Pitting Corrosion

Pitting corrosion is a type of localized corrosion by which local cavities, pits, are formed on an initially smooth metal surface. A pit may be initiated due to surface defects, such as an inhomogeneities in composition or shape, or mechanical abuse resulting in a small scratch or dent. How and if the pit grows depends on a number of factors such as the type of metal, salinity, pH, and temperature of the aqueous electrolyte. A fundamental understanding of the pitting process is paramount for proper material selection in environments susceptible to this type of corrosion.

This tutorial investigates the fundamental mechanisms of pit propagation by simulating electrode kinetics, mass transfer, and the resulting geometry deformation. In the tutorial, the following overall mechanism for the pitting corrosion is assumed:

Oxygen reduction occurs, mainly outside the pit, on the metal surface

(1)

Iron is oxidized, inside and outside the pit, to counterbalance the oxygen reduction reaction

(2)

The combination of the two above reactions gives rise to a mixed electrode potential of the metal surface. Since the electrode area inside the pit is small in comparison to the total surface area of the metal, the oxygen-iron mixed potential can be assumed to be constant; that is, to not be affected by the pitting processes.

Dissolved iron then forms iron hydroxide in the electrolyte close to the electrode surface

(3)

It should be noted that, depending on pH and potentials, other iron containing oxides and hydroxide could also be considered. In this tutorial we will assume a pH ranging from about 10 to 8 in combination with fairly low values for the mixed iron-oxygen potential, which are conditions for which iron hydroxide is the most likely oxidation product.

A result of the iron hydroxide production is that protons are formed by water autoprotolysis to counterbalance the hydroxide ions consumed

(4)

Ions such as Cl- may also be transported in order to maintain electroneutrality. The transport of ions, in combination with the pit shape, determine the local pH.

As a result of the consumption of the hydroxide ions in Equation 3, the pH is reduced close to the electrode surface. If the iron oxidation reaction is catalyzed (depassivated) by H+, a lower pH within the pit will result in faster metal dissolution compared to the metal surface outside the pit.

Model Definition

Figure 1 shows the initial model geometry, defining an electrolyte film covering an iron metal electrode surface and an initial pit. The geometry is defined in 2D with axial symmetry.

Figure 1: Initial model geometry.

The model is defined using the interface, solving for the electrolyte phase potential and the concentrations of the electrolyte species H+, OH-, Cl-, Na+ and Fe2+, using the Nernst–Planck equations assuming electroneutrality and the water autoprotolysis reaction (Equation 4) to be in equilibrium.

Fixed concentrations and electrolyte phase potential are set at the top horizontal electrolyte boundary facing the bulk of the electrolyte.

Iron dissolves at the electrode surface according to Equation 2, with the kinetics being based on a concentration-dependent Butler–Volmer expression, with the exchange current density set to be proportional to the concentration of H+. In this way the iron dissolution reaction gets activated by a lower pH.

The iron metal phase potential is set to fixed value resulting from the mixed iron-oxygen potential, and as discussed above, this is assumed not to be affected by the local pit corrosion.

The iron hydroxide forming homogeneous reaction (Equation 3) is assumed to be irreversible.

Due to the formation of iron hydroxide (and other oxidation products), the pit is assumed to be a porous structure with the electrolyte volume fraction in pit (z < 0) fixed to 2.5%. The transport properties (the ion diffusivities and mobilities) depend on the porosity using a Bruggeman relation so that the effective diffusivity in the pit is about

of that of the bulk of the electrolyte.

That the amount of produced Fe(OH)2(s) does not affect the porosity is a crude simplification of the processes; a possible extension of the model would be to the make porosity a function of Fe(OH)2(s) as it forms dynamically over time.

The geometry of the model deforms as a result of the iron dissolution, with the boundary velocity being proportional to the iron dissolution current density.

The model is solved in a time-dependent solver, simulating the propagation of the pit during 30 days.

Figure 2: Iron dissolution current density after 30 days.

Results and Discussion

Figure 2 shows the iron dissolution current density after 30 days. The current density is larger inside the pit than outside. After 30 days, a pronounced convex-shaped pit as has formed below the metal surface

Figure 3: Electrode dissolution rate along the iron electrode surface at various times.

Figure 3 shows the corrosion rate along the electrode surface (one line per day). The corrosion rate within the pit increases with time.

Figure 4 shows the initial pH. For the initial pit shape, the lowest pH is around 9.5 in the pit.

Figure 5 shows the pH at the end of the simulation. The lowest pH is now about 8.7 at the bottom of the pit. The increased pitting rate over time observed in Figure 3 is a result of the lowered pH.

Figure 4: pH in the pit for the initial conditions.

Figure 5: pH of the pit after 30 days.

