Copyright 2006, Offshore Technology Conference This paper was prepared for presentation at the 2006 Offshore Technology Conference held in Houston, Texas, U.S.A., 1–4 May 2006. This paper was selected for presentation by an OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Papers presented at OTC are subject to publication review by Sponsor Society Committees of the Offshore Technology Conference. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, OTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract This paper addresses the phenomenon of pipeline walking, which can cause cumulative axial displacement of a whole pipeline, leading to potential failures at tie-ins or risers. This phenomenon can massively complicate the design of deep water flowlines and has significantly impacted field layouts on a number of recent projects.

Pipeline walking occurs over a number of start-up and shutdown cycles, under the following conditions: • Tension at the end of the flowline, associated with a steel

catenary riser; • Global seabed slope along the pipeline length; • Thermal transients along the pipeline during start-up and

shutdown. The SAFEBUCK JIP has developed new analytical

equations, from first principles, that predict the rate of walking for all three load conditions. These equations have been successfully validated against FE (finite element) models, and bring welcome simplicity to conceptual design assessments. Introduction The SAFEBUCK JIP was undertaken with the intention of developing a guideline for the design of high temperature pipelines prone to lateral buckling. Part of the JIP included an investigation into the little understood pipeline walking phenomenon, which has occurred in a number of pipelines and lead to at least one failure to date.

The aim of this task within the JIP was to define the key factors that influence pipeline walking and provide guidance for assessing the severity of the walking problem.

This paper summarizes the work done on pipeline walking and presents simple analytic expressions which can be used to assess pipeline walking at a conceptual design stage.

Pipeline Walking Mechanisms When a pipeline is laid on the seabed and heated, it will tend to expand. The expansion is resisted by the friction generated by the seabed. When the pipeline is cooled, it contracts but the effects of seabed friction mean that the pipeline ends cannot contract to the original position. On subsequent heat-up and shutdown cycles, the pipeline ends cycle between the fully heated position and the cool-down position; this behavior is addressed in the traditional approach to pipeline expansion design.

However, in some cases thermal cycling can be accompanied by global axial movement of the pipeline; this global translation of the whole pipeline is termed pipeline walking. Over a number of start-up and shutdown cycles walking can lead to significant global displacement of the pipeline. Walking itself is not a limit state, but without careful consideration can lead to: • Overstressing of spoolpieces/jumpers; • Loss of tension in a SCR (steel catenary riser); • Increased loading within a lateral buckle; • Need for restraint using anchors; • Route curve pullout of restrained systems.

Walking is a phenomenon that can occur in short, high temperature pipelines. The term ‘short’ relates to pipelines that do not reach full constraint in the middle, but instead expand about a virtual anchor point located at the middle of the pipeline. Walking involves a global axial movement which occurs on cyclic load and does not reduce with the number of cycles. There are related axial ratcheting phenomena which can occur in more heavily constrained pipelines, but these tend to reduce to a final equilibrium position over a (relatively) small number of cycles[1].

With the current increase in pipeline operating temperatures, ‘short’ pipelines can be many kilometers in length. The phenomenon can also occur in longer lines where lateral buckling has occurred.

Pipeline walking in short pipelines occurs under the following conditions: • Tension at the end of the flowline, associated with a SCR; • Global seabed slope along the pipeline length; • Thermal gradients along the pipeline during changes in

operating conditions. The three walking mechanisms are treated in turn,

highlighting the parameters that influence walking for each.

OTC 17945

Pipeline Walking—Understanding the Field Layout Challenges, and Analytical Solutions Developed for the SAFEBUCK JIPM. Carr, F. Sinclair, and D. Bruton, Boreas Consultants

2 OTC 17945

Effective Axial Force Profiles The general expansion behavior of a pipeline can be understood by considering the effective axial force profile along the pipe. The effective axial force in the pipeline is made up of the (true) axial force in the pipe wall and the pressure induced axial force. This is defined as:-

iieew ApApSS ⋅−⋅+= (1)

Here tensile forces are positive and all variables are defined in the notation section at the end of this paper. In the remainder of the paper all references to axial force imply the effective axial force; the true wall force can always be recovered using equation (1).

The force at which the axial strain in the pipeline is zero is known as the fully constrained effective force, for a pipeline installed with zero internal pressure this is given by:-

( ) ( ) ( )instsiiL AE21ApSP θ−θ⋅α⋅⋅−ν⋅−⋅⋅−= (2)

Although this is the conventional definition of fully constrained force, the term really applies to sections where the change in strain is zero, i.e. equation (2) defines the force associated with zero strain change from the as-installed condition. The distinction is important here, since we are considering cyclic loading of the pipeline. The change in fully constrained force associated with an unload event is therefore given by

( ) ( ) ( )12si12 AE21AppP θ−θ⋅α⋅⋅−ν⋅−⋅⋅−−=Δ (3)

Where the subscripts 1 and 2 refer to conditions before and after the operating change.

