Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.16 No.2 (June 2015) 1- 8  

ISSN: 1997-4884 

 

 

 

 

Modelling and Optimization of Carbon Steel Corrosion in CO2  

Containing Oilfield Produced Water in Presence of HAc 
 

Aprael S. Yaro and Khalid H. Rashid 

Chemical Engineering Department – College of Engineering – University of Baghdad- Iraq 

 

Abstract  

    Previously, many empirical models have been used to predict corrosion rates under 

different CO2 corrosion parameters conditions. Most of these models did not predict 

the corrosion rate exactly, besides it determined effects of variables by holding some 

variables constant and changing the values of other variables to obtain the regression 

model. As a result the experiments will be large and cost too much. In this paper 

response surface methodology (RSM) was proposed to optimize the experiments and 

reduce the experimental running. The experiments studied effects of temperature (40 

– 60 °C), pH (3-5), acetic acid (HAc) concentration (1000-3000 ppm) and rotation 

speed (1000-1500 rpm) on CO2 corrosion performance of the regression model 

calculated by RSM. The experiments were conducted in saturated solution of CO2 

with 3.5 % NaCl solution. STATISTICA program version 10 was used for data 

analysis. In conclusion a quadratic model is proposed to predict the effect of 

mentioned variables in CO2 environment.  

    
Key Words: CO2 corrosion, regression analysis, optimization, carbon steel, corrosion 

rate, full     factorial experimental design. 

 

Introduction 

   The major concern with CO2 

corrosion in oil and gas industry is that 

CO2 can cause failure on the 

equipment due to the hydration to 

carbonic acid leading to a decrease in 

pH and initiating the CO2 corrosion 

process. Degree of corrosiveness due 

to CO2 gas is influenced by 

environmental conditions such as; 

temperature, CO2 partial pressure, 

corrosion film properties and flow 

conditions [1, 2]. 

   Many studied on CO2 corrosion 

prediction and the effects of species 

like HAc with several other operating 

conditions including above mentioned 

once had been published [3-5]. The 

simultaneous effects of many variables 

in the CO2 corrosion could be 

optimized by using a statistical 

methodology such as design of 

experiment. 

    In CO2 corrosion, iron carbonate 

(FeCO3) film is the chief corrosion 

product formed and is formed through 

the reaction between carbonic acid, 

source of carbonate ions, (CO3
-2

) and 

iron (Fe
+2

) released through corrosion 

of the pipeline. FeCO3 forms on the 

wall of the pipe if the product of 

ferrous ion concentration (Fe
+2

) and 

carbonate ion concentration (CO3
-2

) 

exceeds the solubility product limit. 

The film is known to be protective and 

the corrosion rate drops once the film 

Iraqi Journal of Chemical and 
Petroleum Engineering 

 

University of Baghdad 
College of Engineering 



 Modelling and Optimization of Carbon Steel Corrosion in CO2 Containing Oilfield Produced Water in 
Presence of HAc 

2                                       IJCPE Vol.16 No.2 (June 2015)             -Available online at: www.iasj.net 
 

starts growing. Although iron 

carbonate film formation mechanisms 

and kinetics have been extensively 

studied, it is not known how protective 

the film will be in the presence HAc. 

Moreover it is not known if the film 

failure (if any) is a result of a lower 

system pH or the result of interaction 

between corrosion products and HAc. 

Thus it becomes imperative to 

understand how FeCO3 precipitation is 

affected in the presence of HAc, as 

also by the pH, temperature and ionic 

strength of the solution [6]. 

 

Experimental Work 

 

Electrochemical Set-up & Specimen 

Preparations 

   A typical schematic three–electrode 

set-up used in all electrochemical 

experiments is shown in Fig. (1). A 

rotating cylinder electrode with a speed 

control unit was used as the working 

electrode.  

                  
  Fig.1, Schematic Corrosion Test Cell 

[7]. 

1. Potentiostat 
6. CO2 Gas 
Distributer  

2. Corrosion Test Cell 7. Ammeter 
3. Reference Electrode  8.Voltmeter                                          
4. Counter Electrode 9. Hot Plate 

5. Working  Electrode 
10. CO2 Gas 
Outlet 

Glass cell was fitted with graphite 

electrode as auxiliary electrode and 

SCE as a reference electrode. The 

working electrodes were API X65 

carbon steel and the chemical 

composition is shown in table (1). The 

cylindrical specimens have diameter of 

2.03 cm and 2.08 cm length with 0.13 

cm thickness. Before immersion, the 

specimen surfaces were polished 

successively with 220, 320, 400 and 

600 grit SiC paper, rinsed with 

methanol and degreased using acetone. 

