OTC 4067
MOVEMENTS OF SUBMARINE PIPELINES CLOSE TO PLATFORMS
by Andrew C. Palmer, University of Manchester;
Michael T.S. Ling, Total Oil Marine Limited
©Copyrlght 1981 Offshore Technology Conference
This paper was presented at the 13th Annual OTC in Houston, TX, May 4-7, 1981. The material is subject to correction by the author. Permission to copy Is restricted to an abstract of not more than 300 words.
ABSTRACT
and move towards the piatform:
An analytical model of expansion movements at the
ends of pipelines is developed. A comparison with
measurements on two North Sea pipelines shows that the
analysis is consistent with observed behaviour, and can
be used to assess the results of corrective action. An
alternative mechanism, that of creep deformation in
corrosion coating, is analysed briefly.
Alterations of pressure also cause movements.
Close to the elbow, in the horizontal leg, the
longitudinal stress is tensile, am the combination
of circumferential and longitudinal stress induces a
longitudinal tensile strain, and therefore a
longitudinal movement. Far from the platform, on the
other hand, longitudinal movement is prevented by
friction on the bottom: there the strain is zero and
the longitudinal stress is not the same as it is close
to the elbow.
INTRODUCTION
Expansion due to changes in temperature and
internal pressure can produce substantial movements at
the ends of submarine pipelines l • At platforms, these
movements are important beca~se they can overstress
risers and elbows, and bring the pipe into contact with
the platform itself.
The paper begins by describing the mechanisms that
give rise to expansion movements, and goes on to an
analysis that predicts how much movement is to be
expected. The results are compared with measurements on
two North Sea pipelines. In a few instances, another
mechanism may occur, and the movement may be due to
creep deformation in the corrosi9n coating : this will
be analysed briefly.
MOVEMENTS AT THE END OFA PIPELINE
Consider a straight submarine pipeline connected
to a platform riser (Fig.la). The riser passes through
clamps on the platform, and then has a 900 elbow. At a
short distance from the platform, the pipeline reaches
the bottom, and from then on is continuously in contact
with it.
It is helpful to begin by considering why the
pipeline should tend to move. The operating temperature
and pressure are higher than the temperature and
pressure when the pipe was tied in. Because the
temperature is higher, the pipeline tends to expand.
Far from the platform, the expansion is constrained by
friction between the pipeline and the sea bottom, am
longitudinal expansion stresses are set up. At the
platform, however, the pipeline is only slightly
constrained (by the vertical leg of the riser, which is
relatively flexible) , and there it can expand freely
References and illustrations at end of paper
17
It follows that both temperature and pressure
changes induce movements. At a distance from the
pJ.atform, friction prevents these movements, but it
does not do so close to the platform. The movements
occur within a transition region whose length depends
on the limiting frictional force between the bottom
and the pipeline: if friction is large, the transitior
region is short and the movements are small, but if
friction is small the movements are larger.
If the operating temperature and pressure are
reduced, the movement towards the platform is reversed.
only part of the original movement returns, and there
remains a residual movement towards the platform, even
if the pressure and temperature are returned to their
tie-in values. This is because friction always opposes
motion, so that when the temperature is reduced the
frictional forces do not return to zero, but partially
reverse, holding the pipeline in its extended position
and preventing it from slipping back.
ANALYSIS
The idealizations used in the analysis are those
customary in pipeline engineering, and the errors they
introduce will almost always be negligible in practice.
They are :
(1) that the pipe remains elastic, am that its
material properties are described by Young 1 s modulus E,
Poisson's ratio v and linear thermal expansion
coefficient ll.
(2) that the pipe can be treated as a straight thinwalled circular tube of thickness t and mean radius R
(defined as ~ (outside diameter - t».
(3) that the limiting longitudinal force f per unit
length, between the pipeline and the bottom, is
uniform along the length, independent of the distance
moved, and the same for either direction of motion.
