Corrosion Application Library Manual

Corrosion ModuleApplication Library Manual

C o n t a c t I n f o r m a t i o n

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C o r r o s i o n M o d u l e A p p l i c a t i o n L i b r a r y M a n u a l 19982015 COMSOL

Protected by U.S. Patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; and 8,457,932. Patents pending.

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Version: COMSOL 5.1

CorrosionApplicationLibraryManual.book Page 1 Monday, April 13, 2015 5:05 PM

Solved with COMSOL Multiphysics 5.1

Anod e F i lm Re s i s t a n c e E f f e c t on Ca t h od i c C o r r o s i o n P r o t e c t i o n

Introduction

This example is an extension of the Corrosion Protection of an Oil Platform Using Saovre

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crificial Anodes model. The model exemplifies how the steel corrosion rate increases er time due to build-up of a resistive film on the sacrificial anodes, formed by action products.

odel Definition

he zinc dissolved on a sacrificial anode may react further to form various compounds. ne example is Zn(OH)2 formation according to

(1)

marine saline environments, however, other products may also be formed, for stance chloride and hydroxychloride compounds. This is not included in the model.

this example we assume that 1% of the zinc ions dissolved precipitate as a dense film the zinc anode surface, resulting in a growing film resistance over time.

onstant molar mass, density and conductivity are ascribed to the species forming the sistive film. Note however that in reality these may change over time due to changing rosity of the depositing film.

he model also includes secondary current distribution electrode kinetics on the otected steel structure, defining simultaneous metal dissolution and oxygen duction (mixed potential), in analogy with for instance the Galvanized Nail and the athodic Protection of Steel in Reinforced Concrete examples.

he model is solved in a one year time-dependent simulation. The symmetry of the odel geometry has been considered in order to reduce the problem size, as shown in igure 1.

Zn Zn2+ 2e-+

Zn2+ 2H2O+ Zn(OH)2 2H2+

+


2 | A N O D E F I L

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igure 1: Model geometry. Symmetry was considered to reduce the model size.

esults and Discussion

igure 2 and Figure 3 show the electrode potential vs SHE at the start of the mulation and after one year, respectively. The potential on the steel structure is higher the end of the simulation, resulting in a reduced corrosion protection.


Fi


gure 2: Potential vs SHE at t=0.


4 | A N O D E F I L

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igure 3: Potential vs SHE at t=365 days.

igure 4 shows the resulting anode film thickness after one year. The film thickness is irly uniform.


Fi

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gure 4: Precipitated anode film thickness at t=360 days.

igure 5 shows the steel corrosion current density for two points: one at the upper part one of the legs, and one at the inner bottom part of one of the legs. As can be seen e corrosion rates increase significantly over time and approach the limiting current nsity for oxygen (0.1 A/m2) used in the model.


6 | A N O D E F I L

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igure 5: Corrosion current density vs time.

otes About the COMSOL Implementation

n External Corroding Electrode boundary node is used for the zinc anodes in order define the surface concentration of precipitated products, the film resistance

otential drop, and the zinc oxidation reaction.

odel Library path: Corrosion_Module/Cathodic_Protection/node_film_resistance

odeling Instructions

rom the File menu, choose New.

E W

In the New window, click Model Wizard.


M O D E L W I Z A R D

1 In the Model Wizard window, click 3D.

2 In the Select physics tree, select Electrochemistry>Corrosion, Deformed Geometry>Corrosion, Secondary (corrsec).

3 Click Add.

4 Click Study.

5 In the Select study tree, select Preset Studies>Time Dependent with Initialization, Fixed

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Click Done.

L O B A L D E F I N I T I O N S

rametersOn the Home toolbar, click Parameters.

In the Settings window for Parameters, locate the Parameters section.

Click Load from File.

Browse to the applications Application Library folder and double-click the file anode_film_resistance_parameters.txt.

E O M E T R Y 1

port 1 (imp1)On the Home toolbar, click Import.

In the Settings window for Import, locate the Import section.

Click Browse.

Browse to the applications Application Library folder and double-click the file oil_platform.mphbin.

Click Import.

Locate the Selections of Resulting Entities section. Select the Create selections check box.

On the Geometry toolbar, click Work Plane.

ircle 1 (c1)On the Work Plane toolbar, click Primitives and choose Circle.

In the Settings window for Circle, locate the Size and Shape section.

In the Radius text field, type 50.


8 | A N O D E F I L

4 In the Sector angle text field, type 90.

5 Locate the Rotation Angle section. In the Rotation text field, type 180.

6 Right-click Component 1 (comp1)>Geometry 1>Work Plane 1 (wp1)>Plane Geometry>Circle 1 (c1) and choose Build Selected.

7 Click the Zoom Extents button on the Graphics toolbar.

Extrude 1 (ext1)1 On the Geometry toolbar, click Extrude.

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In the Settings window for Extrude, locate the Distances from Plane section.

In the table, enter the following settings:

In the Model Builder window, right-click Extrude 1 (ext1) and choose Build Selected.

Click the Transparency button on the Graphics toolbar.

ifference 1 (dif1)On the Geometry toolbar, click Booleans and Partitions and choose Difference.

Select the object ext1 only.

In the Settings window for Difference, locate the Difference section.

Find the Objects to subtract subsection. Select the Active toggle button.

Select the objects imp1(6), imp1(33), imp1(2), imp1(8), imp1(31), imp1(17), imp1(1), imp1(12), imp1(3), imp1(22), imp1(24), imp1(4), imp1(35), imp1(30), imp1(27), imp1(38), imp1(39), imp1(16), imp1(36), imp1(19), imp1(14), imp1(11), imp1(9), imp1(5), imp1(21), imp1(40), imp1(25), imp1(41), imp1(32), imp1(23), imp1(10), imp1(7), imp1(13), imp1(15), imp1(26), imp1(20), imp1(37), imp1(29), imp1(18), imp1(34), and imp1(28) only.

Right-click Component 1 (comp1)>Geometry 1>Difference 1 (dif1) and choose Build Selected.

E F I N I T I O N S

ifference 1On the Definitions toolbar, click Difference.

In the Settings window for Difference, type Anodes in the Label text field.

Locate the Geometric Entity Level section. From the Level list, choose Boundary.

istances (m)

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4 Locate the Input Entities section. Under Selections to add, click Add.

5 In the Add dialog box, select Import 1 in the Selections to add list.

6 In the Selections to add list, select Import 1.

7 Click OK.

8 In the Settings window for Difference, locate the Input Entities section.

9 Under Selections to subtract, click Add.

10 In the Add dialog box, select Import 1(41) in the Selections to subtract list.

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In the Selections to subtract list, select Import 1(41).

Click OK.

nion 1On the Definitions toolbar, click Union.

In the Settings window for Union, type Cathode in the Label text field.


Locate the Input Entities section. Under Selections to add, click Add.

In the Add dialog box, select Import 1(41) in the Selections to add list.

In the Selections to add list, select Import 1(41).

Click OK.

nion 2On the Definitions toolbar, click Union.

In the Settings window for Union, type All electrodes in the Label text field.


Locate the Input Entities section. Under Selections to add, click Add.

