ORIGINAL ARTICLE Comparison of computational and analytical methods for evaluation of failure pressure of subsea pipelines containing internal and external corrosions Kwang-Ho Choi 1 • Chi-Seung Lee 1 • Dong-Man Ryu 1 • Bon-Yong Koo 2 • Myung-Hyun Kim 1 • Jae-Myung Lee 1 Received: 2 June 2015 / Accepted: 29 November 2015 / Published online: 15 December 2015 Ó JASNAOE 2015 Abstract In the designing stage of subsea pipelines, the design parameters, such as pipe materials, thickness and diameters, are carefully determined to guarantee flow assurance and structural safety. However, once corrosion occurs in pipelines, the operating pressure should be decreased to prevent the failure of pipelines. Otherwise, an abrupt burst can occur in the corroded region of the pipe- line, and it leads to serious disasters in the environment and financial loss. Accordingly, the relationship between the corrosion amount and failure pressure of the pipeline, i.e., the maximum operating pressure, should be investigated, and then, the assessment guideline considering the failure pressure should be identified. There are several explicit type codes that regulate the structural safety for corroded subsea pipelines, such as ASME B31G, DNV RF 101, ABS Building and Classing Subsea Pipeline Systems, and API 579. These rules are well defined; however, there are some limitations associated with describing precise failure pres- sure. Briefly, all of the existing rules cannot consider the material nonlinearity, such as elastoplasticity effect of the pipeline, as well as the actual three-dimensional corrosion shape. Therefore, the primary aim of this study is to sug- gest a modified formula parameter considering the above- mentioned pipeline and corrosion characteristics. As a result, the material nonlinearity as well as the corrosion configuration, i.e., axial/circumferential corrosion length, width and depth, is reflected in a set of finite element models and a series of finite element analysis considering the operation conditions are followed. Based on the com- parative study between the simulation and analytical results, which can be obtained from the classification society rules, the modified formulae for failure pressure calculation are proposed. Keywords Subsea pipeline Corrosion Finite element analysis Failure pressure Classification society rules 1 Introduction Recently, the installation and operation of onshore and offshore pipelines have been increasing rapidly because of the increased demand for fossil fuel energy, such as crude oil and gas. According to the energy resources-related report, approximately 60,000 km of onshore and offshore pipelines will be installed worldwide between 2014 and 2016 to transport the fossil fuel. The length of subsea pipelines is expected to be at least 18,000 km [1]. However, according to the Pipeline and Hazardous Materials Safety Administration (PHMSA), more than 600 pipeline accidents occurred during the past decade [2]. There are many causes of pipeline accidents. As corrosion and construction defects were found to be main causes of some catastrophic disasters, corrosion was deemed very critical for onshore and offshore pipelines (Figs. 1, 2). Subsea pipelines, specifically, are more significantly affected by corrosion from seawater. In particular, various seawater characteristics, such as seawater temperature, salinity, water velocity and surface roughness, can affect the corrosion state of the pipeline [3, 4]. With a view to ensuring the structural safety of the pipelines during the operation, the relationship between the & Jae-Myung Lee [email protected]1 Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 46241, Republic of Korea 2 Korea Energy Technology Center, American Bureau of Shipping, Busan 47300, Republic of Korea 123 J Mar Sci Technol (2016) 21:369–384 DOI 10.1007/s00773-015-0359-5
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ORIGINAL ARTICLE
Comparison of computational and analytical methodsfor evaluation of failure pressure of subsea pipelines containinginternal and external corrosions
thermal load and other parameters were not considered
during FEA. Hence, these terms were not considered dur-
ing the API 579 calculations.
Level 2 of API 579 Part 5 specified formulae for the
circumferential and longitudinal stresses, and longitudinal
shear stress. The maximum values of the calculated
equivalent stress need to be calculated and are compared to
failure criterion.
Figure 4 shows API 579 definition of internal and
external corrosions. The circumferential stress ðrcmÞ, lon-gitudinal stress at point A ðrAlmÞ, longitudinal stress at pointB ðrBlmÞ and longitudinal shear stress (s) are calculated
using Eqs. 7–10, according to API 579 [13].
