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Copyright © 2012 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofComputational and Theoretical Nanoscience

Vol. 9, 1395–1398, 2012

Numerical Simulation of Transient Process forCorrosion Environment in Coating Crevice

with Cathodic Protection

W. H. Wang1�2�∗, Jun Yi1, Lin Chen2, and X. Y. Li21College of Safety Engineering, Chongqing University of Science and Technology,

Chongqing, 401331, P. R. China2Key Laboratory of Material Corrosion and Protection of Sichuan Colleges and Universities,

Sichuan Province, Zigong, 643000, P. R. China

Potential, current distributions, the chemical and electrochemical environment in crevice aresimulated by transient mathematical model for the system of coating crevices in NaCl solution withcathodic protection. The results indicated that the potential in crevice increases in positive direc-tion and the total current density decreases, pH value in crevice rises monotonously at first andthen reduces, but the chloride ion concentration decreases at first and then increases, oxygen con-centration of solution reduces gradually and then tends to uniformity and conductivity enhancesat first and then reduces with the increasing of crevice length. With the prolonging of polarizationtimes, the potential in crevice decreases in negative direction, the total current density tends touniformity; pH value in crevice rises and the chloride ion concentration decreases gradually, but oxy-gen concentration of solution reduces and conductivity enhances gradually. The comparing resultsbetween the theoretical and experimental data indicated that the mathematical model describedtransient process for corrosion environment with cathodic protection is feasible.

Keywords: Coating Holidays, Electrochemical, Cathodic Protection, Crevice Corrosion.

1. INTRODUCTION

Crevice corrosion refers to the localized corrosion occur-ring on a metallic material in contact with electrolyte in asmall and occluded space (that is, a crevice). Crevices arepresent almost everywhere in practical cases; they may beformed between metallic parts or between a non-metallicpart and a metallic part, or under debris on a metallic part.Crevice corrosion usually associated with a long incuba-tion period, in the breeding period, the speed of metaldissolution in the crevice is small, after the incubationperiod, the crevice corrosion was speeded up and lead topipe corrosion and failure.1–5 Therefore, it is importantthat the incubation period of crevice corrosion behaviorand model for preventing the failure of pipeline corrosion.At present, most crevice corrosion mathematical mod-els were focused mainly on the development process ofcrevice corrosion without potential, the crevice corrosionbehavior and theory with cathodic protection less and one-dimensional potential and current distribution model in

∗Author to whom correspondence should be addressed.

the gap under cathodic protection proposed by Fessler,Schwenk et al., as well as the two-dimensional steady-state model proposed by Chin etc.6–12 The study on crevicecorrosion under cathodic protection were mostly aboutthe distribution of current and potential, the descriptionof current and potential distribution by Laplace equationwere also more,13–15 but most of them were stable statemodel without considering the impact of time parame-ters on the corrosion. The present transient model remainsconcentrated in the nature and develop of crevice corro-sion without cathodic protection, but the current and poten-tial distribution in the gap which derived by mathematicsmodel with cathodic protection and transient mass transferis very limited.In this paper, a transient mathematical model for the

system of crevices with coatings in NaCl solution withcathodic protection was proposed, the effect on the envi-ronment in the crevice by different crevice potentialand different crevice geometry size were discussed, andcathodic protection can be prevented crevice corrosion wasproved correctly.

J. Comput. Theor. Nanosci. 2012, Vol. 9, No. 9 1546-1955/2012/9/1395/004 doi:10.1166/jctn.2012.2209 1395

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Numerical Simulation of Transient Process for Corrosion Environment in Coating Crevice with Cathodic Protection Wang et al.

2. THEORY MODEL AND METHOD

2.1. Crevice Physics Model

In order to simplify the model and solution, a number ofsimilar treatments were made when the physical modelwas set up. Rectangular plane crevice was studied objectbecause of the symmetry of coating peeled of, as well asthe uniformity of the material in the crevice. Commonly,the width of the crevice is small (� ≤ 1 mm), the ratio ofdepth of the crevice to the width is big (≥ 94). So onlythe particles concentration, the local potential and currentalong the one-dimensional depth direction (x-axis direc-tion) changes in the crevice were considered, and the start-ing point of crevice was set as x-axis origin (x = 0).Schematic drawing of crevice model structure was shownas Figure 1.