In the Add dialog box, In the Selections to add list, choose Anodes and Cathode.

Click OK.

O R R O S I O N , S E C O N D A R Y ( C O R R S E C )

lectrolyte 1In the Model Builder window, expand the Component 1 (comp1)>Corrosion, Secondary (corrsec) node, then click Electrolyte 1.

In the Settings window for Electrolyte, locate the Electrolyte section.

From the l list, choose User defined. In the associated text field, type sigma_sea.


10 | A N O D E F I

External Corroding Electrode 11 On the Physics toolbar, click Boundaries and choose External Corroding Electrode.

2 In the Settings window for External Corroding Electrode, type Zinc Anodes in the Label text field.

3 Locate the Boundary Selection section. From the Selection list, choose Anodes.

Surface Properties 11 In the Model Builder window, expand the Component 1 (comp1)>Corrosion, Secondary

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(corrsec)>Zinc Anodes node, then click Surface Properties 1.

In the Settings window for Surface Properties, locate the Corroding Species section.

In the Mccorr text field, type M_ZnOH2.

In the ccorr text field, type rho_ZnOH2.

lectrode Reaction 1In the Model Builder window, under Component 1 (comp1)>Corrosion, Secondary (corrsec)>Zinc Anodes click Electrode Reaction 1.

In the Settings window for Electrode Reaction, type Zn Oxidation in the Label text field.

Locate the Model Inputs section. In the T text field, type T.

Locate the Equilibrium Potential section. In the Eeq text field, type Eeq_Zn.

Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Anodic Tafel equation.

In the i0 text field, type i0_Zn.

In the Aa text field, type A_Zn.

Locate the Stoichiometric Coefficients section. In the nm text field, type 2.

In the ccorr text field, type -lambda.

inc AnodesIn the Model Builder window, under Component 1 (comp1)>Corrosion, Secondary (corrsec) click Zinc Anodes.

In the Settings window for External Corroding Electrode, click to expand the Film resistance section.

Locate the Film Resistance section. From the Film resistance list, choose Thickness and conductivity.

From the s list, choose Total electrode thickness change (corrsec/ede1/sp1).

In the film text field, type sigma_ZnOH2.


Electrolyte-Electrode Boundary Interface 11 On the Physics toolbar, click Boundaries and choose Electrolyte-Electrode Boundary

Interface.

2 In the Settings window for Electrolyte-Electrode Boundary Interface, locate the Boundary Selection section.

3 From the Selection list, choose Cathode.

Electrode Reaction 11

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In the Model Builder window, expand the Electrolyte-Electrode Boundary Interface 1 node, then click Electrode Reaction 1.

In the Settings window for Electrode Reaction, type Steel Oxidation in the Label text field.


Locate the Equilibrium Potential section. In the Eeq text field, type Eeq_Fe.


In the i0 text field, type i0_Fe.

In the Aa text field, type A_Fe.

lectrode Reaction 2On the Physics toolbar, click Attributes and choose Electrode Reaction.

In the Settings window for Electrode Reaction, type Oxygen reduction in the Label text field.


Locate the Equilibrium Potential section. In the Eeq text field, type Eeq_O2.

Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.

In the i0 text field, type i0_O2.

In the Ac text field, type A_O2.

Select the Limiting current density check box.

In the ilim text field, type ilim_O2.


12 | A N O D E F I

C O R R O S I O N , S E C O N D A R Y ( C O R R S E C )

Initial Values 11 In the Model Builder window, expand the Study 1 node, then click Component 1

(comp1)>Corrosion, Secondary (corrsec)>Initial Values 1.

2 In the Settings window for Initial Values, locate the Initial Values section.

3 In the phil text field, type -Eeq_Zn.

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E S H 1

izeIn the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Edit Physics-Induced Sequence.

In the Model Builder window, under Component 1 (comp1)>Mesh 1 click Size.

In the Settings window for Size, locate the Element Size section.

Click the Custom button.

Locate the Element Size Parameters section. In the Maximum element size text field, type 10.

In the Minimum element size text field, type 0.5.

In the Curvature factor text field, type 0.9.

In the Resolution of narrow regions text field, type 0.5.

Click the Build All button.

T U D Y 1

tep 1: Current Distribution InitializationIn the Model Builder window, under Study 1 click Step 1: Current Distribution Initialization.

In the Settings window for Current Distribution Initialization, locate the Study Settings section.

From the Current distribution type list, choose Secondary.

tep 2: Time Dependent, Fixed GeometryIn the Model Builder window, under Study 1 click Step 2: Time Dependent, Fixed Geometry.

In the Settings window for Time Dependent, Fixed Geometry, locate the Study Settings section.


3 From the Time unit list, choose d.

4 In the Times text field, type 0 10 20 30 range(60,60,300) 365.

5 On the Home toolbar, click Compute.

R E S U L T S

Data Sets1 On the Results toolbar, click More Data Sets and choose Solution.

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On the Results toolbar, click Selection.

In the Settings window for Selection, locate the Geometric Entity Selection section.

From the Geometric entity level list, choose Boundary.

From the Selection list, choose Anodes.

On the Results toolbar, click More Data Sets and choose Solution.

On the Results toolbar, click Selection.

In the Settings window for Selection, locate the Geometric Entity Selection section.

From the Geometric entity level list, choose Boundary.

From the Selection list, choose All electrodes.

D Plot Group 3On the Results toolbar, click 3D Plot Group.

In the Settings window for 3D Plot Group, type Potential vs SHE in the Label text field.

Locate the Data section. From the Data set list, choose Study 1/Solution 1 (4).

Click to expand the Title section. From the Title type list, choose Manual.

In the Title text area, type Potential vs SHE (V).

Locate the Plot Settings section. Clear the Plot data set edges check box.

Click the Transparency button on the Graphics toolbar.

tential vs SHERight-click Results>Potential vs SHE and choose Surface.

In the Settings window for Surface, locate the Expression section.

In the Expression text field, type 0 - phil.

On the Potential vs SHE toolbar, click Plot.

Click the Zoom Extents button on the Graphics toolbar.

On the Potential vs SHE toolbar, click Plot.


14 | A N O D E F I

7 In the Model Builder window, click Potential vs SHE.

8 In the Settings window for 3D Plot Group, locate the Data section.

9 From the Time (d) list, choose 0.

10 On the Potential vs SHE toolbar, click Plot.

3D Plot Group 41 On the Home toolbar, click Add Plot Group and choose 3D Plot Group.

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In the Settings window for 3D Plot Group, type Oxide layer thickness in the Label text field.

Locate the Data section. From the Data set list, choose Study 1/Solution 1 (3).

Locate the Plot Settings section. Clear the Plot data set edges check box.

xide layer thicknessRight-click Results>Oxide layer thickness and choose Surface.

In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component 1>Corrosion, Secondary>corrsec.sbtot - Total electrode thickness change.

Locate the Expression section. From the Unit list, choose m.

On the Oxide layer thickness toolbar, click Plot.


D Plot Group 5On the Home toolbar, click Add Plot Group and choose 1D Plot Group.

In the Settings window for 1D Plot Group, type Local corrosion current density in the Label text field.

Click to expand the Title section. From the Title type list, choose None.

