The Mechanism of Alternating CurrentCorrosion of API Grade X65 Pipeline Steel
E. Ghanbari,* M. Iannuzzi,** and R.S. Lillard‡,*
ABSTRACT
In the present work, corrosion rates of API grade X65 pipelinesteel in sodium chloride solutions with and without alternatingcurrents (AC) at different direct current (DC) potentials weremeasured using weight loss analysis. The results show that theeffect of AC is most pronounced near the open-circuit poten-tial; at more positive potentials, the rates approach those of theohmic drop/mass transport-limited DC rates. Correspond-ingly, at negative potentials the rates decrease. Surprisingly,it was found that at all potentials, the AC corrosion rate wasequal to the average AC current in the system. The data gen-erated from weight loss experiments were compared with theresults from a model for AC corrosion that was developed usinga modified Butler-Volmer approach. The model considers theanodic and cathodic Tafel slopes, diffusion limited oxygentransport, interfacial capacitance, and solution resistance.Both experimental and model results showed the importance ofthe interfacial capacitance on the rate of AC corrosion, es-pecially at a frequency of 60 Hz. The models were also used toexplain the observation that the AC corrosion rate was equalto the average AC current in the system.
Increased corrosion rate in the presence of alternatingcurrent (AC) has been known to occur for quite sometime. As long as 100 years ago, investigators from theNational Institute of Science and Technology describedthis in a paper titled, “Influence of Frequency ofAlternating or Infrequently Reversed Current onElectrolytic Corrosion.”1 However, it was not until anaccident on a pipeline in Germany in 1986 that itbecame a widespread industry topic and a safetyconcern. That failure occurred on a polyethylene-coatedpipe installed parallel to a 16.6 Hz powered railway.The pipeline was cathodically protected at −1,000 mVvs. saturated calomel electrode (SCE) using animpressed current system, typical of European industrystandards of the time.2 It was concluded that a lowsoil resistivity of 1,900 Ω·cm from deicing salts was acontributing factor in the failure. Since then, therehave been numerous field cases of AC-induced failuresin pipelines with otherwise adequate cathodicprotection (CP).3 As a result, international and U.S.standards, as well as “best practices,” have beenpublished detailing corrosion protection criteria tomitigate AC-induced corrosion on buried pipelines.3-6
In addition to pipelines, the prospect of AC-inducedcorrosion has prompted the oil and gas industry todevelopmitigation strategies for its subsea operations.7-8
In that application, AC is used for autonomousoperations, as well as to heat pipelines coming from thewell to reduce the formation of hydrates and waxes.
To contribute to the development of standards, alarge number of field studies have been performed to
Submitted for publication: January 13, 2016. Revised and accepted:March 25, 2016. Preprint available online: March 25, 2016, http://dx.doi.org/10.5006/2028.
‡
Corresponding author. E-mail: [email protected].* Chemical and Biomolecular Engineering, The University of Akron,Akron, OH 44325.
** General Electric, Eyvind Lyches vei 10, Sandvika 1338, Norway.
characterize the variables that contribute toAC-induced corrosion on pipelines, such as:AC potential (or AC current), level of cathodic pro-tection, and soil resistivity.9-14 From these studies, it isgenerally agreed that, at the open-circuit potential(OCP), increasing AC pipe potential results in an in-crease in corrosion rate.15 The effect of CP has alsobeen examined for steel in a simulated soil solutioncontaining Cl−, SO4
− , and HCO3− salts and the data
show a very clear relationship between CP potential andcorrosion rate. While some protection is afforded at−0.85 V copper-copper2+ sulfate electrode (CSE), it is notuntil the CP potential is reduced to −1.0 VCSE that theeffects of AC can be sufficiently mitigated.16 The effect ofadditional CP is not known, however, and it has beenproposed that overprotection of pipelines with animpressed AC may occur at these lower potentials,though this has not been confirmed.17 Finally, as notedin the above German failure, there is a clear increasein AC corrosion risk with low soil resistivities.18 Whilepotential, CP, and soil resistivity are among the mostimportant parameters, there are other variables thatinfluence AC corrosion rates, such as surface scalethat occur from the deposition of minerals such ascalcium carbonates and hydroxides.11-20
Gellings was among the first researchers tomodelAC corrosion rates of metals.11 In that work, the in-fluence of parameters such as Tafel slope (i.e., acti-vation vs. transport control) were used to develop ageneralized expression to estimate weight loss.However, neither data nor model validation were pre-sented. Chin, et al., proposed a preliminary theoret-ical approach to explain the polarization behavior ofmild steel in a sodium sulfate solution with asuperimposed AC potential.10 In their model, a Butler-Volmer (B-V) style equation was used. While thecomparison between the calculated polarization curvesand the experimental results was limited at best, theyreported oscillograms of the AC current response (cur-rent vs. time) as a function of frequency that showed adistortion in peak shape away from the “sinusoidalform.” Themagnitude of this distortion was a functionof frequency; however, the frequency dependencewas not explained by the authors. This paper willshow that it may be attributed to the juxtapositionof the reactions occurring at the double layer, namelyoxidation rate, reduction rate, and interfacialcapacitance.
Other theoretical investigations worth mention-ing include the work of Bertocci and later of Bosch, bothof which used a B-V style expression of the form:9,21
i= icorr
�eðEDCþE0 sinðωtÞÞ
βa − e− ðEDC−E0 sinðωtÞÞ
βc
�(1)
where i is current density passing through the system,icorr is the corrosion current density in the absenceof applied alternating voltage, EDC is the applied DC
potential, βa and βc are anodic and cathodic Tafelslopes, E0 is the peak potential, and ω is the angularfrequency of the AC signal. Equation (1) assumesactivation control and does not consider potential dropacross the solution resistance or the effect of doublelayer capacitance. However, Bosch, et al., were amongthe first researchers who considered the effect ofdiffusion phenomena on corrosion rate with applied ACpotential.9 In their analysis, they assumed that ACand DC polarizations do not influence each other and asa result, concentration of oxidants at the electrodesurface consists of two separate DC and AC parts.Based on their model, Bosch, et al., concluded thatthe increase in the corrosion rate was limited by thediffusion-limited current density. This conclusion willbe rebutted in this paper.
