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THERMAL EXPANSION &

GLOBAL BUCKLING

PROF. Ir. Ricky Lukman Tawekal, MSE, PhD

Eko Charnius Ilman, ST, MT

KL4220 PIPA BAWAH LAUT

THERMAL EXPANSION ANALYSIS

1

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Pipe Stress Analyisis

Stress analysis

Thermal

Expansion

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• During operation, pipeline always have variation loading

that create stress

• To ensure the pipeline safe along the design life, stress

analysis need to be conducted

• Pipe stress analysis schematic will be:

• Code is adopted from failure theory. Code development

consists of main aspects like flexibility effect, safety

factor, welding effect, etc in failure theory

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Pipe Stress Analyisis

2

BASIC THEORY

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Stress:

Stress of a material is the internal resistance per unit area to the deformation caused by applied load.

Strain:

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Pipe Stress Analyisis

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∆ = thermal expansion

α = koefisien linier thermal expansion

l = panjang awal

dengan asumsi thermal expansion terjadi pada region elastis material

= thermal expansion stress

E = Modulus elastisitas

∆ = thermal expansion

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Pipe Stress Analyisis

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The purpose of the thermal expansion calculations is to obtain the net thermal expansions at both ends of the pipeline.

Expansion in a subsea pipeline is due to:

• Temperature Effect, due to differential inside & outside temperature • Pressure Effect, end cap effect & poisson effect

• Residual Tension, if any • Soil friction Effect, as resistance

Longitudinal expansion in a pipeline is dependent on the temperature and pressure differentials, and the frictional resisting force between the pipeline and the seabed. At some distance from the hot and cold ends, the pipeline is virtually anchored when the forces producing the expansion are balanced by the cumulative effects of the soil frictional force.

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The purpose of the thermal expansion calculations is to obtain the net thermal expansions at both ends of the pipeline.

Expansion in a subsea pipeline is due to:

Temperature Effect, due to differential inside & outside temperature

Pressure Effect, end cap effect & poisson effect

Residual Tension, if any

Soil friction Effect, as resistance

Longitudinal expansion in a pipeline is dependent on the temperature and pressure differentials, and the frictional resisting force between the pipeline and the seabed. At some distance from the hot and cold ends, the pipeline is virtually anchored when the forces producing the expansion are balanced by the cumulative effects of the soil frictional force.

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Pipe Stress Analyisis

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When the pipeline is long enough, there will be a certain point at some

distance from the pipeline end tie-in point, beyond which the pipeline

can be considered as completely restrained. This is due to the static

equilibrium of the expansion forces, the longitudinal soil friction and

restraining forces.

Riser Clamp Riser Clamp

Pipeline

Restrained Section Unrestrained Section Unrestrained

Section

Virtual Anchor Point Virtual Anchor Point

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Pipe Stress Analyisis

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The methodology used in estimating the pipeline end

expansion is based on the first principle of stress-strain

relation.

The stresses acting in the pipeline wall resulting from the

operating loads and friction resistance depend on whether the

pipeline is unrestrained, partially restrained or fully restrained.

Calculation methodology adopted is based on Ling MTS &

Palmer A. C. (1981) ’Movement of Submarine Pipelines Close to

Platforms’, Paper OTC 4067, 1981.

The net longitudinal

strain in the pipeline

between the free end and

the virtual anchor point is

given by the following

formula:

Where:

NET = ETfr

= Strain due to end cap effect = EE A A P Pi e i    ) (

= Strain due to thermal effect =

= Strain due to Poisson effect =             E t D P Pi e 2 ) (  T    expTx

= Strain due to mobilisation of friction = fE A L Ws s  

= Strain due to residual lay tension = rE A NL

=

E

NET

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Pipe Stress Analyisis

Pi = Design pressure (MPa)

Pe = External pressure (MPa) Ai = Pipe internal area (m2)

D = Pipe outside diameter (without coating) (m) t = Pipe wall thickness (m)

DT = Temperature difference at inlet (°) x = Distance from ‘hot’ end (m)

l = Decay length over which the temperature difference falls to 1/e of its initial value (m) Ws = Submerged weight of pipe (N/m) for unburied pipe

= Submerged weight of pipe + cover (N/m) for buried pipe Ls = Virtual anchor length or ‘friction length’ (m)

A = Steel pipe cross section (m2) N = Residual lay tension (N) n = Poison’s ratio for steel

m = Longitudinal friction coefficient between pipe and soil E = Elastic Young Modulus (MPa)0

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For the restrained section of the pipeline, the stress-strain relation is given by:

= 0 for restrained section NETLR

=

E

NET

T

r

T r

E

= as

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Pipe Stress Analyisis

In the pipeline between free end and virtual anchored point, there is some restraint from soil friction, although not sufficient to prevent total movement. The stress-strain relation within the partially restrained section is given by:

The virtual anchor length, which is the distance between the free end of the pipeline and the virtual anchor point, is given by:

LP

= E

E

f

=

2

s

L

for short pipelines

s r T E

W

E

A

for long pipelines

=

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The end expansions at the hot and cold ends are calculated by integrating the net longitudinal strain and is given by:

∆L

=

LAHOT NET

dL

0

for hot end

=

L

LACOLD NET

dL

for cold end

Where

LAHOT = Virtual anchor point at hot end LACOLD = Virtual anchor point at cold end

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Pipe Stress Analyisis

Typical Temperature Profile

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References

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