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Carbon Dioxide Corrosion in Steel Pipes
Introduction
A flow mixture of water and carbon dioxide passing through a steel pipe can cause significant steel corrosion. Properties such as pH and temperature affect the rate of the corrosion.
This model simulates the corrosion taking place on the steel surface of a pipe for turbulent flow of carbon dioxide and water. The model reproduces results by Nordsveen and others (Ref. 1) and Nesic and others (Ref. 2).
Model Definition
The corrosion is investigated at an arbitrary position within a steel pipe through which a turbulent flow of dissolved carbon dioxide in water passes. A 1D model is used. No variations along the length of the pipe are considered and the interaction of the mixture with the steel is confined to the boundary layer near the steel surface. The boundary layer thickness is considered to be dependent upon the Reynolds number. The model geometry and physical considerations are shown in Figure 1. The diffusion and turbulent sublayers vary and are accounted for with the mass transport parameters.
Figure 1: Description of the boundary layer adjacent to the steel surface.
All species are assumed to be diluted in water and the mass transport is modeled by diffusion. The Electroanalysis interface is used in the model. Carbon dioxide hydration, water dissociation, three reduction reactions, and iron dissolution are accounted for; resulting in seven species in the model. The species and diffusion coefficients are tabulated in Table 1
Table 1: Modeled species with their respective diffusion coefficients.
Species
D (m2/s)·10-9
CO2
1.96
H2CO3
2.00
HCO3-
1.11
CO32-
0.92
H+
9.31
OH-
5.26
Fe2+
0.72
The turbulent sublayer is modeled by adding a turbulent diffusivity term to the diffusion coefficient. The term depends on the flow rate, viscosity, density of the liquid, and distance from the steel surface (Ref. 1).
The Electrode Surface boundary feature is used to calculate the corrosion potential at the steel surface using the mixed potential theory. The net total current of all electrochemical reactions is set to zero, the equation that is solved is described by
(1)
where i (SI unit: A/m2) is the current density of j number of electrochemical reactions. The initial value is set to −0.5 V around the free corrosion potential (Ref. 2).
For the Electroanalysis interface, uniform concentrations of species in chemical equilibrium are used as initial values for concentration for all species (Ref. 1). The outer point of the boundary layer is also set to these equilibrium concentrations for all species. Fluxes of species converted in the electrochemical reactions, ij/F (Faraday’s constant = 96,485 C/mol), are applied on the steel surface.
Equilibrium reactions
The following equilibrium reactions are present in the electrolyte:
where K1 through K4 are the equilibrium constants at 293.15 K(Ref. 1).
These reactions are modeled using the Equilibrium Reaction domain node; one for each reaction. The Equilibrium Reaction nodes solve for one additional degree of freedom each, where the additional degree of freedom represents the local reaction rate required in order to fulfill the equilibrium expression. The equilibrium expressions are based on the reaction stoichiometry and equilibrium constant Kk according to
where ci (SI unit: mol/m3) is the concentration of species i, vik the stoichiometric coefficient of species i in reaction k. The activity of a species, a(ci) is given by dividing the concentration with 1 M.
Electrochemical reactions
The following electrochemical reactions are present at the steel surface (Equation 1):
Iron dissolution
Proton reduction
Water reduction
Carbonic acid reduction
The current densities depend on mass transport limitations and charge transfer resistances as given in Ref. 2.
Study settings
The problem is solved with an auxiliary sweep on a stationary solver in order to investigate the impact of important parameters such as pH and temperature on corrosion.
Results and Discussion
Figure 2 displays the concentration deviation from the bulk of the seven species along the boundary layer at pH 6 and 20ºC. The concentration of iron ions is significantly higher at the steel surface due to the dissolution of iron. The deviation of carbon dioxide and sodium carbonate ions show considerable hydration of the carbon dioxide. All species show little variation in concentration compared to the bulk within a large part of the boundary layer adjacent to the bulk and demonstrating the presence of a turbulent sublayer.
Figure 2: Deviation in concentration of the species compared to the bulk along the liquid boundary layer.
