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Fluid Hammer and Fatigue Analysis for Oil Transport Pipelines With Peak Points
Conference Paper in American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP · July 2014
DOI: 10.1115/PVP2014-28070
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Proceedings of the ASME 2014 Pressure Vessels & Piping Conference
PVP2014
July 20-24, 2014, Anaheim, California, USA
PVP2014-28070
FLUID HAMMER AND FATIGUE ANALYSIS FOR OIL TRANSPORT PIPELINES WITH
PEAK POINTS
Hassan Warda
Mechanical Engineering Department
Alexandria University, Alexandria, Egypt
Sherif Haddara
Ministry of Petroleum and Mineral Resources
Cairo, Egypt
1
Essam Wahba
Mechanical Engineering Department
American University of Sharjah, Sharjah, UAE
ABSTRACT
The SUMED pipeline is a major oil transport pipeline in
the Middle East. It provides an important route for transporting
oil from the Arabian Gulf region to Europe and North America.
The pipeline was subjected to major damage in the 1990s,
which required the replacement of several kilometers at its peak
point. Fluid hammer simulations using the method of
characteristics show that this damage was due to consecutive
shutdown/startup events. Such events led to multiple formation
and collapse of vapor cavities at the peak point. Low cycle
fatigue analysis confirm the finite lifetime of the pipeline due to
the high differential stress resulting from the cavity collapse.
Moreover, a safe valve closure operational scheme is computed
using fluid hammer analysis that would prevent further
formation of cavities and hence ensure safe pipeline operation
in the future.
NOMENCLATURE
A
Pipe cross-sectional area
D
Pipe diameter
Bulk modulus of compressibility for fluid
Ef
Young’s modulus of elasticity for pipe material
Ep
H
Total head
I
Rotational inertia of pump system
K
Valve loss coefficient
Stress concentration factor
Kt
N
Rotational speed of pump system
Fatigue crack initiation life for pipeline
Ni
T
Pump torque
V
Average cross-sectional velocity
a
Wave speed
1. Mechanical Engineering Department, Alexandria University, Alexandria,
Egypt (on leave)
e
f
g
s
t
z
t
S
s
  eqv
Pipe thickness
Darcy-Weisbach friction factor
Gravitational acceleration
Axial location along the pipe
Time
Pipe elevation
Time step size
Nominal stress range
Spatial step size along pipe axis
Equivalent stress range
p


Poisson’s ratio for pipe material
Fluid density
Cavity volume
INTRODUCTION
Over-land transportation of large quantities of oil is
generally carried out using pipelines. With the rapid growth in
the oil industry over the past century, a number of major crosscountry pipelines were constructed worldwide, such as the
Trans-Alaska Pipeline (TAPS) in North America, the Druzhba
(Comecon) pipeline in Eastern Europe and the Yanbu (EastWest) pipeline in Saudi Arabia, to name a few.
The present study is concerned with one of these major
transport pipelines, namely the SUMED (Suez-Mediterranean)
pipeline in Egypt. The SUMED pipeline is a major oil transport
pipeline in the Middle East, running from Ain-Sukhna terminal
on the Red Sea to Sidi-Kerir terminal on the Mediterranean
Sea. It provides an important route for transporting oil from the
Arabian Gulf region to Europe and North America. The API 5L
X60 SUMED pipeline consists of two parallel lines, each with
1
Copyright © 2014 by ASME
a diameter of 42 inches and a length of 320 km. Figs. 1 and 2
show a schematic of the pipeline and its profile, respectively.
The pipeline was first operated in 1977 with an annual capacity
of 40 million tons, which was extended during its second phase
to 60 million tons with the operation of the booster pump
station. Successful operation of the pipeline continued until the
1990s, when results from electronic pigs indicated severe
damage in the pipeline near its peak point. This required the
replacement of several kilometers of the pipeline in this region.
The objective of the present study is to identify the main cause
of failure for the pipeline near its peak point, a region of
supposedly low pressure and hence minimal stresses in the
pipe. With the pipeline operating under start-and-stop
conditions and the failure happening after many years, two
fundamental causes of failure come to attention; fluid hammer
and pipeline fatigue. The present study aims to couple fluid
hammer computations with low cycle fatigue analysis in order
to identify the main cause behind the pipeline failure.
FLUID HAMMER ANALYSIS
‘Fluid hammer’ commonly refers to the generation and
propagation of fluid transients in pipes, as a result of abrupt
changes in flow conditions. Such changes could occur due to
the sudden closure of a valve or shutdown of a pump. The
study of such transients is of great practical importance and
may well provide the design condition for the piping system as
a whole. Severe fluid transients could lead to large fluctuations
in pressure, distributed cavitation along the pipeline, structural
vibrations, and column separation [1].
Fluid Hammer Model and Numerical Methods
One-dimensional (1-D) fluid hammer models are based on
conservation of mass and axial momentum principles. The
model equations are given as follows
1 dp
V
a2
0
 dt
s
dV 1 p
dz
f

