{Numerical modelling of buried pipelines under DC stray current corrosion}
http://dx.doi.org/10.5599/jese.567 125
J. Electrochem. Sci. Eng. 9(2) (2019) 125-134; http://dx.doi.org/10.5599/jese.567
Open Access: ISSN 1847-9286
www.jESE-online.org
Original scientific paper
Numerical modelling of buried pipelines under DC stray current
corrosion
Yaping Zhanga,, Qiong Fenga,d, Xue Hana, Lianqing Yua,, Chi-Man Lawrence Wub,,
Siu-Pang Ngb, Xiao Tangc
aCollege of Science, China University of Petroleum (East China), Qingdao, 266580, P. R. China
bDepartment of Materials Science and Engineering, City University of Hong Kong, Hong Kong, SAR,
P.R. China
cCollege of Mechanical and Electrical Engineering, China University of Petroleum (East China),
Qingdao, 266580, P. R. China
dSemiconductor Lighting Technology Research and Development Center, Institute of
Semiconductors, Chinese Academy of Sciences, Beijing, 100083, P. R. China
Corresponding authors: E-mail zhangyp@upc.edu.cn; iyy2000@163.com; lawrence.wu@cityu.edu.hk
Received: July 7, 2018; Revised: October 29, 2018; Accepted: November 5, 2018
Abstract
Corrosion of buried pipelines caused by stray currents is becoming a serious industrial and
environmental problem. It is therefore necessary to study corrosion mechanisms of buried
pipelines under DC stray currents in order to propose effective anti-corrosion measures.
Since measurement of the potential is one of important ways to identify stray current
intensity, the COMSOL Multiphysics software was used to simulate stray current corrosion
dynamics of buried pipelines. It was also used to calculate the distribution and intensity
changes of electrolyte potential in the cathodic protected system by solving Laplace’s three-
dimensional equation. The obtained results showed that increased applied voltage leads to
more positive shift of a pipeline potential, resulting in acceleration of stray current
corrosion. On the contrary, increased soil resistivity can retard the corrosion process. The
protected pipeline with a sacrificial anode suffers less corrosion interference than
unprotected pipeline. Two crossed arrangement of pipelines makes no difference in
corrosion of protected pipeline, but affects greatly on unprotected pipeline.
Keywords
Stray current corrosion; numerical modeling; buried pipelines
Introduction
Stray currents arising from railway systems can induce corrosion of buried pipeline structures
and result in severe damage [1]. Basically, there are four types of corrosion [2], involving general
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mailto:lawrence.wu@cityu.edu.hk
J. Electrochem. Sci. Eng. 9(2) (2019) 125-134 BURIED PIPELINES UNDER DC STRAY CURRENT CORROSION
126
corrosion (chemical in nature), concentration cell corrosion (caused by differences in the electrolyte
concentration), galvanic corrosion (caused by different metals), and stray current corrosion (caused
by external electrical sources). Among all corrosion types, just the stray current corrosion (SCC) is
considered as the most serious one. SCC is caused by the flow of stray currents through pipelines,
which usually occurs on their external surfaces. The consequences of SCC have been manifested as
severe localized pitting and pin holes formed on metal surfaces at the place where stray currents
leave the pipeline surface [3,4].
A routine way to mitigate the SCC of pipelines is to install sacrificial anodes or apply a current to
inappropriate bedding for protected structures. Both sacrificial anodes and applied current belong
to the cathodic protection procedure. Cathodic protection is benefit for charges transport from the
metal pipeline to the anode [5]. Corrosion easily happens because part of a pipeline in the soil is
anodic and the other part in the air is cathodic. Therefore, the goal of cathodic protection is to apply
a direct current to the steel and provide a sacrificial anode [6]. With the development of technology,
the numerical modeling becomes very convenient and accurate method for dealing with SCC
problems. There are three kinds of numerical analysis for cathodic protection systems, including
finite difference method, boundary element method and finitude method. Among these methods,
the boundary element is suited to off-shore structures as a method capable to infer the distribution
of potential and current densities along the metallic structure/electrolyte interface [7]. At the other
side, the finitude method is well suited to cathodic protected pipelines.
COMSOL Multiphysics is the simulation software based on the finitude method for corrosion
numerical calculations. In this paper, the COMSOL Multiphysics software is used to evaluate the
effect of stray current on the protected/unprotected pipelines resulting from a nearby cathodic
protection system.