The experiments were repeated at least 

twice in order to ensure reasonable 

reproducibility. 

 

Table 1, Composition of API X65  

Carbon Steel in the Experiments 

API X65 wt% 

C 0.15 

Si 0.24 

Mn 1.34 

P 0.01 

S 0.004 

Mo 0.10 

Fe Balance 

 

Cell Solutions 

   The experiments were performed 

both in stagnant and flow solution. The 

total pressure was 1 bar, the glass cell 

was filled with 1 liter of distilled water 

and 3.5% wt. NaCl which was stirred 

with magnetic stirrer. The CO2 gas (> 

99.99 %) was bubbled through the cell 

(at least 1 hr prior to experiment) in 

order to saturate and de aerate the 

solutions. Temperature was set using a 

hot plate. After the solution was 

prepared, the pH was adjusted to reach 

the pH set by using NaHCO3 and HCl, 

as buffer solutions. Simulation of flow 

condition was conducted using rotating 

cylinder electrode (RCE). A cylindrical 

working electrode was screwed on to 

an electrode holder at the center of the 

cell for rotating in the RCE. The 

weight loss technique was used to 

measure the corrosion rate in 

gm/m
2
.day (gmd). 

 

CO2 

(1) 

(7) 

(10) 

(8) 

(6) 

(2) 

(4) 

(3) 

(5) 

(9) 

 

  

 

A   V 



Aprael S. Yaro and Khalid H. Rashid 
                    

-Available online at: www.iasj.net                    IJCPE Vol.16 No.2 (June 2015)                                3 
 

Variable Coding and Experimental 

Design 

   Two levels Full Factorial 

Experimental Design (FFED), with 

four variables, was used to study the 

response pattern and to determine the 

combined effect of variables. The 

effect of independent variables of T 

(°C), pH, HAc concentration CA (ppm) 

and ω (rpm) is shown in table (3). The 

experiments number 17-20 were used 

to allow for estimating for a pure error 

of mean squares. The variables were 

coded according to the following 

Equation [8]. 

      
           

             
                  

 

Where   = coded value of an 
independent variable. 

 

  = real value of an independent 
variable.   

 

Table 2, shows the real and coded 

variables used in RSM study. 

 Real 
T 

(°C) 
pH 

HAc 

(ppm) 

ω 

(rpm) 

 Code x1 x2 x3 x4 
Max. 

Point 
+1 60 5 3000 1500 

Center 
Point 

0 50 4 2000 1250 

Min. 

Point 
-1 40 3 1000 1000 

 

   Table (3) shows a full factorial 2-

levels experimental design, with four 

variables (coded & real) was used to 

study response pattern & to determine 

the combination effects of variables. 

 

Table 3, two-level full factorial experimental design of the independent  

Variables with the observed, predicted values and absolute percentage error for the 

response. 

Run 

No. 

Coded factor Response (gmd) 

Error 

        x1 x2 x3 x4 C.R      
Exp. Error 

     
      

1 -1 -1 -1 -1 48.52 48.72 -0.20 0.41 

2 +1 -1 -1 -1 121.30 121.78 -0.48 0.39 

3 -1 +1 -1 -1 40.06 39.87 0.19 0.47 

4 +1 +1 -1 -1 50.19 49.71 0.48 0.96 

5 -1 -1 +1 -1 51.22 51.21 0.01 0.02 

6 +1 -1 +1 -1 129.39 128.72 0.67 0.52 

7 -1 +1 +1 -1 42.53 42.53 0.00 0.00 

8 +1 +1 +1 -1 56.14 56.82 -0.68 1.21 

9 -1 -1 -1 +1 52.65 52.76 -0.11 0.21 

10 +1 -1 -1 +1 125.15 124.37 0.78 0.62 

11 -1 +1 -1 +1 43.67 43.55 0.12 0.27 

12 +1 +1 -1 +1 51.14 51.93 -0.79 1.54 

13 -1 -1 +1 +1 55.69 55.38 0.31 0.56 

14 +1 -1 +1 +1 130.46 131.43 -0.97 0.74 

15 -1 +1 +1 +1 46.02 46.33 -0.31 0.67 

16 +1 +1 +1 +1 60.14 59.16 0.98 1.63 

17 0 0 0 0 63.81 61.15 2.66 4.17 

18 0 0 0 0 59.72 61.15 -1.43 2.39 

19 0 0 0 0 62.43 61.15 1.28 2.05 

20 0 0 0 0 58.64 61.15 -2.51 4.28 

The mean absolute percentage error               

  