Figure 3 shows the corrosion rate of the steel surface at three different pH for operating temperatures ranging from 20ºC to 80ºC. The corrosion rate is directly proportional to the corrosion current (that is, the iron dissolution current, since no other anodic reaction is considered). Lowered pH and increased temperature increase the rate of corrosion.
Figure 3: Corrosion rate in mm/year for pH 4, 5, and 6 and operating temperatures range of 20ºC–80ºC.
References
1. M. Nordsveen, S. Nesic, R. Nyborg, and A. Stangeland, “A Mechanistic Model for Carbon Dioxide Corrosion of Mild Steel in the Presence of Protective Iron Carbonate Films-Part 1: theory and Verification,” Corrosion, vol. 59, no. 5, pp. 443–455, 2003.
2. S. Nesic, J. Postlethwaite, and S. Olsen, “An Electrochemical Model for Prediction of Corrosion of Mild Steel in Aqueous Carbon Dioxide Solutions,” Corrosion, vol. 52, no. 4, pp. 280–294, 1996.
Application Library path: Corrosion_Module/Galvanic_Corrosion/co2_corrosion
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  1D.
2
In the Select Physics tree, select Electrochemistry>Electroanalysis (tcd).
3
Click Add.
4
In the Number of species text field, type 7.
5
In the Concentrations table, enter the following settings:
cCO2
cH2CO3
cHCO3
cCO3
cH
cOH
cFe
6
Click  Study.
7
In the Select Study tree, select General Studies>Stationary.
8
Click  Done.
Global Definitions
Load the model parameters from a text file.
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file co2_corrosion_parameters.txt.
Definitions
Load the variables from a text file.
Variables 1
1
In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file co2_corrosion_variables.txt.
Geometry 1
The geometry consists of a single interval.
Interval 1 (i1)
1
In the Model Builder window, under Component 1 (comp1) right-click Geometry 1 and choose Interval.
2
In the Settings window for Interval, locate the Interval section.
3
In the table, enter the following settings:
Coordinates (m)
0
delta
4
Click  Build Selected.
Electroanalysis (tcd)
Start defining the physics. The turbulent contribution is accounted for with a turbulent diffusivity, Dt.
Electrolyte 1
1
In the Model Builder window, under Component 1 (comp1)>Electroanalysis (tcd) click Electrolyte 1.
2
In the Settings window for Electrolyte, locate the Diffusion section.
3
In the DcCO2 text field, type DCO2+Dt.
4
In the DcH2CO3 text field, type DH2CO3+Dt.
5
In the DcHCO3 text field, type DHCO3+Dt.
6
In the DcCO3 text field, type DCO3+Dt.
7
In the DcH text field, type DH+Dt.
8
In the DcOH text field, type DOH+Dt.
9
In the DcFe text field, type DFe+Dt.
Initial Values 1
Set the initial values to the concentration of the species in the bulk.
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the cCO2 text field, type cCO20.
4
In the cH2CO3 text field, type cH2CO30.
5
In the cHCO3 text field, type cHCO30.
6
In the cCO3 text field, type cCO30.
7
In the cH text field, type cH0.
8
In the cOH text field, type cOH0.
9
In the cFe text field, type cFe0.
Electrode Surface 1
Use the Dissolving-Depositing species formulation to estimate the corrosion rate. Set the net total current of all the electrochemical reactions to zero. Also, set fluxes according to the electrochemical reactions at the steel surface.
1
In the Physics toolbar, click  Boundaries and choose Electrode Surface.
2
Select Boundary 1 only.
3
In the Settings window for Electrode Surface, click to expand the Dissolving-Depositing Species section.
4
Click  Add.
5
In the table, enter the following settings:
Species
Density (kg/m^3)
Molar mass (kg/mol)
s1
rho_steel
Mw_steel
6
Locate the Electrode Phase Potential Condition section. From the Electrode phase potential condition list, choose Total current.
7
In the Il,total text field, type 0.
8
In the φs,ext,init text field, type -0.5.
Electrode Reaction 1
1
In the Model Builder window, expand the Electrode Surface 1 node, then click Electrode Reaction 1.
2
In the Settings window for Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the n text field, type 2.
4
In the νcFe text field, type -1.