An important consideration in pipeline walking assessment is the level of axial constraint during start-up and shutdown cycling. This can range from a condition of ‘full cyclic constraint’ where no axial displacement occurs over a portion of the pipeline, to ‘fully mobilized’ where axial displacement occurs along the full length of the pipeline; there is also an intermediate condition of ‘cyclic constraint’. Each of these conditions is described in the following figures.

A typical force profile envelope for a fully mobilized ‘short’ pipeline is illustrated in Figure 1.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownHeatupFully Constrained Force

P

f L

ΔP

Sf

Figure 1 - Force Profile Envelope for a Fully Mobilized Pipeline (f/f* <1)

Figure 1 shows the force profiles in the fully heated position and the cool-down position. The slope of the force profiles is defined by the axial friction force, f=μ·W. The change in fully-constrained force, as defined by equation (3), is also showni. For a pipeline to be fully-mobilized on load and unload the change in fully constrained force (∆P) must exceed the height of the force envelope defined by axial friction (f·L). The condition under which cyclic constraint occurs can be expressed in terms of a constraint friction, f*:

LP

f * Δ= (4)

If the friction force is less than f* then the pipeline is fully mobilized (i.e. for f/f*<1). This definition of a ‘short’ pipeline is fundamental, as such lines are the most susceptible to pipe walking.

The force profiles change significantly when a pipeline is long enough for a section of the line to become fully constrained, as illustrated in Figure 2.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownFully Constrained ForceHeatup

ΔP

ΔP

P

S

f

Figure 2 – Force Profile Envelope for Pipeline Reaching Full Constraint (f/f*>2)

Figure 2 shows how the fully-constrained force is insufficient to mobilize axial friction along the full length of the pipeline; for a pipeline to reach full-constraint on first load f/f*>2. A fully constrained section will prevent walking unless the gradient of the thermal transient is extremely high.

There is an intermediate case in which the fully constrained force is sufficient to overcome friction on first load but insufficient to overcome friction on cool-down, as illustrated in Figure 3.

i For simplicity the figure shows the fully constrained force to be constant along the length. In general this will reduce with falling operating conditions. The change in fully constrained force (ΔP) assumes zero effective force following installation.

OTC 17945 3

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownHeatupFully Constrained Force

ΔP

ΔP

f L/2

P

S f

Figure 3 - Force Profile Envelope for a Cyclically Constrained Pipeline (1<f/f*<2)

For the cyclically constrained case in Figure 3 the walking behavior depends upon how close the system is to reaching full constraint. If the system only just reaches cyclic constraint then the walking will be similar to that of the short pipeline. However, as the friction increases the response will tend towards constrained behavior. Pipeline Walking – SCRs In deepwater field developments, it is common for pipelines to be tied into the reception facilities by a SCR. The design of the SCR is such that it pulls the pipeline into tension at the SCR touch down zone. The introduction of a constant tension at the end of the pipeline can cause a short pipeline to walk when it is heated and cooled. This assumes that there is sufficient axial friction along the pipeline for it to be axially stable under the highest axial riser tension.

The force profile envelope for a fully mobilized pipeline attached to an SCR at the cold end is shown in Figure 4.

0 0.25 0.5 0.75 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownFull Temperature

Sr

O L

B

A

A'

B'

Direction of Movement

S

Figure 4 - Force Profile – SCR at Cold End

The SCR applies a constant tension Sr, shown on the right of Figure 4. In practice, this tension will fluctuate with motion of the FPS (floating production system) and to a lesser extent with pipeline end expansion. It is considered safe to assume that dynamic (short time scale) tension fluctuations can be ignored, as the duration of cool-down and start-up operations are expected to last several hours.

The presence of a tension at the end of the pipeline causes asymmetry in the force profile, with the operational virtual anchor (A) located further from the riser and the shutdown anchor (B’) closer to the riser. Between virtual anchors (A-B) the slope of the force profile remains the same on heat-up and

cool-down. The slope of the profile indicates the direction of movement, since it acts to resist movement. This implies that between A and B the pipeline expands towards the SCR on heat-up and contracts towards the SCR on cool-down. Outside this region (O-A and B-L) the force profile reverses between heat-up and cool-down, therefore expansion and contraction are equal. The overall global displacement of the pipeline is therefore governed by the central section (A-B), which causes the whole pipeline to displace towards the SCR with each start-up and shutdown cycle. Analytic Model – SCR

Based upon the walking mechanism outlined above simple equations describing the ‘walk’ per cycle can be developed. The length between the virtual anchors Xab can be calculated by:

fS

X Rab = (5)

On start-up the change in force in the pipeline over the length Xab is:

fLSS Rf ⋅−=Δ (6)

The change in axial strain is related to the force change by:-

EA)PS( Δ−Δ

=εΔ (7)

So the incremental distance walked per cycle can be obtained by integration as:

EAX)PS( abf

R⋅Δ−Δ

=Δ (8)

Equations (5) to (7) are combined to define the walk per cycle due to SCR tension as:

fEASLfSP RR

R ⋅⋅⋅−+Δ

=Δ)(

(9)

FEA Validation - SCR

The analytic model described above has been validated against pipe walking FE models. A 2 km model has been used for the validation. Two riser tensions have been considered, 100 kN and 500 kN, the tensions have been applied at the hot and cold end of the pipeline. The walking per cycle from each of the validation cases is presented in Figure 5.