2.2. Assumption Conditions

In order to simplify the calculation and mathematicsequations, the physical and chemical conditions of thedilute solution were conducted some idealized assump-tions. Mainly including the followings:(1) Bulk solution is dilute NaCl solution, the creviceinside was filled with electrolyte solution, the gap out-side was saturated by the air, the temperature was 25 �C,atmospheric pressure was 101.3 kPa; For the bulk of thesolution was infinite in the cathodic protection process, theconcentration of ions were remained basically unchanged,when reaction happened in the crevice.(2) In the cathodic protection process, the metal anodicdissolution reaction was inhibited in the crevice; thecrevice solution was alkaline, so the chemical reactionsinside the crevice were mainly oxygen and hydrogenabsorption reaction:

O2+2H2O+4e→ 4OH− (1)

H2O+2e→ H2+2OH− (2)

(3) In the case of cathodic protection, electric-ion trans-fer and diffusion process were bonded to happen in thecrevice, for the crevice was thick, crevice solution wasconsidered in a state status, particles convection could beignored. Four particles in the crevice only OH−, Cl−, Na+

and O2 were considered in the condition.

Fig. 1. Schematic drawing of crevice model structure.

(4) Dilute solution used in the experiments meet theNewman electricity neutral theory.16

∑ziCi = 0 (3)

(5) Because of the ratio of the length to width is large, thepotential and concentration gradient along the direction ofcrevice thickness can be considered as zero, so only thecorrosion environment along the direction of the depth wasconsidered.(6) Only current which particles transfer bring was con-sidered, potential of metal with various points were equal.

2.3. Mass Conservation Equations

If the one-dimensional mass transfer was ignored, accord-ing to the dilute solution theory and assumptions of equalpotential in metal, transient mass conservation equationof the particle within the crevice can be expressed asfollows.17–20

�Ci

�t= zF

RTDiCi

(�Ci

�x

��

�x+Ci

�2�

�x2

)

+Di

�2Ci

�x2+ inet

nFA(4)

Where Ferrari constant F = 96500 C/mol, and zi wasCharge number, Ci was Molar concentration of particleswas potential, Di was Diffusion coefficient, Ri = inet/nF ,inet was current density of reactions within crevice. Ri waschemical reaction rate of i in the crevice; n was the num-ber of electron transfer.

2.4. Model and Boundary Conditions

Transient mass transfer conservation equation was appliedto the NaCl solution, for OH−, Cl−, Na+ and O2 four typesof particles, Partial Differential Equations were set up asfollowing.17–18

Where OH− (z1 =−1)

�C1

�t=−FD1

RT

(�C1

�x

�E

�x+C1

�2E

�x2

)+D1

�2C1

�2x+ iO

F(5)

Where Cl− �z2 =−1�

�C2

�t=−FD2

RT

(�C2

�x

�E

�x+C2

�2E

�x2

)+D2

�2C2

�2x(6)

Where Na+ �z3 = 1�

�C3

�t= FD3

RT

(�C3

�x

�E

�x+C3

�2E

�x2

)+D3

�2C3

�2x(7)

Where O2 (z4 = 0)

�CO

�t=DO

�2CO

�2x− iO

4F(8)

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Wang et al. Numerical Simulation of Transient Process for Corrosion Environment in Coating Crevice with Cathodic Protection

Table I. Parameters for simulated computing (T = 298 K, P = 101�3 kPa).

Parameter Value Parameter Value Parameter Value

Crevice width 0.30/0.45/0.60 mm [O] concen. 2�70×10−4 mol/L F 96500 C/molCrevice length 90 mm [O] diffu. coef.c 2.78×10−5 cm2/s R 8.314 J/mol ·kCP potentialsa −0.775/−0�925/−1�075 VSCE Na+ diffu. coef. 1.33×10−5 i0O 1.35×10−8 A/cm2

NaCl concen.b 0.006 mol/L Cl− diffu. coef. 2.01×10−5 �c 0.055pH 7.0 OH− diffu. coef. 5.23×10−5 EOe −0.585 VSCE

Notes: aCP stands for cathodic protection. bConcen. stands for concentration. cDiffu. coef. stands for diffusion coeffient.

0 100000 200000 300000 400000–0.9

–0.8

–0.7

–0.6

–0.5

–0.4

–0.3

–0.2

Pot

entia

l/V(v

s.S

CE

)

Time/(s)

TheoreticalO Experimental

Fig. 2. Distribution of potential in crevice bottom with different time(x = 90 mm).

0.00 0.02 0.04 0.06 0.08 0.10–1.10

–1.05

–1.00

–0.95

–0.90

–0.85

–0.80

–0.75

–0.70

Pot

entia

l / V

(vs.

SC

E)

Crevice length/(m)

TheoreticalO Experimental

Fig. 3. Distribution of theoretical and experimental potential in crevice(time= 80 h).

The four partials meet to Neutral electricity equation;it can be described by formula as follows:

−C1−C2+C3 = 0 (9)

The transient mathematical model equation groupof corrosion behavior within crevice under cathodic

Table II. Compared with theoretical and experimental results for corrosion parameters.

