THERMAL EXPANSION &
GLOBAL BUCKLING
PROF. Ir. Ricky Lukman Tawekal, MSE, PhD
Eko Charnius Ilman, ST, MT
KL4220 PIPA BAWAH LAUT
THERMAL EXPANSION ANALYSIS
1
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
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:
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
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.
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 = ETfr= Strain due to end cap effect = E E A A P Pi e i ) (
= Strain due to thermal effect =
= Strain due to Poisson effect = E t D P Pi e 2 ) ( T expT x
= Strain due to mobilisation of friction = f E A L Ws s
= Strain due to residual lay tension = r E A N L
=E
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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 NET LR
=E
NET
T
r
T r
E
= as2C@MH<G
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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 EW
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 NETdL
0
for hot end=
LLACOLD NET
dL
for cold endWhere
LAHOT = Virtual anchor point at hot end LACOLD = Virtual anchor point at cold end
Pipe Stress Analyisis