g

VV 0
dt  s
ds 2D
(1)
(2)
Using order of magnitude analysis, Wahba [2] and Ghidaoui
et al [3] showed that the nonlinear convective terms could be
neglected from the continuity and axial momentum equations,
since the wave speed is several orders of magnitude larger than
the flow velocity, resulting in
Interior
Valve
Supply
Pump
Booster
Pump
Downstream
valve
Fig. 1 SUMED Pipeline Schematic
1 p
V
 a2
0
s
 t
dz
f
V 1 p
g

VV  0

ds 2D
t  s
(3)
(4)
Pipe elasticity and fluid compressibility are included in the
model through the expression of the wave speed a
500
Ef

a2 
E D
1 f
eE p
Elevation (m)
400
300
200
100
0
0
50
100
150
200
Distance (km)
250
Fig. 2 SUMED Pipeline Profile
300
(5)
Here,  is the fluid density, Ef is the bulk modulus of
compressibility for the fluid, Ep is the Young’s modulus of
elasticity for the pipe material, e is the pipe thickness and D is
the pipe diameter.
The hyperbolic system of equations could be efficiently
solved using the method of characteristics [4]. Other methods
of solution include Runge-Kutta methods [2], implicit methods
[5], Godunov methods [6] and finite element methods [7]. In
the present study, the method of characteristics is applied to
numerically solve equations (3) and (4) resulting in the left and
right running characteristic equations
2
Copyright © 2014 by ASME
dV g dH
f


VV 0
dt a dt 2D
dV g dH
f


VV 0
dt a dt 2D
ds
a
dt
ds
for
 a
dt
(6)
for
(7)
Here, H is the total head at a pipe section. Applying a
standard finite difference discretization procedure along the
characteristic lines would result in
V
V
  ga H
g
 V   H
a
n 1
 Vin1
i
n 1
i
n
i 1
  f2Dt V V
ft
 H 
V V
2D
n 1
 H in1
i
n 1
i
n
i 1
n
i 1
n
i 1
n
i 1
n
i 1
0
0
(8)
(9)
The time step t is taken equal to s/a, where s is the
spatial grid size along the pipe axis. Solving equations (8) and
(9) simultaneously would provide the velocity and total head at
each pipe section at the new time level (n+1).
Supply Pump Boundary Condition
The boundary condition at the supply pump is formulated
using the right running characteristic equation (9), together
with the quasi-steady energy equation (10) and the pump
performance curve (11)
n 1
H in 1  H os  H sp

