DESIGN CONSIDERATIONS OF
HIGH-TEMPERATURE PIPELINES
Wim Guijt M.Sc. Civ.Eng.
ABSTRACT
Nowadays buried pipelines are operated more and more at elevated
temperatures and pressures. Examples of this are flowlines carrying
(untreated) gas or oil from a so-called satellite towards a treatment
facility, both onshore and offshore, and district heating transmission
pipelines.
Design of high-temperature and pressure pipelines requires special
attention, as restrained thermal stresses are high. Due consideration
should also be given to thermal expansion, as stresses in bends of
expansion loops are significant. Modelling of the pipe-soil interaction
using soil characteristics, especially friction and lateral resistance, is
important when designing high-temperature pipelines.
Examples of different high-temperature pipeline systems, such as
bonded Steel-PUR-PE (pre-insulated pipelines) and Pipe-in-Pipe
systems, meeting limit state design criteria as put forward in the Dutch
Design Code NEN 3650, are reviewed in this paper. Results of finite
element calculations, modelling the pipe-soil interaction in detail, are
presented and discussed. Measures such as pre-stressing of pipelines are
highlighted.
Key Words: bonded pre-insulated pipelines, Pipe-in-Pipe, limit state
design, thermal expansion, expansion loop, pipe-soil interaction.
INTRODUCTION
Design of high-temperature pipelines requires special attention.
Experience in designing onshore District Heating pipelines and
flowlines has been gained. Flowlines are typically operated at elevated
temperatures and pressures of above 100 bar, whereas District Heating
systems are designed for pressures ranging from 16 bar up to 30 bar.
Nowadays, two different systems are used for high-temperature
pipelines: insulated Steel-PUR-PE (steel carrier insulated by
polyurethane protected by a polyethylene jacket) and Pipe-in-Pipe
systems. In this paper, design considerations of both systems are
reviewed.
Different sections are distinguished in designing high-temperature
pipelines: fully restrained sections and sliding sections, where the
pipeline expands towards a free end. Furthermore, attention should be
paid to design of loop configurations where thermal expansion from the
sliding sections is taken up.
Paper No: ISOPE-99-AMG-01
The minimum required wall thickness of high-pressure pipelines is
generally governed by the hoop stress criterion, limiting the
circumferential stress caused by internal overpressure to a fraction of
the yield strength. Adopting an allowable stress approach for hightemperature and high-pressure pipelines, by limiting the Von Mises
equivalent stress to a percentage of the yield strength, the equivalent
stress criterion might not be met even at moderate design temperatures
using a wall thickness based on the hoop stress criterion. According to
the Dutch Standard NEN 3650, the hoop stress criterion governs the
minimum required wall thickness even when designing hightemperature and high-pressure pipelines. Design requirements of the
NEN 3650 are reviewed in this paper for an example of a hightemperature and high-pressure pipeline.
A pipeline loaded by temperature and pressure will expand near a
free end such as an expansion loop. The axial movement is counteracted
by soil friction, acting against the outside of the PE casing of the
insulated Steel-PUR-PE pipeline. At a certain distance from the free
end the friction force (summated friction over the moving pipe length)
is in equilibrium with the normal force of the steel inner pipeline. This
is the so-called virtual anchor point, where thermal expansion is fully
restrained. The magnitude of thermal expansion and the bend
parameters determine the stress level encountered in expansion loops.
Results of calculations (expansion analysis and loop design) are
presented in this paper.
Calculations have been made using a finite element program called
PLE-micro-CAD. Pipe-soil interaction can be modelled in detail using
this program by a characterisation of soil reaction forces. When
designing high-temperature pipelines due consideration should be given
to the soil reaction forces, as these are significant.
DESIGN OF A FULLY RESTRAINED HIGH-TEMPERATURE
STEEL-PUR-PE PIPELINE
The design factor for internal pressure, according to the NEN
3650, ranges from 1.39 to 2.22 (equal to 1/0.72 respectively 1/0.45) and
depends on the product being transported (e.g. hot water, oil or gas), as
well as the location class. Normally a design factor F of 1.5 is used for
onshore pipeline design, assuring sufficient safety against the burst limit
state. According to NEN 3650 a de-rated yield stress shall be used when
designing pipelines for temperatures above 50 °C.