The length Z over which movanent occurs can be found ..
f.rom the condition that cr L is continuous at z, and so,
by equating the values of crL in equations (5) and (7),
z is the solution of
(4) that when the line was tied in, its temperature was
the same as that of the sea water during subsequent
operation, that its internal pressure was negligible,
and there was no cold spring.
2
Z = (1TR p/f){1- 2v+ 2E:lt exp(-Z!A)}
(S) that the force differences associated with the
longitudinal pressure gradient are negligible over
the length of pipeline that takes part in the movement
(6) that the temperature of the line is not necessarily
uniform, but can be represented by an exponential
function of distance from the platform, so that
8 (x) = 8 exp (-x/A) • • • • • • • • •
• (1)
1
where 8 (x) is the temperature difference between the
pipeline and the water, at a distance x from the
platform, 8 is the difference at the platform, and A
is a decay length over which the temperature difference
falls to lie (0.369) of its initial value. This assumed
distribution corresponds to the steady state reached if
fluid flows along the pipeline away from the platform
at a uniform rate, and the overall heat transfer
coefficient is independent of time and temperature.
A negative value of A represents flow towards the
platform, and a zero value represents uniform
temperature.
(7) that the shear force in the vertical riser leg is
negligible by comparison with other forces in the
system.
and the change in circumferential stress to the
pressure p·.bY
• • • • •
(3)
vpR/t
Ea8
vpR/t
Eet8 l exp(-x/A)
E:L '" du/dx
• • • • • • • • • • • • • • • • (1.0)
and can be determined by substituting (7) into (2)
and then integrating (10)'. At the platform, the
movement !::. is
!::. =
~:E:L(X) dx
a8 l A{l-exp (-z/A) )+~{ {~-V)pRz/t - f z 2/41TRt}
(11)
and if the temperature is uniform
!::. = 1TRE (a8 l )2t / f { 1 + E:8l
r'~-V)}2
•• (12)
It should be noted that the temperature effect and the
pressure effect interact in a nonlinear manner
the
total expansion movement is not the sum of the
movement that would be induced by pressure alone and
the movement that would be induced by temperature
alone.
2
lI sd = ~y f/1TRtE
(4)
in x ~ Z
If the temperature is uniform, this reduces to
Z = (1TR2 p/f)(I - 2v + 2Ea8 l t/pR)
• (9)
The displacement u, positive away from the platform,
is related to the longitudinal strain by
I
t{
Longitudinal movements are confined to a length z, the
distance from the platform to the (imaginary) 'anchor
point' beyond which no movement occurs. Beyond this,
EL is zero, and so
cr L
(8)
If the temperature and pressure are reduced, a
segment of the pipeline moves away from the platform,
and on that segment the frictional force acts towards
the platform. If the temperature is uniform both
before and after a temperature reduction fran a 1. to a 2
and the pressure is simultaneous1.y raiuced from PI to
P2, analysis by the method described above shows that
reversed movement occurs over a distance y, 1.ess than
z, given by
y =
(~-v) (Pl-P2)1TR2 + Eet1TRt(8 l -8 2 )}
(13)
that at the platform em the reverse movement !::.sd is
The longitudinal strain E: and stress cr , the
circumferential stress cr H and Lthe temperatu~e rise 8
are related by the stress-strain-temperature relation
1.
"'L = E(O"L
- VO"H) + eta
•••• • •
• (2)
cr H = pR/t
•
• • • • • • • • • •
(14)
and that the longitudinal stress is
~P2R/t +
(5)
The longitudinal stress between the platform and the
anchor point is statical1.y determinate. Fig. 1.b shows
the forces that act on a segment of the pipeline and
its contents between section across the riser just
above the elbow and a vertical section at a distance x
from the platform; x is less than z. At the right-hand
end, 21TRtcr L is the longitudinal force in the pipe wall,
and 1TR2p the longitudinal force on the contents. At
the section above the e1.bow, the only horizontal force
is the shear force S, which is negligible. OVer the
length x, the pipeline is moving towards the platform,
and so the bottom exerts on the pipe a force f per
unit length, directed away from the platform. Since
the segment and its contents are in equilibrium, the
resultant horizontal force on it must be zero, and so
o = fx + 21TRtcr L - 1TR 2p
(6)
(7)
crL = ~R/t - fx/21TRt
in x < Z
18
fx/21TRt
in x < Y
cr L = ~lR/t - v (PrP2)R/t + Ea{8 r 8 2 ) - fx/21TRt
iny<x<z
vP2R/t - Ea8 2
in x > z (15)
Fig. 2 shows the distribltions of longitudinal stress,
strain and movement before and after a reduction in
operating temperature and pressure.