4 OTC 17945

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0.0

0.5

1.0

1.5

2.0

2.5

-600 -400 -200 0 200 400 600

Riser Tension

Pipe

line

Wal

king

(m/c

ycle

)

Analytic ResultsFEA results

SCR at Cold End SCR at Hot End

Walking TowardsCold End

Figure 5 - Walking with SCR – Validation Case

Walking due to SCR tension will cease if the friction restraint is sufficient to cause cyclic constraint, i.e. f/f*>1 (as shown in Figure 3). Pipeline Walking – Seabed Slopes Seabed slope along the route can cause walking each time the pipeline is heated and cooled.

For this assessment, a pipeline is laid on a seabed with a constant slope φ, where the slope is positive for a seabed sloping down from the inlet and negative for a seabed sloping up from the inlet, as shown in Figure 6.

φ

Inlet OutletInlet

(+) angle

Figure 6 – Seabed Slope Sign Convention

In this case there is a component of the pipeline weight which acts in the direction of expansion. When the pipe expands up the slope this acts against the expansion and when the pipe expands down the slope this acts with the expansion. This is similar to modifying the friction coefficient in the two directions and the presence of a seabed slope causes an asymmetry in the pipeline force profile. This affects the shape of the force envelope in a similar manner as the SCR tension. The asymmetric force profile envelope for this slope is shown in Figure 7.

0 0.25 0.5 0.75 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownFull Temperature

O L

BA

A' B'

μWcosφ+Wsinφ μWcosφ -Wsinφ

Direction of Movement

S

Figure 7 - Force profile – Sloping Seabed

For a pipeline that slopes downwards from the inlet, the hot anchor (A) is located closer to the hot end and the cold anchor (B’) closer to the cold end. Between anchors (A-B) the

slope of the force profile remains the same on heat-up and cool-down, indicating that the pipeline expands downhill towards B on heat-up and contracts downhill towards B on cool-down. As for the SCR, the overall global displacement of the pipeline is therefore governed by the central section (A-B), which causes the whole pipeline to displace downhill, towards the cold endii. Analytic Model – Seabed Slope

The length between the virtual anchors Xab can be calculated by:

μφ

=tanLXab (10)

The change in force in the pipeline over the length Xab is given by:

)sincos(WLSs φ−φμ−=Δ (11)

Based on these definitions and equation (7) the walk per cycle due to seabed slope is:

( ) ( )[ ] ( )μ

φφμφφ ⋅

⋅⋅⋅⋅⋅−⋅⋅+Δ=Δ

EALLWLWP tancossin

(12)

FEA Validation – Seabed Slope The analytic model described above has been validated against the pipe walking FE models. Three seabed slopes have been considered, 1°, 2° and 5° up and down from the inlet. The walking per cycle from each of the validation cases are presented in Figure 8.

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0.00

0.05

0.10

0.15

0.20

-5 -4 -3 -2 -1 0 1 2 3 4 5

Slope Angle (°)

Pipe

line

Wal

king

(m)

Analytic ResultsFEA results

Down from InletUp from Inlet

Figure 8 - Walking with Slope – Validation Case

Walking due to seabed slope will cease if the friction restraint is sufficient to cause cyclic constraint, i.e. f/f*>1 (as shown in Figure 3).

ii Outside this region (O-A and B-L) the force profile reverses between heat-up and cool-down. Since the friction force is different up and down the slope there will be a slightly different expansion over these sections. This effect will only be significant on steep slopes.

OTC 17945 5

Pipeline Walking – Thermal Transients Thermal Loading and Transients

An important consideration in pipeline walking assessments is the direction of flow and the resultant transients that occur. It is usual to consider the so-called ‘hot end’ of the pipeline to be closest to the wellhead, or manifold, while the ‘cold end’ is at the reception facility or riser. It will be shown that the direction of walking at restart, under thermal transient loading is generally towards the cold end of the pipeline. Cooling usually occurs after the pipeline is shut-in, as the whole system gradually cools to ambient conditions without thermal transient loading. For this reason, walking generally occurs on start-up but there is no reversal of walking on cool down. However, many field developments include shutdown and start-up operations that require the contents of the flowline to be displaced by dead oil to control hydrate formation. For such systems, hot oil is usually introduced at start-up to warm the flowline before bringing in flow from the well. Under these conditions, the hot and cold ends of the flowline can be reversed. This is particularly relevant to pipeline walking, as the steepest thermal transients that drive the walking phenomenon usually occur during initial heating, or sudden cooling of the line.