In comparison, Lalvani, et al., proposed a modelthat considered both potential drop across the solutionresistance and the effect of double layer capaci-tance.22 In that model a simple Randles’ circuit wasassumed, where the total potential drop in the system(ET), was the sum of DC and AC potentials:
ET =EDC þ E0 sin ωt (2)
In this model, ET was equal to the sum of thepotential drop across the electrochemical interface(E) plus the potential drop across the solutionresistance (Rs):
ET =Eþ iTRs (3)
The total current flow (iT) across the interface wasdefined as the sum of the capacitive current (ic) and theFaradaic current (iF):
iT = ic þ iF (4)
where iF is the sum of the anodic (io) and the cathodic (ir)currents,
iF = io þ ir (5)
The current flow through the interfacial capaci-tance (Ci) was defined as:
ic =CidEdt
(6)
Substituting Equations (6) and (5) into Equa-tion (4) and further combination of the result withEquations (2) and (3) yielded a general expression forthe potential drop across the interface:
dEdt
þ ECiRs
þ io þ irCi
=EDC þ E0 sin ωt
CiRs(7)
Lalvani, et al., also considered both anodic andcathodic reactions under activation control. In their
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model, the values of io and ir had their traditional Tafeldefinitions:
io = icorr eðE−EcorrÞ
βa (8)
and
ir = icorr e−ðE−EcorrÞ
βc (9)
where Ecorr is the corrosion potential measured in theabsence of AC.
SubstitutingEquations (8) and (9) into Equation (7)led to their final nonlinear differential equation for E:
dEdt
þ ECiRs
þ icorreðE−Ecorr Þ
βa þ icorre− ðE−Ecorr Þ
βc
Ci
=EDC þ E0 sin ωt
CiRs(10)
Lalvani, et al., obtained numerical solutions forEquation (10) using two different methods, one using alinear model and the other using a perturbationmethod.22-23 Based on their models, it was concludedthat the corrosion current would be lower at higherfrequencies, in agreement with experimental data.24
For the perturbation analysis, they assumed thatthe ratio of DC corrosion current to the double layercapacitance value is much lower than unity and,therefore, could be neglected.22-23 As a resultof assumptions in their numerical solution, the DCpotential does not have any influence on AC corrosionrates, which is in contrast with the results obtainedby others.
In this paper, the mechanism of AC corrosion ofAPI grade X65 pipe steel in sodium chloride solution isinvestigated, presenting corrosion rate data with andwithout AC potentials. To explain the trends observed asa function of AC potential, frequency, and applied DCpotential, a model is developed, building on the work ofLalvani and Equation (7).22 Factors addressed by thenew model that previous models have omitted include:the effect of solution resistance, mixed cathodicreactions such as transport limited oxygen reduction,and hydrogen evolution.
EXPERIMENTAL PROCEDURES
Electrode and SolutionThe samples used in this work were fabricated
from an API grade X65 (UNS K03014)(1) pipe steel. Thechemical composition of thematerial was: C 0.04 wt%,Si 0.2 wt%, Mn 1.5 wt%, P 0.011 wt%, S 0.003 wt%,Mo 0.02 wt%, and Fe balance. The steel was in thequenched and tempered condition. The steel coupons
were cut into 15 × 12 × 5 mm samples with a tappedhole in one end for electrical connection via a threadedrod. Samples were ground with SiC papers, startingfrom 120 grit to 600 grit, and rinsed with acetone,ethanol, and distilled water, sequentially.
All tests were conducted in 0.1 M NaCl. Thesolution volumewas 300mL andwasmade fromanalyticgrade reagents and 18.2 MΩ·cm2 deionized water. Alltests were conducted at ambient temperature (22°C) andopen to air. To assess the effect of ferrous/ferric ioncontent and solution pH on corrosion behavior, threedifferent conditions were examined: (i) static solution,(ii) intermittent batch replacement of solution (250 mLafter each hour), and (iii) constant solution replace-ment at a rate of 8mL/min. Replacement of solution wasperformed using a peristaltic pump, and to ensure thecell was mixed, solution stirring at 60 rpm was used.During the test, an aliquot of solution was takenperiodically to measure pH and Fe ion content. In thosetests, ultraviolet visible spectrophotometer (UVS) wasused to determine ferrous (Fe2+) and ferric (Fe3+) ionconcentration. The Fe3+ content was indirectlyobtained by calculating the Fe2+ concentration, followedby a separate determination of the FeTotal concentra-tion.25-26 Before electrochemical measurements, theworking electrode (WE) was kept in the test solution for24 h at the OCP to ensure steady state.
All tests were performed in triplicate to ensure thereproducibility of the results.
Electrochemical SetupElectrochemical measurements were performed
using a PAR 273A† potentiostat in a conventional three-electrode setup. A platinum mesh was used ascounter electrode (CE) and a SCE as reference (RE).A Luggin capillary was used to prevent cross-con-tamination. The distance between the Luggin capillaryandWEwas approximately 15mm,while the distancebetween the CE and WE was approximately 40 mm. Insome photographic images, the distance between allelectrodes was decreased to capture them in the sameframe but no data were reported for these decreaseddistances: they are for photographic clarity only.
Potentiostatic tests were performed at potentialsof −720, −700, −670, −600, −500, −440, and 0 mVSCE
with and without impressed AC potentials. The ACsignal was generated using a Solartron 1255 FrequencyResponse Analyzer† (FRA). In this configuration, thesignal output from the FRA was connected to the ex-ternal input of the potentiostat. Thus, the AC signalcould be applied between RE and WE through thepotentiostat at a constant potential “on top” of theapplied DC. AC root mean square (RMS) potentials of100, 200, 300, 400, 500, and 600 mV at a frequencyof 60 Hz were used. These nominal signal generatorpotentials and the actual values (as measured by theFRA) varied between 10% and 20% depending onmagnitude.
(1) UNS numbers are listed in Metals and Alloys in the Unified Num-bering System, published by the Society of Automotive Engineers(SAE International) and cosponsored by ASTM International.
† Trade name.
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In order to investigate the effect of AC frequencyon corrosion rate, tests at the OCP using lower fre-quencies (0.01, 0.1 and 1,000 Hz) were performed.The current-time and potential-time response undervarious DC and AC potentials were recorded with anacquisition rate of 0.1 points per second for low fre-quencies (i.e., 0.01 Hz and 0.1 Hz), while higherfrequencies (i.e., 60 Hz and 1,000 Hz) were collected at arate of 250 points per second. Electrochemical im-pedance spectroscopy (EIS) data were taken after eachexperiment with and without AC at OCP in order tomonitor the solution resistance value. The frequencyscans were taken from 100 kHz down to 0.01 Hz with10 mV AC amplitude.
