficiency. A handy 1D finite element program

has been developed to address the need. The program models

the pipeline with pipe element and the pipe-seabed friction

contact with nonlinear spring elements. A fast nonlinear solver

is employed using Newton-Raphson methods. Both latera

stability curve (see Figure 2 which shows axial compression

for heat-up phases and axial tension for cool down phases

compared to curve capacity) and axial displacement curve

(Figure 3) can be plotted as part of the results. The program

also locates the hot spot areas where the lateral curve capacity

is not sufficient.

-6000000

-4000000

-2000000

0

2000000

4000000

6000000

0 2000 4000 6000 8000 10000

Pipe Length (m)

Tension(N)

Ten.Cap.

Comp.Cap

Cyc1-Hu-T

Cyc1-Cd-T

Cyc2-Hu-T

Cyc2-Cd-T

Cyc3-Hu-T

Cyc3-Cd-T

Figure 2: Lateral stability tension curve

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2000 4000 6000 8000 10000

Pipe Length (m)

Displacement(m)

Cyc1-Hu-U

Cyc1-Cd-U

Cyc2-Hu-U

Cyc2-Cd-U

Cyc3-Hu-U

Cyc3-Cd-U

Figure 3: Lateral stability displacement curve

The program has been validated against 2D model created in

commonly used finite element program ANSYS. The 1D

program generates identical lateral stability curve as ANSYS

nevertheless, for a three thousand meter pipeline with six

cycles of thermal loads, only one minute of calculation is

necessary in comparison to one hour in ANSYS.

Free Span identificationAn important aspect of the work performed at FEED stage of a

pipeline project is to determine with a certain accuracy the

number and length of free-spans that the pipeline wouldexperience once laid on sea-bed. This is necessary for a

pipeline contractor answering a Call for Tender to establish his

price, since he needs to know how much intervention works

will be required at the different construction stages, i.e. before

and after laying the pipeline. Intervention works consist of

placing additional supports, such as grout bags or concrete

mattresses on the pipeline route to reduce the spans that are

expected to be too long and unacceptable.

This estimation is quite important since the cost of

intervention works can be very high. When the seabed is

rough and uneven, and the route of the pipeline is long (for

instance one hundred kilometres or more), the theoretica

Curve capacity

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number of spans to be corrected can be very large, and this

may form a significant part of the overall pipeline construction

costs. It is therefore very useful for the oil company to get this

information at FEED stage, in order to know the overall

envelope for the works, and set up the best possible

contractual policy.

Very often, a detailed survey of the pipeline route is

performed concurrently with the FEED activities, whichmeans that a detailed and accurate view of the seabed profile

is available before the end of the FEED.

Software has therefore been developed to take the

opportunity to use the available bathymetric data. It uses the

detailed soil profile, and knowing the geometrical properties

(diameter, wall thickness, and submerged weight) and the

material properties of the pipeline, determines the deformed

shape of the line all along the route. The axial force in

pipeline, in particular the residual laying tension, is also part

of the input data.

The software is based on multiple support beam theory. It

allows modelling the full length of the pipeline, or

alternatively selected sections. The soil profile used as input

data can be directly transferred from the offshore bathymetry

survey datafile, in the form of a file containing the X,Z

coordinates of discrete points. Very long pipelines routes can

be handled, for instance higher than one hundred kilometres.

The soil characteristics are represented by an equivalent

stiffness, which is pre-determined by the user. The pipeline

natural embedment can also be specified as input data, and

included in the calculated response for the determination of

contact or non-contact with soil.

Since the pipeline route can be split in different sections,

the software has quick running times. It performs a 2-

dimensional simulation and provides the following results, for

the different stages simulated (i.e generally pipe empty at

installation, during hydrotest, and in operation): Deformed shape of the pipeline all along the route (see

Figure 4);

Location of the calculated spans (see Figure 4);

Length of the calculated spans;

Height of the pipeline above seabed in the spans;

Bending moments (see Figure 4) and axial force at alldiscrete points modelled.

The length of the calculated spans can then be compared to

the allowable span length, which is determined by independent

methods according to the applicable design code. From this

comparison, the number and locations of the spans to be

corrected is derived.

Additional supports such as grout bags can be modelled bymodifying the Z coordinate of the soil at the relevant location.

A re-run can then be performed to verify the efficiency of the

remedial measure taken.

