Volume 20 Preprint 74
Residual Strength Prediction Model for Corroded Oil Tube based on FEM and Artificial Neural Network
M. Y. Xia, H. Zhang
Keywords: corrosion defects, oil tube, finite element method, residual strength, artificial neural network
Corroded oil tubes are prone to failure under complicated service load. In this study, finite element models of oil tubes with two typical shape of corrosion defects, e.g. elliptical corrosion pits and the axial groove defects, under the service loads were established. Based on the numerical model, parametric analysis were conducted to investigate the effects of corrosion defect position, defect depth, defect width and defect length on tubeâ€™s residual strength. Finally, based on derived numerical results, a BP artificial neural network (ANN) was employed to predict the residual strength of corroded oil tube. Results show that, when the corrosion location depth is shallow, the failure of oil tubes are mainly caused by the axial force. When the corrosion location depth is deep, the failure is mainly caused by the internal pressure. With increase of the depth in well of the corrosion defect, the max von Mises stress in the tube decreases first and then increases. The corrosion defect depth has a great influence on tubeâ€™s max von Mises stress. While the corrosion width and length have small influence on tubeâ€™s max von Mises stress. By validation with numerical results, the proposed BP ANN based residual strength prediction model was accurate and efficiency. This proposed method can be referred in the assessment of oil tubes with corrosion defects.
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Residual Strength Prediction Model for Corroded Oil Tube
based on FEM and Artificial Neural Network
M. Y. Xia*, H. Zhang
College of Mechanical and Transportation Engineering, China University of PetroleumBeijing, Beijing 102249, China
Corroded oil tubes are prone to failure under complicated service load. In this study, finite
element models of oil tubes with two typical shape of corrosion defects, e.g. elliptical
corrosion pits and the axial groove defects, under the service loads were established. Based
on the numerical model, parametric analysis were conducted to investigate the effects of
corrosion defect position, defect depth, defect width and defect length on tube’s residual
strength. Finally, based on derived numerical results, a BP artificial neural network (ANN)
was employed to predict the residual strength of corroded oil tube. Results show that, when
the corrosion location depth is shallow, the failure of oil tubes are mainly caused by the
axial force. When the corrosion location depth is deep, the failure is mainly caused by the
internal pressure. With increase of the depth in well of the corrosion defect, the max von
Mises stress in the tube decreases first and then increases. The corrosion defect depth has
a great influence on tube’s max von Mises stress. While the corrosion width and length have
small influence on tube’s max von Mises stress. By validation with numerical results, the
proposed BP ANN based residual strength prediction model was accurate and efficiency.
This proposed method can be referred in the assessment of oil tubes with corrosion defects.
Keywords: corrosion defects, oil tube, finite element method, residual strength, artificial
Oil tubes play a very important role in oil field development. The complicated working
environments make it vulnerable to external loads. Corrosion is one main threat for these
oil tubes. Fig.1 shows some corroded oil tubes in engineering practice. It is obvious that,
metal losses in the tube’s inner and outer surface. Thus conducting failure analysis or
safety assessment of corroded oil tubes has important practical significance.
Fig.1 Corroded oil tubes
In recent years, there are a series of available literatures on strength analysis of oil
pipelines and tubes with corrosion defects, especially pipelines. Batte et al. proposed a
regression based residual strength prediction model for corroded oil pipes . Choi et al.
and Chen et al. also obtained some simple formulas for limit pressure of pipes with
corrosion defects by numerical analysis [2,3]. Shuai et al. proposed an improved limit
pressure prediction model for both low strength and high strength steel pipes . Stephens
et al., Leis et al., Fekete et al. discussed the effects of geometrical parameters of corrosion
defects on pipe’s residual strength [5, 6, 7]. Xiao et al. and Peng et al. compared the
different assessment methods for corroded pipes adopted by various standards or
guidelines [8, 9]. Zhou et al. discussed the failure criterion of corroded oil tube by
experimental and numerical investigation . Hu et al. established a finite element model
for stress analysis of riser with narrow and long defects, and based on the numerical model,
reliability analysis was also conducted . Liu et al. investigated the failure modes of
corroded N80 oil tubed under different load conditions . Xia et al. conducted parametric
analysis on the residual strength of N80 oil tube with different types of corrosion defect.
Although many researches have be done, few of them focused on the accurate residual
strength prediction of corroded oil tube subjected to service loads, which is of great
importance for engineering practice. To fill this gap, based on finite element method, a
stress analysis numerical model for corroded oil tube subjected to service load was
established by general finite element software package ANSYS. Two common corrosion
defect types were considered in the investigation. A parametric analysis was performed to
derive the quantitative relationship between the influence factors and the max von Mises in
the tube. Finally, an artificial neural network based prediction model was proposed for
predicting the residual strength of corroded oil tube.