Weight loss analysis was conducted in accor-dance with ASTM Standard G1.27 Immersion time wasvaried depending on anticipated weight loss andresolution of the balance. For example, for higher RMSAC potentials and or DC potentials, the initial im-mersion time may have been as short as 2 d. For lowerAC potentials and or cathodic DC potentials, theimmersion time was up to 3 weeks. After potentiostatictests, the corrosion product formed on the couponsurface was removed by both mechanical and chemicalmethods as described in the standard. The me-chanical method included scrubbing with a nylon brushand was used to remove loosely adhered corrosionproduct. To remove tightly bound oxide films, sampleswere immersed several times for 25 s in Clarke’ssolution: concentrated HCl (specific gravity 1.19), 2 wt%Sb2O3, and 5 wt% SnCl2.
RESULTS AND DISCUSSION
Effect of Solution Composition on Corrosion RateGiven that the immersion period of the weight
loss experiments was relatively long, there was concernthat the change in solution properties over time wouldmake interpretation of the results difficult.28-34 Forexample, sustained cathodic reactions over a periodof days in the relatively small volume could have sig-nificant effects on solution pH.28-32 In addition, if thecorrosion rates were high, in some cases large amountsof dissolved Fe2+ could accumulate in the cell. As eachof these factors can influence corrosion rates in pipelinesteels,33-34 a series of experiments were designed tooptimize solution composition. Figure 1 shows thevariation in current density resulting from changes inthe chemical composition of the electrolyte withoutsolution replenishment and stirring. Each solidsymbol represents data points obtained from the meansteady state current density value from potentiostaticsteps at constant DC potential. The solid line representsdata taken using the potentiodynamic polarizationmethod (stirred and replenished only).
As seen in Figure 1, current densities obtained fromsamples in the stagnant solution were consistentlylower than those obtained using solution
replenishment. UVS analysis of aliquots of solution atanodic potentials and solution pH versus charge passedare presented in Figure 2. Charge passed was used asopposed to time, as it is a better reflection of what isoccurring on the corroding sample; for example, onewould anticipate larger Fe2+ concentrations in a stag-nant solution with larger charge passed. In contrastto the stagnant solution, solution replenishment/stir-ring resulted in constant Fe3+ concentration over thecourse of the immersion period (Figure 2[a]) and rela-tively constant pH values of approximately pH = 7.0.Therefore, the lower current density without solutionreplenishment/stirring was attributed to the combi-nation of pH and Fe3+ that decreases corrosion rate.28-34
In the remainder of the work, the decision was madeto use solution stirring and replacement to eliminateany external influences other than imposed AC po-tential on corrosion behavior of carbon steel.
Influence of Combined Alternating Current andDirect Current Potentials on Corrosion Rate
Figure 3 compares corrosion rate with andwithout AC (RMS voltage = 600 mV and f = 60 Hz) as afunction of DC potential. Results were obtained byweight loss analysis after the potentiostatic test. Thevalues of mass loss obtained at each of the DC biaseswere converted to equivalent current densities usingFaraday’s law:
i=m·Ft ·ρ
(11)
where i is current density, m is the mass loss value, F isFaraday’s constant equal to 96,485 C/mol, t is totalexposure time, and ρ is density of carbon steel(7.8 g/cm3).
Weight loss was chosen as it was unclear if thecurrent reported by the potentiostat would reflect thetrue Faradaic current in the system with an applied AC
–1.2
Polarization curve
Potentiostatic (stagnant)Potentiostatic (stirred and replenished)
1E–6
1E–5
1E–4
1E–3
0.01
–1.0 –0.8 –0.6
ESCE (V)
i (A
/cm
2 )
–0.4 –0.2
FIGURE 1. Effect of solution replenishment and stirring on currentdensity.
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signal. In other studies where potentiostats have beenused to measure corrosion current polarization curvesand linear polarization resistance (LPR), investigatorshave used separate AC and DC loops. In those
investigations, an AC voltage was applied between thesample WE and a CE that was separate from thepotentiostat CE, while the potentiostat was used toapply a DC potential between the WE and RE. However,an inductor (of the order of 10 H) was placed betweenthe potentiostat and its CE, preventing the potentiostatfrom “responding” to the potential fluctuations on theWE created by the AC voltage. The result was that onlyDC current flowed in the potentiostat loop. This typeof circuit was first used by Chin and later by Goidanichand others.10,35-36 The use of an inductor in thepotentiostat CE is fundamentally flawed, as the ACcurrent generated by the oxidation reaction (aboveand beyond the oxidation current produced by the DCpotential) is not measured by the potentiostat whenan inductor is used. For example, consider the currentresponse of the WE to a 60 Hz AC perturbation at agiven applied DC potential assuming the electrode canbe modeled as a simple resistor (e.g., a polarizationresistance). In addition to the DC Faradaic current inthe system, Faradaic current at 60 Hz will flowthrough the circuit: recall for an AC potential across aresistor Z(ω) = R. The actual corrosion rate is the sumof these two Faradaic current contributions. However,in setups that use an inductor in the potentiostat CE,the Faradaic component of the AC signal is not part ofthe current measured by the potentiostat. As such,polarization curves, or LPR measured with an inductorin the CE, provide no information with respect tocorrosion rate of the sample resulting from the imposed60 Hz AC voltage. Faradaic and non-Faradaic cur-rents are addressed further in this paper.
