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Electrochimica Acta 258 (2017) 639e652

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Electrochimica Acta

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Acidic corrosion of mild steel in the presence of acetic acid:Mechanism and prediction

Aria Kahyarian*, Alex Schumaker, Bruce Brown, Srdjan NesicInstitute for Corrosion and Multiphase Flow Technology, Department of Chemical and Biomedical Engineering, Ohio University, Athens, OH, 45701, USA

a r t i c l e i n f o

Article history:Received 22 September 2017Received in revised form12 November 2017Accepted 15 November 2017Available online 26 November 2017

Keywords:CorrosionAcidicMild steelAcetic acidMechanism

* Corresponding author.E-mail address: ak702711@ohio.edu (A. Kahyarian

https://doi.org/10.1016/j.electacta.2017.11.1090013-4686/© 2017 Elsevier Ltd. All rights reserved.

a b s t r a c t

The mechanism and the kinetics of mild steel corrosion in deaerated aqueous acetic acid solutions wasinvestigated. The behavior of the steady state voltammograms, obtained at pH 3 to pH 5 and acetic acidconcentrations up to 41.5 mM, showed that the direct reduction of undissociated acetic acid is not sig-nificant, in contrast to what is commonly reported in the literature. Nevertheless, acetic acid was shownto influence the corrosion process, first by increasing the cathodic limiting current through buffering thehydrogen ion concentration at the metal surface, and second by inhibiting the rates of both anodic andcathodic charge transfer reactions by chemically adsorbing onto the metal surface. Considering thesemechanistic observations, a comprehensive mathematical model was developed and verified, using theexperimental results. The counterpoising effect of acetic acid on the limiting current and the rate ofelectrochemical reactions was shown to be able to justify the inconsistent and sometimes contradictorybehavior previously reported in the literature. Additionally, increasing the temperature was shown tohave a synergistic effect with acetic acid concentration on the observed corrosion rates. This behavior is aresult of shifting corrosion currents towards the mass transfer controlled range at elevated temperatures,where acetic acid has a determinant effect.

© 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Besides carbon dioxide (CO2) and hydrogen sulfide (H2S), shortchain organic acids such as formic acid (CHOOH), acetic acid(CH3COOH), and propionic acid (CH3CH2COOH) are amongst thecommon corrosive species encountered in the oil and gas industry[1e5]. Organic acids are commonly reported to be present in the co-produce aqueous phase with concentrations up to several hundredmilligrams per liter [6e9]. Amongst the organic acids, acetic acid(HAc in short) is the most abundant species [6,7,9,10], which hasbeen commonly used to represent the effect of all organic acids incorrosion studies, at least as far as it concerns the oil and gasindustry.

Reports on the significance of organic acids in corrosion ofpipeline steel can be found as early as the 1940s [11], however, thesubject gained little attention until 1980's. To date, there seems tobe a consensus on the significance of acetic acid in corrosion of mildsteel, however, the reported effect of acetic acid on the observed

).

corrosion rates in the literature appears inconsistent or even con-tradictory in some cases, as discussed in the following.

Numerous research studies have focused on elucidating thecorrosion mechanisms related to the presence of acetic acid in oiland gas transmission pipelines. Gulbrandsen and Bilkova [12]studied the effect of acetic acid on CO2 corrosion of X65 mildsteel. The authors reportedmixed behavior of corrosion rates at lowand high temperatures as the concentration of acetic acid wasincreased. Based on their observations at 25 �C, corrosion ratesdecreased with increasing acetic acid concentrations, whereas theopposite behavior was reported at 80 �C. This was justified based onobservation of an inhibitive effect of acetic acid on the anodic re-action. The authors argued that the combination of anodic reactionretardation and increase in cathodic reaction rate, as a result ofdirect acetic acid reduction, leads to this mixed behavior. In 2007,George and Nesic [13] investigated the effect of acetic acid onaqueous X65mild steel corrosion under CO2 and N2 atmospheres incontrolled pH experiments. The reported corrosion rates at pH 4,with or without CO2 present, showed a significant increase withaddition of a 100 ppm (1.66 mM) acetic acid, whereas further in-crease of acetic acid concentration to 1000 ppm (16.6 mM) did notresult in significantly higher corrosion rates. The authors also

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652640

reported that as temperature was increased to 40 �C and 60 �C, theaddition of 100 ppm acetic acid had a more pronounced effect onincreasing the corrosion rates. The increased corrosion rates in thepresence of acetic acid was associated with the direct acetic acidreduction during the corrosion process. The authors also confirmedthe previous reports of a slight inhibitive effect of acetic acid on theiron dissolution reaction. Using a similar approach as George andNesic [13], Okafor et al. [14] studied the effect of acetic acid attemperatures up to 80 �C and acetic acid concentrations up to5000 ppm. It was reported that increasing the acetic acid concen-tration resulted in higher corrosion rates at all the studied condi-tions. The increased corrosion rates were justified by the directreduction of acetic acid, which was claimed to be supported by ahigher activation energy obtained for cathodic reactions whenacetic acid was present. However, the reported cathodic polariza-tion curves in that study appear to be significantly influenced bythe limiting current almost in all conditions, hence, the electro-chemical activation energies could not be obtained with reasonableconfidence. In 2012, Jia et al. studied the effect of acetic acid in CO2corrosion of 3Cr low-alloy steel [15], reporting a significant increaseof corrosion rates by increasing the total acetic acid concentrationfrom 0 to 2000 ppm. The author associated the higher corrosionrates with the direct reduction of acetic acid as well as its effect ondegrading the protective corrosion product layer. Nevertheless, thearguments used to justify the observed behavior could be ques-tioned when considering the lack of proper solution speciationcontrol in their experiments. One should consider that increasingthe acetic acid concentration from 0 to 2000 ppm could decreasethe solution pH dramatically; a key factor when discussing thecorrosion behavior which was not included in analysis of data inthat study [15]. Zhu et al. [16] also studied the CO2 corrosion of N80carbon steel in acetic acid containing solutions with emphasis onelevated temperatures and CO2 partial pressures. A significant in-crease of corrosion rates with increasing acetic acid concentrationsat 90 �C was reported, which were justified by similar argumentsused by Jia et al. [15].

Considering the brief review above, the increased corrosionrates in the presence of acetic acid were commonly justified bypresuming that acetic acid is directly reduced at the metal surface.According to this mechanistic view, as a weak acid, acetic acid isonly partially dissociated in the aqueous phase (Reaction (1)).Hence, both acetate ions (Ac�) and undissociated acetic acid

Fig. 1. The ratio of undissociated acetic acid concentration to total acetate speciesconcentration in 0.1 M NaCl solution for various pH values at 30 �C and 60 �C. Thelabels from left to right show the ratio at pH 3.0, pH 4.0, and pH 5.0.

(molecular HAc) are present in an aqueous solution, while theirrelative concentrations are defined by the solution pH (Fig. 1).

HAcðaqÞ#HþðaqÞ þ Ac�ðaqÞ (1)

In this corrosion mechanism, the anodic iron dissolution (Re-action (2)) is accompanied by two parallel cathodic reactions,namely, hydrogen ion reduction (Reaction (3)) and the directreduction of the undissociated acetic acid (Reaction (4)).