If the pipeline has been in operation, and the
pressure and temperature are then reduced to their
initial tie-in values before start-up, the reversed
movement away from the platform is half the maximum
movement towards the platform, and so half the maximum
movement ranains. It follows that a residual movement
after a complete shutdown does not necessarily imply
creep in the corrosion coating.
A much more complex situation occurs if the
temperature distributions before and after the shutdown
are non-uniform, so that the temperature falls from
used to find the force needed to move it. In this
instance f is taken as 1500 N/m (153 kg/m), which
corresponds to a coefficient of 0.9 and a gas-filled
suhnerged weight of 1670 N/m (170 kg/m), but in
order to check the influence of the choice of
coefficient a Second set of calculations was made with
f equal to 1330 N/m.
6 l exp(-x/Al) to 62exp(-x/A2)' for instance. A segment
of pipeline close to the platform then moves away from
it, but another intermediate segment moves towards the
platform, because of interaction between the nonuniform distribution of thermal strain and a reduction
in axial compressive force that follows from the
reversal of movement. Analysis then leads to coupled
differential equations that have to be integrated step
by step. However, in many practical instances of
temperature and pressure reductions during operation,
the length of pipeline influenced by reversed movement
is small enough for the simple idealization of uniform
temperature to be a reasonable one.
The temperature decay length
A = mc /g
p
It is sometimes necessary to reduce expansion
movements by increasing the resistance to movement
after the pipeline has gone into operation. This can be
done by backfilling gravel or crushed roock over the
pipeline. An important practical case is the following
sequence
first
pressure PI' temperature 6l exP(-x/Al)
then
anchoring backfill is placed over the line,
and increases the limiting resistance to
longitudinal movement by F(x) per unit length
then
the pressure is increased to P3 and the
temperature to 6 3exp(-x/A3) > 6l exp(-x/Al)
On September 30, conditions were as follows :
2
pressure
l3l bars (12.8 MN/m )
38 0c
temperature
flow rate
28 Mcm/day (990 MMscf/d)
+ 2~RtE{(63exP(-v/A3
-6 exp (-v/A )} (16
1
l
and the additional movement at the platform is
t. ad = (~-v) (P3-P J.)RV/Et
+ a(63A3(J.-exp(-v/A3)-61Al (l-exp(-v/A
- 27f~tE1: s: F(~) d~
dx
where m is the mass flow rate, c p the gas specific heat
and g the rate of heat transfer :from the pipeline, per
unit length per unit temperature difference from the
surrounding water : it is assumed that the thermal
resistance between the gas and the steel pipe is small
by comparison with that between the steel and the water
The estimated value of g is 100 W/m degC. The decay
length A is found to be several kIn, even at low flow
rates.
The combination of pressure, temperature and flow
rate that would be expected to induce the maximum
movement occurred on one of three days in the fall of
1979, and each will be examined in turn.
After the anchor is installed, the length v over which
further movement occurs is the solution of the
equation
~:F (x)dx
is determined by
• • • • • • • • (18)
l»
• • • • • • (17)
The sea temperature.is taken as SoC, and so the
temperature rise 61 is 33 dege. Fig. 3 is a graph of
calculated movement at the platform as a function of ,
for the alternative assumed values of f. The estimated
value of A is 8.7 kIn. The calculated and observed
movements are as follows :
z
.movement distance over
which movement
at
platform
occurs
(m)
em)
calculated
f
f
COMPARISON BETWEEN FIELD MEASUREMENTS AND THEORY
The Frigg gas pipeline 1 at treatment platform TPl
in the North Sea provides an unusually favourable
opportunity for comparison between observation and
analysis. The riser is in a vertical shaft inside the
concrete platform; the shaft is usually dry, but is
normally flooded in winter. After an elbow at the
bottom of the riser, the pipeline passes through a seal
and leaves the platform through a horizontal tunnel.