Figure 3 shows the effect of AC potential oncorrosion rate of API grade X65 steel. Each data point inthis figure represents the average of 3 independentweight loss measurements. As seen in Figure 3, bothdata sets with and without AC showed the same trendof increasing corrosion rate with increasing DC potentialabove Ecorr. In addition, the corrosion rate in thepresence of AC was greater at any given DC bias; forexample, the corrosion rate at OCP (–670mV) with ACwas about 10 times higher than that without AC, con-sistent with observations made by other authors.35,37
These results, along with the potentiodynamic polari-zation data shown in Figure 1, are compared inFigure 4. As seen in Figure 4, the current densities frommass loss without AC agreed well with the polariza-tion curve. In addition, Figure 4 suggests that at veryhigh DC biases, as the system approaches a combi-nation of mass transport and IR control, the effect of ACwas negligible. Finally, while it appears that there is a“shift” in the Ecorr during AC, this is a fundamentallyincorrect way of viewing the data. The AC signal is animpressed voltage that does not require the oxidationand reduction reactions to be occurring at steadystate. There will be a potential at which the magnitudeof the oxidation reaction during the positive portionof the sine wave will be equal to the reduction
0.05
6
7
8
9
10
11
–1.5
–1.0
–0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0 M
0
(a)
(b)
1,000 2,000 3,000
Stagnant
Stagnant (Fe3+)
Stirred and replenished (Fe3+)
Stirred and replenished (Fe2+)
Stagnant (Fe2+)
Stirred and replenished
4.0 M 6.0 M 8.0 M 10.0 M
Q (c)
Q (c)
pH
Fe
con
ten
t (m
M/g
. cm
2 )
FIGURE 2. Effect of solution replenishment and stirring on: (a) Fecontent of the electrolyte at DC=−500 mVSCE and (b) pH of theelectrolyte at DC= 0 VSCE.
–0.8100
101
102
102
101
100
10–1
103
104
–0.7 –0.6 –0.5 –0.4 –0.3
With AC RMS = 600 mVNo AC
Ecorr
ESCE (V)
C·R
(m
py)
C·R
(m
m/y
)
–0.2 –0.1 0.0 0.1
FIGURE 3. Effect of AC potential on corrosion rate of carbon steel atdifferent DC biases.
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reaction; however, this is not the same as Ecorr, as thesource of current is not the opposing reaction, rather,the remote power source driving the AC signal. Thepotential at which this crossover point occurs dependson the relative magnitudes of the anodic and cathodicTafel slopes, which is discussed later.
To better understand the relationship between AC,applied DC, and corrosion rate, mass loss experi-ments as a function of applied DC and AC potential wereconducted (Figure 5). As seen in Figure 5, corrosionrates decreased with decreasing AC RMS potential atany given DC potential. In addition, there was adecreasing trend in the AC:DC corrosion ratio withincreasing DC potentials for all AC RMS levels, withthe exception of the OCP. Near the OCP, the effect of ACwas more pronounced as compared to more positiveapplied DC potentials. It is believed that this trend is aresult of a combination of two factors: the magnitude
of the non-Faradaic (capacitive) current and thesolution resistance.
Alternating Current Potentials and FaradaicCurrents
One way of analyzing the corrosion rate dataobtained herein is to compare it with the total ACcurrent in the system. Nominally, the total AC currentvaries with time at 60 Hz and can be separated intothree categories: (1) the average positive AC current(AC(+)), which is the time averaged value of all of thecurrent that is greater than zero; (2) the averagenegative AC current (AC(−)), which is the time averagedvalue of all of the current that is less than zero; and(3) the average AC current (AC(avg)), which is the timeaveraged value of all current (Figure 6[a]). Figure 6(b)compares the current density calculated frommass losswith AC(+), AC(−), and AC(avg). As seen in this figure,the weight loss data diverges sharply from AC(+), anindication that not all of AC(+) contributes to corro-sion reactions; that is, not all of the AC(+) is Faradaic. Incomparison, the weight loss data agreed almost ex-actly with the AC(avg). In fact, the data agreed so wellmost of the points overlapped.
While this phenomenon has been observed beforefor 60 Hz, it has not been explained.38-39 It is
–1.4
1E–6
1E–5
1E–4
1E–3
0.01
0.1
–1.2 –1.0 –0.8 –0.6 –0.4
ESCE (V)
i (A
/cm
2 )
–0.2 0.0 0.2 0.4
Ecorr
Polarization curve
Regression
i, weight loss, no ACi, weight loss, AC
FIGURE 4. Effect of AC potential on current density of carbon steel atdifferent DC biases.
–0.80
2
4
6
8
10
–0.7 –0.6 –0.5 –0.4 –0.3
ESCE (V)
C·R
AC/C
·Rn
o A
C
–0.2
Ecorr
RMS = 600 mV
RMS = 500 mV
RMS = 400 mV
RMS = 300 mV
RMS = 200 mV
RMS = 100 mV
–0.1 0.0 0.1
FIGURE 5. Effect of different RMS values on the ratio of corrosionrate with AC to the corrosion rate without AC at different DCpotentials.
–0.8–0.020
–0.015
–0.010
–0.005
0.000
0.005
0.010
(a)
(b)
0
–0.7 –0.6 –0.5 –0.4
Ecorr
AC(+)
AC(avg)
AC(–)
Weight loss
AC(avg)AC(–)AC(+)
–0.3
ESCE (V)
Time (s)
i (A
/cm
2 )
i (A
/cm
2 )
–0.2 –0.1 0.0 0.1
FIGURE 6. (a) Schematic of sinusoidal AC current density frompotentiostatic test and (b) comparison of current density with 60 HzAC (RMS= 600 mV at different DC biases) from weight loss andAC(+), AC(−), and AC(avg).
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proposed that this finding is specific to mid-range fre-quencies (1 Hz to 100 Hz) and occurs because theFaradaic current generated by the cathodic reaction isnegligible as compared to the anodic reaction. Toevaluate this, consider the equivalent circuit inFigure 7(a) that includes elements for the solutionresistance (Rs), the oxidation and reduction chargetransfer resistances (Ro and Rr), and the interfacialcapacitance (Ci). Here, it is assumed that Ro and Rr areacting as voltage-controlled nonlinear resistors.Specifically, Ro is related to the anodic Tafel slope(βa) and Rr is related to three parameters: (1) the slopeof the oxygen reduction reaction (βc), (2) the transportlimited oxygen reduction current density (iL), and(3) the slope of the hydrogen reduction reaction (βH2
).Both oxidation current (Faradaic) and capacitivecurrent (non-Faradaic) occur during the positive half-cycle of the applied AC signal. Similarly, reductionand capacitive currents coexist during the negative halfcycle of the applied AC signal. The magnitude ofAC(+), Faradaic plus capacitive current, depends on thevalues of Ro andCi (e.g., the RC time constant) and thefrequency of the AC signal. Correspondingly, the valuesof Rr and Ci act independently to control the magni-tude of AC(−). With respect to the capacitive current, the
magnitude of the positive and negative half-cycles areequal and, as such, sum to zero. However, the Faradaiccurrent generated by the oxidation and reductionreactions is independent. Thus, the value of AC(avg) iscontrolled by the rates of these two reactions. In thecase of API grade X65 pipe steel in seawater, the value ofRr is high relative to Ro (βa = 0.089, βc = 0.352, and βH2
= 0.205). As a result, io + ir resembles io. For this reason,AC(avg) approximates the corrosion rate as measuredby weight loss, as observed in Figure 6. The net result isthat the circuit in Figure 7(a) reduces to the oneshown in 7(b). There would be a similar result if therewas a cathodic DC bias on the system and the appliedAC potential was large enough to make io more signif-icant than the ir.