Fe2þðaqÞ þ 2e�#FeðsÞ (2)

2HþðaqÞ þ 2e�#H2 ðgÞ (3)

2HAcðaqÞ þ 2e�#H2ðgÞ þ 2Ac�ðaqÞ (4)

However, in more recent years, evidence has been mountingthat suggests acetic acid is not a significant electroactive speciesand its sole contribution to the cathodic currents is through thehomogeneous Reaction (1). In this mechanistic view, acetic acidmerely acts as a hydrogen ion carrier in the solution and its pres-ence would only increase the mass transfer limit of the cathodiccurrents. This mechanism points to the fact that at mass transferlimiting current, where the surface pH is increased, the chemicalequilibrium of acetic acid (Reaction (1)) shifts towards acetic aciddissociation, therefore, acetic acid acts as an additional source ofhydrogen atoms at the metal surface. In 2011, Amri et al. [17]studied the effect of acetic acid in CO2 corrosion in the context oftop of the line corrosion of X65 mild steel. The authors reportedthat when the corrosion current was controlled by the electro-chemical reaction rates (as opposed to mass transfer limited) atlower pH values, increasing the acetic acid concentration did notsignificantly affect the observed corrosion rates or the corrosionmechanism. It was reported that the effect of acetic acid wasmainlyrelated to increasing the limiting current and that the directreduction of acetic acid was insignificant. It was also suggested thatacetic acid inhibits the anodic reaction and therefore local changesin its surface concentration could trigger localized attack. Inanother, more systematic study, Tran et al. [18] investigated thebehavior of the cathodic polarization curves in mildly acidic envi-ronments, with acetic acid being the only weak acid present insolution. The polarization curves were obtained on 304 stainlesssteel in order to eliminate the interference of anodic reactions onthe observed cathodic current. It was explicitly shown that theconcentration of acetic acid did not affect the charge transfercontrolled portion of the cathodic sweeps. Therefore, the authorsconcluded that acetic acid is not involved in a charge transferprocesses directly, and its main contribution was buffering thesurface hydrogen ion concentration, thereby increasing the limitingcurrents. However, considering the possible influence of thealloying compounds of 304 stainless steel (~20 wt % Cr, and 10 wt %Ni) and the passive layer on the electroactivity of the metal surface,the experimental findings of Tran et al. [18] on stainless steel couldnot be considered valid for mild steel, without further verification.In 2016, Kahyarian et al. [19] investigated the effect of acetic acid onthe polarization behavior of pure iron and X65 mild steel. Based onthe experimental data obtained using rotating disk electrodes andpotentiodynamic measurements, the authors showed that aceticacid did not significantly contribute to the charge transfercontrolled currents for concentrations up to 1000 ppm. Hence, themechanism proposed by Tran et al. [18] was also proven to be validfor iron and mild steel surfaces.

The present study expands on the experimental conditionscovered previously by Kahyarian et al. [19], in order to further

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 641

elucidate the underlying mechanisms of the aqueous mild steelcorrosion in the presence of acidic acid. A quantitative analysis ofthe results, using comprehensive mathematical calculations, isincluded in the present study, to provide a detailed description ofthe mechanistic observations. Ultimately, these mathematical re-lationships can be incorporated into mechanistic corrosion ratepredictive models [20,21] for application in more elaborate corro-sion scenarios.

2. Materials and methods

2.1. Experimental procedure

The experiments were carried out in a 1 L glass cell with aconventional three electrode arrangement and a silver/silverchloride reference electrode, similar to that described in an earlierstudy [22]. The supporting electrolyte was 0.1 M solution of sodiumchloride in deionized water in all of the reported experiments. Thetargeted solution composition was achieved by addition of thedesired amount of glacial acetic acid followed by adjustment of thesolution pH using small amounts of dilute HCl or NaOH solutions.All the chemicals used in the present study were analytical grade.The solution was then purged using nitrogen gas for minimum of90 min while the oxygen content of the outlet gas was monitored(Orbisphere 410). The maximum allowed dissolved oxygen contentbefore introducing the working electrode into the solution was1 ppb.

Theworking rotating disc electrode (RDE) wasmade of an API 5LX65 mild steel disc (composition given in Table 1) with 5 mmdiameter, press-fitted into a Teflon™ electrode holder (Pine in-struments). The electrode was abraded with 1000 grit silicon car-bide paper and further mirror polished using successively finersilicon suspensions, down to 0.25 mm, prior to each test. The elec-trode was then rinsed and sonicated in isopropanol for 5 min anddried with nitrogen gas. The working electrode was inserted intothe glass cell while the nitrogen gas flowwas temporarily increasedand further electrochemically treated as described in detail else-where [19]. As the last step, the open circuit potential (OCP) wasmonitored for 10 min prior to electrochemical measurements inorder to assure a steady OCP reading (maximum allowed drift of±2 mV over 5 min).

The polarization curves were obtained using stair case voltam-metry with the scan rate of 0.5mV s�1 and sampling period of 2 s�1.The anodic and cathodic polarization curves were obtained inseparate experiments, by sweeping the potentials from OCP to-wards more positive and more negative potentials, respectively.The reported results were corrected for ohmic drop using the so-lution resistance obtained from electrochemical impedance spec-troscopy (EIS) measurements, performed after polarizationmeasurements. The EIS measurements were conducted at OCP inthe frequency range of 0.2 Hze5 kHz with an AC perturbation po-tential of ±5 mV.

The reported corrosion rates were obtained from linear polari-zation resistance (LPR) measurements, conducted in separate ex-periments, following the abovementioned preparation procedure.For LPR measurements, the potential range of ±5 mV vs. OCP andscan rate of 0.125 mV s�1 was used. The experimental conditionsare summarized in Table 2.

Table 1Chemical Composition of the X65 Mild Steel in wt%.

S P V C Cr Mo Si Ni Mn Fe

0.009 0.009 0.047 0.13 0.14 0.16 0.26 0.36 1.16 Balance

2.2. Numerical methods and mathematical modeling

2.2.1. Water chemistry calculationThe solution speciation can be obtained considering the chem-

ical equilibria of the involved homogeneous reactions. In anaqueous solution containing acetic acid, the two homogeneousreactions are the acetic acid dissociation shown via Reaction (5) andwater dissociation shown via Reaction (6).

HAcðaqÞ#Ac�ðaqÞ þ HþðaqÞ

CAc�ðaqÞCHþðaqÞ

CHAcðaqÞ¼ KHAc (5)

H2OðlÞ #OH�ðaqÞ þHþ

ðaqÞ COH�ðaqÞCHþ

ðaqÞ¼ Kw (6)

The chemical equilibria corresponding to acetic acid and waterdissociation can be mathematically expressed as Equation (5) andEquation (6), respectively, using the equilibrium constants listed inTable 3.

Assuming that acetic acid concentration in the gas phase wasnegligible, the total acetate concentration (Ct,HAc) may be related toundissociated acetic acid concentration (CHAc) through a massbalance relationship described as Equation (7).