Access to the elbow through the shaft permits accurate
measurements of pipeline movement, without the need to
rely on divers.
1500 N/m, A
= 1330 N/m, A
8.7 kIn
8.7 kIn
observed
1.084
1.192
3430
3780
1.035
The agreement between observed and calculated values
is good.
On October 22, conditions w:ere as follows
pressure
133. bars (13.0 MN/m 2 )
temperature
flow rate
39.5 °c
25 Mcm/day
and the estimated value of A was 7.6 kIn. The calculated
movement is 1.114 m for 1500 N/m longitudinal friction,
and the movement observed was 0.970 m. It is not clear
why the observed movement was 0.065 m less than on
The analysis requires data on the platform
pressure, the gas temperature, and the pipe properties, September 30, but the most likely explanation is that
all readily available and SUbject to little uncertainty. the system temperature had not fully returned to its
steady-state distribution after a brief shutdown on
It also requires the limiting longitudinal frictional
October 21..
force f per unit length, and the temperature decay
length A. These two quantities are more difficult to
On November 16, conditions were as follows
estimate, and it was therefore desirable to investigate
2
pressure
144 bars (14.4 MN/m )
the sensitivity of the results to the assumed values.
temperature
40.3 °c
Since the pipeline was not buried, its limiting
flow rate
30 Mcm/day
frictional resistance could be estimated by multiplying
and the estimated value of A was 9.5 kIn. The calculated
its suhnerged weight by a longitudinal friction
movement was 1.272 m, again for 1500 N/m longitudinal
coefficient. Experience in bottom pull installation of
friction, and the observed movement was 1.090 m.
indicates that if a pipeline has been in place for
some time, a coefficient of between 0.8 and 1 should be
19
The analytical model can be tested further by
comparison between observed and calculated movements
during a shutdown. A brief shutdown lasting 12 hours
took place on November 14 1979, and the observed
reverse movement was 0.230 m after 12 hours. The
pressure drop was not measured, but was estimated to be
4.0 MN/m2 (41 bars) after 12 hours. An estimate of the
rate of temperature drop was made by assuming the heat
transfer rate to be 100 W/m degC, the same as when gas
is flowing (which is reasonable, since most of the
thermal resistance is associated with the concrete,
rather than with heat transfer at the inside wall); the
thermal capacity of the pipeline and the gas is
estimated to be 1.32 MJ/m deg C. After the 12 hours,
the estimated fall in temperature ~1-e2 is 33.7 degC,
and so the temperature had fallen from its initial
value of 400 C almost to the sea temperature of SoC. In
calculating the longitudinal movement, it was assumed
that f was 1500 N/m, and that the effect of variation
of temperature with distance from the platform was
negligible, a reasonable assumption since the distance
over which reversed movement occurs is only 1500 m. The
calculated reverse movement was 0.337 m. The agreement
with the measured value is quite gbod, in the light of
the sensitivity of the result to the changes of
temperature and pressure, neither of which was measured
directly.
After an evaluation of the movements observed at
the platform, it was decided to take action to reduce
the movements that would follow future increases in
operating temperature and pressure. In the early months
of 1980, crushed rock backfill was placed on a number
of sections of the pipeline close to the platform, as
part of a wider program of span correction. The
specified cover above the pipe is 1 m. Taking the
rock particle specific gravity as 2.7, and the in-place
voids ratio as 0.6 (porosity 0.38), the submerged unit
weight is 10.3 kN/m3 (1050 kg/m 3 ). The estimated
add~t~onaL Long~tud~naL res~stance F ~s L4.L kN/m ~f
the pipeline moves through the rock (against the extra
friction generated by the rock's weight) and 12.7 kN/m
if the rock above the pipeline is carried along with
it. However, since the calculation of F involves a
number of uncertain factors (among them the state of
stress in the rock above the pipeline, and the extent
to which arching can transfer the weight of the rock
above the line to the rock on either side), it was
decided to adopt a lower value of 7 kN/m for design
purposes.