Theory
Governing equation
The boundary and initial conditions were set during the simulation, of the protected pipeline and
anode ball constituting a whole [8]. The anode ball acts as an anode and produces the anodic
oxidation reaction which defines the anode boundary condition. The protected pipeline acts as a
cathode for oxygen reduction which defines the cathode boundary condition. The unprotected
pipeline can self-corrode in the soil environment, where anode and cathode reactions occur
simultaneously on the pipeline surface. The electrode boundary conditions should be set in two
ways. The initial value of electrolyte potential is set to -0.90 V, and the electrolyte potential is set
zero at infinity.
The principles of cathodic protection of underground structures have already been discussed in
detail [9]. The soil is treated as a homogeneous medium with a uniform conductivity. The potential
(φ)distribution is governed by the Laplace’s equation
2
0 = (1)
and the current density (i) is related to the electric field by the Ohm’s law as follows
= − i (2)
In eq. (2), is electrical conductivity of the soil.
The boundary conditions are defined as
0 = / m (3)
Yaping Zhang et al. J. Electrochem. Sci. Eng. 9(2) (2019) 125-13434
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where m is the number of electrons transferred directly. Eq. (3) is defined for the region between
the insulation layer of unprotected pipeline without any defect and the soil-air surface.
ia = exp (a / a) (4)
ic = i0,c exp (-c / c) (5)
In boundary conditions defined by eqs. (4) and (5), ia, ic, 0,ai , 0,ci are anodic and cathodic current
and exchange current densities, while a, c and a, c are corresponding Tafel slopes and surface
overpotentials, respectively. The boundary conditions defined by eqs. (4) and (5) represent the
electrode surface kinetics which strictly follows the Tafel kinetics.
Reaction chemistry
Three kinds of electrochemical reactions happen on the steel interface, including iron oxidation,
oxygen reduction, and hydrogen evolution [10].
(1) Hydrogen evolution reaction
Anode reaction: 2Fe→2Fe2++4e-
Cathode reaction: 4H-+4e-→4H2
4H2O+4e-→2H2+4OH-
(2) Oxygen reduction reaction
Anode reaction: 2Fe→2Fe2++4e-
Cathode reaction: O2+4H++4e-→2H2O
O2+2H2O+4e-→4OH-
When stray currents induce pipeline corrosion, the Faraday’ law should be conformed [11]
= nc
J M
K
nF (6)
In eq. (6) Kc is the amount of metal corrosion, Jn is the normal current density, M is atomic mass
of the metal, F is the Faraday’ constant, and n is the number of electrons required for the reaction.
For a given metal and reaction, parameters M, F, and n are constant, and so Kc .Jn
Modeling Configuration
In order to ensure the accuracy of simulation and save computing resources, according to the
length and diameter of actual pipelines, we setup a 1:100 scale model to build up the simulation
model (schematically shown in Figure 1). The length, width and height of the scale model were set
as 500, 800, 500 mm, respectively, and the length of pipelines was set proportional to its diameter.
The distance of sacrificial anode to the pipeline was set proportional to the actual project. The
pipelines are evenly coated with epoxy resin. Epoxy resin coating on pipeline surface should be
strictly in accordance with SHT3022-2011 code for corrosion prevention design of petrochemical
equipment and pipeline coatings.
Models were built up to simulate the corrosion of the protected/unprotected structure due to
stray currents. Two study cases with different arrangements of pipelines were investigated,
involving parallel and crossed arrangements of protected and unprotected pipelines under different
interference conditions. Geometrical, physical and electrochemical model parameters are listed in
Tables 1 and 2. A tank was filled with the soil having measured electrical resistivity of 50.0 Ω·m,
which is consistent with the reference [12]. The protected cathode and unprotected structure were
placed in the tank at a height of 20 cm from the bottom. Two break points were set at both ends of
the pipeline. The copper plates were used to insure the homogeneous potential differences, and a
constant direct voltage was applied to the copper plates. The solution side potential of the
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J. Electrochem. Sci. Eng. 9(2) (2019) 125-134 BURIED PIPELINES UNDER DC STRAY CURRENT CORROSION
128
protected/unprotected structure was scanned with a saturated copper sulfate reference electrode
(CSE). Stray current was picked upon the unprotected pipeline and the protected pipeline was
connected with a sacrificial anode. Physical fields are added to the geometric model, and the
secondary current distribution model (corrosion process satisfy the Ohm's law and activation loss
during charge transfer) in the corrosion module is selected. The anode and cathode reactions in the
corrosion process satisfied the dilute material transfer model in the electrochemical module.