Ct;HAc ¼ CHAc þ CAc� (7)

In a solution without an externally induced electric field, theconcentration of the charged species must also satisfy the elec-troneutrality constraint as shown by Equation (8).Xi

ziCi ¼ 0 (8)

In addition to the four equations discussed above (Equations(5)e(8)), the known solution pH and NaCl concentration can beused to fully resolve the system of equations in order to obtain theconcentration of six chemical species (Hþ

(aq), HAc(aq), Ac�(aq),OH�

(aq), Naþ(aq), Cl�(aq)). Considering that there are no ferrous ionspresent in the solution initially, the concentration of this species inthe bulk solution was arbitrarily taken to be 10�6 M. The resultsobtained from the water chemistry calculation are shown in Fig. 1,where the ratio of undissociated acetic acid to the total acetic acidconcentration is demonstrated for various pH values at 30 �C and60 �C. At low pH values, the high concentration of hydrogen ionshifts the acetic acid dissociation equilibrium towards the left-handside, so that most of the acetate species are in the form of undis-sociated acetic acid. On the other hand, the dissociation equilibriumdictates that the majority of acetate species is in acetate ion form atnear neutral pH values. Fig. 1 also shows that a moderate change intemperature does not profoundly alter the solution speciation.

2.2.2. Electrochemical modelIn order to quantify the polarization behavior of the studied

system and also to ultimately estimate the corrosion rates, acomprehensive mathematical model of electrochemical/masstransfer behavior was developed similar to that discussed in detailelsewhere [20,21]. While the electrochemical reactions at the metalsurface define the observed current/potential response of the sys-tem, the rate of these reactions themselves are dictated by thesurface concentration of the involved electroactive species, whichare determined by the mass transfer towards/away from the elec-trode surface. The mass transfer for a RDE consists of three parallelprocesses. Convective flow of the bulk fluid leading to a flux of thechemical species.Molecular diffusion as a result of the concentrationgradient of the chemical species. Electromigration of the ionic spe-cies arising from the presence of an induced or spontaneous electric

Table 2Summary of the experimental conditions.

Experimental Conditions

Test apparatus Rotating disk electrodeThree-electrode glass cell

Temperature 30 �CRotation rate 2000 RPMElectrode material X65 mild steelSupporting electrolyte 0.1 M NaClpH 3.0, 4.0, 5.0Total acetate concentration 0 mM

1.66 mM (100 mass ppm)8.30 mM (500 mass ppm)16.60 mM (1000 mass ppm)41.50 mM (2500 mass ppm)

Table 3Equilibrium and reaction rate constants where K ¼ kf/kb.

Parameter Reference

KHAc ¼ 10

�� 1500:65

T � 6:50923 �logðTÞ � 0:0076792 �Tþ18:67257

�ðMÞ

[37]

Kw ¼ ð10�3rwÞ2 10��a1þa2

T þa3T2þa4

T3þ�a5þa6

T þa7T2

�logð10�3rwÞ

�ðM2Þ

a1 ¼ -4.098, a2 ¼ -3245.2, a3 ¼ 2.2362, a4 ¼ -3984E7,a5 ¼ 13.957, a6 ¼ -1262.3, a7 ¼ 8.5641E5

[38]

kf ;HAc ¼ 8:7� 105 ð1=sÞ [39]

kb;w ¼ 1:4� 1011 ð1=M:sÞ [40,41]

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652642

field. The flux of any given species i can be described throughEquation (9) [23].

Ni ¼ �ziuiFCiVf� DiVCi þ vCi (9)

The concentration distribution of each chemical species may becalculated by using the species conservation law, which can bemathematically expressed via Equation (10), also known as theNernst-Planck equation.

vCivt

¼ �V:Ni þ Ri (10)

Considering the symmetrical geometry of the RDE, thetangential and radial species flux components of Equations (9) and(10) can be neglected. Furthermore, the mobility of ions can beestimated using Einstein-Smoluchowski relationship (ui¼Di/RT),with diffusion coefficients listed in Table 4. Therefore, for a one-dimensional semi-infinite geometry in the direction x normal tothe metal surface, Equations (9) and (10) can be simplified toEquations (11) and (12) , respectively.

Ni ¼ � DivCivx

� ziDiFCiRT

vf

vxþ vxCi (11)

Table 4Reference diffusion coefficients at 25 �C.

Species Diffusion coefficient � 109 (m2/s) Reference

HAc 1.29 [42]Ac� 1.089 [42]Hþ 9.312 [23]OH� 5.273 [42]Naþ 1.334 [23]Cl� 2.032 [23,42]

Fe2þ 0.72 [23]

vCivt

¼ Div

vxvCivx

þ v

vx

�ziDiFCiRT

vf

vx

�� vx

vCivx

þ Ri (12)

The average bulk movement of the fluid in the direction normalto the surface is accounted for by the convective flow term vxC,where vx describes the velocity profile inside the diffusion layer.For a laminar flow regime of a RDE, the analytical solutions forthe velocity profile (vx) and the diffusion layer thickness (d) areshown as Equation (13), where a ¼ 0.510, and Equation (14),respectively [24].

vx ¼ �au�uy

�1 =

2x2 (13)

d ¼�3Dlim

ay

�1 =

3�uy

��1

=

2(14)

Furthermore, the effect of homogeneous chemical reactions:acetic acid and water dissociation, are reflected by the Ri term inEquation (12). In a generic form, the rate of chemical reaction j(Reaction (15)) can be calculated as shown in Equation (16).

Xnr

r¼1

Cr#Xnp

p¼1

Cp (15)

Rj ¼ kf ;jYnr

r¼1

Cr � kb;jYnp

p¼1

Cp (16)

The rate of production (or consumption) of a species i (Ri inEquation (12)) can be expressed in a matrix format as Equation (17).The kinetic rate constants of the chemical reactions can be found inTable 3.266664

RHþðaqÞ

RHAcðaqÞRAc�ðaqÞROH�

aq

377775 ¼

2664

1 1�1 01 00 1

3775�

�RHAcRw

�(17)

Considering the discussion so far in this section, Equation (12) isapplicable for each chemical species present in the system (Hþ,HAc, Ac�, OH�, Fe2þ, Naþ, Cl�) in order to determine their con-centration distribution inside the diffusion layer. However, for thisset of equations to be complete, the electric potential appearing inthe electromigration term also needs to be specified. This param-eter can be characterized through an additional relationship knownas the “electroneutrality” constraint as described by Equation (8).

2.2.2.1. Initial and boundary conditions. At the initial time (t ¼ 0), itcan be assumed that awell-mixed solution comes into contact withthe metal surface. Hence, the concentrations of the chemical spe-cies throughout the diffusion layer are constant known values,defined by the chemical equilibria of the solution, as discussed inSection 2.2.1.

At the bulk solution boundary, where x¼ d, the concentration ofchemical species remains unchanged at all times (t � 0). Therefore,the boundary condition can be defined based on the known con-centration of species, identical to those of the initial conditions.