The key to the phenomenon is shape of the thermal profile developed over time as the pipeline heats-up. A typical set of heat-up thermal transients is presented in Figure 9.

1 23 4

56

78

910

1112

1314

15

0

0.1

0.20.3

0.40.5

0.6

0.70.8

0.9

1

0 0.25 0.5 0.75 1Distance (x/L)

Tem

pera

ture

(t/T

max

)

Heating steps

Figure 9 - Typical Thermal Transients

The hot fluid enters the pipeline at ‘0’ hereafter called the ‘hot end’. As hot fluids enter the cold pipeline, heat is lost to the surrounding seawater and the fluid quickly cools to ambient temperature. With time, the pipeline gradually warms until hot fluid is discharged at the far end of the line.

Previous investigations[2,3] have shown that the steepness of the thermal transients is the key driver behind walking behavior. The early stages of the heat up, before the cold end of the pipeline rises above ambient (before step 9 in Figure 9), are key.

To examine this phenomena analytically a set of simplified linear transient temperature profilesiii were used, as shown in Figure 10. iii More complex thermal profiles could be used, but these complicate the interpretation of the phenomena. Linear profiles capture the basic physical response and are used

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.25 0.5 0.75 1Length (x/L)

Tem

pera

ture

(t/T

max

)

Figure 10 - Example Thermal Transients

The linear transients exhibit a constant gradient along the pipeline until the full steady state profile is reached. The transients cause the pipeline to expand, resulting in a force profile on first load as shown in Figure 11.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

Heatup

Cooldown

S

Figure 11 - Example Force Profiles – First Heat-up

The profile shows the first heating and cool-down cycle for the pipeline from its as installed positioniv. The compressive axial force gradually builds up in the line as the pipeline heats and more pipe is mobilized. When the pipeline becomes fully mobilized a virtual anchor forms at mid-line and the pipeline expands from this point towards the hot and cold ends.

When cooled globally, the pipeline contracts about the virtual anchor at mid-line. Cooling causes the pipeline to go into effective axial tension (shown as blue). On the second and subsequent heating cycles, the force in the pipeline builds up in a modified manner because of the residual axial tension developed in the pipeline on cool-down (see Figure 12). Walking Mechanism

Pipeline walking occurs over each thermal cycle; although walking occurs on first cycle, it is the second and subsequent cycles which dominate the process. Therefore, the second load response of the pipeline is considered in detail to understand the walking mechanism.

throughout this paper. iv These profiles do not include a change in pressure; this would tend to reduce the walking. However, it is quite normal for shutdowns to occur with relatively small changes in pressure.

6 OTC 17945

The walking mechanism under thermal transient loading is understood by examining the relationship between the thermal transient, the force profile and the displacement of the pipeline at individual time steps during the heat-up process.

Heat-up If we consider Figure 10, the first transient from heat-up

only heats 15% of the pipeline, the remaining 85% is cold. This decay in temperature causes non-uniform expansion of the pipeline. The associated force profile during heating (following a full cooldown) is shown in Figure 12.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

O

L

Location of Virtual Anchor A

Location of Virtual Anchor B

A1

A2A3

A4A5

A6A7

B1

B2B3

B4B5

B6B7

S

Figure 12 - Example Force Profiles – Second Heat-up

As the pipeline heats up and starts to expand at the hot end, a virtual anchor forms (at A1) and expansion occurs towards the hot end between O and A1. In order to maintain force equilibrium a second virtual anchor must form (at B1) and between the virtual anchors the expansion is towards the cold end. Downstream of virtual anchor B1, the pipeline has not been mobilized, therefore there is no change in force along this section of pipe. As the pipeline continues to heat-up the locations of the virtual anchors change, the hot anchor (A1) tends towards the mid-line (A1….A7), whilst the cold anchor tends towards the cold end.

The effect of the transients on the movement of the pipeline can be understood by considering the cumulative displacement through each time increment. Figure 13 presents the cumulative displacement of the pipeline during the start of a typical heat-up cycle, from cool-down (with all displacements set to zero) to the point of full mobilization.

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0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Cum

ulat

ive

Dis

plac

emen

t (m

m)

Full Mobilization (1)

Figure 13 - Cumulative Displacement – Prior to Full Mobilization

As the pipeline heats up the non uniform expansion is evident. Pipe close to the hot end of the line tends to expand towards the hot end whilst the remainder of the line moves towards the cold end. As the pipeline continues to heat-up the cumulative displacement increases and peaks at the centre when the pipeline becomes fully mobilized. Once the pipeline has become fully mobilized, the subsequent expansion is centered on the mid-line virtual anchor point. The cumulative expansion following full mobilization is shown in Figure 14.

