Journal of Power and Energy Engineering, 2014, 2, 594-599
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
How to cite this paper: Xing, P.X., et al. (2014) Potential Calculation on the Oil-Gas Pipeline with Geosynthetic Clay Liners
Based on BEM. Journal of Power and Energy Engineering, 2, 594-599. http://dx.doi.org/10.4236/jp ee.2014.24080
Potential Calculation on the Oil-Gas Pipeline
with Geosynthetic Clay Liners Based on BEM
Pengxiang Xing1, Yu Wang1, Hailiang Lu1, Lei Lan1, Xishan Wen1, Shulin Zhang2
1School of Electrical Engineering, Wuhan University, Wuhan, China
2China Liaohe Petroleum Engineering Co. Ltd., Panjin, China
Received Dec emb er 2013
Put geosynthetic clay liners around underground oil-gas pipelines can reduce the potential dam-
age to environment but it will also affect the distribution of cathodic protection current. Geosyn-
thetic clay liners can be regarded as anisotropic soil structure and the potential distribution on
the pipeline between two adjacent cathodic protection stations was calculated based on boundary
element method (BEM). The calculation results indicate that potential distribution on the pipeline
with geosynthetic clay liner is lower than before. A 1500 m built pipeline with geosynthetic clay
liners was selected to be calculated and to perform field test, which shows that the calculation re-
sults tally well with the field test results and the validity of the arithmetic in this paper was veri-
Oil-Gas Pipeline; Geosynthetic Clay Liner; Cathodic Protection; Boundary Element Method (BE M)
Impressed current cathodic protection is one of the most important measures to prevent corrosion and is widely
used in underground oil-gas pipeline anticorrosion -. With the development of oil-gas pipeline co nst ruc-
tion in China, it has to go through diverse geographical conditions . Put geosynthetic clay liners around un-
derground oil-gas pipelines in environmentally sensitive areas can reduce the potential damage to environment
when pipeline leakage occurred -. Figure 1 shows the location of geosynthetic clay liners around the oil-
gas pip eline.
Geosynthetic clay liners can be regarded as anisotropic soil structure around the pipeline because their resis-
tivity are different from the soil. Potential distribution on the pipeline between two adjacent cathodic protection
station were calculated based on BEM with and without geosynthetic clay liners. A 1500 m built pipeline with
geosynthetic clay liners was selected to model and perform feeder test. Potential variation at the cathodic protec-
tion current inject point, 200 meters away from one head of the pipeline, was calculated and measured. The cal-
culation results tally well with the test results and the validity of the arithmetic in this paper was verified.
P. X. Xing et al.
Figure 1. Sketch map of geosynthetic clay liners’ construction.
2. Calculation Method of Potential Distribution on the Pipeline
First, Geosynthetic clay liners around underground oil-gas pipeline can be model as anisotropic soil structure
and the potential anywhere in the soil can be calculated based on BEM. Here’s the basic idea -:
Resistivity of geosynthetic clay liners are ρ1 and the soil resistivity is ρ2, Γ is the interface of geosynthetic clay
liners and soil, which are marked as Ω1 and Ω2, just as shown in Figure 2.
Arithmetic in this paper based on assumptions as follows:
(1) Interface Γ is divided into m p arts marked
SSS S∆∆∆ ∆
and the surface charge density of every
(I = 1, 2,… m), which can be regard as constant if
(i = 1, 2,… m) is small
is the image of
(2) Underground pipeline is divided into r parts marked
and the linear charge density of
every part is
,their images are
(3) ΔSq is any part on the interface Γ,
is unit normal vector and point from Ω1 to Ω2.
Surface charge density
(q = 1, 2,… m) of any part in the interface Γ is shown as follo ws:
is surface charge density (C/ m2),
is linear charge density (C/m),
is electrical conductivity
(S/m) and E quatio n (1) can be rewrite as follows:
Potential of arbitrary point on the pipeline
(p = 1, 2,… r) is shown as follows:
dL ds ds
Equation (3) can be rewrite as follows:
P. X. Xing et al.
Figure 2. Sketch map of boundary element method.