The boundary condition at the metal/solution interface is basedon the electrochemical reaction rate calculations. For an electro-active chemical species, the flux at the metal/solution boundary isequal to the rate of the corresponding electrochemical reaction.Therefore, for species i involved in electrochemical reaction j, theflux at the metal surface can be described through Equation (18).

Table 5Electrochemical reaction rate relationships and parameters.

Charge transfer rates n a m E0,j vs. SHE (V) k0 j, ref Ea (kJ/mol)

ic;Hþ ¼ �nHþ Fk0 Hþ ðCsHþ ÞmHþ e

��aHþ nHþ FðE�E0 Hþ Þ

RT

�1 0.43 0.5 0.00 7.58 � 10�8 110.6

ia;Fe ¼ nFeFk0 FeðCsOH� ÞmOH� e

�ð2�aFe ÞFðE�E0 Fe Þ

RT

�

pH < 5 or CHAc > 0

2 0.50 1 �0.44 2.27 � 101 29.5

ia;Fe ¼ nFeFk0 FeðCsOH� ÞmOH� e

�2ð1�aFe ÞFðE�E0 Fe Þ

RT

�

pH ¼ 5 and CHAc ¼ 0

2 0.65 0 �0.44 2.05 � 10�5 -

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 643

Nijx¼0 ¼ � sijijnjF

(18)

Based on the analysis of the experimental results (Section 3.1),acetic acid was not considered to be involved in anyelectrochemical reaction. Also, considering that the waterreduction reaction is not significant at the corrosion potential, itwas not included in the model. Hence, the electrochemical re-actions considered in the model consisted only of one cathodicreaction, hydrogen ion reduction (Reaction (3)), and one anodicreaction, iron oxidation (Reaction (2)). Due to negligible con-centration of H2 in the solution (which is stripped out by thenitrogen bubbling through the solution), no significant contri-bution of hydrogen oxidation reaction over the potential range ofinterest is expected. Hence, the current density resulting fromhydrogen ion reduction was calculated in the form shown inTable 5, which considers the cathodic half reaction only. Therelated kinetic parameters, including the transfer coefficient a,the reaction rate constant ko, and the reaction order mHþ,were obtained based on the experimental data as discussed inSection 4.

The current density resulting from iron dissolution (Reaction(2)) can be calculated by considering the anodic half reaction only,since the ferrous ion reduction may also be assumed negligible,because of its low concentration and the potential range of interest.The rate of iron oxidation reaction, at the active dissolution rangeobserved in lower pH values (e.g. below 5), is known to have a firstorder pH dependence [25,26,30]. It is also known that the mecha-nism of iron oxidation reaction at the vicinity of corrosion potentialchanges at near neutral pH values [25,26,28]. Therefore, twodifferent reaction rate relationships were considered, one for lowerand the other for higher pH values, as shown in Table 5. These re-lationships are based on previously reported behavior, with astrong pH dependence in more acidic solutions and no dependenceat higher pH values [25,28]. The change of mechanism is also re-ported to coincide with a change of apparent Tafel slope. The ki-netic parameters reported in Table 5 were obtained based on theexperimental results of the present study, as further discussed inSection 4.

The current/potential relationships used to calculate the rateof electrochemical reactions are listed in Table 5. The negativesign in Equation (18) is due to a sign convention where cathodiccurrents are taken as negative while anodic currents are positive.Furthermore, all the reactions are written in “cathodic” form (e.g.Reactions (2) and (3)), so the reactants on the left hand side arerepresented with a negative stoichiometric coefficient (sij) andthe products on the right hand side are represented as positivevalues.

Equation (18) can be expanded using a matrix notation in orderto include all the electro-active species:

"NFe2þðaqÞ

jx¼0

NHþðaqÞ

jx¼0

#¼�1 00 �1

��

2664iFe2FiHþ

F

3775 (19)

For non-electroactive species, the flux at the metal surface iszero, as it is a non-porous non-reactive barrier:

Nijx¼0 ¼ 0 (20)

The flux Equations (19) and (20) can be used to describe theboundary conditions for all chemical species at the metal surface.

In order to calculate the cathodic and anodic current inEquations (19), the potential at the metal surface (E) needs to beknown. That is true for the case where electrode potential is thecontrolled parameter (such as in potentiodynamic measure-ments). However, when the calculations are done to obtain thecorrosion rates, the potential at the metal surface is not explicitlyknown. In that case, an additional relationship is required torelate the potential at the metal surface to other known param-eters. This can be achieved by introducing the charge conserva-tion at the electrode surface based on the mixed potentialtheory. That suggests the net current resulting from all j elec-trochemical reactions is equal to zero, mathematically expressedas Equation (21).Xj

ij ¼ 0 (21)

2.2.2.2. Numerical solution. Table 6 summarizes all the relevantmathematical equations required to develop a comprehensivemathematical model as discussed above. These equations form a setof non-linear, coupled, partial differential equations to be solvednumerically. Considering a simple one-dimensional computationalspace, the finite difference method can be used to solve the equa-tions. This method is commonplace in mathematical modeling ofelectrochemical systems with similar geometry and has been dis-cussed in detail elsewhere [23,29].

The partial differential equations are discretized using secondorder Taylor's series approximations. The time integration is doneexplicitly, using Euler approximation. The resulting algebraicequations can be written in a matrix format, as a tri-diagonal co-efficient matrix multiplied by the unknown concentrations andsolution potential. The final solution can then be obtained throughdifferent solution algorithms such as Neman's “BAND” open-sourcecode where it is solved by LU decomposition method [23,29]. Thepresence of nonlinear terms, such as those in the electromigrationor chemical reactions relationships, makes some of the terms in thecoefficient matrix to be a function of other concentrations and/orpotential, i.e. they are not explicitly known. In the approach used in

Table 6Summary of equations used in the mathematical model.

Electrode surface boundary

Nijx¼0 ¼ � sij ijnjF

for electroactive species

Nijx¼0 ¼ 0 for non-electroactive speciesPiziCi ¼ 0P

jij ¼ 0 for unknown electrode potential

Diffusion layer

vCivt ¼ Di

vvx

vCivx þ v

vx

�ziDiFCiRT

vfvx

�� vx

vCivx þ Ri

for all species

PiziCi ¼ 0

Bulk boundary conditions

Ci ¼ Cbi

for all species

F ¼ 0 arbitrary reference potential

Fig. 2. Polarization behavior of X65 mild steel in solution of pH 5, at 30 �C, 2000 rpm,0.1 M NaCl, and undissociated acetic acid concentrations 0 mM, 0.6 mM(Ct,HAc ¼ 1.7 mM), 3.0 mM (Ct,HAc ¼ 8.3 mM), and 15.1 mM (Ct,HAc ¼ 41.5 mM).

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652644

the present model, the final solution was obtained iteratively byusing an initial guess for the unknown terms of the coefficientmatrix eusually the last calculated value of the unknown terme

until the desired accuracy (R2¼10�12) was achieved.

