Wet Gas Pipeline Internal General Corrosion Prediction
Based on Improved De Waard 95 Model
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Linshuang Wu 1; Kexi Liao 2; Guoxi He, Ph.D. 3; Min Qin, Ph.D. 4; Zhongyuan Tian 5;
Nan Ye 6; Minan Wang 7; and Jihui Leng, Ph.D. 8
Abstract: Corrosion perforation of wet gas pipelines occurs frequently, threatening the safe production on gas fields and bringing huge
economic losses. Therefore, wet gas pipelines need to use a suitable corrosion prediction model to predict the corrosion rate along the pipeline
and anticipate the corrosion risk. However, current corrosion prediction models have problems such as large errors and inaccurate predictions.
This paper compares four common corrosion prediction models and combines these four models with OLGA multiphase flow simulation
calculations to predict the corrosion condition of the same pipeline under three different conditions. Finally, it compares the model predictions
with the actual corrosion internal detection data. The predicted value of the De Waard 95 model was closer to the corrosion internal detection
data, but the error result still reached 82.03%. To further improve the accuracy of the corrosion prediction model for wet gas pipelines, the
De Waard 95 model was optimized using the linear fitting method to obtain a new corrosion prediction model, W22. And the corrosion
prediction experiment was conducted for the multiphase flow corrosion loop using the W22 model, and the error between the prediction
results and the experimental results was only 6.8%. Compared with the De Waard 95 model, the average error of the W22 model was reduced
by 81.32%. Therefore, the W22 model has high accuracy in predicting wet gas pipeline corrosion, which lays the foundation for improving
the essential safety of wet gas pipeline operation. DOI: 10.1061/JPSEA2.PSENG-1477. © 2023 American Society of Civil Engineers.
Author keywords: CO2 ; Wet gas pipeline; Corrosion prediction; De Waard 95.
Introduction
The problem of corrosion in the industry has long been a major
concern. The typical cost of corrosion is 3%–5% of the gross domestic product of industrialized countries. The cost of corrosion in
the production and manufacturing sector in the United States was
1
College of Petroleum Engineering School, Southwest Petroleum Univ.,
No. 8 Xindu Ave., Xindu District, Chengdu 610500, Sichuan, PR China
(corresponding author). ORCID: https://orcid.org/0000-0003-3461-1427.
Email: 1012232256@qq.com
2
Professor, College of Petroleum Engineering School, Southwest
Petroleum Univ., No. 8 Xindu Ave., Xindu District, Chengdu 610500,
Sichuan, PR China. Email: liaokxswpi@163.com
3
Associate Professor, College of Petroleum Engineering School, Southwest Petroleum Univ., No. 8 Xindu Ave., Xindu District, Chengdu 610500,
Sichuan, PR China. Email: heguoxicup@163.com
4
College of Petroleum Engineering School, Southwest Petroleum Univ.,
No. 8 Xindu Ave., Xindu District, Chengdu 610500, Sichuan, PR China.
Email: 1329314986@qq.com
5
Intermediate Engineer, Hainan Branch of CNOOC (China) Co., Ltd.,
No. 8 Changbin San Rd., Xiuying District, Haikou City, Hainan Province
570312, PR China. Email: 1165729292@qq.com
6
College of Petroleum Engineering School, Southwest Petroleum Univ.,
No. 8 Xindu Ave., Xindu District, Chengdu 610500, Sichuan, PR China.
Email: 1169054068@qq.com
7
College of Petroleum Engineering School, Southwest Petroleum Univ.,
No. 8 Xindu Ave., Xindu District, Chengdu 610500, Sichuan, PR China.
Email: 928787068@qq.com
8
College of Petroleum Engineering School, Southwest Petroleum Univ.,
No. 8 Xindu Ave., Xindu District, Chengdu 610500, Sichuan, PR China.
Email: 383116590@qq.com
Note. This manuscript was submitted on January 19, 2023; approved on
May 25, 2023; published online on September 13, 2023. Discussion period
open until February 13, 2024; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Pipeline Systems
Engineering and Practice, © ASCE, ISSN 1949-1190.
© ASCE
$34.4 billion in 2014, with the oil and gas industry accounting for
more than half of this amount. Corrosion of oil and gas pipelines
directly leads to natural gas leaks and explosions, causing pollution
of the environment and potentially threatening the lives of people.
CO2 internal corrosion is a common phenomenon in oil and gas
gathering and transmission pipelines (Sun et al. 2021). This is
due to CO2 and the water in the transmission medium generating
corrosive carbonic acid (H2 CO3 ), causing pipeline internal corrosion, which causes the pipeline to leak or fail (Mohamed et al.
2012). In addition, changes in flow parameters along the pipeline
leads to different corrosion rates at various locations, especially
with corrosion monitoring equipment usually set up only at the beginning and end of the pipeline. To understand the internal corrosion situation along the pipeline, it is necessary to predict it.
Therefore, the internal corrosion prediction model has become a
focus in the field of internal corrosion protection, and many scholars across the world have studied and optimized the internal corrosion prediction model.