Wim Guijt M.Sc. Civ.Eng.
Page: 1 of 7
Stresses caused by fully restrained thermal expansion are
significant. A temperature differential ∆Τ of 120 °C induces a thermal
compressive longitudinal stress of -290 N/mm2 for carbon steel pipe
(αΕ∆Τ where α is the coefficient of thermal expansion and Ε Young’s
modulus, for carbon steel typically 11.5E-6 mm/mm/°C respectively
210,000 N/mm2). This thermal stress corresponds with the de-rated
yield stress of API 5L X52 steel (Reθ 292 N/mm2 at 130 °C design
temperature). Thermal stresses caused by restrained thermal expansion
are not related to the pipeline wall thickness. It is therefore not effective
to increase the wall thickness of a high-temperature pipeline in order to
meet imposed design criteria.
Combining a tensile stress in circumferential direction (σy) and a
compressive stress in longitudinal direction (σx), results in a high Von
Mises equivalent stress (see Eq. 1, 2 and 3). For illustrative purposes,
other loads than pressure and temperature are ignored, as these loads
are often not significant in designing high-temperature and highpressure pipelines.
p design pressure (N/mm2)
D Pipeline diameter (mm)
t
Wall thickness (mm)
Reθ de-rated yield strength (N/mm2)
F design factor (-)
Von Mises yield curve
600
Eq. 1: Hoop stress criterion
σx = υ
p (D − t )
− α E ∆T
2t
400
200
2
Circumferential stress
Where
p (D − t ) Re θ
<
2t
F
Sy (N/mm )
σy =
because continuity conditions (secondary loads) determine stresses
induced by temperature loading. Internal pressure, however, is a stress
prescribed loading (direct relation between stresses and load via
equilibrium conditions also called primary loads).
The Von Mises yield curves and an illustrative stress history of an
axially restrained pipeline operating at 130 °C and 60 bar is presented
in Figure 1. According to NEN 3650 factored loads (load factor for
internal pressure 1.39, temperature 1.25 and other loads 1.5) have been
used to calculate the stress history, which is shown in the graph.
Results are based on finite element calculations made with PLEmicro-CAD for a 16” carbon steel pipeline, material API 5L X52 with a
yield strength Re of 358 N/mm2 and a de-rated yield strength Reθ of
292 N/mm2. A minimum wall thickness of 6.4 mm is required to fulfil
the hoop stress criterion (design pressure of 60 bar at a design
temperature of 130 °C), using a design factor of 1.5 for internal
pressure according to NEN 3650. Following the allowable stress theory,
a wall thickness of at least 7.8 mm would be required using API 5L
X65 material. Use of API 5L X52 material is not possible, irrespective
of the wall thickness chosen, whereas the minimum required wall
thickness using API 5L X60 material would be 14 mm, adopting an
allowable stress design.
0
-200
Reθ
-400
Where
Re
ν
α
Poisson’s ratio (steel 0.3)
Coefficient of thermal expansion
(carbon steel 11.5E-6 mm/mm/°C)
E Young’s modulus (carbon steel 210,000 N/mm2)
∆T Temperature differential (°C)
Eq. 2: Axial stress of a fully restrained pipeline
σ vM = σ x 2 + σ y 2 − σ x σ y
Eq. 3: Von Mises equivalent stress
Limiting the hoop stress σy to 0.67 Reθ (corresponding with a
design factor F of 1.5 for the hoop stress criterion) and the thermal
stress αΕ∆Τ to Reθ, results in a Von Mises equivalent stress of 1.27
times the de-rated yield strength.
The maximum allowable equivalent stress (typically 0.9 Reθ) is
exceeded by more than 40%, adopting an allowable stress design. The
equivalent stress criterion governs the hoop stress criterion when the
restrained thermal stress αΕ∆Τ exceeds 0.56 Reθ. The wall thickness
should be increased and/or a higher material grade should be used in
order to meet the equivalent stress criterion, leading to (considerably)
higher costs.
