Finite Element Analysis of Galvanic Corrosion of Metals in a Seawater
Environment
by
Megan Elizabeth Turner
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December 2012
© Copyright 2012
by
Megan Turner
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ........................................................................................................ vi
GLOSSARY .................................................................................................................... vii
LIST OF KEYWORDS .................................................................................................. viii
ACKNOWLEDGMENT .................................................................................................. ix
ABSTRACT ...................................................................................................................... x
1. Introduction.................................................................................................................. 1
1.1
Background ........................................................................................................ 1
1.2
Problem Description........................................................................................... 1
1.3
Prior Work.......................................................................................................... 2
2. Methodology ................................................................................................................ 4
2.1
Theory [2]........................................................................................................... 4
2.2
Geometry and Boundary Conditions.................................................................. 4
3. Results and Discussion ................................................................................................ 7
3.1
3.2
COMSOL Model Validation .............................................................................. 7
3.1.1
Using a Linear Expression for Current Density ..................................... 7
3.1.2
Using an Exponential Expression for Current Density .......................... 9
COMSOL Solution for Axisymmetric System ................................................ 11
4. Conclusion ................................................................................................................. 12
5. References.................................................................................................................. 13
6. Appendix A................................................................................................................ 14
iii
LIST OF TABLES
Table 1: Input Data Used for Model Validation [3] ......................................................... 7
Table 2: Input Data Used for Experimental Model Validation [3] ................................. 10
iv
LIST OF FIGURES
Figure 1: Simple Coplanar Model Used for Initial Model Validation [3] ........................ 2
Figure 2: Marine Propulsion Unit Analyzed in Reference [6] Study ............................... 3
Figure 3: 2D Cartesian Geometry ..................................................................................... 5
Figure 4: 2D Axisymmetric Geometry ............................................................................. 5
Figure 5: COMSOL Results for Linear Current Density Distribution on the Electrode
Surfaces (Surface Plot) ...................................................................................................... 8
Figure 6: Results from Reference [3] ............................................................................... 8
Figure 7:
COMSOL Results for Exponential Current Density Distribution on the
Electrode Surfaces (Surface Plot) ...................................................................................... 9
Figure 8: Experimental System Used for Model Validation [3]..................................... 10
Figure 9:
Axisymmetric COMSOL Results for Exponential Current Density
Distribution on the Electrode Surfaces (Surface Plot) ..................................................... 11
Figure 10: COMSOL Results for Linear Current Density Distribution on the Electrode
Surfaces (Contour Plot, 20 lines) ..................................................................................... 14
Figure 11: COMSOL Results for Linear Current Density Distribution on the Electrode
Surfaces (Contour Plot, 9 lines) ....................................................................................... 14
Figure 12:
COMSOL Results for Exponential Current Density Distribution on the
Electrode Surfaces (Contour Plot, 20 lines) .................................................................... 15
Figure 13:
COMSOL Results for Exponential Current Density Distribution on the
Electrode Surfaces (Contour Plot, 9 lines) ...................................................................... 15
v
LIST OF SYMBOLS
𝑖
current density (Am-2)
𝑣
reaction rate
e-
electron
𝑘
rate constant
α
transfer coefficient (V)
ϕ
potential (V)
ϕ0
equilibrium potential (V)
η
overpotential (V)
𝑞
charge density
E
electric field intensity
σ
conductivity (S/m)
vi
GLOSSARY
Galvanic Corrosion –
“…the corrosion that occurs as a result of one metal being in contact with
another in a conducting environment” [2]
Anode –
The portion of a galvanic couple which sees either localized or general metal
dissolution [2]
Cathode –
The portion of a galvanic couple which generally undergoes oxygen reduction
(O2 + e- → O2-), or hydrogen evolution (2H+ + 2e- → H2), or both [2]
Electrolyte –
A solution capable of carrying/transferring charge
(Electrochemical) Potential –
Measure of the voltage in a system
vii
LIST OF KEYWORDS
Galvanic Corrosion
Seawater
COMSOL
viii
ACKNOWLEDGMENT
I would like to thank the Rensselaer faculty and staff for their commitment to educating
their students. I would especially like to thank Professor Gutierrez-Miravete for the
guidance he provided throughout this project.
ix
ABSTRACT
Corrosion is an ever-present problem in all different environments, particularly in
marine applications. The goal of this project is to develop a finite element model that
can be used with experimental data to characterize the corrosion of a galvanic couple in
an electrolyte. This project first addresses a simple system with coplanar electrodes.
The finite element model is developed using COMSOL Multiphysics through derivation
of equations describing corrosion thermodynamics and electrochemical kinetics. The
model is validated through replication of previously determined experimental results and
then applied to the study of some system configurations relevant to marine applications.
x
1. Introduction
1.1 Background
Corrosion is the breakdown of materials, namely metals, through electrochemical
reactions within their environment.
Corrosion is a consideration in virtually all
manufacturing applications. Each year, industries invest time and money into trying to
curtail the effects of corrosion.