In field production, the internal corrosion situation in the middle
part of the pipeline usually cannot be grasped in time, thus the need
to use the corresponding internal corrosion prediction model to predict the corrosion rate along the pipeline. However, there are large
errors between the calculation results of common internal corrosion
prediction models and the actual corrosion situation. To understand
the corrosion situation inside the pipeline and improve the integrity
management of natural gas pipelines, the corrosion prediction
model needs to be further optimized (Olsen et al. 2005). The collection pipeline for the MX gas field discussed in this paper has a
partial pressure of CO2 of over 100,000 Pa. It uses a wet gas transmission process, and the composition of the medium inside the pipe
is complex, along with the topography of the fluctuating. For MX
gas field corrosion rate prediction, this paper summarizes four types
of common CO2 corrosion rate prediction models; compares and
analyzes the applicability, advantages, and disadvantages of each
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model; selects the most applicable corrosion prediction model for
the MX gas field by combining the corrosion internal detection results of the MX gas field; and carries out optimization based on
this model.
The commonly used CO2 corrosion rate prediction models are
mainly divided into mechanistic, empirical, and semiempirical
types (Peng et al. 2020). For different pipe inclinations (horizontal,
vertical, inclined), different fluid media (oil, gas, water) mixing
types and different flow patterns formed a large number of semiempirical, semitheoretical models based on experimental data, and
each model applies to different pipeline parameters and flow
conditions.
The Norsok M506 model was proposed by the Norwegian
Institute of Energy Technology and was established mainly by integrating high-temperature field data and low-temperature test data.
At present, the model has been widely used in China for the selection of external corrosion-resistant materials and corrosion margin
design (He 2019). The De Waard 95 model (DW95 for short) is a
common CO2 corrosion rate prediction model (Gao 2020). This
model is modified based on the Norsok M506 model and takes into
full consideration the influencing factors such as partial pressure of
CO2 , temperature (De Waard et al. 1995), the transfer process of
CO2 dissolved in water, and electrochemical kinetic reaction rate
(Wang et al. 2019). The Srinivasan model introduces a correction
factor on the De Waard 95 model. The first step of this method
is to calculate the system pH. And it can be used for the corrosion
prediction of CO2 and H2 S coexistence solution systems (Srinivasan
and Tebbal 1998). Lafayette Corrosion Research Center proposed
the Lafayette model, which considers the corrosion characteristics
of gas-liquid two-phase flow and calculates the corrosion rate of
annular, intermittent, and stratified flows. In this model, because
the calculation of corrosion rate is related to the flow pattern, the
flow pattern of the pipe needs to be evaluated before predicting the
corrosion rate. Among them, the flow pattern is, in turn, related to
many factors, such as medium composition, content, and liquid
properties (Yao 2012) (Table 1).
Abbas et al. (2018) developed high-pressure work modeling of
high-pressure CO2 corrosion, which required extensive training
using test data from multiple sources conducted under a variety
of experimental conditions and different environments, factors
that introduced uncertainty into the modeling and therefore imposed some limitations on the results predicted by the neural network, resulting in its inability to be widely applied to corrosion
prediction of wet gas pipelines in all environments. The Norsok
M506, De Waard 95, Srinivasan, and Lafayette models apply to
MX gas field wet gas pipeline corrosion rate calculation. However, they are subject to many errors in practical application.
Therefore, there will be errors in the application of the domestic
oil and gas field pipeline corrosion rate prediction process. For the
domestic corrosion prediction model, Long et al. (2008) established a corrosion rate with CO2 partial pressure, temperature,
flow rate, and Cl− concentration of the relationship model, but
only four influencing factors are considered, in addition to the
prediction results and the actual value of a large error. Zhang et al.
(2006) introduced the partial pressure ratio of CO2 and hydrogen
sulfide into the pipeline corrosion prediction model, but the model
only takes into account the influence of CO2 and hydrogen sulfide
on the pipeline, with a single influence factor of corrosion and a
small scope of application. Wu et al. (2006) and Song et al. (2008)
both studied the effect of seven factors on the corrosion of
20# pipe, including the medium flow rate, oxygen content, pH,
mineralization, temperature, partial pressure of carbon dioxide,
and water content of the gathering pipeline, and established the
corresponding corrosion prediction model. However, they both
© ASCE
used a single experimental material, and only for the medium flow
rate of less than 2-m=s pipes. Li et al. (2021a) created a model
based on principal component analysis-artificial bee colony
algorithm-support vector regression (PCA-ABC-SVR) that performs well in corrosion prediction of subsea pipes, and the influences it uses for training were specific to subsea pipes and are not
applicable for predicting long-distance wet gas pipes on land. Li
et al. (2021b) established a computational model for corrosion
under supercritical carbon dioxide conditions based on the
finite-element method, which not only predicts the corrosion rate
over time but also tracks the transient motion of the corrosion surface and deposition interface in real time through the arbitrary
Lagrangian-Eulerian (ALE) technique. However, the model has
a complex calculation process and is more suitable for calculating
the corrosion rate of pipelines under the same working conditions
over short distances. The model is no longer applicable due to the
large differences in conditions along the long-distance transport
pipeline. Qin et al. (2022) also used the multiple linear regression
method to optimize the corrosion prediction model under the
CO2 =H2 S synergistic corrosion mechanism. Through experiments
to verify that the model prediction error was less than 20%, the
reliability of the multiple linear regression method was illustrated.
However, its model contains H2 S, which is not fully applicable to
the corrosion calculation of wet gas pipelines containing only
CO2 . The described seven domestic corrosion prediction models
do not apply to the MX gas field and cannot provide a correct
model for corrosion rate prediction.
In this paper, the common Norsok M506, De Waard 95,
Srinivasan, and Lafayette models were used to predict the corrosion of the same pipeline under different operating conditions.