A further shutdown on March 22 made it possible
to confirm the effectiveness of the backfill. At that
time, rock had been placed over two sections, one of
464 m (from pk 360.136 to 360.600) and one of 93 m
(from pk 359.623 to 359.716); the platform tunnel
entrance is at pk 361.068. Fig'. 4 shows the movements
and temperature and pressure changes that occurred.
The observed movements can be compared with those
calculated under three alternative assumptions, that
the additional longitudinal resistance F generated by
the backfill is 14 kN/m, that it is 7 kN/m, and that it
is zero. The comparison confirms that the presence of
the backfill does reduce the movements significantly,
but the results are not sufficiently sensitive to the
value of F for it to be possible to make an
independent estimate. Another comparison can be made
by calculating the 'forward' movements after restart
at midnight on March 22/23. The calculated movements
are 0.114 m if F is 14 kN/m, 0.118 m if F is 7 kN/m,
and 0.163 m if F is zero, in the first 5 hours of
operation, while the observed movement was 0.125 m.
20
Loeken l has described a second instance of
submarine pipeline movement, in the 36-inch (914.4 rom)
Ekofisk-Emden gas line at platform R. Stephens and
Rawlins2 describe work on the creep movement of an
unspecified 'pipeline E I, but a comparison between the
papers strongly suggests that they are describing the
same line as Loeken. The submerged weight is not
available, but can be estimated at 1860 N/m (190 kg/m)
in operation. The first 400 m from the platform are
unburied, and so in this section the longitudinal
resistance is 1680 N/m if the friction coefficient is
0.9. Beyond that there is 2 to 3 m cover of sand. The
additional resistance generated by this cover is hard
to estimate, but Loeken suggests a value of 44 kN/m for
1.8 m cover and a soil friction angle of 400 • Within
the period covered by the reported movement data, the
maximum movement away from the platform should
correspond to mid-April 1978, when the maximum pressure
was 11.7 MN/m 2 (1700 Ib/in 2 ) and the temperature
reached 42 0 c (l08 0 F). The calculated end movement is
plotted in Fig. 5, as a function of the uncertain
longitudinal resistance F in the buried section. The
observed movement is somewhat less than the calculated
movement, unless F is as low as 10 kN/m (1 tonne/m;
700 lb/ft). The result is sensitive to the amount of
cover between 400 and 800 m from the platform, and
10 kN/m may be a reasonable value, particularly if
arching is significant or if the cover is less than
intended.
CREEP BETWEEN A PIPELINE AND ITS WEIGHT COATING
Some instances of thermal movement may be due to
deformation of bituminous corrosion coating, which
may soften when the pipeline temperature rises as it
goes into operation, and will then deform as a viscous
fluid. That would allow the pipe to expand even though
its concrete coating remained statiQIlary, by shear
deformat~on w~th~ the corros~on coat~ng, and th~s
mechanism is one explanation of movements which
continue to increase after the pipeline is in operation
It is important to make clear that it is not the only
or most likely explanation of such movements : in most
pipelines, the operating pressure, temperature and flow
rate are progressively increased after start-up, and
quite modest increases can produce substantial
additional movements.
A complete analysis of creep deformation is
complicated, because the corrosion coating has a
complex rheological behavior close to its softening
temperature, may be non-Newtonian, and is strongly
temperature-sensitive. However, a simplified model
throws light on the factors that govern creep, and
allows one to determine whether or not it might be
important.