 Modelling and Optimization of Carbon Steel Corrosion in CO2 Containing Oilfield Produced Water in 
Presence of HAc 

4                                       IJCPE Vol.16 No.2 (June 2015)             -Available online at: www.iasj.net 
 

Results and Discussion 

 

Fitting the Model 

    Data from full factorial experimental 

design as given in table (3) was 

analysed by the least squares method 

to fit the second order polynomial 

model given the Eq. (2), which 

represents an empirical relationship (in 

coded values and real units). 

 

                           
             
                

       
 
       

                       
 

Where, T = Temperature (°C) 

pH = Acidity or Strength of CO2 

Saturated Solution 

CA = Concentration of HAc (ppm) 

ω = Rotation Speed (rpm) 

 

Statistical Analyses 

   It appears that the presented model 

significantly represents the data as 

described in table (4). Table (4) shows 

the analysis of variance for corrosion 

in saturated CO2 solution using Full 

Factorial Experimental Design (FFED) 

Methodology. The main factors for the 

coefficient of the linear and square 

models shows significant value at 

confidence level of α = 0.05 (p < 0.5). 

However, for the interaction effect of 

the model is insignificant (p > 0.5) 

except for (T x pH). Furthermore, the 

high value (99.99 %) of the correlation 

coefficient (R
2
) for the responses 

suggests that the model is a good fit. 

 

 

Table 4, Analysis of Variance (ANOVA) for the Fitted Model 

 

 

 

 

Const. 

Estim
d
 

S
o
u
rc

e
 

∑x
2 

Estim. 

Coeff.  

(b) 

Variance 

Sb
2
= 

Sr
2
/∑ x

2
 

F-value  

= b
2
/Sb

2
 

F0.95(1,5) 

 = 6.61 

b1 

L
in

e
a
r 

16 21.5 0.3 1685.9 S 

b2 16 -20.3 0.3 1503.9 S 

b3 16 2.4 0.3 21.6 S 

b4 16 1.6 0.3 9.3 S 

b11 

S
q
u
a
re

 

16 1.9 0.3 14.1 S 

b22 16 1.9 0.3 14.1 S 

b33 16 1.9 0.3 14.1 S 

b44 16 1.9 0.3 14.1 S 

b12 

In
te

ra
c
ti

o
n

 

16 -15.8 0.3 913.3 S 

b13 16 1.1 0.3 4.5 NS 

b14 16 -0.4 0.3 0.5 NS 

b23 16 0.04 0.3 0.01 NS 

b24 16 -0.1 0.3 0.03 NS 

b34 16 0.03 0.3 0.004 NS 



Aprael S. Yaro and Khalid H. Rashid 
                    

-Available online at: www.iasj.net                    IJCPE Vol.16 No.2 (June 2015)                                5 
 

Model Adequacy Checking 

    The accuracy of any empirical 

model can also be done by means of 

statistical parameters, for example, 

correlation coefficient. The correlation 

coefficient (R
2
) is a statistical measure 

of the strength of correlation between 

the predicted and measured values [9]. 

For the current problem, the following 

result is obtained:  R
2
 = 0.999 in 

presence of acetic acid (absence of the 

protective film formation) as shown in 

Fig. (2). 

 

 
Fig. 2, Performance of the Quadratic 

Mathematical Model for API X65 Mild 

Steel in Presence of Acetic Acid 

(Absence of Protective Film 

Formation) 

 

Graphic Analysis of the Model 

   The aim of this study was to find a 

corrosion rate whose features would 

have been previously defined from the 

operative conditions extracted from the 

quadratic mathematical model. 

   Because the direct exploitation of the 

Equation was delicate, it was 

convenient to restore it under a graphic 

representation; while fixing two of the 

four factors of the survey, it was 

possible to represent the response 

surface materializing the surface of 

regression in a three-dimensional 

space. It was also possible to project 

the equation in a design under 

isoresponse curves, interpreted as card 

curves level.  

 
 

 
Fig. 3, Response Surface Plot (top) and 

Contour Plot (bottom) Showing the 

Variation of Response (Corrosion 

Rate) as a Function of the Temperature 

and pH at the Optimum Conditions 

(2178.5 ppm HAc & 1296.6 rpm). 