The effect of the RC time constant (RrCi and RoCi) onAC(avg) and io (mass loss) can be seen in the datacollected at lower frequencies. In Figure 8, the currentvalues calculated from mass loss for API grade X65steel in chloride solution exposed to an AC (600 mVRMS) and a DC potential of 0.17 VSCE vs. OCP areplotted as a function of frequency. As seen in Figure 8,as frequencies decreased from 60 Hz to 0.01 Hz, therewas less agreement between mass loss and AC(avg) andbetter agreement between mass loss and AC(+). Thisoccurs because at low frequencies iC goes to zero, whileio and ir reached their maximum values. Becauseio > ir, AC(+) approximates the mass loss data andAC(avg) with ir now a measureable “error” in theapproximation.
At low frequencies, the mechanism of AC-inducedcorrosion is visible on the electrode surfaces as pe-riodic cycling of bubbles. Figures 9(a) through (f) presentphotographs of both the WE and CE surfaces as afunction of time during an experiment at OCP forf = 0.01 Hz and AC = 600 mV RMS. The electrodes inthe cell have been reconfigured for photographing,resulting in an aberrant RE position and decreased
Ci
Ci
Ic
Ic
ITotal
ITotal
ITotal.Rs
ITotal.Rs
Rs
Rs
(a)
(b)
E
E
Rr
RO
RO
RO2
RH2
Ir,O2
Ir,H2
Ir
Io
Io
FIGURE 7. (a) Full equivalent circuit for an electrode exposed to anAC potential and (b) reduced circuit when the cathodic reaction isrelatively small with respect to the anodic reaction (i.e., mass trans-port limited oxygen reduction).
10–3–0.10
Weight lossAC(+)AC(avg)AC(–)
–0.05
0.00
0.05
0.10
0.15
10–2 10–1 100
Frequency (Hz)
i (A
/cm
2 )
101 102 103
FIGURE 8. Comparison of current density with 60 Hz AC(RMS= 600 mV and DC=−500 mV) from weight loss and AC(+),AC(−), and AC(avg) at different frequencies.
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(a) (b)
(c) (d)
(e)
0.3 0.5
0.0
–0.5
–1.0
–1.5
0.2
0.1
0.0
–0.1
0 10 20 30 40 50Time (s)
i (A
/cm
2 )
E (
V)
log
i
E
cc
b b
a
a
(e)
(f)
d dff
e e
Time (s)60 70 80 90 100 0 10 20 30 40 50
Ecorr
60 70 80 90 100
(f)
(h)
(i)
(g)
(d)(a)
(c)
(b)
FIGURE 9. (a) through (f) Snapshots of the surfaces of working and counter electrode, (g) i-t curve, and (h) E-t curve duringthe experiment with AC (at OCP, RMS= 600 mV) in one cycle at 0.01 Hz, along with (i) schematic of the polarization curvewithout AC.
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solution resistance. As can be seen in Figure 9(a), at thebeginning of the sine wave there was a small positivecurrent and corresponding low density of hydrogenbubbles on the CE surface. At themaximumpotentialof the WE, the density of hydrogen bubbles on the CEreached a maximum (Figure 9[b]). As time continued,the AC potential on the WE decreased, as did the hy-drogen bubble density on the CE (Figure 9[c]). Atapproximately 60 s, the WE changed from anodicpotentials to cathodic; Figure 9(d) shows the corre-sponding image of the WE during oxygen reduction. Asthe WE potential became more negative, the electrodefell below the reversible hydrogen potential and hydro-gen bubbles began to form on the WE surface. Thisperiodic cycling of the WE surface maps the polarizationcurve of API grade X65 pipe steel in seawater. Todemonstrate this, points corresponding to the photo-graphs of the cell are plotted on the experimentalcurrent vs. time and potential vs. time curves (recordedsimultaneously) in Figures 9(g) and (h), respectively.These same points are plotted on the experimental po-larization curve in Figure 9(i). It is seen in these figuresthat the cell current induced by the applied AC potentialwas proportional to the reaction rate at the WE, asindicated by the polarization curve of API grade X65 pipesteel. This effect is most pronounced at cathodicpotentials where there is a combination of transportlimited oxygen reduction and hydrogen evolution. Forcomparison to the low-frequency data in Figure 9, sim-ilar data at 60 Hz were also collected (not shown).Unlike the lower frequency data, there was limited hy-drogen reduction on the WE in these experiments.This likely occurred because the total AC current at thisfrequency was predominantly non-Faradaic (capaci-tive) and the reduction current was small, which isaddressed in the Model Development section.
From these results, it was concluded that an appliedAC potential across an electrochemical interface polar-izes the electrode as a function of time away from its DCpotential along its polarization curve. The net effect ofthis polarization depends on a number of variables in-cluding: AC frequency, AC potential, Tafel slopes, in-terfacial capacitance, solution resistance, and applied DCpotential. For carbon steel in sodium chloride solutionwhere there is a low anodic Tafel slope, transport limitedoxygen reduction, low solution resistance, and highinterfacial capacitance. For example, a 600mV, 60 Hz ACsignal results in increased corrosion rates at all DCpotentials investigated here, greater than −0.25 VOCP.
