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END EXPANSION AND LOCAL BUCKLING

The expansion analysis determines the maximum pipeline expansion at the two termination points and the maximum associated axial load in the pipeline. If a pipeline were free to elongate, the rise in temperature and pressure during operation would result in an increase in length. However, due to the restraint offered by the seabed friction, such pipeline expansions only manifest themselves at the ends, i.e. at the tie-in points to fixed structures. At undisturbed sections(anchor length) of the pipeline the restraint against thermal and pressure induced expansion may cause a compressive pipeline force, which could result in a global buckling mechanism.

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End Expansion Description The operating temperature and pressure are higher than the temperature

and pressure when the pipe was tied in. Because the temperature is higher, the pipe tends to expand. The expansion is constrained by friction force between the pipeline and the sea bottom where the strain is zero (the pipeline not move due to temperature/ pressure).

The movement occur within a transition region whose length depends on the limiting frictional force the bottom and pipeline (i.e. if friction is large the transition region is short and the movement is small, but the friction is small the movements are larger.)

If in operating, the pressure and temperature are reduced the movement toward platform is reserved. This is because friction always opposes motion, so that when the temperature is reduced the friction force do not return to zero, but partially reserve ,holding the pipeline in its extend position and preventing it from slipping back.

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End Expansion Methodology

The maximum pipeline end expansion is based on net longitudinal strain and friction force between the pipeline and the sea bottom.

Longitudinal Strain

Strain due to End Cap

Strain due to Poisson

Strain due to Thermal

Strain due to Friction Force

I. Longitudinal Strain of the Pipeline1. End Cap: The end cap strain is caused by the internal pressure of the fluid in

the pipeline acting at an effectively "closed" end of a pipeline, such as a bend.

Where: Pi, Po: are internal and external pressure E: Elastic Young’s modulus As: Steel Area

End Expansion Methodology

2. Poisson Strain: The Poisson strain is a result of the action of the hoop stress, which radially expands the pipeline.

Where: ν: Poisson's RatioE: Elastic Young’s modulus t: Wall ThicknessPi: Internal PressurePo: External Pressure

3. Thermal Strain: The below formula just is applicable to a

thermal strain profile along the pipeline.

Where Ti: Installation Temperate (assume that the ambient temperature during operation)

Tp: Operating Temperate: Coefficient of Thermal

Expansion.

End Expansion Methodology

4. Frictional Strain: Pipeline Resting on the Seabed: Friction resistance between an object and

the surface it is resting on is given by the Coulomb relationship, resulting from the normal force acting between the surfaces. For a pipeline, the fictional resistance increases linearly with distance, L, from the pipeline free end, in proportion to the cumulative pipe weight. For a pipeline resting on the seabed, the frictional strain is given by:

Pipeline Resting on the Seabed: For buried pipelines, additional resistance to movement is provided by the soil pressure acting around the pipeline.

End Expansion Methodology

Where:f: Friction Strain: Longitudinal Coefficient of FrictionWs: Submerged WeightAs: Steel Areab: Submerged soil densityHb: Depth of pipe below soil surface k0: Coefficient of lateral soil stress at rest: Internal angle of friction of soil

All the coefficient of soil will be detail in the appendix A

Longitudinal Strain of the Pipeline:net = e + p+ t - f

II. Pipeline Expansion:

Expansion at Hot end Expansion at Cold end

End Expansion Methodology

Where:LA: Anchor length (which is the distance between the free end of

the pipeline and the anchor point).Anchor point (no movement occurs) is defined by equating the

applied strain force and frictional force .i.e. ε. Net = ε.e + ε.p + ε.t - ε.f = 0 finding LA

Other method finding LAH based on total friction strain available from hot end

and total friction strain available from cold end

The final friction strain fic applied for total route as minimum of fh and fc (see figure below): after that finding f as minimum between fic and TOT .

TOT

End Expansion Methodology

TOT

LAH LAC

f

The anchor length of pipeline will calculated as equation below:

III. Design spool of pipe to against local bucklingSpool length will be designed by Autopipe software is acceptable to absorb the load due to end expansion. The maximum stress for all load cases and the allowable stress in accordance with DNV-OS-F101. ( The preliminary spool sizing will be design in house software)