Click to expand the Legend section. From the Position list, choose Middle right.

cal corrosion current densityOn the Local corrosion current density toolbar, click Point Graph.

Select Point 18 only.

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 Model>Component 1>Corrosion, Secondary>Electrode kinetics>corrsec.iloc_er1 - Local current density.

Click to expand the Legends section. Select the Show legends check box.

From the Legends list, choose Manual.


6 In the table, enter the following settings:

7 Right-click Results>Local corrosion current density>Point Graph 1 and choose Duplicate.

8 In the Settings window for Point Graph, locate the Selection section.

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Select the Active toggle button.

Select Point 13 only.

Locate the Legends section. In the table, enter the following settings:

On the Local corrosion current density toolbar, click Plot.

egends

ottom of leg


16 | A N O D E F I



A tmo sph e r i c C o r r o s i o n

Introduction

Atmospheric corrosion may occur when thin films of liquid water, in the range of up to hundreds of micrometers, forms on metal surfaces in contact with humidified air. The thickness of the film depends on the relative humidity of the surrounding air, but alcrph

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so on factors such as surface roughness and the presence of particles, especially salt ystals. The thin film of moisture acts as electrolyte, and may cause various corrosion enomena, such as galvanic corrosion of a bimetallic element or crevice corrosion.

his tutorial model studies atmospheric galvanic corrosion as a function of the relative midity of the surrounding air and salt load (NaCl) on a bimetallic aluminum alloy

eel surface. It is assumed that the electrolyte film solution is in equilibrium with solid lt particles, distributed uniformly over the surface at a given load.

he example uses parameter data from Ref. 1, Ref. 2, and Ref. 3.

odel Definition

he model geometry is shown in Figure 1.

gure 1: Model geometry. Each metal surface is 12 mm wide.

he thickness of the electrolyte film depends on both the salt load density and the lative humidity, see Figure 2. The film grows significantly towards 100% relative midity.

Air at given relative humidity

Thin film electrolyte

Steel (oxygen reduction)Aluminum alloy (metal oxidation)

Varying thickness


2 | A T M O S P H E

Fd

To

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igure 2: Thickness of the electrolyte for different relative humidities and salt load ensities. The conductivity varies linearly with the salt load density. (Ref. 1)

he oxygen solubility, oxygen diffusivity, and the electrolyte conductivity also depend n the relative humidity, see Figure 3, Figure 4, and Figure 5.


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gure 3: Oxygen solubility vs relative humidity.(Ref. 1)


4 | A T M O S P H E

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igure 4: Oxygen diffusivity vs relative humidity.(Ref. 2)


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wox(S


gure 5: Electrolyte conductivity vs relative humidity. (Ref. 1)

L E C T R O C H E M I C A L R E A C T I O N S

he less nobler aluminum alloy is oxidized in the cell, with the electrode reaction netics described by a Butler-Volmer expression. On the steel surface, oxygen duction occurs.

he oxygen reduction reaction is limited by oxygen transport through the film. The iting current density, ilim, O2 (SI unit: A/m

2), depends on the film thickness, the ygen solubility and the oxygen diffusivity according to:

here F (96485 C/mol) is Faradays constant, D (SI unit: m2/s) is the diffusivity of ygen in the film, csol (SI unit: mol/m

3) is the solubility of oxygen, and dfilm I unit: m) is the film thickness.

ilim O2,4FDcsol

dfilm---------------------=


6 | A T M O S P H E

By assuming a first order dependency of the oxygen reduction kinetics on the local current density of the oxygen concentration, the following expression for the current density, ilim, O2 (SI unit: A/m

2), can be derived:

where iexpr is the local current density of the electrode reaction in absence of mass tr

R

F0totogin

Fre

iloc O2,ilim O2, iexpr

ilim O2, iexpr+------------------------------------=


ansport limitations. In this model a cathode Tafel expression is used for iexpr.

esults and Discussion

igure 6 shows the local current density of the electrode reactions for a salt load of .5 g/m2 and various relative humidities. The cathodic currents reach a plateau close x=0 at a magnitude that is significantly affected by the relative humidity. This is due a changing limiting current density for oxygen reduction. As the film thickness

rows, the electrolyte transport length for oxygen increases, in combination with an creased oxygen solubility and diffusivity for higher relative humidities.

igure 6: Local current densities along the metal surface at a salt loading of 0.5 g/m2 and lative humidities (RH) spanning from 80 to 98 %.


Figure 7 shows the maximum anodic currents for various salt load densities and relative humidities. For all salt loads, a maximum current density is seen around a relative humidity of 90 %.

Fim

Loxbu


gure 7: Maximum metal oxidation anodic current density on the aluminum alloy etal surface for varied relative humidities and salt load densities (LD).

ooking at the maximum cathodic currents in Figure 8, it is seen that the maximum ygen currents are about one order of magnitude smaller than the anodic currents, t that they follow the same trend with a maximum around a relative humidity of


8 | A T M O S P H E

90 %. These currents are very close to the limiting current densities for oxygen reduction.

Ffo

Fthdh


igure 8: Maximum oxygen reduction cathodic current densities on the steel metal surface r varied relative humidities and salt load densities (LD).

inally, Figure 9 shows the average anode current density, which gives us a measure of e total corrosion rate of the sample, for various relative humidities and salt load

ensities. The maximum is found for a salt load density of 3.5 g/m2 and a relative umidity of 95 %.


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gure 9: Average current densities on the aluminum alloy metal surface for varied lative humidities and salt load densities (LD).

otes About the COMSOL Implementation

he model is implemented using the Secondary Current Distribution interface with o Parametric Sweeps to study the impact of a range of different relative humidities d salt load densities.

eferences

Z.Y. Chen, F. Cui, and R.G. Kelly, Calculations of the Cathodic Current Delivery apacity and Stability of Crevice Corrosion under Atmospheric Environments, J. lectrochemical Society, vol. 155, no. 7, pp. C360368, 2008.

D. Mizuno and R.G. Kelly Galvanically Induced Interganular Corrosion of A5083-H131 Under Atmospheric Exposure Conditions - Part II - Modeling of the amage Distribution, Corrosion, vol. 69, no. 6, pp. 580592, 2013.


10 | A T M O S P H

3. D. Mizuno, Y. Shi, and R.G. Kelly, Modeling of Galvanic Interactions between AA5083 and Steel under Atmospheric Conditions, Excerpt from the Proceedings of the 2011 COMSOL Conference in Boston.

Application Library path: Corrosion_Module/Galvanic_Corrosion/atmospheric_corrosion

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O D E L W I Z A R D

In the Model Wizard window, click 2D.

In the Select physics tree, select Electrochemistry>Secondary Current Distribution (siec).

Click Add.

Click Study.

In the Select study tree, select Preset Studies>Stationary.

Click Done.



Load the model parameters from a text file.



Browse to the applications Application Library folder and double-click the file atmospheric_corrosion_parameters.txt.


G E O M E T R Y 1

Draw the geometry as two adjacent rectangles, each 12 mm wide. The height of the rectangles represents the film thickness. It depends both on the salt load density and the relative humidity, which both will be varied by the parametric sweeps in the Study.