According to NEN 3650 the Von Mises equivalent stress σvM,
determined using factored loads, may even exceed 1.5 times the derated yield stress at design temperature (1.5 Reθ). This is allowed
considering the combination of primary and secondary loads, provided
it is proven that alternating yield does not occur. This is made possible
Paper No: ISOPE-99-AMG-01
-600
-600
-400
-200
0
200
2
400
600
Axial stress Sx (N/mm )
Figure 1: Stress history of an axially restrained pipeline
The pipeline is loaded by soil overburden causing a bending stress
(in circumferential direction). Introducing internal pressure results in a
hoop stress σh as well as an axial tensile stress νσh in the restrained
section. Because of an increase in temperature, an axial compressive
stress starts developing. At a certain temperature, the material starts
yielding. During yielding the stresses do not change and will remain at
the same point on the yield surface for an axially restrained pipeline, as
thermal loading only induces axial strains. Adopting the NEN 3650
approach, alternate yielding does not occur when the thermal stress
1.25*αΕ∆Τ is smaller than the axial stress available within both yield
curves (Re and Reθ), at maximum circumferential stress encountered.
In this case, the maximum circumferential stress calculated
amounts to almost 300 N/mm2, resulting in an available stress range of
390 N/mm2 in axial direction within both yield curves. As the
maximum thermal stress amounts to 360 N/mm2 alternate yielding will
not occur. According to the NEN 3650 factored loads have been
considered for the analysis as described.
Using actual loads, it can be proven that the actual safety factor
regarding alternating plasticity amounts to 1.8. The maximum
circumferential stress, not using load factors, is 220 N/mm2 resulting in
an available axial stress range of 530 N/mm2 within both yield curves.
This is approximately 1.8 times more than the actual axial stress of 290
N/mm2 caused by temperature loading, not using the load factor of 1.25
for temperature.
Wim Guijt M.Sc. Civ.Eng.
Page: 2 of 7
A total strain of 0.13% was calculated, performing a plastic
analysis with PLE-micro-CAD for the fully restrained 16” CS pipeline
operating at 60 bar and 130 °C. Using the NEN 3650 (material)
specifications, an allowable strain of 0.5% can be adopted.
A limit value for the critical buckling strain εcr, applicable for both
the elastic and plastic range, has been derived on basis of experimental
results and is shown in Eq. 4 (t/r’ ratio’s > 1/60). The positive influence
of internal overpressure is neglected in this equation. A critical strain of
0.4% is found for the 16” carbon steel pipeline with a wall thickness of
6.4 mm, taking a conservative ovalisation of 5% of the external
diameter into account.
t
ε cr = 0.25 − 0.0025
r'
La =
Eq. 6: Pipeline active length La

p (D − t ) W L a 

∆x a = L a  α ∆T + (0.5 − ν )
−
2E t
2E A st 

Eq. 7: Maximum expansion ∆xa near free end (expansion loop)
Where
Where
r' =
Where
r
1−
3a
r
t
r’
r
a
Wall thickness (mm)
Pipeline radius, deformed situation (mm)
Pipeline radius (mm)
local ovalisation (mm)
0.7 2 −
∆x a = EA st
2 
3  σh  

 
4  Re θ  

Eq. 5: Limit on thermal strain by Klever, Palmer and Kyriakidis (1994)
It can thus be concluded that the restrained section of the 16” Carbon
Steel pipeline (Material API 5L X52 and a wall thickness of 6.4 mm)
fulfils the requirements of NEN 3650, operating at 60 bar and a
temperature of 130 °C.
EXPANSION ANALYSIS STEEL-PUR-PE PIPELINE
Pipeline active length La (mm), sometimes also called anchor
length, and corresponding maximum expansion ∆xa (mm), caused by a
temperature differential ∆T (°C), a design pressure p (N/mm2) and
counteracted by soil friction W (N/mm), can be determined using Eq. 6
and 7 respectively. Eq. 6 can be obtained from Equilibrium of Forces.
A constant temperature profile has been assumed (no temperature
drop or gradient taken into account), as heat losses of well-insulated
pipelines can be neglected. Lateral soil reaction forces from expansion
loops are also neglected in the formulas below.
Paper No: ISOPE-99-AMG-01
Coefficient of thermal expansion (mm/mm/°C)
Poisson’s ratio (-)
Young’s Modulus (N/mm2)
Pipeline Diameter (mm)
Wall thickness (mm)
Steel cross section area (mm2).