 

(i) Evolution of Corrosion Rate as a 
Function of the Temperature and 

the pH 

     Fig. (3) shows the evolution of the 

corrosion rate as a function of the 

temperature and the pH. It can be seen 

that the temperature has a strong 

influence on the tentative response. 

The minimal corrosion rate is obtained 

for a temperature of -0.5 in coded 

variable, i.e., 45.4 °C in real variable. 

Considering simultaneous effects of 

temperature and pH is presented in Fig. 

(3) contour plot. The Figure shows, in 

low pH (pH 3), the increase of 



 Modelling and Optimization of Carbon Steel Corrosion in CO2 Containing Oilfield Produced Water in 
Presence of HAc 

6                                       IJCPE Vol.16 No.2 (June 2015)             -Available online at: www.iasj.net 
 

corrosion rate is higher than in higher 

pH (pH 5). 

 

 

 
Fig. 4 Response Surface Plot (top) and 

Contour Plot (bottom) showing the 

Variation of Response (Corrosion 

Rate) as a Function of the pH and HAc 

Acid Concentration at the Optimum 

Conditions (45.4 °C & 1296.6 rpm 

 

(ii) Evolution of Corrosion Rate as a 
Function of the pH and HAc Acid 

Concentration 

   Fig. (4), shows the synergism 

between the two factors: the pH and 

HAc acid concentration in corrosion 

rate at temperature 45.4°C and speed 

of rotation of 1296.6 rpm. It can be 

noted that the effect of the HAc acid 

concentration differed according to the 

corrosion rate’s variation. This effect 

becomes positive and even more 

important when the corrosion rate is 

degraded (reduced). Analysis of 

corrosion rate as effects of interaction 

between pH and HAc acetic 

concentration is shown in Fig. (4) 

contour plot. The model shows an 

increase of corrosion rate due to HAc. 

And the decrease of corrosion rate is 

caused by pH. 

 

 

 

 
Fig. 5, Response Surface Plot (top) and 

Contour Plot (bottom) Showing the 

variation of Response (Corrosion Rate) 

as a Function of the Temperature and 

Speed of Rotation at the Optimum 

Conditions (pH 4.8 & 2178.5 ppm). 

 

(iii) Evolution of Corrosion Rate as a 
Function of the Temperature 

and Speed of Rotation 

    Fig. (5) represent the evolution of 

the corrosion rate as a function of the 

temperature and the speed of rotation. 

This Figure shows that the corrosion 

rate decreased when the temperature 

decreased. This evolution was however 

more accentuated for the lower speeds 

of rotation. Considering simultaneous 

 > 80 
 < 76 
 < 66 
 < 56 
 < 46 
 < 36 

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

pH
 

80
01

00
01

20
01

40
01

60
01

80
02

00
02

20
02

40
02

6 0
02

8 0
03

00
03

2 0
0

HAc Acid

Concentration 

(ppm
)

40

50

60

70

80

90

C
o

rro
sio

n
 R

a
te

 (g
m

d
)



Aprael S. Yaro and Khalid H. Rashid 
                    

-Available online at: www.iasj.net                    IJCPE Vol.16 No.2 (June 2015)                                7 
 

effects of temperature and speed of 

rotation is presented in Fig. (5) contour 

plot. The Figure shows, in high speed 

of rotation (1500 rpm), the increase of 

corrosion rate is higher than in lower 

speed of rotation (1000 rpm). 

 

(iv) Evolution of Corrosion Rate as a 
Function of the HAc Acid 

Concentration and Speed of 

Rotation 

   Fig. (6), represent the evolution of 

the corrosion rate as a function of the 

HAc acid concentration and the speed 

of rotation. This Figure shows that the 

corrosion rate decreased when the HAc 

acid concentration and speed of 

rotation decreased.  

 

 
3D Contour Plot 

 
Fig. 6 Response Surface Plot (top) and 

Contour Plot (bottom) showing the 

Variation of Response (Corrosion 

Rate) as a Function of the HAc Acid 

Concentration and Speed of Rotation at 

the Optimum Conditions  

(45.4 °C & pH 4.8) 

   This evolution was however more 

accentuated for the weakest and 

strongest concentrations in HAc acid 

and the lessest and greatest effects of 

speed of rotation. Fig. (6) contour plot 

presents a polynomial surface response 

relating to effect of HAc and speed of 

rotation on corrosion rate. It is shown 

that different corrosion rate is observed 

for HAc concentration and speed of 

rotation. Speed of rotation increased 

corrosion rate from 26-38 gmd along 

the speed setting (1000-1500 rpm). 