Figure 4: Pipeline laid on uneven seabed and associated

bending moment

Pipeline walkingPipeline Walking is a phenomenon which may take place

when a pipeline is subjected to a succession of thermal cycles

such as those occurring when production is stopped (cool

down) and restarted (heat-up) a large number of times. Under

certain conditions, when its length is relatively short, the

pipeline may experience an overall displacement at each

thermal cycle. After several hundred cycles, the accumulated

motion of the line can be quite high (up to a few metres), and

this may lead to irremediable damage to the subsea

installations served. For instance, large movements of a

pipeline connected to subsea wells in deep water can not be

tolerated.

The phenomenon is caused by the presence of a driving

force such as a tension due to a SCR or flexible riser

connected to the line, or a significant seabed slope, together

with thermal gradients.

The walking of a line can also be analysed using a simple

computer tool which models the pipeline in 2D. If available, adetailed soil profile can be used as input data, in the form of a

series of discrete points. Any soil profile can be modelled, and

this is of particular importance if the seabed shows a general

slope towards one end of the pipeline.

Thermal gradients are modelled to simulate the

propagation of temperature along the line during heat-up and

cool down phases (examples of thermal gradients are shown in

Figure 5 and Figure 6).

0

20

40

60

80

100

120

well side riser side

Pipeline length

Temperature(C

)

Figure 5: Temperature profiles during first part of heat-up

phase

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0

20

40

60

80

100

120

well side riser side

Pipeline length

Tem

perature(C)

Figure 6: Temperature profiles during second part of heat-

up phase

Typical data provided to the software are the pipeline

geometrical and material characteristics (diameter, thickness,

submerged weight, Youngs modulus), operational data

(pressure, temperature gradients, number of cyclic thermalsteps), and soil data. The soil data are expressed as a soil

stiffness, an axial friction coefficient and an associated

mobilisation distance.

Optionally, external forces such as a riser tension can be

input to the analysis. There is also possibility to include at

both ends of the line a stiffness element simulating a restraint

due to an expansion spool or anchor.

Usually, a limited number of cycles (about 10) is necessary

to determine whether a pipeline or a flowline is subject to

instability due to thermal and pressure cycles. At FEED stage,

this is generally sufficient to quickly identify the problem, and

take appropriate measures such as challenging the soil data

used, increasing the submerged weight of the line, ordesigning an anchor to make the line fully stable.

The software calculates the motions of the lines at both

ends, and produces diagrams such as those shown in Figure 7

and Figure 8. In the case of a line experiencing small and

constant motions at each cycle, a rate of displacement,

expressed in mm/year can be derived. The estimation of the

total number of cycles during the pipeline lifetime allows then

to determine whether or not the overall motion of the line,

after say 20 or 25 years, would be acceptable.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6 7 8 9

Load step

Displacement(m)

Figure 7: Example of stable displacements at one end of a

pipeline

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Load Step

Co

olEndAxialDisplacement(m)

Figure 8: Example of pipeline displacement slightly

increasing at each step

Lateral buckling

The lateral buckling assessment is based on the theory

developed by Hobbs et al [Ref.1]. Details of the formulations

are given in Appendix A. The assumptions of this theory are:

The theory is based on force equilibrium and displacemencompatibility, once a lateral buckle has formed in a

theoretically straight pipe;

The pipeline material remains elastic;

The pipeline is analysed in two dimensions (flat plane);

The seabed is supposed to be even and uniform.The first step of the method is to evaluate the pipeline

propensity to lateral buckling, by comparing the maximum

effective compression force existing along the pipe with the

Hobbs critical force.

In the simplified approach, the propensity to buckling is

graded as follows: if the effective force does not exceed the

critical force, the pipeline will not buckle. If the effective

force exceeds twice the critical force, the pipe does buckle

And if it is comprised between these two values, it may

buckle.

If a significant part of the pipeline is found to potentially

buckle for the range of soil coefficients of interest, a more

detailed analysis is performed. The aim is then to determine a

mitigation measure, in order to control the position and

formation of the buckles. The one chosen here as an example

is snake lay.

The effective force is calculated at all points along the

pipeline. In the zone where there is a propensity to buckle (i.e

effective force greater than the critical force), the stresses are

checked as if the buckle occurred at any point in the zone

Each axial force is associated with a buckle length for the

different buckle mode shapes (see Figure 9). This buckle

length is then used to derive the bending moment and the axia

force acting within the buckle, using formulae developed byHobbs.

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0

5

10

15

20

0 100 200 300 400 500

Buckling length (m)

Hobbscriticalforce

Mode 1

Mode 2

Mode 3

Mode 4F

Lb 1, 2, 3, 4

Figure 9: Derivation of buckling length from Hobbs curve

These two parameters will then give the level of stress in the

buckle, to be checked with an adequate acceptance design

code.