Imagine a pipeline subject to thermal expansion
alone, so that the pressure effect is negligible. The
temperature increase is e(x,~) at time ~ and distance
x from the platform. The displacement of the pipe itse
tself is u{x,~), and the displacement of the concrete
coating is v(x,~), so u-v is the relative movement
between the pipe and the coating. The thickness of the
corrosion coating is h, and its material is idealised
as a linear viscous fluid with viscosity n at the pipe
temperature. The earlier assumption that the pipe is
thin-walled is extended to include the coating, so
that the radius of the coating is identified with the
mean radius R. Longitudinal forces in the concrete are
assumed to be negligible by comparison with those in
the steel. Fig.6 shows schematically the forces that
act on the different parts of an element dx. At the
u(x,t)= - 2a6 { (~) ~exp (_x 2/4K~) - ~erfc (x 2/4K~)~}
left-hand end of the element, the thermal strain
~
2
component is a6 and the total longitudinal strain is
1 - ~ u(x' ,0) exp -(x-x'
) 2 - exp -" (x+x')
au/ax, and so the longitudinal stress is E(au/ax - a6),
----- }
+ -(~K~)~
0
4K~
4K~
from (2), and the longitudinal force is this stress
multiplied by the wall cross-section 2~Rt. At the right
dx' • (26)
end, the longitudinal force is different, because au/ax
and a6 will in general have different values. The
where
(27)
K
shear force on the outer surface of the pipe is the
(Eth/n) ~ • • • • • • • • •
product of the viscosity n, the velocity gradient
(au/a~ - av/a~)/h and the area 2~Rdx. Since inertia
At the end, the displacement u (0 , ~) at time ~ is
terms are negligible, longitudinal equilibrium of the
pipe element gives the governing differential equation
-2a6
(X)
u(O,~)=
au .- a:r
av
(a 2u a6 )
a:r
= (Eth/n) ~ - a ax
6
1
.~.
•
•
•
•
•
•
•
(20)
for ~ > 0
which is an idealization of rapid start-up at a high
flow rate. The rise in temperature will be followed by
an immediate expansion, because of slip between the
concrete coating and the bottom. The amount of movement
is governed by the analysis described earlier, because
relative movement between the pipe and the concrete
cannot occur instantaneously, since that would imply an
infinite velocity gradient in the corrosion coating. It
follows that, immediate after the temperature rise,
v(x,O+) = u(x,O+) =
where
- ITRt~e)2E(1-x/z)2/f for x < z
(21)
o
for x > z
z = 2~Rta6E/f
• • • •
(22)
Once the instantaneous motion has taken place, viscous
creep begins. Intuition suggests that creep will relax
the longitudinal forces, and that the force between the
concrete coating and the bottom will tend to fall
rather than rise (at least in the zone that slipped
initially). If this is so, we can conjecture that there
will be no further movement of the concrete, so that
for ~ > 0
= 0
•
•
•
(23)
and then, since 6 is uniform, the governing equation
(19) becomes the diffusion equation
au/a~
(Eth/n)a 2u/ax 2
• (24)
(28)
for ~ > 0
This analysis can be generalised to include
pressure, and to allow for temperature gradients. It
has unfortunately not been possible to compare it with
a case of movement that is known to be due to viscous
creep in the corrosion coating.
CONCLUSIONS
Observed movements of submarine"~ipelines are
shown to be consistent with an elastic/frictional
expansion analysis (which is well known in a simple
form). The analysis correctly predicts reversed
movement during shutdowns, and the response to backfill
intended to increase longitudinal resistance. Other
effects, such as the relaxation of 'snaking' and
relative movement in the corrosion coating, may
sometimes be significant, but it is not necessary to
appeal to them to explain the movement of the Frigg
pipeline.
NOTATION
E
f
F
h
p
R
t
\l
V
X
Y
z
a
t:.
The initial condition is (21), and the boundary
condition at the end x equal to zero is given by the
condition that the longitudinal stress at the end be
zero, and is
a6
s: (1_~)2exp{_ ~:~2} d~
where A is the initial displacement at the end, from
(21). The first term in this expression becanes
dominant as ~ increases, and corresponds to the
continued expansion of the pipe through the coating,
while the second term decays from A to zero, and
represents the redistribution of the initial movement.