Over 1,000 corrosion internal detection points were set up along
the pipeline and over 12,000 sets of corrosion prediction data were
calculated using four corrosion prediction models. A new model,
W22, was developed using linear regression and validated with
another pipeline under two different operating conditions in
combination with the multiphase flow corrosion (MPFC) loop
experiments.
Methods
MX8 Wet Gas Pipelines
The MX8 wet gas gathering pipeline contains CO2 acidic gas and
uses a wet gas transport process with complex media composition
inside the pipe. The terrain along the pipeline is undulating, there is
liquid accumulation in the pipeline, and it is difficult to clear the
pipeline. A mileage elevation map along the MX8 pipeline is
shown in Fig. 1. The specific parameters are shown in Table 2. The
three representative operating conditions selected for the OLGA
multiphase flow simulation are shown in Table 3.
OLGA-Based Multiphase Flow Simulation for
Wet Gas Pipelines
The OLGA software version 2020 is the first transient simulation
software developed for the flow of mixed oil and gas transport
pipelines and is at the world’s leading level. This paper uses the
Benedict-Webb-Rubin (BWRS) equation in the OLGA software
for calculations. The fluid package components used in the simulations are shown in Table 4. After multiphase flow simulations,
parameters such as temperature, pressure, velocity of gas flow
and the velocity of liquid flow (UG/UL), partial pressure of carbon
dioxide, and pH along the pipeline were calculated for the three
operating conditions.
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Table 1. Corrosion model formulas and the scope of application
Model
Norsok M506
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De Waard 95
Formula
0.146þ0.0324 logðfco Þ
2
τ
w
fðpHÞt
V corr ¼ Ktf 0.62
co2
19
PCO2 10Pð0.0031−1.4=rÞþ1 p ≤ 250 bars
f co2 ¼
PCO2 10250ð0.0031−1.4=rÞþ1 p > 250 bars
Scope of application
20°C–150°C; CO2 =H2 S > 500; pH
3.5–6.5. It includes several parameters,
including partial pressure P, temperature
T, shear force τ w , and pH value, which
applies to offshore and onshore oil and gas
fields (Liu 2017).
1
1
1
¼
þ
V corr V r V m
1119
þ 0.58 log PCO2 − 0.34ðpHact − pHCO2 Þ
log V r ¼ 4.93 −
t þ 273
u0.8
V m ¼ 2.45 0.2 PCO2
d
pHCO2 ¼ 3.82 þ 0.00384t − 0.5 log PCO2
Srinivasan
pH1 ¼ C1 − logðPH2 S þ PCO2 Þ ðt ¼ 20°CÞ
pH2 ¼ C2 − logðPH2 S þ PCO2 Þ þ logðH2 CO3 Þ ðt ¼ 20°CÞ
logðPCO2−eff Þ ¼ ðC1 − pHÞ=2
logðV corr Þ ¼ 5.8 −
Lafayette
Temperature <80°C.
Considers the transfer process of CO2
dissolved in water and the influence of the
dynamic electrochemical reaction rate of
corrosion (Zhang et al. 2008).
The model is suitable for the coexistence
of CO2 and H2 S, and the concentration of
H2 CO3 is known.
1710
þ 0.67 logðPCO2 Þ
T
1. Stratified flow corrosion rate:
When V L < 0.45 m=s, the expression is (Xu 2018)
V corr ¼ −1.33V 3L þ 1.12V 2L þ 2.53V L þ 2.33
When V L > 0.45 m=s, the expression is
V corr ¼ 1.92V L þ 6.33
2. Calculation of intermittent flow corrosion rate:
Replace all the V L in the two equations for the stratified flow with V LTB .
The corrosion rates of the liquid film and liquid plug portion of the final
pipe determine the corrosion rate of the segment plug flow and is calculated as
(Xue 2016)
1 LS
1 LF
V corrs þ
V corrf
V corr ¼
3
L
U
1.1 3 LU r
12
tyear ¼ 54.91 0.8 þ 5.7
V LTB δ
3. Circumferential flow corrosion rate calculation formula:
1,000r
V corr ¼
tyear
The flow pattern should be judged in
advance, and the flow velocity of liquid
should be known for stratified flow. For
intermittent flow, slug length must be
known; for annular flow, liquid film
velocity and thickness must be known.
Calculation of Corrosion Prediction Models
Models Prediction
Based on the results of the OLGA multiphase flow simulations, the
corrosion rates along the pipeline were calculated by substituting
the parameters of temperature, pressure, gas-liquid flow rate, pH,
and partial pressure of carbon dioxide along the pipeline into the
Norsok M506, De Waard 95, Srinivasan, and Lafayette models.
The predictions from the four models were compared to the corrosion internal detection values, and error analysis was performed.
Fig. 1. Mileage elevation map along the MX8 pipeline.
© ASCE
Error Calculation
By calculating the relative error, the deviation between the corrosion prediction model and the corrosion internal detection value can
be further understood so that the prediction model that is closer
to the corrosion internal detection value can be compared and analyzed. In addition, the standard deviation can also be used as a
measure of uncertainty. The standard deviation of a collection of
measured values represents the accuracy of these measurements.