3. Results and discussion

In general, the reduction of any weak acid in an aqueous solu-tion, including acetic acid used in the present study, is thermody-namically identical to that of hydrogen ion reduction. This can bereadily shown through the reversible potential of the two reactionsbased on the Nernst equation, where the concentration of the weakacid and its conjugate base are defined by the chemical equilibriumof theweak acid dissociation. Therefore, the difference between thehydrogen ion reduction and the direct reduction of the weak acidresides only in the kinetics of these electrochemical reactions. Thetwo reactions can therefore be distinguished by investigating thecathodic polarization behavior of the system in the charge transfercontrolled current range.

The experimental conditions in the present studywere designedso that the electrochemical activity of acetic acid, as an additionaloxidizing species, could be properly distinguished. In these exper-iments, at a fixed solution pH the concentration of acetic acid wasvaried. Since the charge transfer rate from hydrogen ion reductionis constant at a constant pH, any increase in the charge transfercontrolled current density indicates that the direct reduction ofacetic acid is significant and it is occurring in parallel. In contrast, ifthe charge transfer controlled current density remain unchangedfor different acetic acid concentrations, one can conclude that thedirect reduction of acetic acid is not significant.

Furthermore, all the reported polarization curves in this sectionshow a significant increase in mass transfer limiting current, as theconcentration of acetic acid is increased. However, the behavior ofthe mass transfer limiting current is the same irrespective ofwhether acetic acid is directly reduced or not, thus, the variation inthe limiting current density cannot be used to determine theelectrochemical activity of acetic acid. The effect of acetic acidconcentration on change transfer controlled currents is presentedin section 3.1 below, and its effect on limiting currents is discussedin section 3.2.

3.1. Electrochemical activity of acetic acid

The typical polarization curves at pH 3, pH 4 and pH 5 forincreasing acetic acid concentrations are reported in Figs. 2e4. Inthese graphs the anodic polarization curves typically consist of alinear range, just above the OCP, followed by a current maximumand another linear range at more positive potentials. The cathodic

polarization curves also consist of a linear range just below the OCP,associated with the hydrogen ion reduction, followed by the masstransfer limiting current and another linear range at more negativepotentials associated with the water reduction reaction. The dis-cussion below is mostly focused on the electrochemical reactions inthe vicinity of the OCP. That is, the anodic current densities belowthe anodic current maximum and cathodic current densities up tothe limiting current.

Fig. 2 shows the polarization curves obtained at pH 5, where asignificant change was observed by addition of 0.60 mM undisso-ciated acetic acid (Ct,HAc¼ 1.66 mM). The shift of OCP towards morepositive potentials can be explained when considering that thecathodic polarization curve was under mass transfer control in theabsence of acetic acid, and the significant increase of the limitingcurrent by addition of acetic acid leads to an increased OCP. In thepresence of acetic acid, a Tafel behavior is clearly observed in thecathodic polarization curves, particularly when the acetic acidconcentration was further increased. The comparison of the chargetransfer controlled currents did not indicate any increase in chargetransfer rates that could be associated with direct reduction ofacetic acid. Actually, one can observe a slight decrease withincreasing acetic acid concentration, a behavior that will be dis-cussed further below. The cathodic polarization curves obtained atacetic acid concentrations up to 15.1 mM (Ct,HAc ¼ 41.5 mM) furthersupport these observation.

The anodic polarization curves in Fig. 2 show a significantchange in the polarization behavior by addition of 0.60 mM un-dissociated acetic acid. In the presence of acetic acid, a Tafel slopeof approximately 40 mV was observed, which agrees well withthe typical Tafel slopes reported in the literature for anodic irondissolution in acidic solutions [13,25]. The same 40 mV Tafelslope was obtained in the experimental data reported below forlower pH values with or without acetic acid present. However atpH 5, as shown in Fig. 2, a notably different behavior with anapparent ~90 mV Tafel slope and a significantly higher rates ofthe anodic dissolution reaction was observed when no acetic acidwas present. A similar effect has been repeatedly reported in theliterature that suggests a significant change in the electro-chemical behavior of the iron dissolution reaction occurs as thesolution pH is increased towards neutral values (pH 5 and higher)[25,26,30,31]. This can be better understood by considering thewell-known categorization of El Miligy et al. [26] who suggested

Fig. 3. Polarization behavior of X65 mild steel in acidic solution of pH 4, at 30 �C, RDE,2000 rpm, 0.1 M NaCl, and undissociated acetic acid concentrations 0 mM, 1.4 mM(Ct,HAc ¼ 1.7 mM) and 7.1 mM (Ct,HAc ¼ 8.3 mM).

Fig. 4. Polarization behavior of X65 mild steel in acidic solution of pH 3, at 30 �C, RDE,2000 rpm, 0.1 M NaCl, and undissociated acetic acid concentrations 0 mM, 1.6 mM(Ct,HAc ¼ 1.7 mM), and 8.2 mM (Ct,HAc ¼ 8.3 mM).

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 645

that the iron dissolution in mildly acidic environments passesthrough four ranges as the potential is increased towards morepositive values. The four ranges are characterized with differentTafel slopes and reaction orders, depending on the solution pHand the electrode potential [26]. Ordered from more negativetowards more positive potentials, the authors categorized theseranges as active dissolution, characterized by 30e40 mV Tafelslope, transition, characterized by observation of the first currentmaximum, pre-passivation, characterized by a 120 mV Tafel slope,and passivation that occurs after the second current maximum[26]. The 40 mV Tafel slope observed in most conditions in thepresent study is a characteristic behavior of the iron oxidation inthe active dissolution range. The increased Tafel slope at higher pHvalues suggests that the iron dissolution was at the transition/pre-passivation range. Nevertheless, the above discussion does notexplain why the presence of acetic acid shifts the OCP back intothe active dissolution range. The complete picture can only beseen when considering the behavior of cathodic currents as well.The comparison of the cathodic polarization curves in Fig. 2,shows that at pH 5 when no acetic acid was present, the masstransfer limited cathodic currents were extended into the po-tential range well above the OCP, up to �0.425 V (vs. SHE). Thatmeans, the pH at the surface remains significantly higher thanthe pH in the bulk solution even when the electrode was polar-ized anodically. Therefore, the change in the electrochemicalbehavior of the iron dissolution reaction with addition of aceticacid is merely a result of increased cathodic limiting currents andconsequently decreased surface pH to that of the bulk solution atpotentials equal or higher than OCP (anodic potential range).

A smaller, but notable decrease of the anodic dissolution ratewas observed as the acetic acid concentration was furtherincreased. The anodic current densities at these conditions wereslightly retarded while the observed Tafel slopes remained un-changed, what was observed as a slight shift of open circuit po-tentials toward more positive values. This same behavior has beenfrequently reported in the literature, suggesting that acetic acidslightly inhibits the iron dissolution reaction [10,12,17].

The polarization curves at pH 4 with and without acetic acid areshown in Fig. 3. The Tafel behavior is clearly observed in the solu-tions containing acetic acid, with charge transfer controlled cur-rents showing no significant increase with increasing acetic acidconcentration. The inhibiting effect on the anodic dissolution

reaction can be clearly observed with the increase in acetic acidconcentration.