Cl− Oxygen ConductivitypH value (10−3 mol/L) (10−4 mol/L) (103 S/cm2�

CNaCl (mol/L) CP potential (vs. SCE) Time (h) A∗ B∗ A B A B A B

0.0232 −1�075 24 11.5 12.8 4.06 5.21 0.16 0.18 5.62 6.900.0232 −1�075 60 11.9 12.5 2.27 2.98 0.14 0.26 4.15 5.83

Notes: ∗(A= Theoretical; B = Experimental).

protection was composed by Eqs. (5)∼(9), and the bound-ary conditions were confirmed as follows:

�i� t = 0 Ci = Cbi

�i = 0123 0 ≤ x ≤ L� (10)

�ii� x = 0 Ci = Cbi

�i = 0123 E = E�x0�= ECP� (11)

�iii� x = L�Ci

�x= 0

�E

�x= 2�

L−x0+b

�i = 0123 t ≥ 0� (12)

3. RESULTS AND DISCUSSION

According to model equations and boundary conditions,the chemical and electrochemical parameters can be com-puted by Finite Difference Method (FDM) after equationswere be treated by dimensionless. In order to illustrate theaccuracy of the mathematical model, the model simulationresults were compared with the reality of and experimen-tal results. Simulating experimental system is the 20# steelcrevice corrosion experiments in 0.0232 mol/L NaCl solu-tion with cathodic protection, the main experimental con-ditions were as follows: bulk solution is the NaCl solutionwith T = 298 K, P = 101�3 kPa, the depth of crevice is90 mm, the opening size of crevice is 0.45 mm, cathodicprotection potential of crevice is −1�075 V (vs. SCE),experimental methods refers to Ref. [19].The related parameters, including the constants, bulk

concentration and the diffusion coefficient of parti-cles dissolved in NaCl solution, kinetic parameters, thecrevice geometry parameters, seam control potential ofthe oxidation-reduction reaction and hydrogen absorbingreaction on the metal/solution, need to enter to modelsystem in the process of solved the model equations. Theseparameters were listed in Table I.

J. Comput. Theor. Nanosci. 9, 1395–1398, 2012 1397

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Numerical Simulation of Transient Process for Corrosion Environment in Coating Crevice with Cathodic Protection Wang et al.

The measured and simulated potential in crevice bot-tom with time curve, distribution of potential with crevicelength showed in Figures 2 and 3, solution pH and conduc-tivity changes (Table II), it showed that experimental dataand simulation is good agreement with the calculation, soit can be verified that the model can simulate crevice cor-rosion behavior in the experimental conditions well.

4. CONCLUSIONS

According to the results of simulating for the mathematicmodel on transient process for corrosion environment incoating crevice with cathodic protection and experimentalresults, some conclusions can be derived as follows.(1) The mathematic model on transient process for corro-sion environment in coating crevice with cathodic protec-tion can be set up according to the properties of crevicecorrosion and electrochemical theory.(2) The distribution of chemical and electrochemicalparameters with time and depth of the crevice can be gotby finite deference method. Through compared simulationresults with experimental results, the mathematical modelcan forecast the corrosion behavior with that of cathodicprotection, and also explains cathodic protection is feasi-ble for crevice corrosion.

Acknowledgments: This work was supported by theNatrual Science Foundation of Chongqing Science andTechnology Commission (CSTC, 2010BB5283), the Open

Research Fund of Key Laboratory of Material Corro-sion and Protection of Sichuan Colleges and Universities(2010CL02) and the Fund of Chongqing University ofScience and Technology (CK2010B17).

References

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(1993).5. V. Ashworth and C. J. L. Booker, Cathodic Protection: Theory

and Practice, Ellis Horwood Limited, England (1986), Chap. 2,pp. 31–35.

6. R. R. Fessler, A. J. Markworth, and R. N. Parkins, Corrosion 39, 20(1983).

7. D. T. Chin and G. M. Sabde, Corrosion 55, 229 (1999).8. W. Schwenk, Corros. Sci. 23, 871 (1983).9. F. Gan, Z. W. Sun, and G. Sabde, Corrosion 50, 804 (1994).10. T. Kamimura and H. Kishikawa, Corrosion 54, 979 (1998).11. F. M. Song, D. A. Jones, and D. W. Kirk, Corrosion 61, 145 (2005).12. F. M. Song, D. W. Kirk, and D. E. Cormack, Mater. Performance

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(1993).14. F. M. Song, D. W. Kirk, and J. W. Gray, Corrosion 59, 42 (2003).15. J. S. Newman, Electrochemical System, Englewood Cliffs, Prentice-

Hall Inc., NJ (1973).16. J. C. Walton, Corros. Sci. 30, 915 (1990).17. S. M. Sharland, Corros. Sci. 33, 183 (1992).18. R. Brousseau and S. Qian, Corrosion 50, 907 (1994).19. Z. F. Li, F. X. Gan, and X. H. Mao, Corros. Sci. 44, 689 (2002).

Received: 17 August 2010. Accepted: 16 October 2010.

1398 J. Comput. Theor. Nanosci. 9, 1395–1398, 2012