Rectangle 1 (r1)1 On the Geometry toolbar, click Primitives and choose Rectangle.

2 In the Settings window for Rectangle, locate the Size section.

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In the Width text field, type 12[mm].

In the Height text field, type d_film.

Locate the Position section. In the x text field, type -12[mm].

ectangle 2 (r2)Right-click Component 1 (comp1)>Geometry 1>Rectangle 1 (r1) and choose Duplicate.

In the Settings window for Rectangle, locate the Position section.

In the x text field, type 0.

Click the Build All Objects button.

he electrolyte film is much thinner than the geometry width, making it hard to make lections in the actual 2D geometry. Create a user-defined View to view the geometry ing an aspect ratio that corresponds to the graphics window rather than the true ometrical aspect ratio.

E F I N I T I O N S

In the Model Builder window, expand the Component 1 (comp1)>Definitions node.

Right-click Definitions and choose View.

xisIn the Model Builder window, expand the View 2 node, then click Axis.

In the Settings window for Axis, locate the Axis section.

From the View scale list, choose Automatic.


ow create some average and maximum operators. These will be used later on when st-processing the simulation results.

verage 1 (aveop1)On the Definitions toolbar, click Component Couplings and choose Average.

In the Settings window for Average, locate the Source Selection section.


12 | A T M O S P H

3 From the Geometric entity level list, choose Boundary.

4 Select Boundary 2 only.

Maximum 1 (maxop1)1 On the Definitions toolbar, click Component Couplings and choose Maximum.

2 In the Settings window for Maximum, locate the Source Selection section.

3 From the Geometric entity level list, choose Boundary.

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Select Boundary 2 only.

aximum 2 (maxop2)Right-click Component 1 (comp1)>Definitions>Maximum 1 (maxop1) and choose Duplicate.

In the Settings window for Maximum, locate the Source Selection section.

Click Clear Selection.


E C O N D A R Y C U R R E N T D I S T R I B U T I O N ( S I E C )

lectrolyte 1ow start defining the physics. Start with the electrolyte conductivity.

In the Model Builder window, under Component 1 (comp1)>Secondary Current Distribution (siec) click Electrolyte 1.


From the l list, choose User defined. In the associated text field, type sigma.

se Electrolyte-Electrode Boundary Interface nodes to set up the electrode reactions r the two metallic surfaces.

lectrolyte-Electrode Boundary Interface 1On the Physics toolbar, click Boundaries and choose Electrolyte-Electrode Boundary Interface.


lectrode Reaction 1In the Model Builder window, expand the Electrolyte-Electrode Boundary Interface 1 node, then click Electrode Reaction 1.

In the Settings window for Electrode Reaction, locate the Equilibrium Potential section.


3 In the Eeq text field, type Eeq_Al.

4 Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Butler-Volmer.

5 In the i0 text field, type i0_Al.

6 In the a text field, type alphaa_Al.

7 In the c text field, type alphac_Al.

E1

2

E1

2

3

4

5

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7

8

AT

In1

2

3

4

In1




lectrode Reaction 1In the Model Builder window, expand the Electrolyte-Electrode Boundary Interface 2 node, then click Electrode Reaction 1.


In the Eeq text field, type Eeq_Fe.



In the Ac text field, type Ac_Fe.

Select the Limiting current density check box.

In the ilim text field, type ilim.

dd an Initial Values node in order to define different initial values in the two domains. his will shorten the number of iterative steps taken by the solver.

itial Values 2On the Physics toolbar, click Domains and choose Initial Values.

Select Domain 2 only.

In the Settings window for Initial Values, locate the Initial Values section.

In the phil text field, type -Eeq_Fe.

itial Values 1In the Model Builder window, under Component 1 (comp1)>Secondary Current Distribution (siec) click Initial Values 1.


14 | A T M O S P H


3 In the phil text field, type -Eeq_Al.

M E S H 1

Use a mapped mesh for this problem. Since the electrolyte film is very thin we do not expect significant potential drops in the y-direction. Use a mesh with a single element in the y-direction.

MInM

D1

2

3

4

D1

2

3

4

5

6

D1

2

3

4

5


apped 1 the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose apped.

istribution 1In the Model Builder window, under Component 1 (comp1)>Mesh 1 right-click Mapped 1 and choose Distribution.

Select Boundaries 1, 4, and 7 only.

In the Settings window for Distribution, locate the Distribution section.

In the Number of elements text field, type 1.

istribution 2Right-click Mapped 1 and choose Distribution.

Select Boundaries 2 and 3 only.

In the Settings window for Distribution, locate the Distribution section.

From the Distribution properties list, choose Predefined distribution type.

In the Number of elements text field, type 50.

In the Element ratio text field, type 10.

istribution 3Right-click Component 1 (comp1)>Mesh 1>Mapped 1>Distribution 2 and choose Duplicate.

In the Settings window for Distribution, locate the Boundary Selection section.

Click Clear Selection.


Locate the Distribution section. Select the Reverse direction check box.


6 Click the Build All button.

Your finished mesh should now look like this:

S

Tcu

Pa1

2

3

4

5

6

P

L


T U D Y 1

he problem is now ready for solving. Use a Parametric Sweep to study the corrosion rrents for a range of different relative humidities and salt load densities.

rametric SweepOn the Study toolbar, click Parametric Sweep.

In the Settings window for Parametric Sweep, locate the Study Settings section.

From the Sweep type list, choose All combinations.

Click Add.


Click Add.

arameter name Parameter value list Parameter unit

D 0.0005 0.001 0.002 0.0035 0.007[kg/m^2]


16 | A T M O S P H


Decrease the solver tolerance to improve the accuracy of the solutions.

Solution 11 On the Study toolbar, click Show Default Solver.

2

3

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5

R

ER

11

2

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11

Parameter name Parameter value list Parameter unit

RH range(0.8,0.03,0.98)


In the Model Builder window, expand the Solution 1 node, then click Stationary Solver 1.

In the Settings window for Stationary Solver, locate the General section.

In the Relative tolerance text field, type 0.00001.

On the Study toolbar, click Compute.

E S U L T S

lectrolyte Potential (siec)eproduce the plots from the Results and Discussion section in the following way:


On the 1D Plot Group 2 toolbar, click Line Graph.

In the Settings window for Line Graph, locate the Data section.

From the Data set list, choose Study 1/Parametric Solutions 1.

From the Parameter selection (LD) list, choose First.


Click Replace Expression in the upper-right corner of the y-axis data section. From the menu, choose Model>Component 1>Secondary Current Distribution>Electrode kinetics>siec.iloc_er1 - Local current density.

Locate the x-Axis Data section. From the Parameter list, choose Expression.

In the Expression text field, type x.


On the 1D Plot Group 2 toolbar, click Plot.



2 In the Settings window for 1D Plot Group, locate the Data section.

3 From the Data set list, choose Study 1/Parametric Solutions 1.

4 On the 1D Plot Group 3 toolbar, click Global.

5 In the Settings window for Global, locate the y-Axis Data section.


7

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11

2

3

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5

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Expression Unit Description

m

E

m


In the Model Builder window, click 1D Plot Group 3.

In the Settings window for 1D Plot Group, click to expand the Title section.