The polarization curves at pH 3 are shown in Fig. 4. This con-dition is of particular significance, since the Tafel behavior is clearlyobserved even when no acetic acid was present. At this conditionalso, increasing the acetic acid concentration did not result in anyincrease of the charge transfer controlled cathodic current (in theTafel range), further supporting the argument that acetic acid is notdirectly reduced at the steel surface. Actually, an opposite effectwas clearly observed that suggests a significant inhibiting effect ofacetic acid on cathodic currents. The similar effect was noticeable atpH 5 and pH 4 as well (in Figs. 2 and 3), however, it was not asclearly discernible. The inhibitive effect on the anodic dissolutionwas also observed at pH 3 similar to what was shown at higher pHvalues.

Based on the polarization behavior of the studied system, it isreasonable to conclude that acetic acid is not a significantelectroactive species in the conditions considered in the presentstudy (i.e. if there is any cathodic current resulting fromreduction of acetic acid it is overshadowed by its inhibitingeffect on the charge transfer rate of hydrogen ion reduction).Specifically, the results shown at pH 5 and 15.08 mM acetic acid,where CHAc/CH

þz1500, suggest that the reaction rate constant foracetic acid direct reduction is at least three orders of magnitudelower than that of hydrogen ion reduction, considering that theover potential is identical for both reactions [1] (based on theNernst equation with concentration terms defined by acetic acidequilibrium). Therefore, it can be assumed that the contributionof direct acetic acid reduction in the typical conditions encoun-tered in the oil and gas industry would be insignificant ascompared to hydrogen ion reduction. Thereby, the corrosionprocess of mild steel in mildly acidic solutions containing aceticacid is a result of only two electrochemical reactions: hydrogenion reduction as the sole cathodic reaction and the iron disso-lution as the sole anodic reaction. However, the polarizationcurves reported in Figs. 2e4 suggest that the presence of aceticacid significantly affects the corrosion process, first by increasingthe mass transfer limiting current and second, by inhibiting thecharge transfer rate of both the cathodic hydrogen ion reductionreaction and the anodic iron dissolution reaction. These pro-cesses are the subjects of further discussions in the followingsections.

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652646

3.2. Effect of acetic acid on limiting current

The reported polarization curves in Figs. 2e4 showed that thelimiting current density is significantly affected by acetic acidconcentration. As concluded in the previous section, the hydrogenion reduction is the only cathodic reaction in the present discus-sion. The limiting current is therefore a result of the depletion ofhydrogen ion concentration at the metal surface. In accordance tothis local change of pH at the limiting current condition, the localchemical equilibrium of acetic acid (Reaction (1)) at the surfaceshifts towards acetic acid dissociation. Consequently, the acetic aciddissociation is acting as an additional source of hydrogen ions,further increasing the limiting current. Therefore, the cathodiclimiting current is consist of two components:

� The mass transfer of hydrogen atoms from the bulk to the metalsurface followed by their reduction at the surface.

� The mass transfer of undissociated acetic acid followed by ho-mogeneous dissociation to hydrogen ions and acetate ions in-side the diffusion layer, succeeded by reduction of the producedhydrogen ion at the surface.

The effect of acetic acid on mass transfer rates was also studiedin experiments at a fixed solution composition while the rotationspeed of the RDE was varied. Fig. 5 shows the typical polarizationcurves obtained at 125, 500, and 2000, rpm at pH 3 where no aceticacid was present (Fig. 5A) and when the solution contained8.13 mM undissociated acetic acid (Fig. 5B).

For the case where the hydrogen ion reduction reaction followsthe acetic acid dissociation reaction, the limiting current densitycan be expressed through Equation (22), for a RDE flow geometry[32].

ilim ¼nFD

�CbHþ þ Cb

HAc

�

1:61 D13 u� 1

2 n16 þ �

Dðkf ;HAcþkb;HAcÞ

�12

=KHAc

! (22)

In the absence of acetic acid, the second term in the denomi-nator of Equation (22) as well as the acetic acid concentration termdisappear. Hence, Equation (22) reduces to the well-known Levichequation where the limiting current is proportional to u0.5. Theresults obtained in the absence of acetic acid at pH 3 were found toagree well with this expected trend, as shown in Fig. 6.

In the presence of acetic acid, Equation (22) suggests that thebehavior of limiting current vs. u0.5 would depend on the kineticsand the equilibrium constant of the acetic acid dissociation reactionas well. Nevertheless, the linear behavior obtained in the presenceof acetic acid, as shown in Fig. 6, suggests that the flow dependentterm (first term in denominator) has remained significantly largerthan the chemical reaction dependent term, even at rotation speedsas high as 2000 rpm. Considering that the denominator of Equation(22) is defined only by the environmental conditions and physi-ochemical parameters, the limiting currents in the system studiedhere could therefore be represented by the superposition ofhydrogen ion and acetic acid mass transfer from the bulk. That isshown to be indeed the case in Fig. 7, where the limiting current ispresented as a function of the sum of hydrogen ion and undisso-ciated acetic acid concentrations. It should be noted that thedifferent diffusion coefficient of acetic acid and hydrogen ion, as theonly species dependent parameter, should be accounted for in thistreatment. The linear behavior of the trendline and the fact that it iscrossing the origin, justifies this approach. These results suggestthat acetic acid is a strong buffer in the sense that the kinetics andthe equilibrium of its dissociation equilibrium allows this species to

readily dissociate and buffer the hydrogen ion concentration at themetal surface, whenever the hydrogen ion concentration deviatesfrom the equilibrium. In other words, undissociated acetic acid isprimarily a “carrier” for hydrogen ions and increases the effectiveconcentration of hydrogen ions in mild steel corrosion.

4. Estimation of physiochemical parameters

Themathematical model developed in Section 2.2.2, was used toobtain the physicochemical parameters of the studied system. Thiswas achieved by determining appropriate values by fitting themodel to the experimental data. The kinetic parameters of theelectrochemical (hydrogen evolution and iron dissolution) re-actions were obtained by using only the experimental data whereno acetic acid was present. This step was considered necessary toassure that the estimated parameters were free of any interferencedue to the presence of acetic acid. Fig. 8 shows the comparison ofthe model (dotted black lines) with the experimental data at pH 3to pH 5, using the estimated parameters shown in Table 5.

The transfer coefficient for the hydrogen ion reduction (0.43)was slightly lower than the commonly accepted theoretical value of0.5, however, similar deviations have been previously reported[33,34]. The iron dissolution reaction showed a significant changein the kinetic parameters at pH 5 (compared to pH 3 and pH 4)where the Tafel slope increased from 40 mV at pH 4 to approxi-mately 90 mV at pH 5. As discussed above, this behavior has beenfrequently reported in the previous studies [25,26,30,31], andsuggests that at this environmental condition the mechanism ofiron dissolution in the vicinity of corrosion potential is no longer inthe active dissolution range. Based on this observation, a differentcharge transfer relationship was used for this particular condition(Table 5). As noted in section 3.1, this behavior was only observed atpH 5 when no acetic acid was present.