MODEL DEVELOPMENT
In this section a new model is presented to predictcorrosion rates of carbon steel in the presence of an ACpotential. The model is, in part, based on the work byLalvani (Equation [10]).22 One of the assumptions inEquation (10) is that the Faradaic currents io and ir canbe described by activation control. However, at moderate
overpotentials and near-neutral solutions, the ca-thodic reaction is typically controlled by diffusion limitedoxygen reduction (ir,O2
), while at lower potentials byhydrogen evolution (ir,H2
, Equation [12]). As such, amodified B-V function is presented that describes theanodic reaction under activation control, while the ca-thodic reaction is assumed to be under mixed control:
ir = ir,O2þ ir,H2
(12)
where themass transport limited oxygen reduction rate isgoverned by the expression:40
ir,O2= icorr
e2.3ðE−Ecorr Þ
βc
1 − icorril
þ icorrile2.3
ð−EþEcorrÞβc
(13)
where iL is the limiting current density of oxygen re-duction and the remaining terms take the usualmeaning. The hydrogen evolution reaction rate is gov-erned by the Tafel equation (Equation [14]):41
ir,H2= i0H2
e2.3
ð−EþE0 ÞβH2 (14)
where i0H2is hydrogen exchange current density and is a
function of the nature of the cathode, E0 is the hy-drogen standard equilibrium potential that is equal tozero in the standard hydrogen scale (SHE), and βH2
isthe Tafel slope of the hydrogen evolution reaction.
Substituting Equations (13) and (14) in Equa-tion (12) and the combination of Equations (6), (10), and(12) leads to the nonlinear equation for potential drop(E) across the Faradaic resistance:
dEdt
þ ECiRs
þ ξ
Ci=
EDC þ E0 sin ωtCiRs
(15)
where
ξ= icorr
�e2.3
ðE−Ecorr Þβa −
e2.3ð−EþEcorrÞ
βc
1 − icorril
þ icorrile2.3
ð−EþEcorr Þβc
�
þ i0H2e2.3ð−E−0.244Þ
βH2 (16)
MODEL RESULTS
Even though the number of assumptions inEquation (15) has been minimized, finding the analyt-ical solution for this expression would be very diffi-cult. Thus, a numerical solution using MATLAB† soft-ware and ODE23S† solver based on Runge-KuttaFehlberg method was used.42 Using the potential dropacross the Faradaic resistance from Equation (15),one may easily calculate the time averaged of oxidationcurrent density (io-model) along with the total currentdensity passing through the system. Specific details areavailable in the Appendix.
1204 CORROSION—SEPTEMBER 2016
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Relationship Between Average Current andMassLoss
It was shown in Figure 6 that AC(avg) agreed wellwith mass loss data. Figure 10 compares io from themodel for two different capacitance values with thecurrent densities obtained from experimental data. Theother input values used for solving Equation (15) canbe found in Tables 1 and 2. These values were obtainedfrom IR corrected polarization data without AC(i.e., anodic and cathodic Tafel slopes, corrosion currentdensity, corrosion potential, and oxygen limitingcurrent density shown in Table 1), and EIS data. Forapplied potentials greater than the OCP, the experi-mental data approached the model values for aninterfacial capacitance of 1 mF. However, at appliedpotentials below OCP, the experimental data were moreclosely represented by a model using Ci = 0.1 mF. Asall of the Ci values are higher than the normal range ofdouble layer capacitances (20 F/cm2 to 50 F/cm2), it
is likely that Ci is composed of a series combination ofthe double layer and oxide capacitances.43-44 Thiscapacitance is associated with both double layer andoxide layer. Wren, et al., studied the influence of theoxide film on carbon steel on corrosion rate and Ci
values for three different potential regions: regionI ( ≤ −0.6 VSCE), region II (−0.5 V ≤ ESCE ≤ −0.2 V), andregion III (0.0 V < ESCE < 0.4 V). At different potentialsin mildly alkaline solution, a unique value of Ci wasmeasured. In addition, the oxide films in each of thoseregions were identified as Fe3O4, Fe3O4 layer with Fe2O3,and FeOOH, respectively. It was concluded that Ci wasrelated to the composition of the oxide films. Further, itwas concluded that the oxide also influenced thenature of the double layer capacitance.44 Thus, as itrelates to the results in this paper, the value of Ci islikely a combination of double layer capacitance andoxide capacitance. From a model perspective, in orderto accurately solve Equation (15) for all DC potentials at60 Hz, a series of empirical values of capacitance as afunction of potential would be needed.
Fitted values of Ci for each experimental data point inFigure 10 were obtained and the results are shown inTable 2. By using these values along with the othervalues from Table 1 as input for solving Equation (15),AC(+), AC(−), and AC(avg) were calculated and plotted inFigure 11. Figure 11 is analogous to Figure 6 but formodel data only. In addition to these values, the oxida-tion current passing through Ro (io) has also beencalculated. This current involves oxidation reactions onlyand would be analogous to a current calculated frommass loss and Faraday’s Law. As in Figure 6, it is seenthat AC(avg) from the model was in a good agreementwith the oxidation current as described earlier.
Influence of Frequency and Capacitance onCorrosion Rate with Alternating Current
It is apparent that one of the key parameters inAC corrosion is the value of Ci. For a given anodic Tafel
0.01Ecorr
iO-model, Ci = 0.001 F
iO-model, Ci = 0.001 F
iW
1E–3
1E–4
1E–5
1E–6–0.8 –0.7 –0.6
ESCE (V)
i (A
/cm
2 )
–0.5 –0.4
FIGURE 10. Comparison of experimental mass loss data at 60 Hzand the solution of the Equation (15) for two different capacitancevalues (0.01 F and 0.001 F).
TABLE 2Experimental Data and Input Variables in Solving Equation (15) to Obtain Figures 10 and 11
EDC (V) RMS (V) f (Hz) Rs (Ω·cm2) Ci (μF/cm2) (fitted value)
slope, the value of Ci determines two factors: (1) themagnitude of the Faradaic current at a given frequencyand (2) the high-frequency break point at which noFaradaic current is passed. In this section, the responsefrom the model will be explored as a function of ACfrequency and Ci. The model predictions will be com-pared with results for several cases.
The effect of capacitance on each component ofthe current for frequencies of 0.01 Hz, 60 Hz, and1,000 Hz (0.6 V RMS) and an anodic potential of−0.5 V is shown in Table 3. Similar trends were observedat a cathodic potential of −0.7 V. As seen in this table,at both high frequency and low frequency there was littleeffect of capacitance on the individual components ofthe current density. For example, the relative magni-tudes of each component of current at 0.01 Hz wasthe same for Ci = 0.0001 F and Ci = 0.001 F. However, at60 Hz, the difference between the two values of Ci wasdramatic. For example, io at Ci = 0.0001 F was a factor oftwo as compared to Ci = 0.001 F. This occurs because60 Hz for this system was close to the high-frequencybreak point. From a practical standpoint, this findingimplies that the growth of an oxide or scale on thesurface of the material (owing to a corrosion productor mineral deposition from solution/soil) that alters theinterfacial capacitance will greatly impact the ACcorrosion rate of the material.
