COMSOL 6.4 - Estimation of Corrosion Kinetics Parameters

Estimation of Corrosion Kinetics Parameters

A common challenge in corrosion modeling is to accurately describe the electrode kinetics as a function of electrode potential. This tutorial shows how to use the Parameter Estimation study node to perform electrode kinetics parameter estimations based on polarization data.

A zero-dimensional electrode polarization model is constructed using an anode Tafel expression for the metal dissolution reaction and a cathode Tafel expression for the oxygen reduction kinetics in combination with an oxygen reduction limiting current density.

Parameter estimation is performed using a global least-squares objective function based on three different sets of polarization data (Ref. 1) recorded for the following metals:

•

70-30 Cu-Ni alloy (SAE/ASTM UNS number CA7150)

•

90-10 Cu-Ni alloy (C70600)

•

Ni-Al bronze (C95800)

The experimental data was recorded using potentiodynamic scans at 30°C for fresh metals in a controlled sea water flow (8.0 ft/s) environment.

Model Definition

The metal dissolution reaction is described by an anodic Tafel expression according to:

(1)

where i0, Me (A/m2) is the exchange current density and AMe (V) is the anodic Tafel slope of the metal dissolution reaction, respectively. The overpotential of the metal dissolution reaction, ηMe (V), is defined as:

(2)

where Eeq, Me is the equilibrium potential of the metal dissolution reaction. Note that the choice of Eeq, Me (which is generally unknown) is arbitrary in this model since the cathodic part of the metal dissolution reaction is neglected. Eeq,Me = 0 is used in this model.

For the oxygen reduction reaction, the following cathodic Tafel expression is used:

(3)

where i0,O2 (A/m2) is the exchange current density and AO2 (V) is the cathodic Tafel slope of the oxygen reduction reaction, respectively. The overpotential of the oxygen reduction reaction, ηO2 (V), is defined as:

(4)

The equilibrium potential for oxygen reduction is defined to be dependent on the pH according to the Nernst equation:

(5)

where T (K) is the temperature. (But note that here also the actual choice of Eeq,O2 is arbitrary). A pH of 7.7 is used in the model.

Furthermore, the current density of oxygen is assumed to be limited by diffusion, resulting in:

(6)

where iO2,lim (A/m2) is the limiting current density for oxygen reduction.

Finally, the total current density at the electrode surface, iloc (A/m2), is:

(7)

Note that for low potentials one should also consider hydrogen evolution as an additional cathodic reaction. That reaction is however not included in this tutorial.

The model is formulated as a set of parametric expressions in 0D and the Parameter Estimation study node is used to create a least squares objective function used for optimization, based on the experimental data.

Results and Discussion

The experimental polarization curves for the 70-30 Cu-Ni alloy and the corresponding fitted model values are shown in Figure 1 and Figure 2, using a linear or a logarithmic scale for the current density values, respectively.

Figure 3 and Figure 4 show the polarization curves in logarithmic scale for the 90-10 Cu-Ni and the Ni-Al bronze. In all cases, the model seems to be able to capture the salient features of the polarization behavior.

Table 1 shows the fitted parameter values for the polarization data for the three different metals. The two Cu-Ni alloys exhibit fairly similar values, whereas the values for the Ni-Al bronze are more different. The limiting current density for oxygen reduction are similar for all cases. This is expected since the experiments where conducted for fresh metals in a controlled flow environment.

Table 1: Optimization parameters and corresponding estimated values for the three different alloys.
Parameter	Unit	70-30 Cu-Ni	90-10 Cu-Ni	Ni-Al bronze
AMe	mV	63	68	70
AO2	mV	-170	-166	-125
i0,Me	A/m2	103.3	102.8	103.5
i0,O2	A/m2	10-7.1	10-7.3	10-10
iO2,lim	A/m2	-13	-15	-15

Figure 1: Polarization curve (linear scale) for the 70-30 Cu-Ni alloy.

Figure 2: Polarization curve (log scale) for the 70-30 Cu-Ni alloy.

Figure 3: Polarization curve (log scale) for the 90-10 Cu-Ni alloy.

Figure 4: Polarization curve (log scale) for the Ni-Al bronze.

Reference

1. Atlas of Polarization Diagrams for Naval Materials in Seawater. Harvey P Hack. Carderock Division, Naval Surface Warfare Center, CARDIVNSWC-TR-61 -94/44, April 1995.

Corrosion_Module/General_Corrosion/corrosion_parameter_estimation

Modeling Instructions

From the menu, choose .

New

In the window, click

Add Component

In the toolbar, click

and choose .

Global Definitions

Load the model parameters from a text file.

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file corrosion_parameter_estimation_parameters.txt.

Definitions

Interpolation 1 (int1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the text field, type 7030CuNi_pol.csv.

Click

Interpolation 2 (int2)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type 9010CuNi_pol.csv.

Click

Interpolation 3 (int3)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the text field, type NiAlBronze_pol.csv.

Click

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar three times.

In the toolbar, click

to close the window.

Study 1

Use the study step to specify the polarization data (70-30 Cu-Ni) used by the optimization solver. The objective function will be created automatically by the study step.

Parameter Estimation

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 7030CuNi_pol.csv.

Click

Locate the section. In the table, click to select the cell at row number 1 and column number 2.

From the list, choose .

In the table, click to select the cell at row number 2 and column number 3.

In the text fields that appear below the table, enter the following values:

In the text field, type iloc.

In the text field, type iloc_exp.

In the text field, type A/m^2.

From the list, choose .

In the text field, type max(abs(comp1.int1(E)),1e-2).

Locate the section. Click

five times.

Row by row, select a parameter name in the first column and set the corresponding initial value and scale as follows:


Parameter	Initial value	Scale	Unit
A_O2 (Cathodic tafel slope for oxygen reduction)	-200[mV]	0.1	V
A_Me (Anodic tafel slope for metal dissolution)	100[mV]	0.1	V
i_O2_lim (Limiting current density for oxygen reduction)	-15[A/m^2]	10	A/m^2
log10_i0_O2 (log10 of exchange current density for oxygen reduction)	-9	1
log10_i0_Me (log10 of exchange current density for metal dissolution)	0	1