A general solution is complex, because of the
strong dependence of viscosity on temperature. It is
useful to examine a simplified problem. Imagine that
the temperature 6 is rapidly raised to 61' and then
held uniform along the pipeline and constant with time,
so that
o
for ~ < 0
•
(~K~~Z2)'i
• • • • • • (19)
The group Eth/n has the dimensions of (length)2/time,
and is a diffusivity, analogous to thermal diffusivity
in heat transfer theory and coefficient of
consolidation in soil mechanics. Stephens and Rawlins 2
derived the same group, in a rather different way.
6 (x,~)
(K~/~)I:!
{
e:
n
K
(25)
The solution of (24) subject to these initial and
boundary conditons is elementary, and is
A
6
'V
~
(J
21
Young's modulus
limiting longitudinal friction per unit length
additional limiting longitudinal friction provided
by backfill
coating thickness
pressure
mean radius
wall thickness
displacement of pipe
displacement of concrete coating
distance from platform
distance over which reversed movement occurs
during shutdo"W11
distance over which expansion movement occurs
linear thermal expansion coefficient
movement at platform
strain
viscosity
(diffusia:ity)I:!
decay length for exponential distribution of
temperature
Poisson's ratio
integration variable
stress
ACKNOWLEDGEMENT
REFERENCES
The authors thank Total Oil Marine Limited for
permission to publish this paper.
1. Loeken, P.A. 'The "creep" on the Ekofisk-Emden 36"
gas pipeline', Proceedings, 12th Annual Offshore
Technology Conference, Houston, 1980, paper OTC
3783, 393-40l.
2. Stephens, H.G. and Rawlins, C.E. 'Axial movement of
warm buried pipelines', Proceedings, Interpipe 1980,
Houston, 146-161.
a: CLAMP
w
(j)
a:
-.8
fx
•
x
Fig. 1 - DEFINITION SKETCH (a) geometry (b) forces on a segment.
b...J
Cf)
Cf)
ill
a:
I-
Cf)
...J
W
z
:;;:
0:
I-
Cf)
I-
z
y
(13)
(9)
y
z
x
x
m
b.Sd]
::2
ill
o>
::2
y
z
DISTANCE FROM PLATFORM
Fig. 2 - STRESS, STRAIN AND MOVEMENT AT THE END OF A PIPELINE
Solid lines represent condition after a reduction in temperature
and pressure, dashed lines condition before; numbers refer to
equations in text.
Fig. 3 - RELATION BETWEEN CALCULATED MOVEMENT AND TEMPERATURE DECAY LENGTH.
•
bars
w
140
a:
::)
C/)
C/)
°c
•
••
• •• •
0
0
•
0
120
w
a::
a...
<.,0-'<;.
~e
-.
•
·\e~
0
El
100
1200
MARCH 22
• ~'\.e
?r eSsure_
•
MIN
MARCH 23
0
•
100
I-
Z
w
:2:
w
200
> 300
0
:2: mm
Fig. 4 - MOVEMENTS DURING A SHUTDOWN
Solid symbols represent measured values, open symbols calculated values.
0.6
I-
z
OBSERVED _
m
w 0.4
w
~
CALCULATED
>
0 0.2
:2:
10
20
30
40
50 kN/m
LIMITING LONGITUD INAL RESISTANCE
IN BURIED SECTION
Fig. 5 - RELATION BETWEEN CALCULATED MOVEMENT AND LIMITING RESISTANCE.
dx
. . LJ----,,;::..p--'iP=-e_-l'
+ E(~~ + BdX - "S -' ,,~! dX) 21fRt
r-=-=:::!~=-....;(n(h)(~~ - ~n 21fRdx
-
coating
I
c oncrete
b ottom
Fig. 6 - DEFINITION SKETCH
FORCES ON AN ELEMENT OF PIPELINE.
30 w
a:
::)
l-
20 «
a::
w
a..
10 :2:
w
I-