Service load of oil tube
Under service condition, the oil tube is under complicated load condition . In the
vertical direction, it is under the gravity load and other kinds of load. In the circumferential
direction, it is under internal pressure load. In some special cases, there will be additional
bending load on the tube, which is not considered in this study.
For the applied vertical load on the tube, it is composed of the gravity load induced by the
tube σ1, the buoyancy force induced by the well fluid σ2, the gravity load induced by the
fluid σ3, the friction load between the plunger and bush σ4, the friction load between the
pumping rod and the tube σ5 . So the max axial load in the tube can be obtained as
1 2 3 4 5
For the internal pressure, it can be easily derived as:
P 0 gh 0
Where, h is the depth position of the defect in the tube, 0 is the density of the oil, g is the
gravity acceleration, 0 is the pressure at the well ahead.
In the numerical model, true stress-strain of P110 steel was adopted in the numerical
analysis. The multi-linear isotropic hardening model in ANSYS was utilized simulating this
relationship. And according to API Specification 5CT, Specification for Casing and Tubing
, typical material parameters for P110 steel are as follows. The Young’s modulus E is
207GPa, the yield strength is 758MPa, the ultimate strength is 862MPa, the Possion ratio is
Finite element model
For oil tube corrosion defects, it has three main geometrical parameters, the corrosion
depth d, the corrosion length L, the corrosion width W, as shown in Fig.2.
Fig.2 Geometrical parameters of corrosion defect
For the model is symmetric, only one fourth of the tube need to be modelled in numerical
analysis. In the numerical model, 20 node continuum solid element SOLID 186 was adopted
to simulate the pipe. In the corrosion area, a fine mesh was used. In the radial direction, the
tube was divided into four elements. The mesh details of the finite element model was
shown in Fig. 3.
Fig.3 Finite element model for corroded tube
For oil tube, rupture will occur when the von-Mises stress in the structure reaches the
ultimate strength of the steel. This failure mechanism is similar for both oil tubes and
pipelines. Thus in this section full scale experimental results for burst test of high strength
pipelines were used to validate the accuracy of the presented model. Parameters of the
experiment specimens were listed in Table 1. The finite model was modified geometrically
to conduct these analysis, and results were compared with the experimental and previous
numerical results, as illustrated in Fig.4. It can be found that, results obtained by proposed
finite element model agrees well with the other results, which proves this numerical model
Table 1 Parameters for experiment corroded pipes
Defect length /mm
Fig.4 Comparison results of proposed numerical model with previous experimental and numerical
In this section, parametric analysis was performed using the established numerical model to
investigate the trends of the max von Mises stress σmax with the influence factors. In this
study, Typical P110 oil tube used in the Tahe oil field in China was considered. Thus the
service load was calculated by the field data. Key parameters are as followed: the total
depth of the well is 4500m, the density of completion fluids in the well is 973kg/m3, the
viscosity of completion fluids in the well is 0.025Pa·s, the pressure of the well head is
3.4MPa. In numerical analysis, the axial load and internal pressure in the tube are linear
with the depth position of the corrosion defect in the tube.
Effects of load conditions
As mentioned above, with the increase of the depth position of the defect in tube h, the
axial load in the tube decreases linearly, while the internal pressure increases linearly. In
this section, two typical shapes of corrosion were considered to investigate the relationship
of max von Mises stress in the tube σmax with the depth position of defect in tube h. The
first kind of corrosion defect is ellipsoidal pit defect, its geometrical parameters are listed
as follows: L=20mm, W=16mm, d=4mm. another kind of corrosion defect is the narrow
and long defect, its geometrical parameters are also listed as follows: L=60mm, W=16mm,
Fig. 5 shows trends of the max von mises stress σmax with the depth position in the tube h.
It can derived that, for both kinds of defects, σmax increases with h first, and then decreases.
By comparing the two curves, it can be found that, when h<2250m, the max stress of tube
with ellipsoidal pit defect is larger than that with narrow and long defect.
Fig. 6 illustrates the detailed von Mises contours of the defect areas at different depth
positions in tube for both types of defect. when h=500m, the max von Mises stresses
concentrated at the axial central line and axial end of the defect area for ellipsoidal pit
defect and narrow and long defect, respectively. While, when h=4000m, the max von Mises
stresses concentrated at the circumferential central line for both types of defect. Thus if h is
small, tube may rupture in axial direction, and if h is large enough, the tube may rupture in
circumferential direction. The two failure phenomenon in engineering practice were shown
in Fig. 7.