4.1. Inhibiting effect of acetic acid

Considering that the direct acetic acid reduction was shown tobe insignificant in the conditions of the present study, the modeldeveloped above based solely on hydrogen ion reduction and irondissolution reactions, should be able to describe the steady statevoltammograms obtained in the presence of acetic acid. However,the inhibiting effect of undissociated acetic acid on the chargetransfer rates also needs to be quantified for more accurate pre-diction of both the polarization curves and corrosion rates.

The inhibiting effect of acetic acid on the anodic and cathodiccharge transfer rates was quantified in terms of its adsorption onthemetal surface acting as aweak corrosion inhibitor that results inblockage of the active sites of the electron transfer reactions.However, considering numerous surface active species, such aswater, chloride ions, as well as anodic and cathodic reaction in-termediate species and the non-uniformity of the steel surface, adetailed mechanistic description of this phenomena is well beyondthe scope of the present study, hence, a semi-empirical approachwas employed. In this approach, the rate of electrochemical re-actions in the presence of acetic acid was assumed to followEquations (23) and (24):

iHþ;HAc ¼ iHþ ð1� qcÞ (23)

iFe;HAc ¼ iFeð1� qaÞ (24)

Since the reaction rate constants were known from the condi-tion without acetic acid present, the surface coverage of acetic acid(q) could be determined by the apparent rate constants from theexperimental data as shown in Equation (25). Here k0,HAc is the

Fig. 5. Polarization behavior of X65 mild steel in acidic solution of pH 3, at 30 �C, 0.1 M NaCl, and various rotation speeds. A) CHAc¼0 mM, B) CHAc¼8.2 mM.

Fig. 6. The behavior of the limiting current density vs. square root of rotation speed inacidic solution of pH 3, at 30 �C, 0.1 M NaCl.

Fig. 7. Limiting current density at various hydrogen ion and undissociated acetic acidconcentrations on X65 RDE, 2000 rpm, 30 �C, 0.1 M NaCl and CHAc from 0 mM to8.2 mM.

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 647

apparent reaction rate constant in the presence of acetic acid and k0is the reaction rate constant at similar conditions but when aceticacid was not present.

k0;HAck0

¼ ð1� qÞ (25)

As noted in Equation (25), the calculation of q required the k0where no acetic acid was present to be known explicitly. As shownin Figs. 2e4, pH 3 was the only condition where the pure chargetransfer controlled cathodic current was observed without aceticacid being present, and the anodic polarization curves were notaffected by local pH due to cathodicmass transfer limitation. Hence,the k0 values could be obtained from the experimental data,directly. Thereby, pH 3 was selected as the base condition for thediscussion on the inhibitive effect of acetic acid on the chargetransfer rates. Fig. 9 demonstrates the values of surface coverageobtained as described via Equation (25), using the experimentaldata at pH 3 and extended acetic acid concentrations.

The coverage effect associated with the acetic acid adsorptionshows a logarithmic trend with the undissociated acetic acid

Fig. 8. Comparison of the experimental and calculated (dotted back lines) polarizionbehavior of X65 mild steel in acidic solutions in the absence of HAc, at 30 �C, 0.1 MNaCl, RDE, 2000 rpm, and various pH values.

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652648

concentration, as shown in Fig. 9. Transforming this functionality(Equation (26) to Equation (27)) shows that acetic acid follows aTemkin type adsorption isotherm.

q ¼ A lnðCHacÞ þ B (26)

eðrqÞ ¼ KCHac (27)

where K ¼ eB=A and r ¼ 1

=A. However, the observed inhibiting effect

was different for the cathodic and anodic reactions. That is due tothe semi-empirical treatment of these parameters where the effectof the numerous surface active species and non-uniform steelsurface are all lumped into the two constants of Equation (26). Thedifference in the observed inhibitive effect on the cathodic andanodic currents suggests a competitive adsorption scenario. Atanodic currents, acetic acid is competing with electrochemicalhydroxide adsorption as the reactions intermediate of the irondissolution [25,35,36], while at cathodic currents it is the electro-chemical hydrogen ion adsorption in competition with acetic acid.

Fig. 10 is a comparison of the experimental results at pH 3 withthose calculated by the model. The agreement of the resultsshowed that the inhibitive effect of acetic acid was properly re-flected through the Temkin type adsorption isotherms discussedabove.

4.2. Temperature effect

An increase in temperature affects the charge transfer and themass transfer rates as well as the adsorption of acetic acid, and thesolution speciation (as discussed in section 2.2.1). Fig. 11 shows theexperimental polarization curves obtained at pH 3 for 30 �C, 40 �Cand 50 �C, A) in the absence and B) in the presence of acetic acid.

The effect of temperature on mass transfer rate is through tem-perature dependence of the terms in the Nernst-Planck equation,which includes the diffusion coefficient in molecular diffusion andelectromigration terms. The flow velocity (vx) in convective flowterm is affected by the temperature dependence of physical prop-erties of water, such as viscosity and density. The temperaturedependence of these parameters are summarized in Table 7.

The effect of temperature on charge transfer rate can be

Fig. 9. The variation of q, defined by Equation (25), as a function of undissociated aceticacid concentration for cathodic currents (green diamonds) and anodic currents (redsquares). Error bars are based on the standard devation of at least three repeats. (Forinterpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)

characterized by an Arrhenius law type of expression and theactivation energy of the electrochemical reactions. Fig. 12 showsthe temperature dependence of the apparent reaction rate con-stants, where the slope of the trendline represents the activationenergy of a given reaction (Ea/R). Therefore, the temperaturedependence of the electrochemical reactions can be expressedthrough van't Hoff's law:

k0 j ¼ k0 j;ref e

�� Ea

R

�1T� 1

303

(28)

The effect of temperature on inhibition by acetic acid can be dis-cussed in terms of the parameter q as shown in Equation (27),where K is the adsorption equilibrium constant with an Arrheniustype temperature dependence (K¼K0 e

-Ea/RT) and r¼b/RT. Therefore,Equation (26) can be restated as Equation (29) to accommodate forthe temperature effect.

q ¼ RTb

ðlnð½HAc�Þ þ lnðK0ÞÞ �Eab

(29)

The only unknown parameter in Equation (29) is Ea, the acti-vation energy of the acetic acid adsorption equilibrium constant. Asshown in Equation (29), Ea is represented by the intercept of thetrendline (-Ea/b) in a q vs. T graph as shown in Fig. 13. From theseresults, the temperature effect on the inhibition by acetic acid isexpressed by the last two equations shown in Table 7.

The temperature dependence of the physiochemical parame-ters, as summarized in Table 7, were incorporated into the modeland the predicted voltammograms were compared with experi-mental data. Fig. 11A shows the comparison for the case withoutany acetic acid present, while the predicted voltammograms for asolution at pH 3 and 8.2 mM undissociated acetic acid concentra-tion is shown in Fig. 11B. Here again a reasonable agreement wasfound while at more negative potentials close to limiting currentdensities, slight deviations between the predicted apparent Tafelslopes and the measurements were observed.