A large standard deviation represents a large difference between
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Table 2. Pipeline parameters of MX8
Parameter
Value
External diameter
Length
Wall thickness
Steel grade
Design pressure
Carbon dioxide content
273 mm
2.50 km
8 mm
20#
8.5 MPa
1.990%
Table 3. Pipeline working conditions of MX8
Pipeline name
Working condition
Inlet temperature (°C)
Outlet temperature (°C)
Operating pressure (MPa)
Flow (kg=s)
1
2
3
30.90
27.80
30.00
26.90
22.30
26.00
6.82
6.45
6.68
5.37
5.26
5.07
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MX8
was 529.4 MPa, and the average elongation was 26.31% as measured by a tensile tester. A pendulum impact tester was used to
measure the average impact work of 41.38 J. The average hardness
of the pendants was 156.54 HV measured by a Vickers hardness
tester, and the tensile stress, impact force, and hardness of 20# steel
coupons all met the requirements. 20# steel was cut into a 15 ×
10 × 2-mm corrosion coupon and placed in the MPFC annulus
for corrosion weight loss experiments. Fig. 2. shows 20# steel
metallographically under a microscope; 20# steel is mainly composed of ferrite and lamellar pearlite, with uniform tissue distribution and good material properties.
The size of 20# steel specimen was 15 × 10 × 2 mm, and three
pieces were used for corrosion rate calculation in each group of
experiments. Before the experiments, the specimens were polished
with 60#, 400#, 800#, 1000#, 1200#, and 1500# sandpapers. Then
the specimens were cleaned with petroleum ether and alcohol. After
drying, the specimens were weighed. At the end of the experiment,
the specimens were de-filmed.
Table 4. Fluid composition
Substance fraction
Content (molar %)
96.621
0.140
1.961
0.923
0.355
CH4
C2 H6
CO2
N2
He
most values and their mean, indicating poor predictive accuracy.
The calculation formula of error value and the average error are
shown in Eqs. (1) and (2), and the formula for calculating the standard deviation is shown in Eq. (3)
ðPvalue − Mvalue Þ
× 100%
M value
Pn
E
EAvalue ¼ i¼1 value i
n
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rP
n
2
i¼1 ðEvalue i − EAvalue Þ
σ¼
n
Evalue ¼
ð1Þ
ð2Þ
MPFC Loop Experiments
The schematic diagram of the MPFC loop channel experiment is
shown in Fig. 3. The 100-L solution prepared in the section “Solution Preparation” was poured into the reservoir, which was capped
with an empty finger gap, and carbon dioxide was continuously
passed into the liquid to keep the liquid oxygen-free. A controller
was used to control the pump speed and display the temperature of
the annulus solution. After the experiment had been carried out for
12 h, the specimens were removed. The MPFC experimental loop
working conditions are shown in Table 6.
ð3Þ
MPFC Loop Experiment
In terms of flow corrosion experiments, the MPFC loop experiment
is mainly used to study the corrosion of pipelines under field
conditions.
Corrosion Rate Assessment
The three coupons were immersed in the film removal solution and
cleaned with an ultrasonic cleaner for 10 min to remove the corrosion product film from the surface of the specimens. They were
then cleaned with alcohol, dried, and weighed. The corrosion coupons were weighed using a Sartorius (Shanghai, China) electronic
balance with an accuracy of 0.0001 g (parts per million) and the
weighing was repeated three times to prevent errors caused by reduced weighing. The following is a general corrosion rate calculation formula of the sample (Dong et al. 2020):
Solution Preparation
One hundred liters of the solution was required for the ring channel.
Deionized water and NaCl were used to prepare the solution in proportion to the Cl− concentration of 6,000 mg=L. N2 was used to
deoxygenate the solution for 2 h before the experiment to ensure an
oxygen-free environment. After the end of deoxidation, CO2 was
passed into the solution for 1 h until the CO2 concentration reached
saturation.
Sample Materials
The experiments were carried out using 20# steel for the MX
collector piping, the elemental composition of which is shown
in Table 5. The average tensile strength of 20# steel coupons
V corr ¼ 8.76 × 104
Δm
ρ · A · ti
ð4Þ
Table 5. 20# steel chemical composition
Element
Fe
Mn
Si
C
Cr
Cu
P
S
Ni
% by weight
≥98
0.35–0.65
0.17–0.37
0.17–0.27
≤0.25
≤0.25
≤0.035
≤0.035
≤0.030
© ASCE
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2
Optimization of DW95-Based Corrosion Prediction
Model for CO2 Wet Gas Pipelines
In the DW95 formula, as the formula for the reactive corrosion
rate involves the most factors, including temperature, CO2 pressure,
actual pH, and the pH of the CO2 -saturated solvent, the formula
for the reactive corrosion rate V r is finally selected for numerical
optimization using linear regression in this paper.
Linear regression is a statistical analysis method that uses
regression analysis to determine the quantitative interdependent
relationship between two or more variables and is widely used.
First, the along-line parameters Pco2 , u, and d from the multiphase
flow simulation in the MX8 pipe are substituted into the third equation in the DW95 model to obtain the value of V m . Then t and Pco2
are substituted into the fourth equation of the model to obtain
pHCO2 , whereas V m and V corr are brought into the first equation of
the model to obtain V r . Second, the calculated V r , pHCO2 , and the
multiphase flow simulation results t, Pco2 , and pHact are substituted
into the second equation of the model, and linear regression is
performed as shown in Eq. (5)
6 1
6
6 :::
6
6
6 :::
6
4
1
1
t þ 273 1
:::
3
log PCO2 1
:::
:::
:::
1
log PCO2 4,395
t þ 273 4,395
× ½ ε A B C T ¼ ½ log ðV r Þ1
:::
ðpHact − pHco2 Þ1 7
7
7
:::
7
7
:::
7
7
5
ðpHact − pHco2 Þ4,395
: : : log ðV r Þ4,395 T
ð5Þ
Let log V r be y; 1=ðt þ 273Þ be X 1 ; log Pco2 be X 2 ; and
(pHact − pHCO2 ) be X 3 . At the same time, multiple linear regressions are fitted to the constants ε, A, B, and C of the DW95
model based on 4,395 sets of corrosion data along the MX8 pipeline under three different operating conditions predicted by the
DW95 model.