HAc concentration from 1000-3000 

ppm has increased corrosion rate from 

26-42 gmd. [10] and [11] have studied 

effects of speed of rotation on 

corrosion rate. They believed effects of 

mass transfer, hydrodynamic and 

diffusion coefficient that influenced 

corrosion rate.  

 

Conclusions 

1- The second order polynomial 
regression analysis of the objective 

function (corrosion rate) describe 

the behavior of the process in 

absence of the protective film 

formation with mean absolute 

percentage error 1.2 % in terms of 

temperature, solution pH, HAc acid 

concentration and speed of rotation. 

2- The corrosion rate of API X65 mild 
steel in CO2 saturated, 3.5 wt% 

NaCl solution in presence of acetic 

acid, increases with increasing 

temperature, acetic acid 

concentration and speed of rotation, 

and decreased with increasing of 

solution pH. 

3- The optimum conditions as 
predicted from Eq. (2) are 45.4 °C, 

pH 4.8, 2178.5 ppm HAc and 

1296.6 rpm in absence of the 

protective film formation. 

4- The analysis of statistical Full 
Factorial Experimental Design 

(FFED), generally, shows that the 

square and interaction effects on the 

corrosion rate by weight loss 



 Modelling and Optimization of Carbon Steel Corrosion in CO2 Containing Oilfield Produced Water in 
Presence of HAc 

8                                       IJCPE Vol.16 No.2 (June 2015)             -Available online at: www.iasj.net 
 

technique (within the studied range) 

is less pronounced compared with 

the main variables except the high 

interaction effect of  (T x pH) in 

presence of acetic acid. 

5- The effect of the temperature, 
solution pH, HAc acid 

concentration and speed of rotation 

on the corrosion rate in absence of 

the protective film formation in the 

following order: 

Temperature > pH > HAc Acid 

Conc. >   Speed of rotation  

 

References 

1- Abd El-Lateef, H.H., Abbasov, V. 
M., Aliyeva, L.I. and Ismayilov, 

T.A., (2012), “Corrosion Protection 

of Steel Piplines against CO2 

Corrosion- A Review”, Chemistry, 

Vol.2, Issue 2, pp. 52-63. 

2- Nesic, S., (2007), “Key Issues 
Related to Modelling of Internal 

Corrosion of Oil and Gas Pipelines- 

A Review”, Corrosion Science, 

Vol. 49, No. 12, pp. 4308-4338. 

3- Zhang, G. and Cheng, Y., (2009), 
“On the Fundamentals of 

Electrochemical Corrosion of X65 

Steel in CO2-containing Formation 

Water in the Presence of Acetic 

Acid in Petroleum Production”, 

Corrosion Science, No. 51, pp.87-

94. 

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(2009), “Effect of Low 

Concentration Acetic Acid on CO2 
Corrosion in Turbulent Flow 

Conditions”, Corrosion, Vol. 34, 

No. 12, pp.129-149. 

5- Mokhtar, I.C., (2005), “Prediction 
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acetic acid”, Ph.D. Thesis, UMIST, 

United Kingdom. 

6- Sun, Y., George, K. and Nesic, S., 
(2003),“The Effect of Cl

- 
and Acetic 

Acid on Localized CO2 Corrosion in 

Wet Gas Flow”, Corrosion, No. 

3327, NACE, Houston, Texas. 

7- Rashid, K.H., (2014), “Corrosion 
Behavior of Carbon Steel in CO2 – 

Containing Oilfield Produced 

Water”, Ph.D. Thesis, University of 

Baghdad.     

8- Box, G.E.P. and Draper, N.R., 
(1987), “Empirical Model Building 

and Response Surfaces”, John 

Wiley & Sons, New York. 

9- Devore, P., (2005), “The 
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5
th 

Edition, Thomson Learning, 

Belmont, USA. 

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Transfer Coefficients and Fluid 

Shear Stresses between the Rotating 

Cylinder Electrode and Pipe”, 

Corrosion, No. 6, Vol. 6, p.515. 

11- De Waard, C., Lotz, U. and 
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Liquid Flow Velocity on CO2 

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Model”, Corrosion, No. 128, 

NACE, Houston, Texas.