From the Title type list, choose Manual.

In the Title text area, type Maximum Anode Current Density.

Locate the Plot Settings section. Select the x-axis label check box.

In the associated text field, type Relative Humidity (1).

Select the y-axis label check box.

In the associated text field, type Current Density (A/m2).

Click to expand the Legend section. From the Position list, choose Upper left.


D Plot Group 4Right-click 1D Plot Group 3 and choose Duplicate.

In the Model Builder window, expand the 1D Plot Group 4 node, then click Global 1.

In the Settings window for Global, locate the y-Axis Data section.



In the Settings window for 1D Plot Group, locate the Title section.

In the Title text area, type Maximum Cathode Current Density.


axop1(siec.iloc_er1) A/m^2

xpression Unit Description

axop2(-siec.iloc_er1) A/m^2


18 | A T M O S P H

1D Plot Group 51 In the Model Builder window, under Results right-click 1D Plot Group 3 and choose

Duplicate.

2 In the Model Builder window, expand the 1D Plot Group 5 node, then click Global 1.

3 In the Settings window for Global, locate the y-Axis Data section.


5

6

7

8

E

a



In the Settings window for 1D Plot Group, locate the Title section.

In the Title text area, type Average Anode Current Density.


xpression Unit Description

veop1(siec.iloc_er1) A/m^2


C a t h od i c P r o t e c t i o n o f S t e e l i n R e i n f o r c e d Con c r e t e

Introduction

Cathodic protection (CP) is a common strategy for retarding the corrosion of reofun

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inforcing steel in concrete structures, such as bridges and parking garages. By the use CP the potential of the corroding surface is lowered, thereby decreasing the rate of desired anodic corrosion reaction.

his example models the cathodic protection of a steel reinforcing bar (rebar) in ncrete. The corrosion cell consists of a zinc anode, the concrete, acting as

ectrolyte, and the steel surface. Iron oxidation, water reduction (hydrogen olution) and oxygen reduction are considered on the steel surface, whereas oxygen d charge transport are accounted for in the concrete electrolyte.

he anode and the steel surface are connected electrically via a potentiostat that ntrols the cell voltage.

oncrete is a porous material, and an effect of this is that its transport properties for ns and gases vary with the moisture content. Therefore the electrolyte conductivity d oxygen diffusion coefficient are modeled to vary with the concrete pore saturation

vel using empirical data.

he corrosion rate for various moisture contents is investigated.

he model example is based on a paper by Muehlenkamp et al. (Ref. 1).

or a more detailed description for how to build this model, including screen shots, e the Introduction to the Corrosion Module.

odel Definition

E O M E T R Y

igure 1 shows the model geometry. The geometry modeled represents a two mensional cross section of a repeating unit cell in a larger structure where three mmetry planes (top, bottom and right) have been used in order to reduce the model ometry. The zinc anode has been coated onto the concrete by thermal spraying and

assumed to be permeable to air.


2 | C A T H O D I C

F

C

UTF

F

OS

Rebar cathode (steel)

Electrolyte (concrete)

Anode (zinc)

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igure 1: Model geometry. One electrolyte domain and two electrode surfaces.

O N C R E T E D O M A I N E Q U A T I O N S

se a Secondary Current Distribution interface to model the electrochemical currents. he electrolyte conductivity depends on the pore saturation level according to igure 2.

igure 2: Electrolyte conductivity (S/m) as function of the concrete pore saturation level.

xygen transport in the concrete domain is modeled using the Transport of Diluted pecies interface. The oxygen diffusivity depends on the pore saturation level


according to Figure 3.

Fi

B

Cthse

Seto

Cox


gure 3: Oxygen diffusivity (m2/s) in the concrete as function of pore saturation.

O U N D A R Y C O N D I T I O N S

hoose the electrical potential of the Zn anode as ground for the system. By assuming e kinetics of the Zn anode to be very fast the polarization is neglected in the model, tting the electrolyte potential to

t the concentration of oxygen at the Zn anode to atmospheric conditions according

onsider three different electrode reactions on the steel rebar boundary: iron idation, oxygen reduction, and hydrogen evolution:

l Zn, Eeq Zn, s Zn,+ Eeq Zn,= =

cO2 Zn, cO2 ref,=

Fe Fe2+ 2e-+

O2 2H2O 4e-

+ + 4OH-

2H2O 2e-

+ H2 2OH-

+


4 | C A T H O D I C

Model the reaction kinetics for these reactions with an Electrolyte-Electrode Boundary Interface node in the Secondary Current Distribution interface, on which the external electric potential of the steel bar, , is set to the applied cell potential of -1 V.

The electrode kinetics of the steel bar reactions are described by Tafel expressions according to

uca

TFth

A

I N

Sat

U

TA

P

E

E

T

s steel,

iFe i0 Fe, 10

FeAFe--------

=


sing the parameters shown in Table 1, where the overpotential for each reaction is lculated as

he oxygen reduction reaction causes a flux of oxygen at the steel surface according to aradays law. Model this using an Electrolyte-Electrode Interface Coupling node in e Transport of Diluted Species interface.

pply Symmetry conditions on all other boundaries.

I T I A L V A L U E S

et the electrolyte potential initial value to the same value as in the boundary condition the Zn anode.

se atmospheric concentration as initial value for the oxygen concentration variable.

BLE 1: ELECTRODE REACTION PARAMETERS

ARAMETER UNIT Zn Fe O2 H2

quilibrium potential, Eeq V -0.68 -0.76 0.189 -1.03

xchange current density, i0 A/m2 - 7.110-5 7.710-7 1.110-2

afel slope, A V/decade - 0.41 -0.18 -0.15

iO2cO2

cO2 ref,----------------i0 O2, 10

O2AO2---------

=

iH2 i 0 H2, 10

H2AH2---------

=

s steel, l Eeq=


S T U D Y

Solve the model using a parametric sweep over a stationary study step, solving for a range of pore saturation values from 0.2 to 0.8.

Results and Discussion

Figure 4 shows the electrolyte potential for a pore saturation level of 0.8. The electrolyte potentials is lower towards the back (the right side) of the rebar.

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gure 4: Electrolyte potential for a pore saturation (moisture) level of 0.8.

igure 5 shows the oxygen concentration in the electrolyte for a pore saturation level 0.8. The concentration is very low close to the rebar, indicating that the oxygen duction kinetics should be mass transport limited for this pore saturation level. The ncentration is lower towards the back of the rebar.


6 | C A T H O D I C

F

Apapel


igure 5: Oxygen concentration for a pore saturation (moisture) level of 0.8.

n important factor for the corrosion rate of the rebar is the operating electrode otential, which is the difference between the electric potential (here the potential plied by the potentiostat) and the electrolyte potential. Figure 6 shows the operating ectrode potential for various pore saturation levels for three different points (front,


middle and back) of the rebar surface. The potential drops considerably at a pore saturation level of 0.65.

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Fle


gure 6: Operating electrode potential for three points at the rebar-concrete interface.

igure 7 shows the local oxygen concentration at the rebar for various pore saturation vels. The concentration drops significantly towards higher saturation levels. This is


8 | C A T H O D I C

an effect of the decreasing diffusivity of oxygen in the concrete for higher saturation levels.