Many different corrosion environments have been
studied and monitored to develop corrosion control methods [1].
There are different types of corrosion, including galvanic corrosion. Galvanic corrosion
is an electrochemical process that occurs when two dissimilar metals are in electrical
contact with one another, and are in a conducting environment known as an electrolyte
[2]. Galvanic corrosion is particularly prevalent in marine applications because seawater
acts as a naturally free flowing electrolyte.
1.2 Problem Description
The amount and rate of corrosion can be correlated to the electrochemical potential
distribution within a system. The goal of this project is to develop a finite element
model that can be used in conjunction with experimental data to characterize the
corrosion of a galvanic couple in an electrolyte. There are a number of factors that can
contribute to the amount of corrosion within a system from material factors (e.g.
geometry) to environmental factors (e.g. type of electrolyte present) [1]. To limit the
effects of all these factors, this project first utilized a simple model of coplanar
electrodes as shown in Figure 1. Utilizing a simple geometry allowed the initial focus to
be on development of the boundary conditions rather than generation of geometry
representing a specific system.
1
Figure 1: Simple Coplanar Model Used for Initial Model Validation [3]
1.3 Prior Work
There is a lot of past precedent of scientists taking an interest in corrosion, looking to
understand what causes it and what limits or accelerates the process. Numerous studies
have been conducted; some take a more global outlook as in Reference [4], whereas
some take a more focused approach as in Reference [5].
The study conducted in Reference [4] looked at many different galvanic couples
commonly used in seawater applications. The study focused on developing reasonable
models for systems experiencing varying periods of exposure. The studies were also
conducted under potentiostatic and potentiodynamic scenarios.
The potentiostatic
experiment allowed for analysis of the corrosion under the natural potentials of the
system. While the potentiodynamic experiment introduced potential to the electrodes to
analyze the impacts of changing the electrode potential on the corrosion.
Other studies sought to analyze corrosion for a specific system geometry and
environment. Generally these investigations look to develop methods to prevent or
minimize corrosion of that specific system. This is most commonly achieved through a
process known as cathodic protection. This process involved introducing an additional
part, known as a sacrificial anode, to the system. The sacrificial anode is generally
2
another piece of metal that is introduced into a system so that it will corrode prior to
other elements.
Reference [5] looked at developing a method to model cathodic
protection of a carbon steel pipe in seawater using one or two aluminum sacrificial
anodes. Reference [6] looked utilizing a sacrificial zinc anode to cathodically protect the
marine propulsion unit shown in Figure 2.
Figure 2: Marine Propulsion Unit Analyzed in Reference [6] Study
3
2. Methodology
2.1 Theory [2]
The potential distribution within a galvanic solution is fundamentally based on the
continuity equation for conservation of charge [2] in the electrolyte.
−∇. 𝑖 =
In a steady state system,
𝜕𝑞
𝜕𝑡
𝜕𝑞
𝜕𝑡
[1]
= 0 and ∇. 𝑖 = 0
The relationship between the electric field intensity and the electric potential is
𝐸 = −∇𝜙
[2]
𝑖 = 𝜎𝐸
[3]
and Ohm’s Law is
where σ is the conductivity of the electrolyte.
From the above, the continuity equation becomes
∇𝜎∇𝜙 = 0
[4]
and for uniform isotropic conductivity this yields
∇2 𝜙 = 0
[5]
which is Laplace’s Equation for the potential distribution within the electrolyte.
2.2 Geometry and Boundary Conditions
The model geometry must be representative of the system being analyzed and must be
subjected to appropriate boundary conditions.
There are generally three types of
boundary conditions that can be considered at electrodes: linear, logarithmic (Tafel) and
exponential (Butler-Volmer).
This project utilized the finite element program COMSOL Multiphysics to solve
Equation [5] for each system. The geometry was developed to represent the system
being modeled. During initial model and boundary condition development, simple 2D
geometries as shown in Figure 1 and Figure 8 were used. This initial coplanar model
4
was created using a 2D Cartesian geometry as shown in Figure 3. A 2D Axisymmetric
geometry was developed, as shown in Figure 4.
Figure 3: 2D Cartesian Geometry
Figure 4: 2D Axisymmetric Geometry
5
In accordance with Equation [1] at a steady state, it can be assumed that there is no
current flow normal to the insulating boundaries [3] because the charge within the
system cannot change. This allows for a “Zero Flux” boundary condition to be applied
to edges 1-2, 2-3, and 3-4, in Figure 3and Figure 4.
Edges 4-5 and 5-1 are the electrode surfaces. The electrode boundary conditions were
assigned by using a “Flux/Source” boundary condition for either a linear, logarithmic
(Tafel) or exponential (Butler-Volmer) relationship.
6
3. Results and Discussion
3.1 COMSOL Model Validation
The geometry that is used in the model reflects the configuration shown in Figure 1. The
input data that was used is shown in Table 1 [3].