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0

50

100

150

200

0 0.2 0.4 0.6 0.8 1

Length (x/L)C

umul

ativ

e D

ispl

acem

ent (

m)

ContinuedHeating (3)

Full Temperature (4)

Full Mobilization (1)Cold EndExpansion (2)

Figure 14 - Pipeline Expansion Following Full Mobilization.

Once full mobilization has occurred (the blue line in Figure 14, is the same as in Figure 13) the cold end begins to expand as the temperature continues to rise. In this particular example the end expansion at full load is about 1100mm; the figure is truncated to focus on the walking displacement. Because of the expansion asymmetry earlier in the heat-up cycle, the middle of the pipeline has moved towards the cold end (in this case by 45 mm). This displacement is the ‘walk’. Once full mobilization occurs, the midline remains stationary and walking stops for the remainder of the heat-up cycle.

Cooldown When the pipeline cools, it typically does so at a uniform

rate along the whole line, this leads to contraction about the mid-line virtual anchor point. The force profile during unload is presented in Figure 15.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

O L

2nd Load

2nd UnloadS

Figure 15 - Force Profile – Unload

The pipeline unloads symmetrically about the centre of the pipeline. The cumulative displacement of the pipeline from one unload to the next unload is presented in Figure 16.

OTC 17945 7

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0

50

100

150

200

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Cum

ulat

ive

Dis

plac

emen

t (m

m) Continued

Heating (3)

Full Temperature (4)

Unload (5)

Figure 16 - Pipeline Movement Following Unload.

Because the pipeline cools uniformly along its length, there is no reversal of the displacement at the pipeline centre, i.e. the global shift of the centre is not recovered. When the pipeline is re-heated, the process starts again. The transients cause asymmetric expansion along the length of the pipeline, the mid point moves towards the cold end, full mobilization occurs and the mid-line becomes an anchor, on cool-down the pipe contracts equally about the midline anchor. So with each cycle, the pipeline walks towards the cold end.

The displacement of the centre of the pipeline over five heat-up/cool-down cycles is presented in Figure 17.

0

50

100

150

200

250

0 1 2 3 4 5Load Cycle Number

Mid

-Lin

e D

ispl

acem

ent (

mm

)

Walk per cycle

Figure 17 - Mid-line Displacement for 5 Load Cycles Analytic Model –Thermal Transients

The analytical model considers a simplified approach to the walking problem with the following key assumptions: • Linear transient temperature profiles, with constant

gradient throughout heat-up; • No pressure variation is included (pressure = 0); • Axial friction mobilization displacement not modeled; • Pipe is fully mobilized (‘short’); f/f*<1; • Axial friction force less than the force associated with the

thermal gradient (f<fθ = EAα qθ); • Considers second and subsequent heat-ups only.

An incremental solution is developed in which the position of the hot anchor point is allowed to move from the inlet to the centre of the pipeline (after which walking ceases) in k equal

steps of xA. An arbitrary stage in the heat-up is considered; the temperature and force profiles are shown in Figure 18.

θ -θw L

xθk

qθ

Temperature Profile

S1st LoadProfile for xθUnload

f

k·xA L/2-k·xAL/2

Force Profile

Figure 18 – Force and Thermal Profiles

At this stage in the heat up the hot anchor point is at a position k·xA and the temperature is above ambient for a distance xθk. By considering the force change as k increases to k+1, equations for the strain and displacement change along the pipeline can be developed. These equations have one unknown, the length of heat-up xθk. Imposing the condition that the displacement at the anchor points is zero yields

( ) ( )θ

θθ−⋅⋅⋅

+−⋅+⋅=− f

xLxf2xxkxkx AA2

AA 1kk (13)

To start the analysis the thermal transient is taken at the location of the anchor point, i.e. Axx

0=θ . Once the kxθ are

known the displacement at the centre of the line is then given by:-

( )

( )

( ) ( ) ( )( )2Lx

EA2xxxxLf

EA1k2fx

x2Lx

EA22Lxf

EA1k2fx

2Lx1k2

EAfx

w

1k

1kkk1k

k1k

k

k

222A

2

2A

2A

k

>−+−⋅

−−⋅

≤<⎟⎠⎞

⎜⎝⎛ −⋅

−−⋅

≤−⋅

=Δ

−

−−

−

θθθθθθ

θθ

θθ

θ

And the total walk is given by:-

∑Δ=Δk

kT w (15)

When a sufficient number of increments are considered, the solution shows good agreement with the FEA, as illustrated in Figure 19.