Results
OLGA Multiphase Flow Simulation Results of MX8 Wet
Gas Pipeline
The pipeline has an elevation minimum of approximately 500 m,
but the overall trend is upward. As can be seen from Fig. 4, the
pipeline starts at a pressure of 6.82 MPa and ends at 6.52 MPa with
a total pressure drop of 0.3 MPa. There is an upward pressure trend
at approximately 500 m due to the large undulations in the pipeline
here. The start temperature is 30.9°C and the end temperature is
20.9°C, with a temperature drop of 10.0°C. The maximum gas flow
Table 6. MPFC multiphase flow experimental loop pipe working
conditions
Fig. 2. 20# steel under a microscope.
Working
condition
PCO2 (MPa)
Temperature
(°C)
Velocity
(m=s)
Experimental
duration (h)
1
2
3 × 10−2
1 × 10−2
30
35
0.5
1.0
12
12
Fig. 3. MPFC multiphase flow experimental loop diagram.
© ASCE
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rate is 3.59 m=s and the minimum is 2.50 m=s. The maximum
liquid flow rate is 3.05 m=s, and the minimum is −0.20 m=s. This
is due to the presence of uphill piping here and the backflow of the
accumulated liquid, which the flow simulation specifies as a negative flow rate (Xu and Wang 2021). The CO2 partial pressure is
mainly related to the CO2 content and total pressure in the pipe and
therefore decreases gradually along the line, reaching a peak at
500 m. The CO2 partial pressure decreases gradually from 7.32 ×
10−2 MPa at the inlet to 6.99 × 10−2 MPa at the outlet. The pH
fluctuates with the ebb and flow of the pipe. When the fluid is
at the lower part of the pipe, the partial pressure of CO2 is higher
and the amount of CO2 dissolved in the accumulated fluid is higher,
so the pH decreases rapidly. In the rising section of the pipe, the
partial pressure of CO2 is lower and the amount of CO2 dissolved in
the fluid decreases, so the pH rises rapidly.
As can be seen from Fig. 5, the starting pressure of the pipeline
is 6.45 MPa and the end pressure is 6.14 MPa, with a total pressure
drop of 0.31 MPa. There is an upward pressure trend at approximately 500 m, which is due to the large undulations in the pipeline
here. The start temperature is 27.8°C and the end temperature is
22.6°C, with a temperature drop of 5.2°C. The gas flow rate ranges
from a maximum of 2.87 m=s to a minimum of 2.59 m=s. The
liquid flow rate ranges from a maximum of 3.05 m=s to a minimum
of 9.33 × 10−2 m=s. The partial pressure of CO2 is mainly related
to the CO2 content and total pressure in the pipe and therefore
decreases gradually along the line, reaching a peak at 500 m.
The partial pressure of CO2 decreases gradually from 6.92 ×
10−2 MPa at the inlet to 6.59 × 10−2 MPa at the outlet. The pH
fluctuates with the ebb and flow of the pipe. The pH trend pattern
is consistent with Working condition 1.
As can be seen from Fig. 6, the starting pressure of the pipeline
is 6.68 MPa and the end pressure is 6.35 MPa, with a total pressure
drop of 0.33 MPa. There is an upward pressure trend at approximately 500 m, which is due to the large undulations in the pipeline
here. The start temperature is 30.0°C and the end temperature is
26.0°C, with a temperature drop of 4.0°C. The maximum gas flow
rate is 3.38 m=s, and the minimum is 2.42 m=s. The maximum
liquid flow rate is 2.88 m=s, and the minimum is 8.96 × 10−2 m=s.
The partial pressure of CO2 is mainly related to the CO2 content
and total pressure in the pipe and therefore decreases gradually
along the line, reaching a peak at 500 m. The partial pressure of
CO2 decreases gradually from 11.35 × 10−2 MPa at the inlet to
10.81 × 10−2 MPa at the outlet. The pH fluctuates with the ebb and
flow of the pipe. The pH trend pattern is consistent with Working
condition 1.
Models Prediction Results
Under Working condition 1 (Fig. 7), the corrosion internal detection data vary evenly and with a flat amplitude. The average
Fig. 4. OLGA simulation results (Working condition 1).
© ASCE
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Fig. 5. OLGA simulation results (Working condition 2).
corrosion rate is 0.163 mm=y. The maximum value of the corrosion internal detection is 0.351 mm=y, and the minimum is
0.059 mm=y. The Lafayette model corrosion prediction results
fluctuate, with many sudden drops and increases. The maximum
value is 9.907 mm=y, the minimum is 2.540 mm=y, and the average is 3.233 mm=y, the highest average among the four models.