5
In the Stoichiometric coefficients for dissolving-depositing species: table, enter the following settings:
Species
Stoichiometric coefficient (1)
s1
-1
6
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Erev_Fe.
7
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Anodic Tafel equation.
8
In the i0 text field, type i0_Fe.
9
In the Aa text field, type b_Fe.
Electrode Surface 1
In the Model Builder window, click Electrode Surface 1.
Electrode Reaction 2
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
In the Settings window for Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the νcH2CO3 text field, type -1.
4
In the νcHCO3 text field, type 1.
5
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Erev_H2CO3.
6
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.
7
In the i0 text field, type i0_H2CO3.
8
In the Ac text field, type -b_H2CO3.
9
Select the Limiting current density check box.
10
In the ilim text field, type ilimH2CO3.
Electrode Surface 1
In the Model Builder window, click Electrode Surface 1.
Electrode Reaction 3
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
In the Settings window for Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the νcH text field, type -1.
4
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Erev_H2.
5
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.
6
In the i0 text field, type i0_H2.
7
In the Ac text field, type -b_H2.
8
Select the Limiting current density check box.
9
In the ilim text field, type ilimH2.
Electrode Surface 1
In the Model Builder window, click Electrode Surface 1.
Electrode Reaction 4
1
In the Physics toolbar, click  Attributes and choose Electrode Reaction.
2
In the Settings window for Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the νcOH text field, type 1.
4
Locate the Equilibrium Potential section. From the Eeq list, choose User defined. In the associated text field, type Erev_H2O.
5
Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.
6
In the i0 text field, type i0_H2O.
7
In the Ac text field, type -b_H2O.
Equilibrium Reaction 1
Set four equilibrium reactions.
1
In the Physics toolbar, click  Domains and choose Equilibrium Reaction.
2
In the Settings window for Equilibrium Reaction, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Equilibrium Condition section. In the Keq text field, type KH2O.
5
Locate the Stoichiometric Coefficients section. In the νcH text field, type 1.
6
In the νcOH text field, type 1.
Equilibrium Reaction 2
1
In the Physics toolbar, click  Domains and choose Equilibrium Reaction.
2
In the Settings window for Equilibrium Reaction, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Equilibrium Condition section. In the Keq text field, type KCO2H.
5
Locate the Stoichiometric Coefficients section. In the νcCO2 text field, type -1.
6
In the νcH2CO3 text field, type 1.
Equilibrium Reaction 3
1
In the Physics toolbar, click  Domains and choose Equilibrium Reaction.
2
In the Settings window for Equilibrium Reaction, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Equilibrium Condition section. In the Keq text field, type KH2CO3.
5
Locate the Stoichiometric Coefficients section. In the νcH2CO3 text field, type -1.
6
In the νcHCO3 text field, type 1.
7
In the νcH text field, type 1.
Equilibrium Reaction 4
1
In the Physics toolbar, click  Domains and choose Equilibrium Reaction.
2
In the Settings window for Equilibrium Reaction, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Equilibrium Condition section. In the Keq text field, type KHCO3.
5
Locate the Stoichiometric Coefficients section. In the νcHCO3 text field, type -1.
6
In the νcCO3 text field, type 1.
7
In the νcH text field, type 1.
Concentration 1
Set bulk concentrations at the rightmost boundary.
1
In the Physics toolbar, click  Boundaries and choose Concentration.
2
Select Boundary 2 only.
3
In the Settings window for Concentration, locate the Concentration section.
4
Select the Species cCO2 check box.
5
Select the Species cH check box.
6
Select the Species cFe check box.
7
In the c0,cCO2 text field, type cCO20.
8
In the c0,cH text field, type cH0.
9
In the c0,cFe text field, type cFe0.
Mesh 1
Build a user-defined mesh with a maximum element size in the domain of 1e-6 and at the leftmost boundary 1e-7.
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Mesh Settings section.
3
From the Sequence type list, choose User-controlled mesh.
Size
1
In the Model Builder window, under Component 1 (comp1)>Mesh 1 click Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. In the Maximum element size text field, type 1e-6.
Size 1
1
In the Model Builder window, right-click Edge 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundary 1 only.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section. Select the Maximum element size check box.
7
In the associated text field, type 1e-7.