372 J Mar Sci Technol (2016) 21:369–384
123
rcm ¼ MAWP
RSF � cos aD
D0 � Dþ 0:6
� �ð7Þ
rAlm ¼ MCs
Ec
Aw
Am � Af
MAWPð Þ þ F
Am � Af
�
þ yA
IXFyþ yþ bð Þ MAWPð ÞAw þMx½ � þ xA
IYMy
�ð8Þ
rBlm ¼ MCs
Ec � cos aAw
Am � Af
MAWPð Þ þ F
Am � Af
�
þ yB
I �XF�yþ yþ bð Þ MAWPð ÞAw þMx½ � þ xB
I �YMy
�ð9Þ
s ¼ MT
2 At þ Atfð Þ tmm � FCAð Þ þV
Am � Af
ð10Þ
MCs ¼
1� 1MC
t
� �dtc
� �1� d
tc
� � ð11Þ
MCt ¼ 1:0þ 0:1401ðkcÞ2 þ 0:002046ðkcÞ4
1:0þ 0:09556ðkcÞ2 þ 0:00025024ðkcÞ4ð12Þ
kc ¼1:285cffiffiffiffiffiffiffi
Dtcp ð13Þ
whereMAWP is the maximum allowable working pressure;
RSF remaining strength factor computed based on the flaw
Flaw & Damage Mechanism Identification
Applicability and Limitations of the FFSAssessment Procedures
May used when a flaw is not acceptable in its currentcondition
In-service monitoring is one method whereby futuredamage or conditions leading to future damage can beassessed or confidence in the remaining life estimate can
be increased
A general rule A practitioner should be able to repeatthe analysis from documentation without consulting an
individual originally involved in the FFS assessment
STEP DETAIL
Fig. 3 General FFS assessment procedure of API 579 [13]
J Mar Sci Technol (2016) 21:369–384 373
123
and damage mechanism in the component; a the cone half-
apex angle in conical type pipe, which is 0 for a cylindrical
pipe; D the cylinder’s inside diameter: cone (at the location
of the flaw), sphere or formed head; D0 the cylinder’s
outside diameter, corrected for LOSS and FCA as appli-
cable; Ec the circumferential weld joint efficiency; Aw the
effective area on which pressure acts; Am the metal area of
the cylinder’s cross section; Af the cross-sectional area of
the region of local metal loss; yA the distance from the x–x
axis measured along the y-axis to Point A on the cross
section; yB the distance from the x–x axis measured along
the y-axis to Point B on the cross section; IX the cylinder’s
moment of inertia about the x–x axis; IX the moment of
inertia of the cross section with the region of local metal
loss about the x-axis; IY the moment of inertia of the cross
section with the region of local metal loss about the y-axis;
F the applied net-section axial force for the weight or
weight plus thermal load case; �y the location of the neutral
axis; b the location of the centroid of area, Aw, measured
from the x–x axis; Mx the applied section bending moment
yx
x
y,yMetal Loss
tmm
x
x
A
Df
2
Do
2
B
D2
yLx
tc
My
c
FMx
MT
P
(a)
y, y Metal Loss
xx
x
Do
2
D2
x
tmm
Df
2
AB
yLx
y
tc
(b)
Fig. 4 Parameters used in API
579 for defining a internal
corrosion and b external
corrosion [13]
374 J Mar Sci Technol (2016) 21:369–384
123
for the weight or weight plus thermal load case about the x-
axis;My the applied section bending moment for the weight
or weight plus thermal load case about the y-axis; xA the
distance along the x-axis to Point A on the cross section; xBthe distance along the x-axis to Point B on the cross sec-
tion; MT the applied net-section torsion for the weight or
weight plus thermal load; At the mean area to compute
torsion stress for the region of the cross section without
metal loss; Atf the mean area to compute torsion stress for
the region of the cross section with metal loss; tmm the
minimum remaining thickness determined at the time of
the assessment; FCA the future corrosion allowance
applied to the region of local metal loss; and V the applied
net-section shear force for the weight or weight plus ther-
mal load case; MCs ;M
Ct Folias factor or the bulging cor-
rection factor; c the circumferential extent or length of the
region of local metal loss.
The equivalent stress is defined as
rAe ¼ rcmð Þ2� rcmð Þ rAlm
þ rAlm 2þ3s2
h i0:5ð14Þ
rBe ¼ rcmð Þ2� rcmð Þ rBlm
þ rBlm 2þ3s2
h i0:5ð15Þ
where rAe and rBe are the equivalent stresses at point A and
B, respectively. The maximum stress in the corroded pipe
was chosen by one of the larger values in these two:
re ¼ max rAe ; rBe
� �ð16Þ
3 Sample pipelines and computational analysisprocedures
3.1 Sample pipeline and case studies
A series of computational analyses were conducted to
predict the structural behavior and failure pressure. The
targeted subsea pipeline experiences both internal and
external pressures. The computational analysis was carried
out using the commercial FEA software tool ABAQUS.