8 OTC 17945

0

5

10

15

20

2530

35

40

45

50

0 0.2 0.4 0.6 0.8 1f/f*

Wal

k Pe

r Cyc

le (m

m)

FEA ResultsApproximate SolutionIncremental Solution

Analytic SolutionValid Range

Figure 19 - Analytic Model Validation

The figure presents the walk as a function of the axial friction force; this is normalized against the constraint friction, f*. The walking rate is low for very low axial friction because the pipeline becomes fully mobilized before much of the transient has passed along the pipeline. The peak walking occurs when the pipeline reaches full-mobilization close to when the transient reaches the cold end of the pipeline.

The analytic model can be used to accurately predict the rate of walking over its range of validity. The range is shown in Figure 19 and the limit can be calculated using Equation 16.

5.1ff

≥θ (16)

The figure also shows the predictions of a simpler approximate solution for the distance walked per cycle, which is given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−⋅

⋅⋅

≅Δ θθ 4ff

ff24

EA16Lf 2

T if 6

θff >

EA8Lf 2

T ⋅⋅

≅Δ if6

θff < (17)

The walk per cycle varies with the friction force, f, and there is a given friction force at which the rate of walking peaks, as defined in Equation 18:

θ⋅= f83fmax (18)

The results from the approximate solution show reasonably good agreement with the FEA.

The model development assumes that the transients exhibit a constant gradient along the pipeline until the full steady state profile is reached. In reality the gradient reduces as the pipe heats up (Figure 9). The incremental solution can be used with a changing thermal transient gradient, as long as the change in gradient over an increment is small. Effect of Thermal Gradient

The thermal gradient applied to the flowline has a significant effect on the rate of walking. To illustrate this three thermal gradients have been considered with a 2 km pipeline model, 10, 20 and 30°C/km. Figure 20 presents the

pipeline walk versus friction force for the three thermal gradient cases. The results are presented for the FEA and analytic models.

05

101520253035404550

0 0.2 0.4 0.6 0.8 1f/f*

Wal

k Pe

r Cyc

le (m

m)

30°C/km - FEA20°C/km - FEA10°C/km - FEA30°C/km - Incremental Solution20°C/km - Incremental Solution10°C/km - Incremental Solution

Figure 20 - Effect of Thermal Gradient – 2km Pipeline

The amount of walking per cycle is strongly dependant on the gradient of the thermal transients. Indeed, the peak pipeline walk is a linear function of the transient slope, i.e. the peak displacement of the 30°C/km is 3 times that of the 10°C/km case. Effect of Pipeline Length

From the approximate analytic solution the peak walk per cycle is proportional to the pipeline length squared. The relationship is illustrated in Figure 21 for two pipeline lengths and a transient slope of 30°C/km.

020

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120140

160180

200

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6f/f*

Wal

k Pe

r Cyc

le (m

m)

FEA - 2 kmFEA - 4 kmApproximate Solution - 2 kmApproximate Solution - 4 km

Fully mobilised

Thermal transient =30 ºC /km

Figure 21 - Effect of Pipeline Length on Walking

The FEA results confirm the relationship between length and walk. However, as the length of the pipeline increases the likelihood of reaching a position of constraint increases, which modifies the behavior. Behavior of Constrained Pipelines

Pipeline walking is known to occur in ‘short’ (fully mobilized) pipelines. If the thermal gradient is steep enough then walking can also persist through a section of full constraint. The response is controlled by the ratio of the thermal transient gradient force to the friction force, fθ/f. If fθ/f> 1 then walking can persist even though the pipeline is fully constrained at its centre, as illustrated in Figure 22.

OTC 17945 9

050

100150200

250300350

400450

0 0.5 1 1.5 2 2.5 3f/f*

Wal

k (m

m/c

ycle

)

fθ/f*=1.13fθ/f*=1.51fθ/f*=1.89fθ/f*=2.26fθ/f*=2.64

Fully Mobilised Cyclic Constraint First Load Constraint

Analytic FEA

Figure 22 - Walking Limits – Analytic and FEA model comparison

For a pipeline with a significant fully constrained length (f/f* >3) the rate of walking is given by:-

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅

⋅Δ

=Δθf1

f1

EA2P 2

T (19)

For most pipelines this is unlikely to be a practical problem and full constraint will arrest walkingv. In the example considered in Figure 22 a gradient of 60ºC/km is required to continue the walk through the constrained section. Effect of Mobilization Displacement

The amount by which a pipeline will walk is also affected by the axial friction mobilization displacement. The mobilization displacement is defined as the amount of axial elastic displacement that occurs before the full friction force is generated. To illustrate this, a 2 km pipeline with a thermal transient gradient 30°C/km and a friction force of 300 N/m is considered.

Figure 23 presents the movement of the mid-line over five load cycles for a range of mobilization displacements from 0.1 mm to 20 mm.