Table 1: Input Data Used for Model Validation [3]
Property
Value
Units
αA anodic reaction of metal A
0.05
V
αB anodic reaction of metal B
0.05
V
βA cathodic reaction of metal A
0.05
V
βB cathodic reaction of metal B
0.05
V
C conductivity of the electrolyte
10
Ω-1m-1
𝑖0(𝐴) free current density of metal A
1
Am-2
𝑖0(𝐵) free current density of metal B
1
Am-2
a surface length of metal A
0.01
m
b surface length of metal B
0.01
m
w thickness of the electrolyte
0.01
m
EA free corrosion potential of metal A
0.5
V
EB free corrosion potential of metal B
-0.5
V
Tafel Parameters:
3.1.1
Using a Linear Expression for Current Density
Using linear approximations for the current densities at the electrode surfaces produced
the potential distribution shown in Figure 10.
The COMSOL results correlate
qualitatively well to the results in Reference [3], as shown in Figure 6. However, there
are discrepancies in the values for the potential within the system.
This linear
approximation is only appropriate when there is a very small overpotential in the system
(generally <0.01V), which is not applicable in this case. The linear approximation gives
7
produces conservative results for the potential distribution.
This system is more
appropriately represented by an exponential potential distribution within the electrolyte.
Figure 5: COMSOL Results for Linear Current Density Distribution on the Electrode Surfaces
(Surface Plot)
Figure 6: Results from Reference [3]
8
3.1.2
Using an Exponential Expression for Current Density
Using exponential approximations for the current densities at the electrode surfaces
produced the potential distribution shown in Figure 10.
Figure 7: COMSOL Results for Exponential Current Density Distribution on the Electrode
Surfaces (Surface Plot)
9
Figure 8: Experimental System Used for Model Validation [3]
Table 2: Input Data Used for Experimental Model Validation [3]
Property
Value
Units
αCu anodic reaction of Copper
0.001
V
αZn anodic reaction of Zinc
0.025
V
βA cathodic reaction of Copper
0.05
V
βB cathodic reaction of Zinc
0.05
V
0.42
Ω-1m-1
𝑖0(𝐶𝑢) free current density of Copper
1
Am-2
𝑖0(𝑍𝑛) free current density of Zinc
1
Am-2
0.0075
m
0.02
m
0.002 and 0.02
m
ECu free corrosion potential of Copper
-0.845
V
EZn free corrosion potential of Zinc
-0.985
V
Tafel Parameters:
C conductivity of HCl solution
a surface length of Copper
b surface length of Zinc
w thickness of the HCl solution
10
3.2 COMSOL Solution for Axisymmetric System
Figure 9: Axisymmetric COMSOL Results for Exponential Current Density Distribution on the
Electrode Surfaces (Surface Plot)
11
4. Conclusion
Summary of findings
Consistency with fundamentals
12
5. References
[1]
Zhang, X. G. (2011). Galvanic Corrosion. In Uhlig's Corrosion Handbook (Third
ed., pp. 123-143). John Wiley & Sons, Inc.
[2]
Oldfield, J. W. (1988). Electrochemical Theory of Galvanic Corrosion. In H. P.
Hack (Ed.), Galvanic Corrosion, ASTM STP 978 (pp. 5-22). Philadelphia, PA:
American Society for Testing and Materials.
[3]
Doig, P., & Flewitt, P. E. (1979). A Finite Difference Numerical Analysis of
Galvanic Corrosion for Semi-Infinite Linear Coplanar Electrodes. Journal of The
Electrochemical Society , 126 (12), 2057-2063.
[4]
Hack, H. P., & Scully, J. R. (1986). Galvanic Corrosion Prediction Using Longand Short-Term Polarization Curves. Corrosion , 42 (2), 79-90.
[5]
Yan, J. F., Pakalapati, S. N., Nguyen, T. V., & White, R. E. (1992).
Mathematical Modeling of Cathodic Protection Using the Boundary Element
Method with a Nonlinear Polarization Curve. J. Electromchem. Soc. , 139 (7),
1932-1936.
[6]
Astley, D. J. (1988). Use of the Microcomputer for Calculation of the
Distribution of Galvanic Corrosion and Cathodic Protection in Seawater
Systems. In H. P. Hack (Ed.), Galvanic Corrosion, ASTM STP 978 (pp. 53-78).
Philadelphia, PA: American Society of Testing and Materials.
13
6. Appendix A
Additional COMSOL Plots
Figure 10: COMSOL Results for Linear Current Density Distribution on the Electrode Surfaces
(Contour Plot, 20 lines)
Figure 11: COMSOL Results for Linear Current Density Distribution on the Electrode Surfaces
(Contour Plot, 9 lines)
14
Figure 12: COMSOL Results for Exponential Current Density Distribution on the Electrode
Surfaces (Contour Plot, 20 lines)
Figure 13: COMSOL Results for Exponential Current Density Distribution on the Electrode
Surfaces (Contour Plot, 9 lines)
15