8
Click  Build Selected.
Study 1
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, locate the Study Settings section.
3
Clear the Generate default plots check box.
Parametric Sweep
Use parametric sweep to investigate the impact of pH and temperature.
1
In the Study toolbar, click  Parametric Sweep.
2
In the Settings window for Parametric Sweep, locate the Study Settings section.
3
Click  Add twice.
4
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
pH (Operating pH)
4 5 6
 
T (Operating temperature)
293.15[K] 323.15[K] 353.15[K]
K
5
From the Sweep type list, choose All combinations.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, click Stationary Solver 1.
4
In the Settings window for Stationary Solver, locate the General section.
5
In the Relative tolerance text field, type 1e-4.
6
In the Study toolbar, click  Compute.
Results
The following steps reproduces the plots from the Results and Discussion section.
Concentrations
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Concentrations in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
4
From the Parameter selection (pH) list, choose Last.
5
From the Parameter selection (T) list, choose First.
6
Click to expand the Title section. From the Title type list, choose Manual.
7
In the Title text area, type pH=6, T=20<sup>\circ</sup>C.
8
Locate the Plot Settings section. Select the x-axis label check box.
9
In the associated text field, type Distance from steel surface (m).
10
Select the y-axis label check box.
11
In the associated text field, type Concentration deviation (mol/m<sup>3</sup>).
Line Graph 1
1
Right-click Concentrations and choose Line Graph.
2
In the Settings window for Line Graph, locate the Selection section.
3
From the Selection list, choose All domains.
4
Locate the y-Axis Data section. In the Expression text field, type cCO2-cCO20.
5
Click to expand the Title section. From the Title type list, choose None.
6
Locate the x-Axis Data section. From the Parameter list, choose Expression.
7
In the Expression text field, type x.
8
Click to expand the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
CO<sub>2</sub>
Line Graph 2
1
Right-click Line Graph 1 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cH2CO3-cH2CO30.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H<sub>2</sub>CO<sub>3</sub>
Line Graph 3
1
Right-click Line Graph 2 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cHCO3-cHCO30.
4
Locate the Legends section. In the table, enter the following settings:
Legends
HCO<sub>3</sub><sup>-</sup>
Line Graph 4
1
Right-click Line Graph 3 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cCO3-cCO30.
4
Locate the Legends section. In the table, enter the following settings:
Legends
CO<sub>3</sub><sup>2-</sup>
Line Graph 5
1
Right-click Line Graph 4 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cH-cH0.
4
Locate the Legends section. In the table, enter the following settings:
Legends
H<sup>+</sup>
Line Graph 6
1
Right-click Line Graph 5 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cOH-cOH0.
4
Locate the Legends section. In the table, enter the following settings:
Legends
OH<sup>-</sup>
Line Graph 7
1
Right-click Line Graph 6 and choose Duplicate.
2
In the Settings window for Line Graph, locate the y-Axis Data section.
3
In the Expression text field, type cFe-cFe0.
4
Locate the Legends section. In the table, enter the following settings:
Legends
Fe<sup>2+</sup>
5
In the Concentrations toolbar, click  Plot.
Corrosion rate
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Corrosion rate in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 1/Parametric Solutions 1 (sol2).
4
Locate the Title section. From the Title type list, choose None.
5
Locate the Plot Settings section. Select the x-axis label check box.
6
In the associated text field, type Operating temperature (<sup>\circ</sup>C).
7
Select the y-axis label check box.
8
In the associated text field, type Corrosion rate (mm/year).
Point Graph 1
1
Right-click Corrosion rate and choose Point Graph.
2
Select Boundary 1 only.
3
In the Settings window for Point Graph, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Electroanalysis>Dissolving-depositing species>tcd.vbtot - Total electrode growth velocity - m/s.
4
Locate the y-Axis Data section. From the Unit list, choose mm/yr.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
In the Expression text field, type T.
7
From the Unit list, choose degC.
8
Click to expand the Legends section. Select the Show legends check box.
9
From the Legends list, choose Manual.
10
In the table, enter the following settings:
Legends
pH=4
pH=5
pH=6
11
In the Corrosion rate toolbar, click  Plot.