Notes About the COMSOL Implementation

The node is used to define the pit as a porous structure.

Linear elements are used to reduce memory usage and reduce the computation time.

The model is solved in two steps. The first study step solves for the stationary concentration and potential fields for the initial pit shape. The study step solves for the pit growth during 30 days, using the stationary solution for initial values.

Corrosion_Module/Crevice_and_Pitting_Corrosion/pitting_corrosion

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the text field, type 3.

In the table, enter the following settings:


cNa
cCl
cFe

Click

Global Definitions

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 pitting_corrosion_parameters.txt.

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type R_pit*20.

In the text field, type R_pit*10.

Click

Click the

button in the toolbar.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type R_pit.

In the text field, type H_pit.

Locate the section. In the text field, type -H_pit.

Click

Union 1 (uni1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select both objects.

In the window for , locate the section.

Clear the check box.

Click

Fillet 1 (fil1)

In the toolbar, click

Click the

button in the toolbar.

On the object , select Points 4 and 5 only.

In the window for , locate the section.

In the text field, type R_pit.

Click

Tertiary Current Distribution, Nernst-Planck (tcd)

Change the charge transport model to . This will add the water auto protolysis as an equilibrium reaction as well as the proton and hydroxide ion concentrations to the equation system, and save for the two concentrations algebraically.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

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

Tertiary Current Distribution, Nernst-Planck (tcd)

Species Charges 1

In the window, under click .

In the window for , locate the section.

In the zcNa text field, type 1.

In the zcCl text field, type -1.

In the zcFe text field, type 2.

The pit is assumed to be porous, with a non-unit volume fraction of electrolyte. The node may be used to specify the porosity.

Separator 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the DcNa text field, type D_Na.

In the DcCl text field, type D_Cl.

In the DcFe text field, type D_Fe.

In the DcH text field, type D_H.

In the DcOH text field, type D_OH.

Locate the section. In the εl text field, type epsl.

Reactions 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the RcFe text field, type -R_FeOH2.

In the RcOH text field, type -2*R_FeOH2.

Use a and an node to define the boundary toward the bulk of the electrolyte, at the top of the geometry.

Concentration 1

In the toolbar, click

and choose .

Select Boundary 3 only.

In the window for , locate the section.

Select the check box.

In the c0,cNa text field, type cNa_0.

Select the check box.

In the c0,cCl text field, type cCl_0.

Select the check box.

In the c0,cFe text field, type cFe_0.

Electrolyte Potential 1

In the toolbar, click

and choose .

Select Boundary 3 only.

Electrode Surface 1

In the toolbar, click

and choose .

Select Boundaries 4, 5, 7, and 8 only.

In the window for , click to expand the section.

Click

In the table, enter the following settings:


Species	Density (kg/m^3)	Molar mass (kg/mol)
Fe	rho_Fe	M_Fe

Clear the check box.

Locate the section. In the φs,ext text field, type E_metal.

Electrode Reaction 1

In the window, click .

In the window for , locate the section.

In the n text field, type 2.

In the νcFe text field, type -1.

In the table, enter the following settings:


Species	Stoichiometric coefficient (1)
Fe	1

Locate the section. In the Eeq,ref(T) text field, type Eeq_Fe.

Locate the section. In the i0,ref(T) text field, type i0_ref_Fe*(tcd.cH/cH_ref).

In the αa text field, type 0.25.

Initial Values 1

In the window, under click .

In the window for , locate the section.

In the cNa text field, type cNa_0.

In the cCl text field, type cCl_0.

In the cFe text field, type cFe_0.

Multiphysics

Nondeforming Boundary 1 (ndbdg1)

Switch to zero normal displacement for the non-deforming boundaries. This is a more stable boundary condition for the deformation, but it can only be used for straight boundaries.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Tertiary Current Distribution, Nernst-Planck (tcd)

In the window, under click .

In the window for , click to expand the section.

Using linear elements instead of quadratic saves memory and speeds up the computation for this model.

From the list, choose .

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Size 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 4, 7, and 8 only.

Locate the section. From the list, choose .

Size 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Point 2 only.

Locate the section. From the list, choose .

Click

Root

For solving the model we will first compute a stationary current and concentration distribution for this initial shape of the pit. The we will use this solution as initial values for a 30-day time-dependent simulation.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Right-click and choose .

In the toolbar, click

to close the window.

Study 1

Step 1: Stationary

In the window for , locate the section.

In the table, enter the following settings:


Physics interface	Solve for	Equation form
Deformed geometry (Component 1)		Automatic

In the table, enter the following settings:


Multiphysics couplings	Solve for	Equation form
Nondeforming Boundary 1 (ndbdg1)		Automatic (Stationary)
Deforming Electrode Surface 1 (desdg1)		Automatic (Stationary)