The Srinivasan model corrosion prediction results gradually decrease with mileage, but the downward trend is gentle. The maximum value of corrosion prediction is 0.948 mm=y, the minimum is
0.848 mm=y, and the average is 0.896 mm=y, which are higher
than the corrosion internal detection data. The De Waard 95 model
corrosion prediction results are relatively flat, except near the 150-,
250-, and 2,150-m peaks. This because at 150 and 250 m near the
station, the temperature and pressure are high, and the gas-liquid
flow rate is large, so the corrosion prediction rate peaks. At
2,150 m, as the total pressure along the pipeline gradually decreases, the gas in the pipe expands, and the pipeline elevation
fluctuates, so the gas-liquid flow rate becomes larger, resulting in
the corrosion prediction rate reaching the peak. The average value
of the De Waard 95 model is 0.022 mm=y, and the predicted results
are relatively close to the corrosion internal detection data, with a
maximum of 0.219 mm=y and a minimum of 0.008 mm=y. The
corrosion prediction results of the Norsok M506 model have
a gentle trend. The corrosion prediction maximum value is
0.004 mm=y, the minimum is 0.002 mm=y, and the average is
0.003 mm=y. The results are lower than the corrosion internal
© ASCE
detection data, and the average value is the lowest of the four
prediction models.
Under Condition 2 (Fig. 8), the corrosion internal detection data
vary evenly and with a gentle amplitude. The average corrosion rate
is 0.163 mm=y, the maximum corrosion internal detection value is
0.348 mm=y, and the minimum corrosion internal detection value
is 0.058 mm=y. The Lafayette model corrosion prediction results
fluctuate, with many sudden drops and increases. The maximum
value is 9.365 mm=y, the minimum is 2.511 mm=y, and the average is 3.139 mm=y, the highest average value of the four prediction
models. The Srinivasan model corrosion prediction results gradually decrease with mileage, but the declining trend is gentle. The
maximum value of corrosion prediction is 0.777 mm=y, the minimum is 0.691 mm=y, and the average is 0.732 mm=y, which are
higher than the corrosion internal detection data. The De Waard 95
model corrosion prediction results are relatively flat except near the
150- and 2,150-m peaks. This is because close to the station at
150 m, there are high temperature and pressure and the gas-liquid
flow rate is large, so the corrosion prediction rate peaks. At 2,150 m
as the total pressure along the pipeline gradually decreases, the gas
expansion in the pipe, and the pipeline elevation fluctuates, so the
gas-liquid flow rate becomes larger, resulting in the corrosion prediction rate reaching a peak. The average value is 0.020 mm=y
(the prediction result is relatively close to the corrosion internal
detection data), the maximum is 0.227 mm=y, and the minimum
is 0.007 mm=y. The Norsok M506 model corrosion prediction
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Fig. 6. OLGA simulation results (Working condition 3).
Fig. 7. Comparison between calculation results of four corrosion prediction models and actual monitored values (Working condition 1).
© ASCE
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Fig. 8. Comparison between calculation results of four corrosion prediction models and actual monitored values (Working condition 2).
Fig. 9. Comparison between calculation results of four corrosion prediction models and actual monitored values (Working condition 3).
results trend is flat. The maximum value is 0.002 mm=y, the minimum is 0.001 mm=y, and the average is 0.001 mm=y. The results
are lower than the corrosion internal detection data, and the average
value is the lowest of the four prediction models.
© ASCE
Under Working condition 3 (Fig. 9), the corrosion internal detection data vary evenly and with a gentle amplitude. The average
corrosion rate is 0.163 mm=y, the maximum corrosion internal detection value is 0.351 mm=y, and the minimum corrosion internal
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detection value is 0.060 mm=y. The Lafayette model corrosion prediction results fluctuate, with many sudden drops and increases.
The maximum is 8.182 mm=y, the minimum is 2.467 mm=y,
and the average is 2.957 mm=y, the highest average value of
the four prediction models. The Srinivasan model corrosion prediction results gradually decrease with mileage, but the downward
trend is gentle. The maximum value of corrosion prediction is
0.951 mm=y, the minimum is 0.825 mm=y, and the average is
0.885 mm=y, which are higher than the corrosion internal detection
data. The De Waard 95 model corrosion prediction results are
relatively flat, except near the 1,000-, 1,500-, and 1,600-m peaks.
This is due to the gradual reduction of the total pressure along the
pipeline, the expansion of the gas in the pipe, and pipe elevation
fluctuations, so the gas-liquid flow rate becomes larger, resulting
in the corrosion prediction rate reaching a peak. The DW95 model
has an average corrosion prediction value of 0.024 mm=y. The
prediction results are relatively close to the corrosion internal detection data; the maximum is 0.250 mm=y, and the minimum
is 0.009 mm=y. The Norsok M506 model corrosion prediction results trend flat. The maximum is 0.002 mm=y, the minimum is
0.001 mm=y, and the average is 0.001 mm=y. The results are lower
than the corrosion internal detection data, and the average value is
the lowest of the four prediction models.
As can be seen from Figs. 7–9, the values of the De Waard 95
prediction model are relatively close to the corrosion internal inspection values, with an error of 82.03% and a standard deviation
of 48.48%. The De Waard 95 model is followed by the Norsok
M506 model and the Srinivasan model, with average errors of
94.86% and 2,087.10% and standard deviations of 3.14% and
625.72%, respectively. The Lafayette model results differed significantly from the corrosion internal inspection results, with a mean
error of 9,189.58% and a standard deviation of 16,129.51%. From
the peak prediction of the DW95 model in Working conditions 1–3,
the DW95 model has inaccuracies in its calculations, which is due
to the limited parameters considered in the DW95 model, and the
coefficient values in the formula applied to the MX pipeline still
have deviations. The overall trend is that the corrosion rate calculated by the Norsok M506 corrosion model is small. The corrosion
rate calculated by the Srinivasan prediction model is large, and the
corrosion rate calculated by the Lafayette corrosion model is too
large. This is because the Lafayette corrosion model does not consider the fluid medium but focuses on the flow rate. In the Lafayette
calculation formula, even if the flow rate is 0 m=s, the corrosion
prediction value reaches 2.33 mm=y. In general, the aforementioned four corrosion prediction models have large errors and cannot provide effective corrosion prediction for domestic gas fields.