 
n 1
H sp
 f Q in 1  f Vin 1

(10)
(11)
where Hos is the time-invariant total head at the upstream
terminal and Hsp is the supply pump head. The three equations
are solved simultaneously to compute the velocity Vin 1 , the
details about the supply pump boundary condition could be
found in [4].
Booster Pump Boundary Condition
The boundary condition at the booster pump is formulated
similar to the supply pump. However, in case of the booster
pumps, we have four equations instead of three, with the
addition of the left running characteristic equation (8). The four
equations are solved simultaneously to compute the velocity
Vin 1 , the total head at the pump suction H isn 1 , the total head
n 1
,
at the pump discharge H id
Interior Valve Boundary Condition
The boundary condition at the interior valve is formulated
using the left and right running characteristic equations (8) and
(9), together with the quasi-steady energy equation
n 1
n 1
H iu
 H id
K
Percent Open
100
90
80
70
60
50
40
30
20
10
0
(12)
Here, I is the rotational inertia of the supply pump system.
Based on equation (12), the new rotational speed N could be
evaluated as follows
60 n
T t
2I
(13)
The supply pump performance curve is constructed at each
time level from the steady-state performance curve using the
affinity laws [4]. The non-return valve on the discharge side of
the pump is simulated by checking the direction of flow
velocity; if the velocity is negative then it is set to zero. More
(14)
2g
Table 1
Loss Coefficient for Through-Conduit Gate Valve
governed by
N n 1  N n 
n 1 2
i
n 1
n 1
and H id
, at the valve. In case of a negative
heads, H iu
velocity at the interior valve, the quasi-steady energy equation
is reformulated based on flow in the reverse direction, and the
system of equations is re-solved. It should be noted here that
the interior valve is a through-conduit gate valve and its valve
loss coefficient K is provided in table (1) as a function of the
percentage valve opening.
n 1
H sp
. Pump acceleration/deceleration due to restart/failure is
2 dN
I
60 dt
V 
The three equations are solved simultaneously to compute
the velocity Vin 1 and the upstream and downstream total
total head at the pump discharge H in 1 and the pump head
T
and the booster pump head
n 1
H bp
.
1/K
5.27
2.5
1.25
0.625
0.333
0.179
0.1
0.0556
0.0313
0.0167
0
Downstream Valve Boundary Condition
The boundary condition at the downstream valve is
formulated using the left running characteristic equation (8)
and the quasi-steady energy equation
3
Copyright © 2014 by ASME
H in 1  H od  K


2
Vin 1
(15)
2g
Here, Hod is the head at the downstream terminal which is
equal to 50 m. The two equations are solved simultaneously to
compute the velocity Vin 1 and the total head H in 1 at the
valve. In case of a negative velocity at the downstream valve,
the quasi-steady energy equation is re-written based on the
reverse flow direction and the two equations are re-solved
simultaneously. Similar to the interior valve, the downstream
valve is also a through-conduit gate valve and its valve loss
coefficient is given in table (1).
Discrete Vapor Cavity Model (DVCM)
Column separation occurs during a fluid transient when the
pressure drops to the vapor pressure at specific locations along
the pipe, such as peak points and dead ends. As a result, a
vapor cavity starts to develop at this specific location, which
would split the liquid column in the pipeline. The collapse of
this vapor cavity and the re-joining of the liquid column would
result in an abrupt rise in pressure, which could present a
significant threat to the structural integrity of the pipeline.
Several incidents are documented in the literature regarding
catastrophic failure of piping systems due to column separation
[8], [9].
The discrete vapor cavity model (DVCM) [10]-[13] allows
the formation of cavities at any of the pipe cross sections
whenever the computed pressure at this section becomes equal
to or lower than the vapor pressure. Under such condition, the
pressure head at this section is set equal to the vapor pressure
head as follows
Hi  H v
(16)
The upstream and downstream velocities, Viun 1 and Vidn 1 ,
for the cavity are computed from the left and right running
characteristic equations, respectively. The growth/collapse of
the cavity is then computed from principles of mass
conservation as follows

 V  V Adt
t
t0
id
(17)
iu
Here,  represents the cavity volume and t0 is the time at
which the cavity starts to form. Trapezoidal rule is used to
numerically integrate equation (17) as follows
 