Rewrite Equations (2) and (4) as matrix form:
whe re A, B, C, D are coefficient matrix, U is voltage vector of every section of the pipeline, when the section is
small enough its potential can be regard as constant and the potential of section k can be regard as the average
potential of the two attached nodes:
where V is voltage vector of the pipeline nodes, K is coefficient matrix, if node i connect node j, kij = 0.5, othe r-
wis e kij = 0. Replace branch voltage in Equatio n (6) with node voltage in Equatio ns (6) and (7) can be rewrite as
Branch current can be divided into two equal parts and allocated to attached nodes, then we can get Equatio n
If node j connect branch k, ck,j = 1, other wise ck,j = 0. Equivalent node current dissipate matrix J can be ex-
pressed in Eq uation (10).
J KI= ⋅
According to electrostatic analogy, electric density on the interface of pipeline and current dissipate can be
expressed in Equation (11).
Rewrite it as matrix as follows:
If the node current vector is F, we can get Equation (13) based on node voltage method in circuit theory.
Equation (13) can be rewrite as follows combined Equations (10) and (12).
P. X. Xing et al.
Potential and current dissipate of each section of the pipeline can get from the simultaneous solution of Equa-
tions (5) (8) and (14).
3. Calculation and Analyse of Pipeline Potential Distribution
Model pipeline potential calculation is based on BEM according to part two. The length of the steel underground
pipeline is 8500 meters, with a outside diameter 323.9 mm and a thickness 5.6 mm, relative resistance of the
pipeline is 10 and the relative permeability is 636; soil resistivity is 593 Ω·m and the resistivity of geosynthetic
clay liners is 200 Ω·m with a thickness 5 cm. Cathodic protection current at two ends of the pipeline are 50 mA,
100 mA, 150 mA and 200 mA. The varied potential distribution on the pipeline with and without geosynthetic
clay liners are shown in Figure 3, represented by and separately, where l is the length of the
pipeline (m), ΔU is the varied potential (V).
Calculation results indicate that the varied potential increased with cathodic protection current and the varied
potential distribution on the pipeline seems to be inverted U, namely higher in the two ends and lower in the
middle, and the voltage variation gradient in the two ends are much bigger than middle parts. Potential distribu-
tion on the pipeline with geosynthetic clay liners has overall declined compared to it used to be. The ratio of ΔU
and its previous potential is defined as potential decrease percentage and the maximum value 10% occured at the
two ends of the pipeline, namely the cathodic protection current inject points. So cathodic protection current
should increased properly when geosynthetic clay liners are put around the underground pipeline.
4. Feeder Test and Analyse
In order to verify the accuracy of the arithmetic in this paper, field feeder test was performed in China and
Myanmar oil-gas pipeline Jinning extension, the test pipeline is 1500 meters long and has been covered with
geosynthetic clay liners. Feeder test method - is shown in Figure 4.
Temporary anode bed in the field test was made up by 6 angle steels with a length of 1 meter, which are pa-
rallel co nne cted with each other, the temporary anode bed was 100 meters away in vertical distance from the test
pipeline. Anode of the DC power was linked to the temporary anode bed and the cathode of the DC power was
linked to the pipeline by a test pile 200 meters away from one head of the pipeline. Spontaneous potential of the
01000 2000 3000 4000 5000 6000 7000 8000
010002000 30004000 5000 6000 70008000
010002000 30004000 5000 600070008000
01000 2000 3000 4000 5000 6000 7000 8000
Figure 3. Potential distribution on the pipeline with different cathodic protection current.
P. X. Xing et al.
1—underground pipeline; 2—geosynthetic clay liners
3—connected cable; 4—temporary anode
5—copper sulfate reference electrode
Figure 4. Sketch map of pipeline feeder test.
pipeline was −1 V and the pipeline potential became −1.2 V when adjust cathodic protection current to 120 mA,
potential variation ΔU = −0.2 V. Based on the arithmetic in this paper, the calculation result of cathodic protec-
tion current is 113 mA when potential variation ΔU at the current inject point is −0.2 V, relative error is 5.83%,
which indicate that the calculation result agree well with the test result.
Potential distribution on the pipeline with geosynthetic clay liners was calculated based on BEM in this paper
and it indicated that the pipeline potential get a slight decline when geosynthetic clay liners were put around the
pipeline. Both the maximum potential variation and the maximum potential decrease percentage were occurred
at the cathodic protection current inject point. Validity of the arithmetic in this paper to calculate potential dis-
tribution on the pipeline with geosynthetic clay liners was verified by the comparison with field test.
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