Fig.5 Trends of the max von Mises stress with the depth position of the defect in tube
(a)The ellipsoidal pit defect
(b)The narrow and long defect
Fig.6 The von Mises stress contours of defect areas at various depth positions in tube
(a) Aixal rupture (b) Circumferential ruptrue
Fig.7 Failure tubes with axial and circumferential rupture
Effects of defect depth
The defect depth was described by the ratio of the defect depth with tube wall thickness in
this study. The corrosion defect was set to be 4000m depth in well, thus the axial load was
148.65 MPa and the internal pressure was 41.54MPa.
Fig. 8 illustrates the trends of the maximum von Mises stress with the defect depth for two
different shape defects. Obviously, with increases of the defect depth, the maximum von
Mises stress increases. And it increases faster with a larger defect depth. This phenomenon
is similar for defects with different width. For the ellipsoidal pit defect, the maximum stress
became larger than the yield strength of tube, when d/t=0.65. For the narrow and long
defect, the maximum stress became larger than the yield strength of tube, when d/t=0.5.
Von Mises contours of the two defects with different defect depth were shown in Fig. 9. It
can be obtained that, the stress distribution is similar for the two defects. And with increase
of the defect depth, stress concentration become more severe in central area of the defect.
Effects of defect width
Fig. 10 illustrates the relationship of the max von Mises stress with the defect width for two
types of corrosion defect. The trends of max stress with defect width are similar for the two
kinds of defects. When the depth of defect d/t is small, max von Mises stress σsmax have
very small variations with the increase of defect width. When d/t is larger, σsmax decreases
with the increase of the defect width. The main reason of this phenomenon is that, with the
increase of defect width stress concentration can be reduced to some extent.
(a) The ellipsoidal pit defect
(b) The narrow and long defect
Fig.8 Trends of the max von Mises stress with the depth of defect
(a)The ellipsoidal pit defect
(b)The narrow and long defect
Fig.9 The von Mises stress contours of defect areas with different defect depth
The von Mises stress contours for tubes with different defect width were also plotted in Fig.
11. For the ellipsoidal pit defect, with increase of the defect width, the max von Mises
stress position transferred from the circumferential central line to the central defect area.
For the narrow and long type defect, the von Mises stress distribution has no obvious
difference, when the defect width increases.
(a) The ellipsoidal pit defect
(b) The narrow and long defect
Fig.10 Trends of the max von Mises stress with width of the defect
(a)The ellipsoidal pit defect
(b)The narrow and long defect
Fig.11 The von Mises stress contours of defect areas with different defect width
Effects of defect length
Fig. 12 describes the influence of defect length L on the max von Mises stress in tube σsmax.
Results show that, with the increase of defect length, σsmax increases. And with a larger
defect depth, the increase rate is larger. Especially, when d/t=0.6, σsmax increases with L
obviously. When d/t=0.2, σsmax varies a little with defect length increasing.
Fig.12 Trends of the max von Mises stress with the length position of the defect
The von Mises stress contours for tubes with different defect lengths were shown in Fig. 13.
For both conditions, the max von Mises stress concentrated in the circumferential central
area of the defect. But with the increase of defect length, axial length of high stress area
Fig.13 The von Mises stress contours of defect areas with different defect length
Residual strength prediction based on artificial neural network
In the previous section, parametric analysis was conducted by 264 cases with different
combination of influence factors. Through this investigation, quantitative relationships
between the max von Mises stress in tube with the influence factors were derived. In this
section, a residual strength prediction model was proposed using BP artificial neural
Basic procedure for BP ANN
BP artificial neural network (ANN) is a kind of multilayer perceptron, which is also known as
feed forward multilayer neural network. It has three different layers, e.g. input layer, hidden
layer and output layer. For hidden layer, it can be one layer or multi layers. Fig. 14 illustrate
the algorithm of training procedure of BP ANN.
Fig. 14 Training procedure for BP neural network
In this study, the neural network was established by the commercial software MATLAB,
which has a neural network toolbox. The BP artificial neural network can be easily trained
by the function ‘trainlm’ supported by MATLAB .
From the parametric analysis, effect factors of residual strength of corroded oil tube can be
concluded as defect location (Load condition), tube wall thickness, defect width, defect
length, defect depth. Thus they are adopted as five input parameters in the input layer. And
the residual strength was set to be the output. In this model, the structure of the neural
network was set as 5-11-1, as shown in Fig. 15.
Residual strength of tube
（11 artificial neurons）
Fig. 15 Neural network structure for limit pressure predicting of corroded pipes
264 case results were used to train the network. Fifteen percent of all cases were used as
validation and another fifteen percent of all cases were used as test. The network training
was completed at epoch 27 as shown in Fig. 16. The normalized results for the trained
network was also illustrated in Fig. 17, which shows that the proposed model is accurate in
residual strength prediction.