Figure 12 shows model results for the individualcomponents of current in the system at two frequenciesin the form of current vs. time data. The data at 60 Hz arepresented in Figures 12(a) through (c), where (a) is theoxidation current, (b) is the reduction current, and (c) isthe capacitive current. The data at 0.01 Hz are pre-sented in Figures 12(d) through (f), where (d) is the oxi-dation current, (e) is the reduction current, and (f) is thecapacitive current. The data were calculated for the inputvalues from Tables 1 and 3 at OCP. These results showthat at 60 Hz most of the current is non-Faradaic, that is,most of the current passes through the interfacialcapacitance (Figure 12[c]). Comparison of the oxidation
and reduction currents (Figures 12[a] and [b]) showsthat the reduction current, which is controlled primarilyby the diffusion limited oxygen current density, isnegligible relative to the oxidation current. Because thecapacitive current sums to zero and ir is negligible, thetotal current is equal to io. This is consistent with thediscussion of Figure 6 and is further confirmation thatthe average current at 60 Hz (AC(avg)) is a good repre-sentation of the mass loss of the sample. However, thisis limited to DC potentials where the reduction current iscontrolled primarily by the diffusion limited oxygencurrent density. In comparison to the 60 Hz data, thewaveforms at 0.01 Hz (Figures 12[d] through [f]) arequite different in magnitude and shape. At this frequencythe total current is dominated by the Faradaic currentio and ir, while the iC is negligible. From this finding, onewould conclude that at this frequency AC(avg) is not agood representation of themass loss of the sample. This isin agreement with the observation during experimentwith AC at lower frequencies (Figure 8).
The total current in the system calculated from themodel is compared with the experimental results inFigure 13. In Figure 13, the input values to this modelwere kept constant (Table 4, the same as Figure 12)for frequencies of 60 Hz and 0.01 Hz. As seen inFigure 13, at these frequencies, there was goodagreement in both magnitude and waveform shape be-tween the proposed model and the experimental data.It should be noted that it is not possible to experimentallycollect the individual waveforms for the oxidation andcapacitive currents presented in Figure 12.
Comparison between the applied potential (ET) at60 Hz and 0.01 Hz and the corresponding potentialacross the Faradaic resistance (E) is shown in Figure 14(parameters from Table 4 as in Figures 12 and 13).The data were generated for an applied potential equalto the OCP, approximately −0.67 VSCE, and is shownin each figure. As seen in these figures, for both cases ET
was higher than E. This is a result of a combination ofparameters including the magnitude of the Tafel slopes,the capacitive current in the system, and ohmic drop(Rs). These findings reinforce the idea that the potentialdrop across the system drives the Faradaic reactionsin proportion to the anodic and cathodic Tafel slopes;
–0.8
–0.020
–0.015
–0.010
–0.005
0.000
0.005
0.010
0.015Ecorr
–0.7 –0.6
iO-model
AC(+)-modelAC(avg)-modelAC(–)-model
ESCE (V)
i (A
/cm
2 )
–0.5 –0.4
FIGURE 11. Model Results for 60 Hz AC and 0.6 V RMS for AC(+),AC(−), AC(avg), and io (Equation [15]).
TABLE 3Effect of Frequency and Capacitance on Faradaic and Non-Faradaic Current at 0.6 V RMS and DC Biases of −0.5 V for
Rs= 48 Ω·cm2(A)
F (Hz) Ci (F) io (A/cm2) ir (A/cm2) iT (A/cm2)
0.01 0.001 5.3 × 10−3 −7.1 × 10−4 4.6 × 10−3
0.0001 5.3 × 10−3 −7.1 × 10−4 4.6 × 10−3
60 0.001 1.3 × 10−3 −4.2 × 10−5 1.2 × 10−3
0.0001 4.0 × 10−3 −1.4 × 10−4 3.8 × 10−3
1,000 0.001 1.1 × 10−3 −4.0 × 10−5 1.1 × 10−3
0.0001 1.1 × 10−3 −4.0 × 10−5 1.1 × 10−3
(A)Table 1 used as Input values (Equation [15]).
1206 CORROSION—SEPTEMBER 2016
CORROSION SCIENCE SECTION
0.00Time (s)
i o-m
od
el (
A /c
m2 )
i o-m
od
el (
A /c
m2 )
i r-m
od
el (
A /c
m2 )
0.00
0.01 0.02
0.02
–0.020.03 0.04
0.04
0.06(a) (b)
(c) (d)
(e) (f)
0.05 0.00–0.0015
0.08
0.04
0.00
0.0001
0.0000
–0.0001
–0.0010
–0.0005
–0.0000
Time (s)0.01 0.02 0.03 0.04 0.05
0.00Time (s)
i c-m
od
el (
A /c
m2 )
i c-m
od
el (
A /c
m2 )
i r-m
od
el (
A /c
m2 )
–0.05
0.01 0.02
0.00
–0.10
0.03 0.04
0.050.10
–0.01
–0.02
–0.03
0.00
0.05
0Time (s)
50 100 150 200 300250
0
Time (s)50 100 150 200 300250
0Time (s)
50 100 150 200 300250
FIGURE 12.Comparison of the Faradaic and non-Faradaic currents at two different frequencies from the model. At 60 Hz: (a)anodic current, (b) cathodic current, and (c) capacitive current. At 0.01 Hz: (d) anodic current, (e) cathodic current, and(f) capacitive current.
0.00 0 50 100 150 200 250 3000.01 0.02Time (s) Time (s)
0 50 100 150 200 250 300Time (s)
0.03 0.04 0.05
0.00 0.01 0.02Time (s)
0.03 0.04 0.05
–0.10
–0.04
–0.05
0.00
0.00
0.04
0.08
0.12
0.05
–0.04
0.00
0.04
0.08
0.12
0.10(a) (b)
(c) (d)
i T (
A /c
m2 )
–0.10
–0.05
0.00
0.05
0.10
i T-m
od
el (
A /c
m2 )
i T-m
od
el (
A /c
m2 )
i T (
A /c
m2 )
FIGURE 13. Comparison of the total current from the experiment at (b) 60 Hz and (d) 0.01 Hz, and corresponding calculatedcurrent from the model ([a] and [c], respectively).