 n 1   n  0.5 Vidn 1  Viun 1  0.5 Vidn  Viun At
(18)
If the cavity volume  becomes zero or negative, the
cavity disappears and the numerical procedure reverts back to
the standard method of characteristics.
LOW CYCLE FATIGUE ANALYSIS
Fatigue represents the main failure mode for mechanical
structures subjected to variable loading. Starting with the
pioneering work of Wohler (1860), high cycle fatigue (HCF)
was studied by numerous researchers in order to determine the
fatigue limit for metallic materials. This was mainly done
through establishing S-N curves, which represent the relation
between the load and the number of cycles to failure. In the
1960s, researchers developed special interest in studying low
cycle fatigue (LCF). Instead of the stress-based approach used
in HCF, Manson [14], [15] and Coffin [16], [17] independently
proposed a strain-based approach for LCF. The strain-based
model is known as the Manson-Coffin relation
 p
2
  'f 2 N f c
(19)
where p and Nf are the plastic strain range and the
number of cycles to failure, respectively. Moreover,  'f and c
are the fatigue ductility coefficient and the fatigue ductility
exponent, respectively.
Most pipelines operating under start-and-stop conditions
are subjected to low-cycle fatigue [18]-[20]. With the aid of
experimental tests performed on X60 pipeline steel specimens
with single edge notches, Zheng et al [21], [22] developed a
modified Manson-Coffin relation using an energetic approach.
The modified relation for X60 pipeline steel is expressed as
follows


N i  1.96  1015  eqv 2 / 1 n   4412 / 1 n 

2
(20)
Here, Ni is the fatigue crack initiation life, n is the
hardening exponent and  eqv is the equivalent stress range
which is calculated from


1
 eqv   1 n 
1 n  
1  R  
 2
1/ 2
K t S
(21)
in which Kt is the stress concentration factor, S is the
nominal stress range and R is the stress ratio, which is
evaluated from the minimum and maximum internal pressures
as follows
R
4
Pmin
Pmax
(22)
Copyright © 2014 by ASME


 

cracks do not initiate and the fatigue life is infinite. In the
present study, the equivalent stress range  eqv is evaluated


as 1260 MPa from the fluid hammer analysis, while the
given by Zheng [22] to be 441 MPa. Hence, as a result of
cavity collapse during pipeline startup, fatigue cracks would
initiate and the pipeline would have a finite fatigue life. The
fatigue crack initiation life is estimated from equation (20) to
be 7.7x103 cycles.
1800
Pipe profile
Steady−state total head (t=0)
Maximum total head
Minimum total head
1600
1400
1200
Head (m)
Fluid Hammer and Fatigue Analysis Results
Fluid hammer analysis is carried out to simulate a pipeline
shutdown event. In this simulation, the interior and downstream
valves are closed in 200 s and both the supply and booster
pumps are shutdown. The flow rate through the pipe
corresponds to an annual capacity of 60 million tons and the
density and kinematic viscosity of crude oil are 870 kg/m3 and
20 cSt, respectively. Grid-independent results are obtained
with the use of 100 parts along the pipe axis.
Fig (3) shows the resulting maximum and minimum total
heads generated along the pipeline during the transient event.
Fig (3) clearly indicates that with such shutdown scenario, the
maximum heads generated at the pipeline peak points are not
high enough to cause failure in this region. Hence, one would
argue that the pressure transient generated during the pipeline
shutdown process is not the main cause for the pipeline failure
at its peak point.
Further investigation is carried out by plotting the total
head along the pipe after 1000 s from the initiation of the
transient in fig (4). This would provide the static head in the
pipe after the transient has been damped out considerably. As
can be seen from fig (4), column separation occurs at the peak
point, and a large cavity is formed in this region. The collapse
of such cavity during the startup of the pipeline could cause
abrupt and significant rise in pressure.
To evaluate the possible pressure rise as a result of the
cavity collapse, a second fluid hammer simulation is performed
to model pipeline startup. Results from the simulations show
that at the instant of cavity collapse, the pressure head at the
pipe peak point reaches 950 m. In its design, SUMED pipeline
was designed with telescopic thickness, where the pipeline
thickness varies from 17.48 mm in regions of high pressure to
9.52 mm in regions of low pressure. At the peak points,
pressures are supposedly low and the thickness is 9.52 mm.
With the high pressure rise due to cavity collapse and the low
thickness at the peak point, significant stresses are developed in
this region. Using equation (21) in conjunction with the ASME
B31.4 thin pressure vessel design formula for pipelines
transporting liquid hydrocarbons [23], the equivalent stress
range is calculated to be 1260 MPa.
Zheng [22] showed that when  eqv   eqv th , fatigue