Best Validation Performance is 0.0032674 at epoch 27
Mean Squared Error (mse)
Fig. 16 Training process of the BP artificial neural network
Output ~= 0.97*Target + -0.0097
Output ~= 1*Target + 0.0014
Output ~= 0.98*Target + -0.005
Output ~= 0.92*Target + -0.025
Fig. 17 Proposed BP neural network results
Corssion is a main threat for oil tubes. In this paper, a refined numerical model for residual
strength analysis of P110 oil tube with corrosion defects under serive load was established.
Effects of common factors on tube’s residual strength were derived by parametric analysis.
What’s more, a residual strength prediction model was propsod using BP artifical nueral
networks. Some conclusions can be drawn:
The defect depth has more obvious effect on tube’s strength comparing with the
defect length and width. Thus, monitoring the depth of corrosion defects is more
essential in engineering parctice.
With increase of the depth of corssion defect location in tube, the max von Mises
stress in the tube decreases first and then increases for both ellipsoidal pit defect
and narrow and long defect.
If location of the defect in tube is shallow, corrosion area may rupture in axial
direction, and if location of the defect in tube is deep, corrosion area may rupture in
The proposed residual strength prediction model is accurate for corrored P110 oil
tube, which can be referenced in the safety assessment and equipment maintainence
in oil filed.
The work was financially supported by China National Key Research and Development
Project (Grant No. 2016YFC0802105). Science Foundation of China University of Petroleum,
Beijing (Grant No. 2462015YQ0408, No. C201602 and No. 2462015YQ0403), National
Natural Science Foundation of China (Grant No. 51309236), the Opening Fund of State Key
Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (Grant No. 1314), Opening
Fund of State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin
University) (Grant No. HESS-1411), Opening Fund of State Key Laboratory of Coastal and
Offshore Engineering (Dalian University of Technology) (Grant No. LP1507).
‘New methods for determining the remaining strength of corroded pipeline’, A. Batte,
B. Fu, M. Kirkwood, et al., International Conference on Offshore Mechanics and Arctic
Engineering. OMAE. Yokohama, Japan, pp221-228, 1997.
‘Development of limit load solutions for corroded gas pipelines’, J. Choi, B. Goo, J.
Kim, et al. International Journal of Pressure Vessels and Piping, 80, pp121-128, 2003.
‘Limit load capacity of pipes with long longitudinal corrosion’, Y. Chen, X. Li, J. Zhou,
Journal of Ship Mechanics, 13, 5, pp748-756, 2009.
‘Prediction of failure pressure in corroded pipelines based on non-linear finite
element analysis’, J. Shuai, C. Zhang, F. Chen, Acta Petrolei Sinica, 29, 6, pp933-937, 2008.
‘An alternative approach to assess the integrity of corroded line pipe-Part I: current
status and Part II: alternative criterion’, B. Leis, D. Stephens, Proceedings of the 7th
International Offshore and Polar Engineering Conference, Honolulu, USA, May 25-30, 1997.
‘Development of an alternative criterion for residual strength of corrosion defects in
moderate to high-toughness pipe’, D. Stephens, B. Leis, Proceedings of International
Pipeline Conference, Calgary, Alberta, Canada, September, pp10-13, 2000.
‘The effect of the width to length ratios of corrosion defects on the burst pressures
of transmission pipelines’, G. Fekete, L. Varga, Engineering Failure Analysis, 21, pp21-30,
‘Study on failure assessment for X80 high-grade pipeline with corrosion defects’, G.
Xiao, M. Feng, H. Zhang, et al. Journal of Safety Science and Technology, 11, 6, pp126-131,
‘Study on characteristics of safety assessment model on pipeline corrosion’, S. Peng,
H. Tang, Y. Ding, et al., Journal of Safety Science and Technology, 3, pp172-178, 2015.
‘Study the waste standard of the defective oil pipe by finite element method’, S. Zhou,
D. He, Z. Lu, Oil Field Equipment, 2006, 35, 6, pp19-22, 2006.
‘Reliability analysis of marine risers with narrow and long corrosion defects under
combined loads’, X. Hu, C. Zhou, M. Duan, et al. Petroleum Science, 11:139-146, 2014.
‘Residual Strength Analysis of Oil Tubes with Corrosion Defect’, M. Xia, Q. Duan,X.
Liu et al., Materials Science Forum, 850:950-956, 2016.
‘Failure Analysis of Oil Tubes Containing Corrosion Defects Based on Finite Element
Method’, X. Liu, H. Zhang, et al., International Journal of Electrochemical Science, 11, 51805196, 2016.
ISO/TR 10400, the International Organization for Standardization, 2007.
API Specification 5CT, Specification for Casing and Tubing, 2005.
‘A finite-element-based analysis of the accuracy in bursting tests predicting the
ultimate load of a buried pipeline’, B. Ma, J. Shuai, D. Liu, et al., Natural Gas Industry. 33, 6,
‘Neural network toolbox for use with MATLAB. User’s guide’, D. Howard and B. Mark,