F

Tmle


igure 7: Local oxygen concentration at the rebar-concrete interface.

he local oxygen reduction current densities at the rebar are shown in Figure 8. The agnitude of the oxygen reduction current density is highest around a pore saturation vel of 0.6 0.65. Up to this point the current densities are increasing due to


increased electrolyte conductivity, but for higher pore saturation levels the current densities decrease due to decreased oxygen diffusivity.

Fi

Tiselev


gure 8: Local oxygen reduction current densities at the rebar-concrete interface.

he hydrogen evolution current densities are shown in Figure 9. Hydrogen evolution very limited below a PS level of 0.65, which is the saturation level at which the ectrode potential gets below the equilibrium potential (1.03 V) for the hydrogen olution reaction, see Figure 6.


10 | C A T H O D I

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igure 9: Local hydrogen evolution current densities at the rebar-concrete interface.

inally, the iron oxidation current densities are shown in Figure 10. Corrosion current ensities are higher for low PS levels, which is in line with the higher electrode otential for low PS levels (Figure 6). It should be noted that the magnitude of iron xidation current density is considerably smaller than oxygen reduction and hydrogen olution current densities at the steel rebar indicating the effectiveness of zinc coating

nto the concrete in protecting the steel rebar from corrosion.


Fi

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1.SpC

Aca

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N

1


gure 10: Iron corrosion current densities at the rebar-concrete interface.

eference

E.B. Muehlenkamp, M.D. Koretsky, and J.C. Westall, Effect of Moisture on the atial Uniformity of Cathodic Protection of Steel in Reinforced Concrete,

orrosion, vol. 61, no. 6, pp. 519533, 2012.

pplication Library path: Corrosion_Module/Cathodic_Protection/thodic_protection_in_concrete



E W



12 | C A T H O D I



2 In the Select physics tree, select Electrochemistry>Secondary Current Distribution (siec).

3 Click Add.

4 In the Select physics tree, select Chemical Species Transport>Transport of Diluted Species (tds).

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8

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L

Pa1

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Cas

In1

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Click Add.

Click Study.

In the Select study tree, select Preset Studies for Selected Physics Interfaces>Stationary.

Click Done.


oad the model parameters from a text file.




Browse to the applications Application Library folder and double-click the file cathodic_protection_in_concrete_parameters.txt.

E F I N I T I O N S

reate interpolation functions for the electrolyte conductivity and oxygen diffusivity functions of the pore saturation level. Load the data from text files.

terpolation 1 (int1)On the Home toolbar, click Functions and choose Local>Interpolation.

In the Settings window for Interpolation, locate the Definition section.

From the Data source list, choose File.

Click Browse.

Browse to the applications Application Library folder and double-click the file cathodic_protection_in_concrete_sigma.txt.

Click Import.

In the Function name text field, type sigma.


8 Locate the Units section. In the Function text field, type S/m.

9 Click the Plot button.

The plot should look like Figure 2.

Interpolation 2 (int2)1 On the Home toolbar, click Functions and choose Local>Interpolation.

2 In the Settings window for Interpolation, locate the Definition section.

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From the Data source list, choose File.

Click Browse.

Browse to the applications Application Library folder and double-click the file cathodic_protection_in_concrete_D_O2.txt.

Click Import.

In the Function name text field, type D_O2.

Locate the Units section. In the Function text field, type m^2/s.

Click the Plot button.

The plot should look like Figure 3.

E O M E T R Y 1

ow create the geometry by using a rectangle and a circle.

ectangle 1 (r1)On the Geometry toolbar, click Primitives and choose Rectangle.

In the Settings window for Rectangle, locate the Size section.

In the Width text field, type W.

In the Height text field, type L.

Right-click Component 1 (comp1)>Geometry 1>Rectangle 1 (r1) and choose Build Selected.


ircle 1 (c1)On the Geometry toolbar, click Primitives and choose Circle.

In the Settings window for Circle, locate the Size and Shape section.

In the Radius text field, type R_rebar.

Locate the Position section. In the x text field, type S+R_rebar.

In the y text field, type L.


14 | C A T H O D I

6 Right-click Component 1 (comp1)>Geometry 1>Circle 1 (c1) and choose Build Selected.

Difference 1 (dif1)1 On the Geometry toolbar, click Booleans and Partitions and choose Difference.

2 Select the object r1 only.

3 In the Settings window for Difference, locate the Difference section.

4 Find the Objects to subtract subsection. Select the Active toggle button.

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EN

1

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E1

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To


Select the object c1 only.

On the Geometry toolbar, click Build All.

E C O N D A R Y C U R R E N T D I S T R I B U T I O N ( S I E C )

lectrolyte 1ow set up the physics for the current distribution. Start with the electrolyte settings.

In the Model Builder window, expand the Component 1 (comp1)>Secondary Current Distribution (siec) node, then click Electrolyte 1.


From the l list, choose User defined. In the associated text field, type sigma(PS).

lectrolyte Potential 1On the Physics toolbar, click Boundaries and choose Electrolyte Potential.


In the Settings window for Electrolyte Potential, locate the Electrolyte Potential section.

In the l,bnd text field, type -Eeq_Zn.



In the Settings window for Electrolyte-Electrode Boundary Interface, locate the Boundary Condition section.

In the s,ext text field, type E_app.hree different reactions occur at this electrode surface: oxygen reduction, iron xidation and hydrogen evolution.


Electrode Reaction 11 In the Model Builder window, expand the Electrolyte-Electrode Boundary Interface 1

node.

2 Right-click Electrode Reaction 1 and choose Rename.

3 In the Rename Electrode Reaction dialog box, type Oxygen reduction in the New label text field.

4 Click OK.

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In the Eeq text field, type Eeq_O2.


In the i0 text field, type c/C_O2_ref*i0_O2.

The exchange current density depends on the oxygen concentration, which is solved for in the Transport of Diluted Species interface.

In the Ac text field, type A_O2.


In the Model Builder window, under Component 1 (comp1)>Secondary Current Distribution (siec)>Electrolyte-Electrode Boundary Interface 1 right-click Electrode Reaction 2 and choose Rename.

In the Rename Electrode Reaction dialog box, type Iron oxidation in the New label text field.

Click OK.


In the Eeq text field, type Eeq_Fe.



In the Aa text field, type A_Fe.



16 | C A T H O D I

2 In the Model Builder window, under Component 1 (comp1)>Secondary Current Distribution (siec)>Electrolyte-Electrode Boundary Interface 1 right-click Electrode Reaction 3 and choose Rename.

3 In the Rename Electrode Reaction dialog box, type Hydrogen evolution in the New label text field.

4 Click OK.

5 In the Settings window for Electrode Reaction, locate the Equilibrium Potential

6

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9

InCel

1

2

T

Cth

1

2

Tr1

2

3

Tco


section.

In the Eeq text field, type Eeq_H2.


In the i0 text field, type i0_H2.

In the Ac text field, type A_H2.

itial Values 1omplete the current distribution model by specifying the initial value for the ectrolyte potential.


In the phil text field, type -Eeq_Zn.

R A N S P O R T O F D I L U T E D S P E C I E S ( T D S )

ontinue by setting up the model for the oxygen transport in the concrete. Start with e domain transport properties.