020

4060

80100

120

140

160

180

200

0 1 2 3 4 5Load Cycle

Mid

Lin

e D

ispl

acem

ent (

mm

)

0.1mm Mobilisation5mm Mobilisation10mm Mobilisation20mm Mobilisation

Figure 23 - Effect of Mobilization Displacement on Walking

The walking displacement is reduced as the axial mobilization displacement increases; the peak walk per cycle occurs when the mobilization displacement is close to zero (this is the condition addressed by the analytic model). The

v This observation may not hold true in XHPHT developments.

reason can be illustrated by considering the 20 mm mobilization displacement case, Figure 24.

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Load Cycle

Mid

Lin

e D

ispl

acem

ent (

mm

)

20mm Mobilisation

Permanent Walk

Elastic RecoveryPeak Displacement

Figure 24 - Mid-Line Walk 20mm Mobilization displacement

The figure shows that the mid line displacement reaches a peak followed by a reduction from that peak. The reduction is termed the ‘elastic recovery’ of the soil and its magnitude is very close to that of the mobilization displacement of the soil. In this assessment the FEA assumes that the mobilisation displacement is wholly elastic, in reality this may not be the case. Clearly the selection of mobilization displacement is critical when performing a walking analysis using FEA. Effect of Internal Pressure

The model outlined above is based on temperature loading only. Changes in internal pressure ahead of thermal loading will cause a degree of mobilization of the pipeline before the thermal transients pass, and will reduce the walk associated with the thermal transients. This is illustrated in Figure 25.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

CooldownPressure onlyFull Temperature

Apply InternalPressure

TransientHeat-up

S

Figure 25 - Force Profile Including Pressure Step

The effect of pressure can be incorporated into the models by defining a reduced effective length over which the transients act. However, in many cases the difference between operating pressure and shut-in pressure is small, thus pressure will have limited benefit in reducing walking. In addition, if the pipeline has been depressurized, it is usual to increase pressure after heating has commenced to control hydrate formation; so that mitigating the rate of pipeline walking by pressurization ahead of heating is usually unacceptable for operational reasons. Combined Loading Walking can be driven by each of the three mechanism discussed above. For many pipelines more than one

10 OTC 17945

mechanism may be active. In this case the mechanisms can add to increase the rate of walking, or subtract to reduce it. For example if the SCR is attached at the top of a slope it will act to reduce the slope induced downhill movement. For systems in which more than one mechanism is active, the analytic models derived here can be used in isolation and then combined to provide an estimate of the overall walk. Implications for Field Architecture Pipeline walking is an important phenomenon that can threaten the integrity of a pipeline system. The severity of the phenomena increases as the operating conditions become more severe. As operating temperatures increase pipelines become more susceptible to walking and the walking magnitude with each cycle increases.

Shutdown and start-up cycles that lead to pipe-walking may require some form of mitigation if, over a number of cycles, this movement would lead to excessive global axial displacement of the pipeline. Axial displacement is excessive if it compromises the design of pipeline end terminations, in-line connections or riser configurations. To illustrate how serious an issue pipeline walking can be Table 1 presents the walk associated with different drivers for an 8-inch surface laid pipeline operating at 110ºC, that is subjected to 200 full start-up-shutdown cycles over its lifetime.

Length Driver Walk/cycle Walk/Life

2km 10°C/km transient 15 mm 3 m 2km 30°C/km transient 45 mm 9 m 4km 30°C/km transient 180 mm 36 m 2km 100kN SCR tension 350 mm 70 m 2km 5° Slope 170 mm 34 m

Table 1 – Example Walking Results In each of these examples the walk per cycle can appear to

be small but considered over the entire field life, the total axial displacement can become excessive.

The most common method of mitigation is the installation of flowline anchors to control or limit the maximum axial displacement. The size of such anchors can be significant, typically being in the range of 50 to 350 tonnes. Provision for anchoring is important to address in the layout of multiple flowline end terminations at a manifold.

End of line anchors are generally considered simpler to install than a mid-line anchor. A unidirectional anchor is preferred to a fixed anchor, as this reduces the required anchor capacity by allowing thermal expansion towards the anchor whilst limiting excessive walking displacement away from the anchor. This configuration also avoids increasing compressive loads in any lateral buckles along the pipeline. Anchor design capacity can be further reduced by incorporating anchor flexibility in the analysis and the anchor size can possibly be reduced by designing the anchors to sustain loading only during relatively infrequent pipeline shutdowns. Anchor loads and walking susceptibility can be also moderated by increasing pipe weight but this approach is case specific.

A major concern raised by the use of holdback anchors to control pipe walking, is the additional tension in the pipeline generated at shutdown by the restraining anchors. The concern is that tension in these pipelines could be sufficient to cause lateral instability (ratcheting lateral displacement) of the pipeline at a route-curve. Except for the shallowest of curves, this instability can pullout the route-curve, allowing further pipe to walk axially, until the curvature is small enough to be laterally stable. The minimum stable radius of curvature may be so large as to compromise field architecture. The tension profiles, anchor loads and susceptibility of a pipeline to curve-pullout should be addressed in front-end engineering design, to ensure that field architecture is not compromised. In some cases, it may be necessary to include a mid-line tie-in to overcome route curve instability.