A limit on thermal strain, in order to avoid alternate yielding and
ratcheting, is defined by Klever, Palmer and Kyriakidis (1994) and is
presented in Eq. 5. As the hoop stress σy is limited to 0.67 Reθ for the
16” pipeline (corresponding with a design factor F of 1.5 for the hoop
stress criterion), the design is still adequate if the thermal strain α∆T is
limited to 0.17%. This strain corresponds with a maximum allowable
temperature difference of 145 °C, assuring that alternate yielding and
ratcheting is avoided.
2

3  σh 
Re θ 
−
+
1


E 
4  Re θ 

α
ν
E
D
t
Ast
The maximum expansion encountered at a free end of a pipeline is half
of the free expansion over the anchor length. Substitution of Eq. 6 in
Eq. 7 and rewriting of terms yields Eq. 8.
Eq. 4: Critical buckling strain (NEN 3650)
α ∆T <
A st 
p (D − t ) 
 α E ∆T + (0.5 − ν )

W 
2t 
2 
(α ∆T ) 1 +
2W



(0.5 − ν ) p (D − t ) 
2t
α E ∆T
2




Eq. 8: Influence of internal pressure on expansion
From Eq. 8 it can be concluded that the maximum displacement at
a free end is inversely proportional to soil friction and proportional to
the square of the temperature difference.
In case the hoop stress of a high-temperature and high-pressure
pipeline is limited to 0,67 Reθ and the thermal stress is equal to Reθ the
expansion increases by almost 30% due to internal pressure (last term in
Eq. 6 between brackets).
Expansion is directly proportional to the steel cross section area.
Use of high-grade materials, limiting the wall thickness required and
thereby the steel cross section area, is favourable in order to limit the
displacement imposed on expansion loops.
Due consideration should be given to the influence of the
coefficient of thermal expansion. This coefficient is typically 11.5E6
mm/mm/°C for carbon steel. A considerably larger coefficient is found
for stainless steels. Duplex Stainless Steel, frequently used for
flowlines, has a coefficient of thermal expansion of 13E6 mm/mm/°C,
resulting in an increased thermal expansion of some 30% compared
with carbon steel.
The NEN 3650 uses a load factor of 1.25 for temperature loading
and 1.39 for internal pressure. The use of load factors has a significant
impact on the expansion calculated. Considering the load factor for
temperature only results in an increase of the calculated expansion by
56% compared with the actual expansion.
An expansion analysis has been performed for standardised
District Heating pipelines using Eq.6 and 7. Material properties of
carbon steel, a design temperature Td 130 °C and a design pressure pd
of 25 bar have been assumed for the analysis. An average soil friction
W of approximately 5 kN/m2 typical for sandy soils, corresponding with
a cover of 1 metre, has been used. Standardised pipeline dimensions of
Steel-PUR-PE District Heating pipelines are summarised in Table 1.
Results of the expansion analysis are summarised in Table 2 and Figure
2.
Wim Guijt M.Sc. Civ.Eng.
Page: 3 of 7
4”
8”
12”
16”
24”
114.3
219.1
323.9
406.4
609.6
3.6
4.5
5.6
6.3
8
200
315
450
520
780
12" insulated Steel-PUR-PE pipeline, cold installed
DN 300/450 mm, Td = 130 C, pd = 25 bar
250
Expansion (mm)
Pipeline Diameter
Diameter
steel
pipeline (mm)
Wall
thickness
(mm)
Outside Diameter
PE casing (mm)
Table 1: Standardised dimensions of District Heating pipelines
200
150
100
50
0
0
8”
12”
16”
24”
137
203
250
299
348
97
146
181
218
256
250
400
200
300
150
200
100
100
50
0
0
4
8
12
16
20
24
Pipeline Diameter
Active Length La
Td and pd (metres)
Expansion
prestressing (mm)
Expansion
Td and pd (mm)
Cooling down, p=0
Warming up, pd
4”
8”
12”
16”
24”
70
106
131
157
185
-23
-34
-41
-49
-56
26
39
50
60
72
Table 3: Results of expansion analysis for standardised (pre-stressed at
70 °C) District Heating pipelines
200
100
100
50
0
0
-100
-50
-200
28
-100
0
4
8
12
16
20
24
28
Pipeline Diameter (inch)
La (metres)
Expansion (mm)
Figure 2: Pipeline active length La and corresponding maximum
displacement ∆xa
Paper No: ISOPE-99-AMG-01
175
Large expansions can often be avoided by pre-stressing of a
pipeline. The pipeline is heated to a temperature, just in between the
installation temperature and the design temperature, in an open trench.