In the Settings window for Transport of Diluted Species, locate the Transport Mechanisms section.

Clear the Convection check box.

ansport Properties 1In the Model Builder window, expand the Transport of Diluted Species (tds) node, then click Transport Properties 1.

In the Settings window for Transport Properties, locate the Diffusion section.

In the Dc text field, type D_O2(PS).

he concrete is in contact with air at the left, and the concentration is therefore nstant at this boundary.


Concentration 11 On the Physics toolbar, click Boundaries and choose Concentration.

2 Select Boundary 1 only.

3 In the Settings window for Concentration, locate the Concentration section.

4 Select the Species c check box.

5 In the c0,c text field, type C_O2_ref.

Couple the flux of oxygen to the oxygen reduction current at the electrode surface.

E1

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StSe


lectrode-Electrolyte Interface Coupling 1On the Physics toolbar, click Boundaries and choose Electrode-Electrolyte Interface Coupling.


eaction Coefficients 1In the Model Builder window, expand the Electrode-Electrolyte Interface Coupling 1 node, then click Reaction Coefficients 1.

In the Settings window for Reaction Coefficients, locate the Model Inputs section.

From the iloc list, choose Local current density (siec/eebii1/er1).


In the c text field, type -1.

itial Values 1In the Model Builder window, under Component 1 (comp1)>Transport of Diluted Species (tds) click Initial Values 1.


In the c text field, type C_O2_ref.

E S H 1

se the physics-controlled mesh settings, with an extra fine mesh size.

In the Model Builder window, under Component 1 (comp1) click Mesh 1.

In the Settings window for Mesh, locate the Mesh Settings section.

From the Element size list, choose Extra fine.

T U D Y 1

ep 1: Stationaryt up an auxiliary continuation sweep for the 'PS' parameter.


18 | C A T H O D I

1 In the Model Builder window, under Study 1 click Step 1: Stationary.

2 In the Settings window for Stationary, click to expand the Study extensions section.

3 Locate the Study Extensions section. Select the Auxiliary sweep check box.

4 Click Add.


6

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ETfr

11

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Parameter name Parameter value list Parameter unit

P

L

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B


On the Home toolbar, click Compute.

E S U L T S

lectrolyte Potential (siec)he model is now solved. Follow the remaining steps below to reproduce the plots om the Results and Discussion section.


On the 1D Plot Group 3 toolbar, click Point Graph.

Select Points 35 only.

In the Settings window for Point Graph, locate the y-Axis Data section.

In the Expression text field, type E_app-phil.


From the Legends list, choose Manual.


In the Model Builder window, right-click 1D Plot Group 3 and choose Rename.

In the Rename 1D Plot Group dialog box, type Rebar electrode-electrolyte potential in the New label text field.

Click OK.

S range(0.2, 0.05, 0.8)

egends

ront

iddle

ack


Rebar electrode-electrolyte potential 11 Right-click Rebar electrode-electrolyte potential and choose Duplicate.

2 In the Model Builder window, under Results right-click Rebar electrode-electrolyte potential 1 and choose Rename.

3 In the Rename 1D Plot Group dialog box, type Oxygen concentration in the New label text field.

4 Click OK.

O1

2

O1

2

3

4

O1

2

O1

2

3

4


xygen concentrationIn the Model Builder window, expand the Results>Oxygen concentration node, then click Point Graph 1.

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 Model>Component 1>Transport of Diluted Species>c - Concentration.

xygen concentration 1In the Model Builder window, right-click Oxygen concentration and choose Duplicate.

Right-click Oxygen concentration 1 and choose Rename.

In the Rename 1D Plot Group dialog box, type Oxygen reduction currents in the New label text field.

Click OK.

xygen reduction currentsIn the Model Builder window, expand the Results>Oxygen reduction currents node, then click Point Graph 1.

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 Model>Component 1>Secondary Current Distribution>Electrode kinetics>siec.iloc_er1 - Local current

density.

xygen reduction currents 1In the Model Builder window, right-click Oxygen reduction currents and choose Duplicate.

Right-click Oxygen reduction currents 1 and choose Rename.

In the Rename 1D Plot Group dialog box, type Iron oxidation currents in the New label text field.

Click OK.


20 | C A T H O D I

Iron oxidation currents1 In the Model Builder window, expand the Results>Iron oxidation currents node, then

click Point Graph 1.

2 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 Model>Component 1>Secondary Current Distribution>Electrode kinetics>siec.iloc_er2 - Local current

density.

3

Ir1

2

3

4

H1

2

3


On the Iron oxidation currents toolbar, click Plot.

on oxidation currents 1In the Model Builder window, right-click Iron oxidation currents and choose Duplicate.

Right-click Iron oxidation currents 1 and choose Rename.

In the Rename 1D Plot Group dialog box, type Hydrogen evolution currents in the New label text field.

Click OK.

ydrogen evolution currentsIn the Model Builder window, expand the Results>Hydrogen evolution currents node, then click Point Graph 1.

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 Model>Component 1>Secondary Current Distribution>Electrode kinetics>siec.iloc_er3 - Local current

density.

On the Hydrogen evolution currents toolbar, click Plot.


Ca r bon D i o x i d e Co r r o s i o n i n S t e e l P i p e s

Introduction

A flow mixture of water and carbon dioxide passing through a steel pipe can cause sico

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gnificant steel corrosion. Properties such as pH and temperature affect the rate of the rrosion.

his model simulates the corrosion taking place on the steel surface of a pipe for rbulent flow of carbon dioxide and water. The model reproduces results by ordsveen et al. (Ref. 1) and Nesic et al. (Ref. 2).

odel Definition

he corrosion is investigated at an arbitrary position within a steel pipe through which turbulent flow of dissolved carbon dioxide in water passes. A 1D model is used. No riations along the length of the pipe are considered and the interaction of the ixture with the steel is confined to the boundary layer near the steel surface. The undary layer thickness is set to 0.001 mm. The model geometry and physical nsiderations are shown in Figure 1. The diffusion and turbulent sublayers vary and e accounted for with the mass transport parameters.

gure 1: Description of the boundary layer adjacent to the steel surface.

ll species are assumed to be diluted in water and the mass transport is modeled by ffusion. The Electroanalysis interface is used in the model. Carbon dioxide dration, water dissociation, three reduction reactions, and iron dissolution are counted for; resulting in seven species in the model. The species and diffusion

x

Boundary layer

Turbulent sublayer

BulkSteel

Diffusion sublayer


2 | C A R B O N D

coefficients are tabulated in Table 1

Tdan

Tthel

wT

Fcore

E

T

w

TABLE 1: MODELED SPECIES WITH THEIR RESPECTIVE DIFFUSION COEFFICIENTS.