It is common now for high temperature pipelines to be designed to buckle laterally on the seabed. Designing a long pipeline to laterally buckle effectively splits the pipeline into a number of shorter lines between buckles[3]. This is illustrated in Figure 26.

0 0.2 0.4 0.6 0.8 1

Length (x/L)

Effe

ctiv

e A

xial

For

ce

Buckled Pipe - Unload Straight Pipe - UnloadBuckled Pipe - Load Straight Pipe - Load

S

Virtual AnchorLateral Buckle

Figure 26 -Force Profile in Laterally Buckled Pipeline

The buckles effectively split a long pipeline, which may not walk, into a series of shorter pipelines which could walk. The analytic expressions can be used to quickly assess whether walking may occur in a buckled pipeline by modifying the effective pipeline length to match the spacing between lateral buckles. The use of holdback anchors can affect lateral buckling behavior and influence loading in the lateral buckles. The interaction between lateral buckling and pipeline walking is complex and requires the use of FEA to investigate the phenomena fully.

Finally, the walking behavior is critically dependant upon the axial friction force. In most situations decreasing the axial friction results in an increased susceptibility to walking. It is therefore crucial to select a suitable range of axial friction coefficients at the design stage. It is common practice to define very low lower bound axial friction coefficients; this is particularly true in soft clays where axial friction coefficients of 0.2 are regularly employed. For such low friction coefficients, full mobilization will occur for very long lengths of pipe and the walking mechanisms outlined here will all be active.

However, recent work carried out by the SAFEBUCK JIP suggests that the axial friction that develops in practice is very unlikely to be this low. Selecting a more appropriate lower

OTC 17945 11

bound can fundamentally modify the severity of the walking problem.

Conclusions This study has determined the key parameters that effect pipeline walking and developed some simple analytic equations for use in conceptual design, to assess the likelihood of walking occurring.

The key parameters that affect walking are: • Axial pipe-soil friction; • Gradient of the thermal transients; • Steady state operating conditions, which defines the range

of effective force; • Seabed slope; • Tension at the flowline end due to a SCR.

This phenomenon can massively complicate the design of deep water flowlines and has significantly impacted field layouts on a number of recent projects.

Acknowledgements The authors would like to thank the participants in the SAFEBUCK JIP. BP, ConocoPhillips, ExxonMobil, Petrobras and Shell, as well as the US Government through the MMS participated in Phase I, while installation contractors and suppliers were represented by Allseas, JFE-Metal One, Technip and Tenaris. Additional participants including Chevron, Statoil and Stolt Offshore have joined Phase II, which will run through 2005 and 2006. Abbreviations FEA Finite Element Analysis FPS Floating Production System JIP Joint Industry Project SCR Steel Catenary Riser XHPHT Extreme High-pressure High-temperature Nomenclature

Ae Cross sectional area of Pipe OD (m2) Ai Cross sectional area of Pipe ID (bore) (m2) As Cross sectional area of Pipe wall (m2) E Youngs Modulus (N/m2) EA Axial Stiffness (N) f Axial Friction force f=μW (N/m) fθ Force generated by the thermal transient EAαqθ

(N/m) f* Friction force at which cyclic constraint occurs

(N/m) fmax Friction force at which max walk occurs (N/m) L Pipeline Length (m) pi Internal Pressure (Pa)

pe External Pressure (Pa) P Fully Constrained Effective Force (N) ΔP Change in Fully Constrained Force (N) qθ Thermal gradient (°C/m) S Effective Axial Force (N) SL Residual Lay Tension (N) SR SCR Tension (N) Sw Axial Wall Force (N) ΔS Change in Effective Axial Force (N) ΔSf Change in Effective Axial Force over Xab (SCR) (N) ΔSs Change in Effective Axial Force over Xab (Slope) (N) W Submerged Unit Weight (N/m) Xab Distance between virtual anchors (m) α Coefficient of Thermal Expansion (1/°C) ΔR Total Walk per cycle due to SCR Tension (m) Δφ Total Walk per cycle due to Seabed Slope (m) ΔT Total Walk per cycle due to Thermal Transients (m) ε Axial Strain φ Seabed Slope (°)

θ Operating Temperature (°C) θinst Installation Temperature (°C) μ Axial Friction Coefficient ν Poisson’s Ratio

References

1. Konuk, I. “Expansion of Pipelines under Cyclic Operational Conditions” OMAE 1998.

2. Tornes, K., Jury, J., Ose, B., Thompson. “Axial Creeping of High Temperature Flowlines Caused By Soil Ratcheting” OMAE 2000.

3. Carr M., Bruton, D. and Leslie, D. “Lateral Buckling and Pipeline Walking, a Challenge for Hot Pipelines” Offshore Pipeline Technology Conference, Amsterdam. 2003.