Corrosion was defined in accordance with Fig. 5. This
approach had already been verified by several researchers,
e.g., Netto et al. [5]. Netto et al. introduced two corrosion
idealized models in the FEA: the exact defect-shape model
(EDSM) and the simplified defect-shape model (SDSM). As
shown in Fig. 1, the EDSM is elliptical, which reflects the
actual corrosion shape. In contrast, the SDSM is rectangu-
lar, which provides efficiency for modeling the corrosion
shape. An analysis was conducted, and the results were
compared with those from an actual failure pressure test.
The failure pressure of the EDSM and SDSM models had
acceptable average errors of 10 and 15 %, respectively. The
failure pressures of the EDSM and SDSM were slightly
overestimated and underestimated, respectively. The SDSM
has limitations such as the stress concentration because of
its rectangular shape. However, the underestimation ten-
dency could be an advantage for safety assessment.
Therefore, the SDSM was adopted in this study. It was
postulated that the corrosion had taken place at the center of
the pipe, away from the boundaries of the FEM model.
Table 1 presents the 43 analysis cases to investigate
effects of both external and internal corrosions with vary-
ing depth, width and length corrosion. The corrosion depth
and length are expressed as ratios over the initial pipe
thickness and diameter, respectively. The degree of cor-
rosion width denotes an arc length of the corroded region in
the pipe’s cross section.
3.2 Material properties and dimensions of pipeline
The subsea pipeline used in this study was made of carbon
manganese steel grade API 5L X65. Figure 6 is an example
of the strain–stress curves of this material. Table 2 shows
its material properties and dimensions. A piecewise linear
material model was used to represent the nonlinear material
behavior.
Fig. 5 Configuration of internal
and external corrosion in a
subsea pipeline
J Mar Sci Technol (2016) 21:369–384 375
123
3.3 Finite element model loading and boundary
conditions
Figure 7 shows the FE model. The number of FE is
approximately 17,600. The selected element was
reduced integration 20-node hexahedral element
(C3D20R in ABAQUS). To reduce the computation
time, only a half in cross section and a half in lengths
were modeled and symmetric boundary conditions were
applied. Moreover, to avoid rigid body motion during
Fig. 12 Relationship between equivalent pressure and von Mises
stress predicted assuming elastic and elastoplastic material
characteristics
J Mar Sci Technol (2016) 21:369–384 381
123
corrosion, was used to investigate the geometrical effect
and compare with the FEA results. To distinguish dominant
factors, aforementioned process was carried out. As shown
in Eqs. 7–10, Level 2 of Part 5 in the API 579 code has
terms of geometrical information, such as the neutral axis,
the moment of inertia of the pipe and corrosion. Because
the calculation results of API 579 were represented as
equivalent stress values, not failure pressure, the FEA
results were adopted as von Mises stress values and com-
pared with the calculation results of the API 579 code. The
internal pressure condition of the FEA was fixed to only
12 MPa, which is a subsea pipeline’s operating pressure
[20]. Other conditions were the same as those of the con-
ducted FEA. To calculate the API 579 code, the maximum
allowable working pressure (MAWP) value was required,
which is the value of the internal pressure load. However,
because the FEA results considered both the external and
internal pressure load, MAWP should be changed to the
equivalent pressure load that indicates the same as loading
condition of FEA. As described above, the internal pressure
load was 12 MPa and the external pressure load was
30 MPa, which is the hydrostatic load at 3,000 m water
depth. Then, the equivalent pressure load was 18 MPa.
Each direction of pressure is in the opposite way.
However, when the magnitude of the equivalent pressure
load was the same, the direction of the equivalent pressure
did not affect structure behavior in the pipe significantly.
Additional analysis, which only had a difference of load
direction for corrosion depths of 25 and 50 %, was per-
formed and its results were 374.1 and 434.92 MPa,
respectively. The results had a 5 and 6 % error, respec-
tively, compared with the corresponding results in Table 5.
Because there was no significant difference between them,
18 MPa was adopted as MAWP. The calculation results
were represented in accordance with the procedures of the
API 579 code (Table 5; Fig. 13).