After back filling, the pipeline is cooled down. This way the restrained
thermal stress is divided over a tensile and compressive stress, instead
of a compressive stress only for a cold installed pipeline. The risk of
buckling of high-temperature pipelines, when excavating a pipeline
over some length, can also be minimised by pre-stressing.
An expansion analysis has been performed for standardised
District Heating pipelines (Table 1) with a design temperature Td of
130 °C, pre-stressed at 70 °C and a design pressure pd of 25 bar, using
an average soil friction W of approximately 5 kN/m2. Results of the
expansion analysis performed for pre-stressed District Heating pipelines
are summarised in Table 3 and Figure 3.
Pipeline Diameter (inch)
La (metres)
150
Expansion analysis prestressed
standardised District Heating Pipelines
Expansion (mm)
Pipeline active
Length La
(metres)
Expansionanalysis coldinstalled
standardisedDistrict HeatingPipelines
500
125
Figure 3: Hysterese behaviour of a cold installed pipeline
The thermal expansion as calculated for a so-called cold installed
pipeline will only develop the first time during start-up. Due to the
reversal of friction forces the pipeline will only retract to approximately
half of the maximum expansion encountered during first start-up.
Shown graphically in Figure 3 is the hysterese behaviour of a 12” SteelPUR-PE District Heating pipeline. The analysis was performed with
PLE-micro-CAD. A soil friction of approximately 4.5 kN/m2 has been
used for these calculations. The expansion calculated using Eq. 7 and 8
(203 mm) is in good agreement with results of the detailed analysis
(201 mm).
300
100
Temperature (degrees Celsius)
Due to the large temperature difference of 120 °C, the active
length of a 12” Steel-PUR-PE pipeline is 250 metres. The mid section
of the pipeline is only fully restrained if the distance between both free
ends (expansion loops) is more than 500 metres. The corresponding
expansion is approximately 180 mm, considerably more than could be
taken up by a buried expansion loop. Therefore, the distance between
expansion loops is often limited. In practice cold installation of long
straight sections is limited to small diameter pipelines or pipelines
operating at lower temperatures (typically some 90 °C).
600
75
Warming up 1st time, pd
Table 2: Results of expansion analysis for standardised (cold installed)
District Heating pipelines
0
50
Expansion (mm)
4”
Pipeline active
Length La
(metres)
Pipeline Diameter
Active Length La
(metres)
Expansion ∆xa
Td and pd (mm)
25
Expansion Td and pd
Expansion cooling down p=0
Figure 4: Pipeline active length La and corresponding maximum
displacement ∆xa
Total expansion of a 24” high-temperature District Heating
pipeline over the full temperature range is limited to 128 mm (72+56
Wim Guijt M.Sc. Civ.Eng.
Page: 4 of 7
mm), if the pipeline is pre-stressed. This expansion can be taken up by a
buried expansion loop. The hysterese behaviour of a pre-stressed
pipeline is shown in Figure 5. Results of the detailed calculations made
are in excellent agreement with expansions calculated using Eq. 7 and
8.
12" insulated Steel-PUR-PE pipeline, prestressed
DN 300/450 mm, Td = 130 C, pd = 25 bar
Expansion (mm)
150
100
50
0
-50
-100
0
25
50
75
100
125
150
175
(compression to 50% of the original thickness requires approximately
100 kPa typically). Back filling with soft soils near expansion loops in
case sandy soils are encountered along the projected routing is also an
option.
Detailed calculations have been made using the finite element
program PLE-micro-CAD for a U-loop buried in sand. The legs of the
U-loop have a length of 10 metres each. Calculations have been made
according to NEN 3650 for the 16” carbon steel pipeline operating at
60 bar and a temperature of 130 °C, as described previously in the
paragraph: “Design of a fully restrained high-temperature Steel-PURPE pipeline”. An expansion of 90 mm is imposed on the expansion
loop. The bend parameters (radius R and wall thickness t) have been
varied. Also considered was the use of expansion cushions (sandy soils
or reduced stiffness using expansion cushions). A bend radius R of
2000 mm (5D) in combination with a wall thickness 9.5 mm was used,
resulting in a dimensionless bend parameter h of 0.46, as defined below
in Eq. 9. Stresses in a bend with a radius of 1200 mm (3D) and a wall
thickness of 6.4 mm (h=0.19) have also been investigated.