Although the DW95 corrosion prediction model is relatively
close to the corrosion internal detection data, the error is calculated
by Eq. (1), and the average error of the DW95 corrosion prediction
model has been calculated as high as 82.03% by Eq. (2).
Optimization Results of DW95-Based Corrosion
Prediction Model for CO2 Wet Gas Pipelines
Optimization Model Based on De Waard 95—W22
After processing, the values of the parameters of the obtained linear
regression model are shown in Table 7. The substitution of the
parameters leads to Eq. (7). The final W22 model is shown in
Eqs. (6)–(9)
1
1
1
¼
þ
V corr V r V m
Table 7. Linear regression processing results
Parameter
Value
ε
A
B
C
−4.54
−167.85
−0.16
1.68
167.85
− 0.16 log PCO2
t þ 273
þ 1.68ðpHact − pHCO2 Þ
ð6Þ
log V r ¼ −4.54 −
ð7Þ
Fig. 10. Experimental steel corrosion macroscopic appearance: (a) Working condition 1; and (b) Working condition 2.
© ASCE
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Fig. 11. Shape and energy spectrum of 20# steel under SEM.
Table 8. Comparison of experimental results with the predicted results of
W22 model
Working
condition
1
2
Average corrosion
rate (mm=y)
W22 model prediction
data (mm=y)
Error
0.298
0.334
0.271
0.305
9.06%
8.60%
V m ¼ 2.45
u0.8
PCO2
d0.2
ð8Þ
pHCO2 ¼ 3.82 þ 0.00384t − 0.5 log PCO2
ð9Þ
Verification Based on MPFC Loop Experiment
After 12 h of MPFC loop experiments, the macroscopic morphology of 20# steel before going to the film under different working
conditions is shown in Fig. 10. The products on the surface of the
steel sheet are mainly black. The structure is loose and porous, and
the products have more local bump accumulation. The microscopic
morphology and structure of the products were further tested and
© ASCE
Fig. 12. Mileage elevation map along the MX204 pipeline.
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Table 9. Pipeline parameters of MX204
Parameter
External diameter
Length
Wall thickness
Steel grade
Design pressure
Carbon dioxide content
219 mm
2.53 km
7.1 mm
20#
8.5 MPa
1.46%
Value
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Table 10. Pipeline working conditions of MX204
Table 11. Fluid composition
Pipeline
name
Working
condition
Inlet
temperature
(°C)
Outlet
temperature
(°C)
Operating
pressure
(MPa)
MX204
1
2
35.80
34.20
21.10
20.02
7.28
7.14
analyzed by scanning electron microscopy (SEM). In the experiments, the corrosion rate of the hanging sheet is 0.298 mm=y
for Condition 1 and 0.344 mm=y for Condition 2. The hanging
sheets in both conditions have very serious corrosion. As the flow
rate increases and the temperature increases, the uniform corrosion
rate of 20# steel increases. This is because the increase in flow rate
increases the rate of material and charge transfer. The temperature
increase also accelerates the corrosion reaction.
This experiment contained only CO2 corrosive gas. The fact
that corrosion of CO2 facilitates the formation of a denser film
of corrosion products, to a certain extent, prevents the corrosion
of steel. Fig. 11(a) shows 20# steel under Condition 1 with the
surface microstructure of corrosion products; Fig. 11(b) shows
the energy spectrum analysis. The microscopic morphology and
energy spectrum under Condition 2 are shown in Fig. 11(c) and
Fig. 11(d), respectively. The results show that the corrosion products are mainly round particles stacked on the surface of the specimen, and the substrate has a certain degree of protection. Corrosion
product elements are C, O, Mn, and Fe. Corrosion product adhesion
is good, and corrosion rate is uniform. Corrosion product energy
spectrum results show that the product elemental composition is
more consistent, and corrosion products are mainly composed of
iron oxides, with a small amount of FeCO3 .
MPFC Loop Test Verification Results
The parameters were substituted into the W22 model to predict the
corrosion rate of 20# steel under the experimental conditions, and
the results are shown in Table 8. The average error of W22 model
prediction results is only 8.83%.
Substance fraction
CH4
C2 H 6
C3 H 8
iC4 H10
nC4 H10
iC5 H12
nC5 H1
Cþ
6
CO2
N2
He
Content (molar %)
84.905
6.486
2.818
0.458
0.911
0.231
0.673
0.945
1.959
0.600
0.014
Fig. 13. Comparison diagram between W22 model and DW95 model
(Working condition 1).
Discussions
To further verify the accuracy of the W22 model, the W22 model
was applied to the wet gas pipeline field in this paper. For the
MX204 pipeline in the MX gas field, the terrain along the pipeline
is undulating, and the map of the mileage elevation along the
MX204 pipeline is shown in Fig. 12. The pipeline parameters and
pipeline working conditions are shown in Tables 9 and 10. The
contents of the different gases in the pipeline are shown in
Table 11. In this paper, two working conditions were selected
for OLGA multiphase flow simulation, and the results of flow
velocity and partial pressure of carbon dioxide along the line were
directly substituted into the W22 model and compared with the
predicted results of DW95. Finally, the error calculation Eqs. (1)
and (2) were used to calculate the error between the predicted
values of the DW95 and W22 models and the corrosion internal
detection results, and the comparison results are shown in
Figs. 13–15.