As shown in Figure 2, the sacrificial anode has more positive potential, and so, electric field lines
are emitted from it and terminate at the cathodically polarized structure having more negative
potential. The current in the structure flows towards the anode, and regions where currents enter
will be at a more negative potential, protecting thus the structure from corrosion. Sacrificial anode
protection is equivalent to a direct current flowing to the pipeline compulsively, resulting in negative
potential shift and reducing the corrosion rate of the structure.
Fig. 1. Schematic view of models: (a) parallel pipelines; (b) crossed pipelines
Table 1. Specification of physical model parameters
Quantity Value
Protected pipeline length 400 mm
Unprotected pipeline length 400 mm
Protected pipeline diameter 4 mm
Unprotected pipeline diameter 4 mm
Anode diameter 2 mm
Soil resistivity (if not specified) 50.0 Ω·m
Anode current density (if not specified) 100 A/m²
Yaping Zhang et al. J. Electrochem. Sci. Eng. 9(2) (2019) 125-13434
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Table 2. Electrochemical model parameters
Parameter name Value Description
F 96485 C/mol Faraday constant
Eeq_Fe -0.76 V Equilibrium potential of Fe-Fe2+
i0_Fe 7.1×10-5 A/m2 Exchange current density of Fe-Fe2+
𝛽Fe 0.41 mV/decade Ion Reduction Tafel Slope
Eeq_H2O -1.03 V Equilibrium potential of H2O-H2
i0_H2O 0.11 A/m2 Exchange current density of H2O-H2
𝛽H2O 0.15 mV/decade H2O reduction Tafel slope
Eeq_O2 0.189 V Equilibrium potential of O2 and OH-
i0_O2 7.7×10-7 A/m2 Exchange current density of O2 and OH-
𝛽O2 -0.18 mV/decade Oxygen reduction Tafel slope
gap 5×10-4 m Gap between coating and steel surface
phi0 -0.9 V Measuring potential of body phase
Fig. 2. Scheme of pipeline protection by sacrificial anode
Results and discussions
Parallel pipelines
Figure 3 shows the calculated potential distributions for parallel pipelines in a cathodic protection
system, with a voltage of 10 V applied between the anode and the protected cathode, which is
consistent with literature data [8,9] and actual project construction. Different colors represent
potential magnitudes, where red and blue mean positive and negative values, respectively. As
shown in Figure 3, the potential at the position of 0 ~ 20 cm is much higher than at other parts of
the tank along the pipeline direction. Figure 3(b) shows the potential contour profile surrounding
the parallel pipelines in detail. As shown in Figure 4, currents flow into the cathodically protected
pipeline and return to the anode through the unprotected pipeline where corrosion occurs due to
the dissolution reaction of the anode. Because there is potential gradient surrounding the anode,
anode will interfere with the current flow path, that is, protected pipeline can accept current near
the anode and then leading to current flowing along the pipeline. That is why the protected pipeline
has more negative potential than the unprotected pipeline.
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Fig. 3. Calculated potential distributions for parallel pipelines: (a) profile of equipotential
surfaces; (b) chart of equipotential lines
Fig. 4. Current flow direction for parallel pipelines
Yaping Zhang et al. J. Electrochem. Sci. Eng. 9(2) (2019) 125-13434
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a b
c d
Fig. 5. Potential profiles along the parallel pipeline axial length: protected pipeline at
(a) different voltage and (c) different soil resistivity; unprotected pipeline at
(b) different voltage and (d) different soil resistivity
Dependences of potential profiles on positions of protected/unprotected pipeline for different
voltages are shown in Figure 5. The potential of the unprotected pipeline is more positive than the
protected pipeline, which suggests that the unprotected pipeline will be corroded firstly. At the
voltage of 10 V, the potential of the protected pipeline ranges from -0.30 V to 0.17 V. For the
unprotected pipeline at 10 V, however, the potential values are higher, and ranged between 0.00 V
and 1.00 V. According to the calculated data, it is proved that the sacrificial anode protection is
effective. With voltage increase, the potentials show a positive trend of changes. According to Figure
5(a), at the position of 10 cm, the potential rises from -0.20 V to 0.20 V when the applied voltage
increases from 5 V to 20 V. Likewise, as shown in Figure 5(c) and (d), the potential profile shifts
positively when the soil resistivity decreases, what can accelerate charge transfer and facilitate the
process of corrosion.