equivalent endurance limit  eqv th for X60 pipeline steel is
1000
800
600
400
200
0
0
50
100
150
200
Distance (km)
250
300
Fig. 3 Maximum and minimum total heads along the pipe
(Scheme 1)
1800
Pipe profile
Steady−state total head (t=0)
Transient total head (t=1000 s)
1600
1400
1200
Head (m)
RESULTS AND DISCUSSION
In the present section, results from the fluid hammer/low
cycle fatigue analysis are presented and used to identify the
main cause of failure for the SUMED pipeline at its peak point.
Moreover, after identifying the main cause of failure, fluid
hammer simulations are performed to identify a safe valve
closure scheme that would prevent further damage to the
pipeline in the future.
1000
800
600
400
200
0
0
50
100
150
200
Distance (km)
250
300
Fig. 4 Transient total head at time t=1000 s
(Scheme 1)
Safe Valve Closure Scheme
In the previous section, both the interior and downstream
valves were closed in 200 s. This resulted in a relatively low
static head in the pipeline after shutdown, which led to column
separation and cavity formation at the peak point. The objective
5
Copyright © 2014 by ASME
1800
1400
1200
200
Downstream Valve (s)
200
30
200
Although scheme 2 provides high static head after
shutdown as can be seen from fig (6), however, fig (5) shows
that the scheme also results in excessive pressures along the
pipeline due to the relatively fast valve closure time, 30 s, for
both valves. On the other hand, figs (7) and (8) show that
scheme 3 provides enough static head to prevent cavity
formation after the pipe shutdown while limiting the maximum
pressures to some extent, as compared to scheme 2. Hence, the
implementation of valve closure scheme 3 would result in the
elimination of cavity formation at the peak point after pipe
shutdown, which would prevent the subsequent events of
cavity collapse and the high stress levels which could lead to
eventual failure due to low cycle fatigue.
800
400
0
0
50
100
150
200
Distance (km)
250
300
Fig. 6 Transient total head at time t=1000 s
(Scheme 2)
1800
Pipe profile
Steady−state total head (t=0)
Maximum total head
Minimum total head
1600
1400
1200
Head (m)
Interior Valve (s)
200
30
50
1000
600
Table 2
Closure Time for the Different Valve Closure Schemes
Scheme No.
1
2
3
Pipe profile
Steady−state total head (t=0)
Transient total head (t=1000 s)
1600
Head (m)
of the present section is to use fluid hammer simulations to
identify a safe valve closure scheme that would result in a
higher static head in the pipeline after shutdown. This would
prevent cavity formation at the peak point, and hence eliminate
the large stresses that arise due to cavity collapse at startup.
Besides the valve closure scheme discussed in the previous
section, two other schemes are considered herein. A summary
of all three valve closure schemes is provided in table (2).
Results for scheme 2 are given in figs (5) and (6), while results
for scheme 3 are given in figs (7) and (8).
1000
800
600
400
200
1800
1400
50
100
150
200
Distance (km)
250
300
Fig. 7 Maximum and minimum total heads along the pipe
(Scheme 3)
1200
Head (m)
0
0
Pipe profile
Steady−state total head (t=0)
Maximum total head
Minimum total head
1600
1000
800
600
400
200
0
0
50
100
150
200
Distance (km)
250
300
Fig. 5 Maximum and minimum total heads along the pipe
(Scheme 2)
CONCLUDING REMARKS
A coupled fluid hammer\low cycle fatigue analysis is used
in the present study to identify the main cause of failure for the
SUMED pipeline at its peak point. The analysis shows that the
consecutive shutdown/startup events for the pipeline resulted in
the formation and subsequent collapse of cavities at the peak
point of the line. The cavity collapse would lead to high
pressure rise, which under low cycle fatigue conditions, would
result in the failure of the pipeline in this region. Moreover,
fluid hammer simulations are used to identify a safe valve
closure scheme for the pipeline that would prevent column
separation events at the peak point and hence ensure safe
operation of the pipeline in the future.
6
Copyright © 2014 by ASME
1800
Pipe profile
Steady−state total head (t=0)
Transient total head (t=1000 s)
1600
1400
10.
Head (m)
1200
1000
11.
800
600
400
12.
200
13.
0
0
50
100
150
200
Distance (km)
250
300
Fig. 8 Transient total head at time t=1000 s
(Scheme 3)
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