© ASCE
Fig. 14. Comparison diagram between W22 model and DW95 model
(Working condition 2).
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Fig. 15. Comparison diagram of relative error between W22 model and DW95 model.
Figs. 13 and 14 show that the W22 model prediction results are
consistent with and close to the corresponding corrosion internal
detection data fluctuation trend, unlike the case for the DW95
model.
From the error comparison chart (Fig. 15), it can be seen that the
error value domain of the W22 model is always small, ranging from
0.03% to 24%, with an average error of 8.30%. In contrast, the
DW95 model has a larger error, ranging from 1.39% to more than
930.01%, with an average error of 89.62%. In addition, the standard deviation of the DW95 model is 42.95%, whereas the standard
deviation of the W22 model is 5.25%. Therefore, the accuracy of
the model W22 presented in this paper is higher, and the error is
reduced by 81.32% on average compared to the DW95 model.
Conclusions
Based on the comparison of the corrosion prediction values of wet
gas pipelines with the field corrosion internal detection values by
the Norsok M506, De Waard 95, Srinivasan, and Lafayette models,
the De Waard 95 model with the lowest error was selected. The
coefficients of De Waard 95 were optimized by linear regression
method to obtain the W22 model, which is more suitable for wet
gas pipeline corrosion prediction. Finally, the W22 model was validated using MPFC multiphase flow loop experiments and field
applications, and its prediction error was less than 10% on average
in the working condition range.
1. Norsok M506, De Waard 95, Srinivasan, and Lafayette are
common corrosion prediction models. Norsok M506 is a purely
empirical model, and the prediction results are relatively
conservative. The De Waard 95 corrosion prediction model pioneered the resistivity model, and taking into account the steel
structure and corrosion products film and other factors, the
scope of application is wide. The Srinivasan model can be used
for CO2 and H2 S coexistence solution systems, but the pH value
of the environment must be known. The Lafayette model can
calculate the corrosion rate under the stratified, segment plug,
and annular flow types, but the key parameters of the relevant
© ASCE
flow type must be known. Each of the four types of models has a
different scope of application, theoretically all applicable to
MX gas field wet gas pipeline.
2. The corrosion prediction results of the four models for the field
pipeline are as follows: The De Waard 95 prediction model
value is the closest to the corrosion internal detection value,
with an average error of 89.62%, followed by Norsok M506,
Srinivasan, and Lafayette.
3. The experiments verified that the experimental corrosion rate of
the MPFC loop differed from the corrosion rate predicted by the
W22 model by an average of only 6.80%. In field applications,
the DW95 model predicted an error of 89.62%, whereas the W22
model had an average error of only 8.30% in corrosion prediction
values. Overall, the average error of the W22 model was 81.32%
lower than that of the DW95 model, indicating that the W22
model has higher accuracy in predicting wet gas pipe corrosion.
4. The W22 model was optimized based on field data from the MX
gas field and is suitable for CO2 -corroded pipelines in 20# steel
and without H2 S. The pressure range is approximately 6.45–
7.28 MPa, the temperature range is approximately 20.02–
35.80°C, and the partial pressure of carbon dioxide ranges from
approximately 65,850–113,790 Pa. Overall, its applicability is
somewhat limited, but this paper mainly provides a model optimization method for corrosion prediction of specific objects. We
hope that more researchers will continue to optimize on this basis in the future to expand its applicability.
Data Availability Statement
All data, models, and code generated or used during the study
appear in the published article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (52174062).
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Notation
The following symbols are used in this paper:
A = area of sample (cm2 );
d = pipeline internal diameter (m);
Evalue = error value;
EAvalue = average error value;
FCO2 = modified partial pressure of CO2 (bar);
fco2 = fugacity coefficient of CO2 ;
fðpHÞt = pH influence factor;
H2 CO3 = H2 CO3 concentration (meq=L);
h = pitting depth (μm);
K t = constant that depends on temperature;
LF = length of liquid film (m);
LS = length of plug (m);
LU = length of slug element (m);
M value = corrosion internal detection value;
PCO2 = partial pressure of CO2 (bar);
PCO2 -eff = effective partial pressure of CO2 (bar);
PH2 S = partial pressure of H2 S (bar);
Pvalue = corrosion prediction value;
p = absolute pressure of system (MPa);
pH1 , pH2 = pH of environment;
pHact = actual pH;
pHco2 = pH of CO2 -saturated solvent;
r = pipe wall thickness (m);
T = temperature (K);
t = medium temperature (°C);
tc = corrosion time (day);
ti = immersion time (h);
tyear = failure time (year);
u = flow velocity of a liquid medium (m/s);
V corr = corrosion rate (mm=y);
V corrf = corrosion rate of liquid film (mm=y);
V corrL = local corrosion rate (mm=y);
V corrs = liquid plug corrosion rate (mm=y);
V LTB = liquid film velocity (m/s);
V r = reaction rate (mm=y);
V m = mass transfer rate (mm=y);
Δm = weight loss of sample (g);
δ = thickness of liquid film (m);
ρ = density (g=cm3 );
σ = standard deviation; and
τ w = wall shear stress (Pa).
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