Temperature (degrees Celsius)
Cooling down (prestressing), p=0
Warming up, pd
h =
Cooling down, p=0
Figure 5: Hysterese behaviour of a pre-stressed pipeline
Where
4tR
D2
t
R
D
Wall thickness (mm)
Bend Radius (mm)
Pipeline Diameter (mm)
EXPANSION LOOP DESIGN OF STEEL-PUR-PE PIPELINES
Eq. 9: Definition of bend parameter h
Limitation of thermal expansion and proper choice of bend
parameters (bend radius, wall thickness) is of the utmost importance in
designing buried expansion loops. High loads are imposed on loops as
the deformation of the loop is counteracted by lateral soil reaction.
Furthermore, ovalisation of bends induces high bending stresses.
Bending stresses in bends are mainly governed by three bend
parameters: Bend radius R, pipeline diameter D and wall thickness t of
the bend. To a certain extent, the bending stresses are also influenced
by the bend angle. Use of thin walled, small radius bends results in high
bending stresses, caused by cross sectional ovalisation (stress
intensification factor). Expansion cushions are often placed alongside
the legs of expansion loops, especially in sandy soils, in order to limit
the lateral soil reaction on the expansion loop. A typical displacementsoil pressure diagram of sand is shown in Figure 6. Use of expansion
cushions reduces the overall stiffness considerably and therefore
reduces stresses in bends of expansion loops.
2
Lateral soil pressure (kN/m )
Lateral soil pressure - horizontal displacement response
of a buried 16" Steel-PUR-PE pipeline
200
150
soil reaction
expansion cushion
System total
100
50
0
0
25
50
75
100
125
150
Horizontal displacement (mm)
Figure 6: Lateral soil reaction in combination with expansion cushions
It is not required to use expansion cushions in soft soils as the
maximum lateral soil resistance and stiffness of soft soils (wet clay or
peat) is sufficiently low, comparable with a stiff expansion cushion
Paper No: ISOPE-99-AMG-01
Bend parameter
h = 0.46
Sandy soils
Reduced soil stiffness
h = 0.19
2
436 N/mm
576 N/mm2
2
431 N/mm2
328 N/mm
Table 4: Maximum Von Mises equivalent stress in bend
Use of expansion cushion reduces the Von Mises equivalent stress
by 25%, whereas the reduction of the bend parameter results in a 30%
increase. The requirement of NEN 3650 σvM < 1.5 Reθ is just met (Von
Mises equivalent stress σvM, determined using factored loads) for API
5L X52 material, adopting a bend radius of 5D and a wall thickness of
9.5 mm (h=0.46), not using expansion cushions.
A plastic analysis has been performed for the bend with a radius
R=5D and 9.5 mm wall thickness (h=0.46). A total strain of 0.5 % was
calculated not using expansion cushions in sandy soils. In case the soil
stiffness is reduced, either using expansion cushions or back-filling
with soft soils near the expansion loop, a total strain of only 0.19 % is
calculated. Soil reaction forces have a significant effect on stresses and
strains of bends in expansion loops.
Draft Standard CEN TC107/TC267/JWG1 Design, Calculation
and Installation for Pre-insulated Bonded Pipes for District Heating
mentions allowable stresses ranging from 400 up to 900 N/mm2 even
for API 5L Grade B materials. An elastically calculated (fictive) stress
is used as a measure for inelastic strains. As the number of load cycles
in District Heating systems is limited (typically some 250 up to 2500
full load cycles) fatigue curves are used to determine the allowable
stress range. The maximum stress calculated for the bend with a radius
R=3D and a wall thickness of 6.4 mm (h=0.19) meets the criteria of the
draft Standard TC107.
The fatigue curve, as adopted by CEN TC 107, is compared with
test results of Markl in figure 7. A reduction of 25% in stresses results
in a 3 times larger number of cycles to failure.