CORROSION—Vol. 72, No. 9 1207
CORROSION SCIENCE SECTION
however, ET is not the same as the potential dropacross the Faradaic resistances E.
CONCLUSIONS
Corrosion rates of API grade X65 pipeline steel insodium chloride solutions with and without 60 Hz AC atdifferent DC potentials were measured using weightloss analysis. These data were compared with theresults from a model for AC corrosion that was de-veloped using a modified Butler-Volmer approach. Themodel considered the anodic and cathodic Tafelslopes, diffusion limited oxygen transport, interfacialcapacitance, and solution resistance. Good agree-ment with the results was demonstrated. From thisinvestigation, it was concluded that:v The presence of an applied AC potential increasescorrosion rates at all cathodic and anodic DC poten-tials between −0.725 VSCE and 0.0 VSCE, with the
most pronounced increase being at potentialsnear OCP.v The corrosion ratemeasured via weight loss agreedmost closely with the average AC current passed acrossthe electrochemical interface and not with the averagepositive AC current. This was shown to be a result ofseveral factors, including a large capacitive current at60 Hz and a relatively low reduction current limited byoxygen mass transport.v An applied AC potential across an electrochemicalinterface polarizes the electrode as a function of timeaway from its DC potential along its polarizationcurve. The net effect of this polarization depends on anumber of variables including: AC frequency, ACpotential, Tafel slopes, interfacial capacitance, solutionresistance, and applied DC potential.v A frequency of 60 Hz is close to the high-frequencybreakpoint for electrochemical systems. As such, it is ina critical frequency range as it relates to corrosion
0.00 0.01 0.02
OCP
OCP OCP
OCP
Time (s) Time (s)0.03 0.04 0.05 0 50 100 150 200 250 300
Time (s)0 50 100 150 200 250 3000.00
–1.5
–1.0
–0.5
0.0
0.5
0.01 0.02Time (s)
E-m
od
el (
V)
–1.5
–1.0
–0.5
0.0
0.5
E-m
od
el (
V)
–1.5
–1.0
–0.5
0.0
0.5(a) (b)
(c) (d)
ET (
V)
–1.5
–1.0
–0.5
0.0
0.5
ET (
V)
0.03 0.04 0.05
FIGURE 14.Comparison of the applied potential at (a) 60 Hz and (b) 0.01 Hz, and corresponding calculated potential acrossthe Faradaic resistance obtained from solving Equation (15) ([c] and [d], respectively).
TABLE 4Input Variables for Solving Equation (15) Used to Obtain Figures 12 Through 14
EDC (V) RMS (V) f (Hz) Rs (Ω·cm2) Ci (μF/cm2)
−0.67 0.6 60 8.7 638−0.67 0.6 0.01 6.72 638
1208 CORROSION—SEPTEMBER 2016
CORROSION SCIENCE SECTION
rate. Below the high-frequency break point, corrosionrates can vary widely depending on parameters suchas interfacial capacitance and solution resistance.Above the high-frequency breakpoint, no change incorrosion rate with AC would be observed.
ACKNOWLEDGMENTS
The authors wish to acknowledge the financialsupport of Dan Dunmire and Rich Hayes, Department ofDefense Corrosion Policy and Oversight ContractNo. W9132T-11-1-0002. We also thank Prof. NathanIda, Prof. Joe Payer, and Prof. Dmitry Golovaty for theirinsightful discussions, and Dr. Maurico Rincon Ortiz forhis help with some of the initial experiments.
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21. U. Bertocci, Corrosion 35 (1979): p. 211-215.22. H. Xiao, S.B. Lalvani, J. Electrochem. Soc. 155 (2008): p. C69.23. R. Zhang, P.R. Vairavanathan, S.B. Lalvani, Corros. Sci. 50 (2008):
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Examination of Water and Wastewater, 18th ed. (Washington, DC:AWWA, 1992).
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NOMENCLATURE
icorr Corrosion current density (A/cm2)Ecorr Corrosion potential (V)βa Anodic Tafel slope (V/decade)βc Cathodic Tafel slope for oxygen reduction
reaction (V/decade)E Potential across the Faradaic resistance (V)il Oxygen limiting current density (A/cm2)i0H2
Hydrogen exchange current density (A/cm2)βH2
Cathodic Tafel slope for hydrogen evolutionreaction (V/decade)
Rs Solution resistance (Ω·cm2)Ro Oxidation resistance (Ω)Rr Reduction resistance (Ω)Ci Interfacial capacity (F/cm2)iw Current density obtained from mass loss
(A/cm2)io Oxidation current density (A/cm2)ir Reduction current density (A/cm2)iC Capacitive current density (A/cm2)iT Total current density passing through the
system, capacitive + Faradaic (A/cm2)ET Total applied potential (V)EDC DC potential (V)E0 Peak potential (V)r Ratio of anodic to cathodic Tafel slopesRMS Root mean square valueAC(+) Time-averaged positive AC current density
(A/cm2)AC(−) Time-averaged negative AC current density
(A/cm2)AC(avg) Time-averaged AC current density (A/cm2)f Frequency (Hz)
CORROSION—Vol. 72, No. 9 1209
CORROSION SCIENCE SECTION
APPENDIX A: MATLAB SOLUTION FOR EQUATION (15)
%All electrochemical potentials are vs. SCE.
%inputs unitsR %Ω·cm2 (solution resistance).C %F/cm2 (interfacial capacitance).i_corr %A/cm2 (corrosion current density without AC).E_corr %V (corrosion potential without AC).B_a %V/decade (anodic Tafel slope).B_c %V/decade (cathodic Tafel slope).E_DC %V (DC bias potential).i_lim %A/cm2 (oxygen limiting current density).E_AC %V (AC potential amplitude).f %Hz (frequency).t0 %S (initial time).tf %S (final time).dt %S.B_H %V (Hydrogen Tafel slope).i_H %A/cm2 (Hydrogen exchange current density).w=2*pi()*f; %angular frequency.tspan=[t0:dt:tf];