The code chosen here is the DNV OS-F101. The

simplified approach uses the verification for local buckling

under Load Control Condition (LCC), with modified factors.

As a first approach, the load condition factor is set to 0.82 andthe functional load factor to 1.1, which means that only the

load combination b is verified.

The zone over which the utility check is above 1.0

indicates where buckling shall not be allowed to occur

spontaneously, i.e. where control or mitigation measures, such

as snake lay, are required. Snake lay consists of laying the

pipeline with preformed imperfections, so as to ensure that the

compression in the pipeline will be released in a controlled

manner at predetermined locations.

In the zone of snake lay, the route is defined with snake

cycle lengths equal to an acceptable length between buckles,

i.e. a length that should ensure that the buckles, once fully

formed, would be acceptable. This is equal to the spacing ofvirtual anchor points, which is determined as follows:

VAS

Virtual anchor points

BuckleBuckleBuckle

Figure 10: Defnition of Virtual Anchor Spacing

The determination of the required VAS is an iterative

process.

First, an initial virtual anchor spacing is assumed, fromwhich, the difference between the Hobbs critical force, Po,

and the axial force within the buckle, P, is calculated as

illustrated in Figure 11.

Po

P

Axialforce

Pipeline length

VAS/2

Figure 11: Illustration of Axial force

This assumes that the buckle length itself is small

compared to the feed-in length.

The buckle length is then derived from the Po-P curve

given by the Hobbs equations, as shown on the following

figure.

-10000

0

10000

20000

30000

40000

50000

60000

70000

80000

0 50 100 150 200 250 300 350 400 450

Buckle length Lb (m)

Po-P(kN)

Po-P calculated

Correspondingbuckle length

Figure 12: Derivation of buckling length

As previously outlined, the bending moment and the axialforce within the buckle are calculated from the buckle length

and stress check is performed.

If the pipe can not sustain this stress, the initial VAS is

decreased, and the method is reiterated, as shown on the flow

chart below:

VAS assumed

(Po-P) derived fromsoil friction

Buckle length

interpolated

Bending moment andforce within the

buckle calculated

Verification of

acceptance criteria Criteria not met

Criteria met

Buckle spacing is

acceptable

Figure 13: VAS calculation flowchart

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This preliminary method for assessing the lateral buckling

stability allows deriving snake lay configurations that will be

studied in more detail by Finite Element Analyses.

ValidationThe validation consists in using Finite Element analyses to

perform more accurate checks of the different simplified

analyses.The same overall method is applied, separating the

problem into 2D analyses. The main features of the detailed

FE analyses are presented hereafter.

Lateral Stability

Validation is performed using the general purpose finite

element program ANSYS to perform 2D longitudinal stability

checks. An interface program has been developed between

ANSYS and Excel spreadsheets to ease the input of pipeline

configuration and other data. The program mainly allows the

user to perform the following tasks:

Use real survey coordinates to specify the line

configuration; Specify pipeline design data including both single pipe andpipe-in-pipe options (mixed designed options allowed for

one line);

Meshing of the pipeline with user specified pipelineelement length;

Checking of line configuration inputs with line plots;

Specify loads including tension, pressure and cyclicthermal loads including heatup and cooldown temperature

profile throughout the pipeline operation conditions;

Generation of clean ANSYS macros to perform the majoranalysis work;

Post-processing of the ANSYS calculated force and

displacement results with plotted single load step plot ormultiple load step plots.

The program use contact elements to model pipeline-seabed

contacts and can consider the pipeline with elasto-plastic

materials.

Free Span identification

The same approach as for lateral stability checks is used, but

the bathymetry data along the curvilinear route of the pipeline

is used.

The initial state of the pipeline is defined by modelling the

laying of the pipe onto the seabed. Each step of the life of the

pipeline (filling, hydrotest, hot oiling, thermal and pressure

cycles, etc) is then simulated.

This is the most time consuming part of the validation due

to the large number of elements in the models.

Pipeline Walking

The same FE model is used, but soil friction coefficients are

varied in order to assess the possible extents of axial pipeline

movements.

Lateral buckling

To validate the lateral buckling preliminary assessment, FEA

study is performed to confirm the snake lay configuration. The

software used is ANSYS [Ref.2].

The finite element model is built on the same basis as the

one used for lateral stability, as this gives the axial forces

required to analyse buckles, but with the following

parameters: Perfectly plastic element using typical beam properties bu

allowing in addition to consider the constant hoop stress

caused by the external/internal pressure loadings;

Seabed modelled as 2D rigid flat surface;

Pipeline routing including simulation of snake lay withstraight lengths between short radius curves;

Mesh refined in the curved sections (1 x OD elementlength) and straight sections in coarser mesh (10m element

length);

Orthotropic friction modelled with rigid-rigid contacpairs, manually defined between individual pipeline node

(termed contact node) and seabed surface.