Wim Guijt M.Sc. Civ.Eng.
Page: 5 of 7
Eq 11: Normal force of jacket pipe near fixed point
Fatigue curves
La =
Allowable stress range (N/mm2)
10000
FFP , j + α EA st , j∆Tj
W
Eq. 12: Active length of Pipe-in-Pipe system
CEN TC 107
Markl
1000
∆ FP =
(
)
FFP, j + α EA st , j∆Tj 2
WL2a
=
2EA st , j
2WEA st , j
Eq. 13: Displacement of fixed points near both free ends
100
10
100
1000
Number of cycles to failure (N)
10000
design pressure (N/mm2)
Temperature differential (°C)
Pipeline Diameter (mm)
Wall thickness (mm)
Steel cross section area (mm2).
Poisson’s ratio (steel 0.3)
Coefficient of thermal expansion (carbon steel
11.5E-6 mm/mm/°C)
E Young’s modulus (carbon steel 210,000 N/mm2)
LFP Length between fixed points
La Active length
∆FP Expansion at fixed point location
Where
p
∆T
D
t
Ast
ν
α
Figure 7: Fatigue curves
EXPANSION ANALYSIS OF PIPE-IN-PIPE SYSTEMS
The subscripts c and j are used for the carrier pipe
respectively the jacket pipe.
Eq. 10, 11 and 13 can be solved using an iterative numerical
method. A program has been made for easy calculation purposes (quick
check of normal forces and expansion). Results of the program are in
good agreement with finite element calculations made for Pipe-in-Pipe
systems as discussed below.
Results of calculations made for a 1 kilometre long carbon steel
12”/22” Pipe-in-Pipe system with a design temperature of 160 °C
operating at 25 bar are presented in Figure 8 and 9. A wall thickness of
5.6 mm has been used for both the 12” carrier and 22” jacket pipe. The
calculated displacement of both fixed points for a cold installed Pipein-Pipe system is 152 mm. If the Pipe-in-Pipe system is pre-stressed at
100 °C both fixed points will retract 55 mm and will expand 35 mm, a
total displacement range of only 90 mm. A Pipe-in-Pipe system also
shows histeresis behaviour similar to Steel-PUR-PE pipelines.
Expansion analysis 12"/22" Pipe-in-Pipe system,
fixed point at free end only
200
Expansion (mm)
Pipe-in-Pipe systems have been frequently used over the last
decades for district heating pipeline transmission systems as well as
high-temperature (typically above 150 °C) systems transporting steam,
hot water or oil. Nowadays they are also used for so-called highintegrity systems for safety reasons (e.g. chlorine pipelines). Pipe-inPipe systems are often shop pre-fabricated. The insulated steel carrier
pipe is centralised within a PE-coated steel jacket pipe using bearings
such as shoe supports or roller bearings. The steel carrier pipe is
insulated using pre-formed mineral wool shells, specially impregnated
to provide a high degree of water repellence. As an alternative, glass
wool or calcium silicate can be used as insulating materials. The
insulating properties of the Pipe-in-Pipe system can be improved
further by vacuuming of the free space between the carrier and jacket
pipe.
Different Pipe-in-Pipe systems can be distinguished. If the distance
between expansion loops is limited, the free expansion of the carrier
pipe, operating at elevated temperatures, is absorbed within the
(enlarged) jacket pipe. A single intermediate fixed point between the
expansion loops guides the expansion towards both free ends.
Temperature loading is absorbed by free expansion of the carrier pipe
and bending of the expansion loops of the carrier pipe, inside the jacket
pipe. The jacket pipe is loaded by soil overburden and traffic loads.
In case long straight sections are present, expansion of the carrier
pipe is limited utilising fixed points near both free ends of the straight
section. Fixed points are constructions where (a part of) the restrained
thermal expansion forces of the carrier pipe are transferred to the jacket
pipe. Both carrier pipe and jacket pipe can move at the fixed point,
there is only no relative displacement between carrier and jacket pipe.
The Pipe-in-Pipe system may also be pre-stressed in order to limit both
the compressive force of the carrier pipe and the expansion. Expansion
of Pipe-in-Pipe systems with a single fixed point near both free ends,
thus no intermediate fixed points, can be calculated using Eq. 10, 11, 12
and 13. It is also assumed that the casing pipe is fully restrained, as this
is an assumption used in Eq. 13.