The calculated potential distributions for crossed pipelines at a voltage of 10 V are shown in
Figure 6. The protected pipeline is situated along y-axis. It can be seen that the potential of the
pipeline parallel to y-axis decreases progressively along the positive y-axis and the color changes
from red to blue.
Potential versus position profiles for different voltages and soil resistivities of protected/un-
protected pipelines are shown in Figure 7. For protected pipelines, the trend of potential change in
Figures 7(a) and (c) is similar to Figures 5(a) and (c) and shows monotonous potential decrease.
0 5 10 15 20 25 30 35 40
-0.4
-0.2
0.0
0.2
0.4
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
5 V
10 V
15 V
20 V
0 5 10 15 20 25 30 35 40
0.0
0.5
1.0
1.5
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
10 V
15 V
20 V
25 V
0 5 10 15 20 25 30 35 40
-0.4
-0.3
-0.2
-0.1
0.0
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position,cm
70.63 m
52.54 m
30.94 m
0 5 10 15 20 25 30 35 40
0.2
0.4
0.6
0.8
1.0
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
70.63 m
52.45 m
30.94 m
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132
Crossed pipelines
Fig. 6. Calculated potential distributions for crossed pipelines
a b
c d
Fig. 7. Potential profiles along the crossed pipeline axial length: protected pipeline at
(a) different voltage and (c) different soil resistivity; unprotected pipeline at
(b) different voltage and (d) different soil resistivity
The stray current transfers from one broken side of protected pipeline to another broken side
where corrosion occurs seriously. Potential distributions for unprotected pipelines shown in Figures
0 5 10 15 20 25 30 35 40
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
10 V
15 V
20 V
25 V
0 5 10 15 20 25 30 35 40
-0.2
0.0
0.2
0.4
0.6
0.8
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
)
Position, cm
10V
15V
20V
25V
0 5 10 15 20 25 30 35 40
-0.4
-0.3
-0.2
-0.1
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
70.63 m
52.45 m
30.94 m
0 5 10 15 20 25 30 35 40
0.2
0.4
0.6
0.8
1.0
P
o
te
n
ti
a
l,
V
v
s
.
C
S
E
Position, cm
70.63 m
52.45 m
30.94 m
Yaping Zhang et al. J. Electrochem. Sci. Eng. 9(2) (2019) 125-13434
http://dx.doi.org/10.5599/jese.567 133
7(b) and (d) are, however, significantly different from that shown in Figures 5(b) and (d). Both
potential profiles exhibit a sharp downturn with the change of position, reaching a minimum value
in the middle of pipeline and then begin to increase. Simply speaking, the potential distribution is
presented as a letter “V”. In other words, the potential on the unprotected pipeline is symmetrical
perpendicular to the protected pipeline. As shown in Figure 7(a) and (b), in the middle position at
20 cm, the potential of the unprotected pipeline reaches -0.20 V, what is more positive than -0.42
V attained for the protected pipeline. Thus, the unprotected pipeline will suffer from severely
concentrated corrosion. The corrosion reaches the maximum in the middle zone where the current
flows out from the unprotected pipeline. As shown in the scheme drawn in Figure 8, the current
flows out from the anode, enters the unprotected pipeline at the remote areas and then escapes
from the crossed point of two pipelines. Since the potential of the unprotected pipeline is generally
positive, a minimal potential value can be obtained at the position of current flowing out.
Fig. 8. Current direction for crossed pipelines
Conclusions
A mathematical model was developed to solve Laplace’s three-dimensional equation with
nonlinear boundary conditions for a cathodic protection system, and applied for considering the
interference of DC stray current corrosion. Two different arrangements of protected and
unprotected pipelines (parallel and crossed) were studied, and potential distributions of buried
pipelines were for both arrangements obtained by simulations. It was shown that the type of
protected/unprotected pipelines arrangements have a great impact on the potential distribution of
the unprotected pipeline. The results also showed that both applied voltage and soil resistivity are
crucial factors impacting stray current corrosion. Again, the sacrificial anode protection in a cathodic
protection system was certified as an effective way for corrosion prevention.
Acknowledgements: The work described in this article was supported by grants from the National
Natural Science Foundation of China (No.21476262), Technology Project of Qingdao 14-2-4-108-jch.
The authors also acknowledge the associated support service by Associate Professor Xiao Tang’s
research group.
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