Three types of study can be performed.

Firstly, an isolated buckle can be modelled with a straigh

pipeline, to assess the level of strain within the most severe

buckle, and to determine whether the deformation may be

above the elastic range.

Figure 14 shows a typical buckle displacement:

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

4200 4300 4400 4500 4600 4700 4800 4900 5000 5100

pipeline length (m)

Lateraldispla

cement(m)

Figure 14: Buckle profile

Figure 15 shows axial force developed in the pipeline due

to the buckle, and Figure 16 the associated bending moment:

-5 000 000

-4 500 000

-4 000 000

-3 500 000

-3 000 000

-2 500 000

-2 000 000

-1 500 000

-1 000 000

-500 000

0

500 000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pipe Length (m)

EffectiveAxialForce(N)

Figure 15: Axial force developed in the pipeline

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-6 000 000

-5 000 000

-4 000 000

-3 000 000

-2 000 000

-1 000 000

0

1 000 000

2 000 000

3 000 000

4 000 000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pipe Length (m)

Be

nding

Momen

t(N*m)

Figure 16: Bending Moment developed in the pipeline

Secondly, the study of buckle interaction can be made with

short and long models, as required by the pipeline and snake

lay configuration.

Several snake cycles are modelled as defined in the

analytical method, and the pressure and temperature

conditions are applied. Compared to the previous isolated

buckle results, there is interaction between several buckles, asshown in Figure 17:

-15

-10

-5

0

5

10

15

0 2000 4000 6000 8000 10000

Pipeline length (m)

Buc

kleamp

litude

(m

Figure 17: Profile of several interacting buckles

The effective force is released, as shown in Figure 18:

-2 500 000

-2 000 000

-1 500 000

-1 000 000

-500 000

0

500 000

0 2000 4000 6000 8000 10000

Pipe length (m)

EffectiveAxialforce(N)

Figure 18: Axial force with interacting buckles

As a final step, a sensitivity study can be performed on the

radius and pitch of the snake lay configuration, in order to get

the most optimised snake lay shape.

ConclusionsThis approach to the problems of pipeline stability through

simplified methods enables many pipeline routings and soi

conditions to be analysed to determine a robust field layout. A

set of more accurate Finite Element analyses provides

confidence in the selected solution to be proposed for the nex

phase of project development.

References1. R.E. Hobbs and F.Liang Thermal Buckling of

Pipelines Close to Restraints (OMAE 1989)

2. ANSYS 10.0 Program Manual

APPENDIX A Formulations for lateral buckling

The effective force N along the pipeline is defined by the

following equation:

TEAApHN sii = )21(0

WithH0 Residual laying tension

pi Differential internal pressure acting on

pipeline section w.r.t. installation

Ai Internal pipe area

Poissons ratio

As Steel section

Thermal expansion coefficient

E Youngs modulus

T Differential temperature w.r.t. installation

The Hobbs critical force P0is given by:

)1))(

1((2

52

23 +=

cA

bLc

bAEI

WLEAkWLkPPo

With

P0 Hobbs critical force

P Axial force within the buckle

k2, k3 Hobbs constants

a Axial friction coefficient

W Pipeline submerged weight

Lb Buckle length

Ac Steel area

l Lateral friction coefficient

E Youngs modulusIc Pipeline inertia

The bending moment M within the buckle is defined by:

2

5 ... bl LWkM =

With

k5 Hobbs constant

l Lateral friction coefficient

W Pipeline submerged weight

Lb Buckle length

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The axial force P within the buckle is defined by:

21

..

b

c

L

IEkP=

With

k1 Hobbs constant

E Youngs modulusIc Pipeline inertia

Lb Buckle length

The difference (P0-P) between Hobbs critical force and the

axial force within the buckle is defined by:

2)( VAS

WPPo a =

With

P0 Hobbs critical force

P Axial force within the buckle

a Axial friction coefficient

W Pipeline submerged weightVAS Virtual Anchor Spacing

Buckle length derived from P0-P curve:

)1))(

1((2

52

23 +=

cA

bLc

bAEI

WLEAkWLkPPo

With

P0 Hobbs critical force

P Axial force within the buckle

k2, k3 Hobbs constants

a Axial friction coefficient

W Pipeline submerged weight

Lb Buckle length

Ac Steel area

l Lateral friction coefficient

E Youngs modulus

Ic Pipeline inertia