150
100
50
0
-50
-100
-150
-200
0
Fc = υ
2EA st , c ∆ FP
p (D − t )
− α EA st , c ∆Tc +
2t
L FP
Eq. 10: Normal Force of carrier pipe
FFP , j = − Fc + 0.5
200
400
600
Carrier pipe
1000
Jacket pipe
Figure 8: Expansion of a 12”/22” Pipe-in-Pipe system, 2 fixed points
p (D − t )
− α EA st , j ∆Tj
2t
Paper No: ISOPE-99-AMG-01
800
Length (m)
Wim Guijt M.Sc. Civ.Eng.
Page: 6 of 7
Equivalent Stress of 12"/22" Pipe-in-Pipe
5 fixed points spacing 25 m at both free ends
Equivalent Stress of 12"/22" Pipe-in-Pipe
fixed point at free end
Von Mises equivalent
2
stress (N/mm )
400
Von Mises equivalent
2
stress (N/mm )
400
350
300
250
200
150
100
350
300
250
200
150
100
50
0
50
0
0
0
200
400
600
800
200
400
600
800
1000
1000
Length (m)
Length (m)
Carrier Pipe Jacket pipe
Carrier Pipe
Jacket pipe
Figure 9: Equivalent Von Mises stress (N/mm2) of a 12”/22” Pipe-inPipe system, 2 fixed points
CONCLUSIONS
INFLUENCE OF MULTIPLE FIXED POINTS
For offshore Pipe-in-Pipe systems, fixed points or so-called bulkheads are generally placed every 24 metres. Calculations performed
show that the thermal expansion of the Pipe-in-Pipe system is hardly
reduced placing bulk-heads every 24 metres, instead of using a single
fixed point at either free end. Thermal stresses of the carrier pipe are
increased as the free length between fixed point is reduced.
Expansion analysis 12"/22"Pipe-in-Pipe system,
5 fixed points spacing 25 metres at both free ends
Expansion (mm)
200
150
100
50
0
-50
-100
-150
-200
0
200
400
600
Figure 11: Equivalent Von Mises stress (N/mm2) of a 12”/22” Pipe-inPipe System, 10 fixed points
800
1000
Adopting the design approach of NEN 3650 the minimum wall
thickness required is governed by the hoop stress criterion for highpressure and high-temperature pipelines. A limit state approach or a
strain based design is more adequate in designing high-temperature
pipelines, compared with an allowable stress design.
Use of high-grade materials favours the design of high-temperature
pipelines, as it limits the wall thickness required and provides more
safety against alternate yielding. Limiting the wall thickness also
reduces expansion imposed on expansion loops.
When designing high-temperature pipelines, due consideration
should be given to pipe-soil interaction. Stresses and strains caused by
soil loading (especially lateral soil reaction near expansion loops) are
significant and must be taken into account.
The choice of design factors has a significant impact on the
(calculated) thermal expansion. It is not yet clear what the actual safety
factor gained is, utilising the present design practice. Load and safety
factors should therefore be determined based on modern risk and
reliability based limit state design methods and not based on historical
backgrounds.
Criteria are required for alternating loadings, such as temperature
and pressure loading. In the Netherlands, analytical models have been
developed over the years.
Length (m)
REFERENCES
Carrier pipe
Jacket pipe
Figure 10: Expansion of a 12”/22” Pipe-in-Pipe system, 10 fixed
points
Paper No: ISOPE-99-AMG-01
Draft Standard CEN/TC107/TC267/JWG1 (1997). “Design,
Calculation and Installation for Pre-insulated Bonded Pipes for
District Heating”.
Gresnigt, AM (1986). “Plastic Design of buried steel pipelines in
settlement areas”, HERON, Vol. 31 no. 4.
Klever, F.J., Palmer, A.C. and Kyriakides S. (1994). “Limit-state design
of high-temperature pipelines”, Offshore Mechanics and Arctic
Engineering (ASME), Pipeline Technology, Vol. 5, pp. 77-92.
NEN 3650 (1992). “Requirements for steel pipeline transportation
systems”, Nederlands Normalisatie Instituut.
Wim Guijt M.Sc. Civ.Eng.
Page: 7 of 7