SPECIES D (m2/s)109

CO2 1.96

H2CO3 2.00

HCO3- 1.11

CO32- 0.92

H

O

F

CorrosionApplicationLibraryManual.book Page 2 Monday, April 13, 2015 5:05 PMI O X I D E C O R R O S I O N I N S T E E L P I P E S

he turbulent sublayer is modeled by adding a turbulent diffusivity term to the iffusion coefficient. The term depends on the flow rate, viscosity, density of the liquid, d distance from the steel surface (Ref. 1).

he Electrode Surface boundary feature is used to calculate the corrosion potential at e steel surface using the mixed potential theory. The net total current of all ectrochemical reactions is set to zero, the equation that is solved is described by

(1)

here i (SI unit: A/m2) is the current density of j number of electrochemical reactions. he initial value is set to -0.5 V around the free corrosion potential (Ref. 2).

or the Electroanalysis interface the outer point of the boundary layer is set to the bulk ncentrations of the species. Fluxes of species converted in the electrochemical actions, ij/F (Faradays constant = 96485 C/mol), are applied on the steel surface.

Q U I L I B R I U M R E A C T I O N S

he following equilibrium reactions are present in the electrolyte:

here K1 through K4 are the equilibrium constants (Ref. 1).

+ 9.31

H- 5.26

e+ 0.72

ijj 0=

H2O(l) H+(aq) OH-(aq)+ K1 6.418 10

-15=

CO2 aq( ) H2O aq( )+ H2CO3(aq) K2 2.580 103

=

H2CO3(aq) H+(aq) HCO3

- (aq)+ K3 1.251 104

=

HCO3- (aq) H+(aq) CO+ 3

2-(aq) K4 1.382 10

-10=


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

wcoth

E

T

Ir

P

W

C

Tre

S

Tinco

Kk a ci( )vik

i=


here ci (SI unit: mol/m3) is the concentration of species i, vik the stoichiometric

efficient of species i in reaction k. The activity of a species, a(ci) is given by dividing e concentration with 1 M.

L E C T R O C H E M I C A L R E A C T I O N S

he following electrochemical reactions are present at the steel surface (Equation 1):

on dissolution

roton reduction

ater reduction

arbonic acid reduction

he current densities depend on mass transport limitations and charge transfer sistances as given in Ref. 2.

T U D Y S E T T I N G S

he problem is solved with an auxiliary sweep on a stationary solver in order to vestigate the impact of important parameters such as pH and temperature on rrosion.

Fe(s) Fe2+ 2e-+

H+ e- H+

H2O e-

+ H OH-+

H2CO3 e- H HCO3

-++


4 | C A R B O N D

Results and Discussion

Figure 2 displays the concentration deviation from the bulk of the seven species along the boundary layer at pH 6 and 20 C. 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 tu

Fbo

Fopoth


rbulent sublayer.

igure 2: Deviation in concentration of the species compared to the bulk along the liquid undary layer.

igure 3 shows the corrosion rate of the steel surface at three different pH for perating temperatures ranging from 20 C to 80 C. The corrosion rate is directly roportional to the corrosion current, that is, the iron dissolution current since no ther anodic reaction is considered. Lowered pH and increased temperature increases e rate of corrosion.


Fira

R

1.CF

2.ofn

Aco

M

F


gure 3: Corrosion rate in mm/year for pH 4, 5, and 6 and operating temperatures nge of 20 C-80 C.

eferences

M. Nordsveen, S. Nesic, R. Nyborg, and A. Stangeland, A Mechanistic Model for arbon Dioxide Corrosion of Mild Steel in the Presence of Protective Iron Carbonate ilms-Part 1: theory and Verification, Corrosion, vol. 59, no. 5, pp. 443455, 2003.

S. Nesic, J. Postlethwaite, and S. Olsen, An Electrochemical Model for Prediction Corrosion of Mild Steel in Aqueous Carbon Dioxide Solutions, Corrosion, vol. 52,

o. 4, pp. 280294, 1996.

pplication Library path: Corrosion_Module/Galvanic_Corrosion/2_corrosion




6 | C A R B O N D

N E W

1 In the New window, click Model Wizard.



2 In the Select physics tree, select Electrochemistry>Electroanalysis (elan).

3 Click Add.

4

5

6

7

8

G

T

In1

2

3

4

G

Pa1

c

c

c

c

c

c

c


In the Number of species text field, type 7.

In the Concentrations table, enter the following settings:

Click Study.

In the Select study tree, select Preset Studies>Stationary.

Click Done.

E O M E T R Y 1

he geometry consists of a single interval.

terval 1 (i1)On the Geometry toolbar, click Interval.

In the Settings window for Interval, locate the Interval section.

In the Right endpoint text field, type 100e-6.

Right-click Component 1 (comp1)>Geometry 1>Interval 1 (i1) and choose Build Selected.



Load the model parameters from a text file.

CO2

H2CO3

HCO3

CO3

H

OH

Fe


2 In the Settings window for Parameters, locate the Parameters section.

3 Click Load from File.

4 Browse to the applications Application Library folder and double-click the file co2_corrosion_parameters.txt.

D E F I N I T I O N S

Variables 11

2

3

4

E

Stdi

Tr1

2

3

4

5

6

7

8

9

InSe

1


In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.

Load the variables from a text file.

In the Settings window for Variables, locate the Variables section.


Browse to the applications Application Library folder and double-click the file co2_corrosion_variables.txt.

L E C T R O A N A L Y S I S ( E L A N )

art defining the physics. The turbulent contribution is accounted for with a turbulent ffusivity, Dt.

ansport Properties 1In the Model Builder window, under Component 1 (comp1)>Electroanalysis (elan) click Transport Properties 1.

In the Settings window for Transport Properties, locate the Diffusion section.

In the DcCO2 text field, type DCO2+Dt.

In the DcH2CO3 text field, type DH2CO3+Dt.

In the DcHCO3 text field, type DHCO3+Dt.

In the DcCO3 text field, type DCO3+Dt.

In the DcH text field, type DH+Dt.

In the DcOH text field, type DOH+Dt.

In the DcFe text field, type DFe+Dt.

itial Values 1t the initial values to the concentration of the species in the bulk.

In the Model Builder window, under Component 1 (comp1)>Electroanalysis (elan) click Initial Values 1.


8 | C A R B O N D


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

Sac

E1

2

3

4

5

6

E1

2

3

4

5

6

7

8

E1


In the cFe text field, type cFe0.

et the net total current of all the electrochemical reactions to zero. Also, set fluxes cording to the electrochemical reactions at the steel surface.

lectrode Surface 1On the Physics toolbar, click Boundaries and choose Electrode Surface.


In the Settings window for Electrode Surface, locate the Boundary Condition section.

From the Boundary condition list, choose Total current.

In the Il,total text field, type 0.

In the s,ext text field, type -0.5.

lectrode Reaction 1In the Model Builder window, expand the Electrode Surface 1 node, then click Electrode Reaction 1.


In the Eeq text field, type Erev_Fe.



In the Aa text field, type b_Fe.


In the cFe text field, type -1.



2 In the Settings window for Electrode Reaction, locate the Equilibrium Potential section.

3 In the Eeq text field, type Erev_H2CO3.

4 Locate the Electrode Kinetics section. From the Kinetics expression type list, choose Cathodic Tafel equation.

5 In the i0 text field, type i0_H2CO3.

6 In the Ac text field, type -b_H2CO3.

7

8

9

10

E1

2

3

4

5

6

7

8

9

E1

2

3

4

5

6

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Corrosion Application Library Manual

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