Apparently, stresses based on API 579 are much lower
than those of FEM. The same trend was found in other
investigated codes. In addition, the calculation results of
API 579 show a gradually rising slope, while the nonlinear
FEM shows a more complex pattern. Differences were
considered to be due to the material’s nonlinearity, which
is not explicitly considered in API 579 code or other codes.
5.2 Suggestion of including material nonlinearity
in API 579 code
A RSF factor may be introduced as a dimension less
measure of strength of corroded pipe. RSF was defined as
the ratio of the non-damage to the damage value. The
failure pressure could be predicted using RSF, if the failure
pressure of the intact pipe was known. The failure pressure
of the intact pipe was determined by FEA, taking into
account the material’s nonlinearity. Equations 17–20 show
the RSF calculations, which were provided in the API 579
code.
RSF ¼1� A
A0
1� 1Mt
AA0
ð17Þ
A0 ¼ s � tc ð18Þ
Mt ¼ 1:0010� 0:014195kþ 0:29090k2 � 0:096420k3
þ 1:4656 10�10
k10 þ 0:020890k4
� 0:0030540k5 þ 2:950 10�4
k6 � 1:8462 10�5
k7
þ 7:1533 10�7
k8 � 1:5631 10�8
k9 ð19Þ
k ¼ 1:285sffiffiffiffiffiffiffiDtc
p ð20Þ
where A is the allowable remaining strength factor, A0 the
original metal area based on s, tc the corroded wall thick-
ness away from the region of local metal loss,Mt the Folias
Table 5 Results of API 579 and FEA
Corrosion depth (%) Calculated result
RSF MAWPra (MPa) API 579b (MPa) FEAc (MPa) Failure pressure using RSF (MPa)
10 0.94 18.81 234.44 272.26 76.17
20 0.88 17.50 252.36 339.11 70.88
25 0.84 16.80 263.19 395.62 68.04
30 0.80 16.07 275.64 421.33 65.07
40 0.72 14.48 307.10 440.91 58.66
50 0.64 12.73 351.84 463.06 51.55
60 0.54 10.77 420.11 526.15 43.62
65 0.49 8.57 469.53 626.36 39.30
a Reduced permissible maximum allowable working pressure of the damaged componentb Equivalent stress of pipe calculated in accordance with the API 579 proceduresc Maximum von Mises stress
382 J Mar Sci Technol (2016) 21:369–384
123
factor or bulging correction factor based on the longitudi-
nal extent of the local thin area (LTA) for a through-wall
flaw, and k the longitudinal or meridional flaw length
parameter. The FEA’s failure pressure for the intact pipe
was 81 MPa. The failure pressure calculated using this
value and the RSF value are presented in Table 5 and
Fig. 14.
Up to a 60 % corrosion depth, the results had a high
degree of comparison, with an error between 1 and 9 %.
The RSF equations (Eqs. 17–20) resemble the hoop stress
equation. However, there was a distinct difference between
the calculation results. Therefore, corrosion assessment
that used the RSF and failure pressure values of the intact
pipe, which reflect the material’s nonlinearity, could be
more accurate than the existing assessment codes.
6 Conclusions
This paper summarizes a study on the strength of a cor-
roded pipe under inflow-induced (internal) as well as
hydraulic pressure (external). Extent of corrosion pipe was
defined by corrosion depth (radius), width (angle) and
length (height). The corrosion location (internal and
external) was also investigated.
A series of linear and nonlinear FEM analyses was
performed to investigate the failure of corroded pipeline
and the influences of corrosion and material properties on
the failure pressures. These FEA results were compared
with various assessment codes.
The following conclusions could be drawn:
• Whether corrosion takes place on divided external or
internal surface, the behavior of the pipeline remains
same.
• Corrosion depth was the most significant factor for
safety of subsea pipes. With the increase in corrosion
depth, the maximum von Mises stress on the corroded
pipe increased drastically and the failure pressure
decreased rapidly.
• Effect of material nonlinearity becomes more pro-
nounced when corrosion depth is high. However, this
effect was not explicitly considered in the existing
codes of ASME, DNV, ABS and API. A suggestion
was made to adjust the API 579 prediction of failure
pressure using a calibrated factor to take into account
the effects of material nonlinearity.
Acknowledgments This work was supported by the National
Research Foundation of Korea (NRF) Grant funded by the Korea
government (MSIP) through GCRC-SOP (No. 2011-0030013). This
research was supported by Basic Science Research Program through
the National Research Foundation of Korea (NRF) funded by the
Ministry of Education (NRF-2013R1A1A2A10011206).
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RSF
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