Page 1
1
Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected]
Lecture 12 – Thermal Expansion
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Lecture Goals
Students will be able to: define pipeline engineering design cases for
thermal expansion, and calculate thermal expansion stress and strain
for subsea pipelines
2
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Reading List
3
# Document 12.1 DNV OS-F101 Submarine Pipeline Systems. Offshore Standard, 240p.
[2007_DNV_OS_F101.pdf]
Section 4 B109 Section 5 D604, E206, E400, E414, G202, G504
12.2 Palmer, A.C. and Ling, M.T.S. (1981). “Movements of submarine pipelines close to platforms.” Proc., OTC-4067, pp.17-24.
Page 2
2
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Thermal Expansion Differential Temperature
Pipeline operating temperature is different than the installation tie-in temperature
Pipeline Deformation Linear, area, or volume
expansion Statically indeterminate
and depends on boundary condition
4
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Full Axial Restraint Design Case
Anchor block Thermal stress effect
Δ100°C ⇒ 240MPa ~60% SMYS X60
Design Equation Hooke’s law
5
σl σl
εl = Δ = 0 εl = Δ = 0
σh =
pi Di − pe De( )2 t
σ l = νσh − Eαθ =
ν2 t
pi Di − pe De( ) − Eαθ
ε l =
1E
σ l −νσh( ) +αθ = 0
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
End Free Boundary Condition Design Case
Frictionless sleepers 90° bend to riser
Design Equation Hooke’s law
6
σl σl
σ l =
pi Di − pe De
4 t
ε l =
1E
σ l −νσh( ) +αθ =piDi − peDe
4 t E1− 2ν( ) +αθ
Δ = ε l dx
L∫ =
L2
piDi − peDe
4 t E1− 2ν( ) +αθ
⎛
⎝⎜⎞
⎠⎟
εl, Δ εl, Δ
σh =
pi Di − pe De( )2 t
Page 3
3
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Partial Axial Restraint Design Case
Surficial seabed, spans and buried contact
Structural supports, objects, restraints (e.g. rock dump, clamps)
Tie-in points with platform riser, PLEM, PLET, etc.
Expansion spool Shore approach
7
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Partial Axial Restraint – Anchor Length
Design Case Soil forces buried
pipeline Frictional forces
structural support
8
x
x=z=π p R2
f1− 2ν +
2 tp R
Eαθ⎛⎝⎜
⎞⎠⎟
Δ =
p R2E t
1− 2ν( ) +αθ⎡
⎣⎢
⎤
⎦⎥ z −
f z2
4π E R t
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Thermal Expansion Loops Configuration
U-shape L-shape Circular Zig-Zag
9
Page 4
4
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Ring Expansion Loop Analysis
Energy Methods Vertical deflection at load P
Horizontal deflection at load P
10
r P
δV = −
2P r 3
EI
δH =
π P r 3
2EI
δV =
dUd Pi
=1
E IM
dMd Pi
ds =0
2π
∫1
E IPr sinθ −r + r cosθ( ) r dθ
0
2π
∫
θ
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Multiple Ring Expansion Loop
Moment Equations [Eq.1]
11
Ref: Ugural and Fenster (1987)
M1
M2
M3
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Multiple Ring Expansion Loop
Minimize Energy End deflection [Eq.2]
End slope [Eq.3]
12
Ref: Ugural and Fenster (1987)
Page 5
5
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Multiple Ring Expansion Loop End Deflection
[Eq.4] Substitute moment
equations [Eq.1] into end deflection equation [Eq.2]
13
Ref: Ugural and Fenster (1987)
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Multiple Ring Expansion Loop
End Slope [Eq.5] Substitute moment equations [Eq.1] into slope
equation [Eq.3]
14
Ref: Ugural and Fenster (1987)
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Multiple Ring Expansion Loop Compatibility Equation
[Eq.6] Deflection at Point E (End
Restraint)
Solve Eq. 4, 5 & 6 Expansion loop geometry,
expansion coefficient and temperature gradient know
Solve for axial forces (N), section moments (M) and end deflection (eEN)
15
eEN = EET = αθ L
Ref: Ugural and Fenster (1987)
M1
M2
M3
Page 6
6
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
Example 12-01 A 273.1 mm DNV SMLS 450 arctic
pipeline with a 9.525 m wall thickness traverses 2.5 km from the gravity based platform to the shore approach with a maximum water depth of 12 m. The design pressure is 10 MPa at 5 m reference height and operates at 100 °C with a tie-in temperature of -40 °C. The oil is API 38°. The soil has an undrained shear strength of 25 kPa.
Calculate the virtual anchor point, axial strain and end deflection due to thermal expansion for a buried pipeline.
Check the equivalent stress using a design factor of 0.9.
16
ENGI 8673 Subsea Pipeline Engineering – Lecture 12 © 2009 S. Kenny, Ph.D., P.Eng.
References Ugural, A.C and S.K. Fenster. (1987). Advanced Strength
and Applied Elasticity, 2nd SI Edition. Prentice Hall, ISBN 0-13-500901-4
17