The effect of increased temperature in the presence of aceticacid is demonstrated in Fig. 14 based on the prediction of the modelat pH 5. These results shows a synergistic effect of temperaturewith undissociated acetic acid concentration on the corrosion ratesthat further elucidates the inconsistent behavior of corrosion ratesin the presence of acetic acid as reported in the literature (see

Fig. 10. Comparison of the experimental and calculated (dotted black lines) polarizionbehavior of X65 mild steel in acidic solutions demonstrating the inhibitive effect ofacetic acid of pH 3, at 30 �C, 0.1 M NaCl, RDE, 2000 rpm.

Fig. 11. Comparison of the experimental and calculated (dotted black lines) polarizion behavior of X65 mild steel in acidic solutions demonstrating the temperature effect at pH 3,0.1 M NaCl, 2000 rpm RDE at 30 �C (blue line), 40 �C (green line), and 50 �C (red line). A) 0 ppm HAc, B) 500 ppm HAc. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

Table 7Temperature dependence of the physiochemical properties.

Parameter Relationship Reference

Water density (kg/m3) rw ¼ 753:596þ 1:87748 T � 0:003562 T2 [28]Water viscosity (cP)

m ¼ mref 10

0B@1:1709 ðTref �TÞ�0:001827ðTref �TÞ2

ðT�273:15Þþ89:93

1CATref ¼ 293:15 K; mref ¼ 1:002 cP

[43]

Diffusion coefficient Di ¼ Di;refTTref

mrefm

[23]

HAc adsorption, cathodicqc ¼ 8:86� 102 T

303:15

�lnðCHAcÞ þ 10:61þ �61385

R

�1T � 1

303:15

��This study

HAc adsorption, anodicqa ¼ 1:57� 10�1 T

303:15

�lnðCHAcÞ þ 9:02þ �2248

R

�1T � 1

303:15

��This study

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 649

Section 1). Fig. 14 shows that a maximum corrosion rate exists ateach condition, which is increased at higher temperatures and isgreatly influenced by acetic acid concentration. The decreasingtrend of corrosion rates, observed in Fig. 14 is a result of acetic acid

Fig. 12. Temperature dependance for the reaction rate constant without acetic acidpresent at pH 3, 0.1 M NaCl, for hydrogen ion reduction (blue diamonds) and ironoxidation (red squares). Error bars are based on the standard devation of at least threerepeats. (For interpretation of the references to colour in this figure legend, the readeris referred to the web version of this article.)

inhibitive effect on the charge transfer cathodic and anodic currentswhen the corrosion current is controlled by the rate of electro-chemical reactions. Whereas, the increasing effect on the corrosionrate stems from the buffering ability of acetic acid and the resultingincrease in limiting currents, when the corrosion current is undermass transfer control. At elevated temperatures, the increased rateof anodic and cathodic reactions shifts the corrosion current to-wards the mass transfer limiting range, as readily observed in thepolarization behavior in Fig. 11. This combined effect leads toextremely high corrosion rates at elevated temperatures in thepresence of acetic acid.

5. Corrosion rate prediction

The performance of the mathematical model developed in theprevious sections was further examinedwith the comparison of theestimated corrosion rates with the experimental data. Fig. 15 is thecomparison of the corrosion rate data obtained by linear polariza-tion measurements at pH 3, pH 4, and pH 5 with and without aceticacid present. At pH 3 and pH 4 where the corrosion current ismostly under charge transfer control, increasing acetic acid con-centration decreased the corrosion rates. At pH 5 and in the absenceof acetic acid, the corrosion current was under mass transfer con-trol (Fig. 2), therefore, by addition of 0.6 mM undissociated aceticacid, the corrosion rate was rapidly increased, but further increaseof acetic acid resulted in a slightly lower corrosion rate. The effect ofacetic acid on the observed corrosion rates shown in Fig. 15 was in

Fig. 13. Temperature dependance for acetic acid adsorption at pH 3, 0.1 M NaCl, andCHAc ¼ 8.2 mM, for hydrogen ion reduction (blue diamonds) and iron oxidation (redsquares). Error bars are based on the standard devation of at least three repeats. (Forinterpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)

Fig. 15. Comparison of the experimental and calculated corrosion rates of X65 mildsteel in acidic solutions, at 30 �C, 0.1 M NaCl, 2000 rpm, at various pH and Ct,HAc values.Dashed boxes show the predicted values. Error bars are based on the standard devationof at least three repeats. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652650

complete agreement with the expected behavior as discussed inSection 3.

The performance of the model was further examined in theparity plot shown in Fig. 16 where the experimental datawas compared with the calculated corrosion rates for a widerrange of environmental conditions and solution compositions(22 �C < T < 60 �C, 2 < pH < 5, 0 mM < Ct,HAc < 16.6 mM,125 rpm < rotation speed < 2000 rpm). Most of the calculated datapoints are within 20% of the measured values and in almost everycase within a factor of two.

6. Conclusions

- The experimental results and the quantitative analysis reportedin the present study showed that the direct acetic acid reductiondoes not significantly contribute to the cathodic currents inacidic solutions.

- Acetic acid was shown to be a strong buffer which was fullydissociated under mass transfer limiting conditions, meaning

Fig. 14. The estimated corrosion rates for mild steel in pH 5, 0.1 M NaCl, 2000 rpm RDEwith respect to temperature and total acetic acid concentration.

Fig. 16. Comparison of the predicted corrosion rates with experimental results for awide range of parameters. 22 �C < T < 60 �C, 2 < pH < 5, 0 mM < Ct,HAc < 16.6 mM,125 rpm < rotation speed <2000 rpm. Additional experimental data from Zheng et al.[44] and George et al. [13]. Dashed lines and the dotted dashed lines represent 20% andone fold deviation, respectively. Error bars are based on the standard devation of atleast three repeats.

that the kinetics of the dissociation reaction were not ratedetermining.

- The inhibitive effect of acetic acid was explained through itsadsorption on the metal surface, which was well defined by aTemkin type adsorption isotherm. Different adsorption con-stants over the anodic and cathodic current suggested acompetitive adsorption scenario depending on the electrodepotential and the dominant electron transfer reaction.

- The results reported in the present study suggest that thepresence of acetic acid affects the acidic corrosion of mild steelthrough two mechanisms:� Acetic acid increases the corrosion rate through buffering theHþ concentration at the metal surface, if the corrosion currentis under mass transfer control.

A. Kahyarian et al. / Electrochimica Acta 258 (2017) 639e652 651

� Acetic acid decreases the corrosion rate by inhibiting thecharge transfer rates, if the corrosion current is under chargetransfer control.

- Elevated temperatures were shown to have a synergistic effecton acetic acid corrosion by shifting the corrosion current to-wards the mass transfer limiting condition, where acetic acidhas a determinant effect.

Acknowledgments

The authors would like to acknowledge the financial supportfromAnadarko, Baker Hughes, BP, Chevron, CNOOC, ConocoPhillips,DNV GL, ExxonMobil, M-I SWACO (Schlumberger), Multi-Chem(Halliburton), Occidental Oil Company, Petrobras, PTT, Saudi Ara-mco, Shell Global Solutions, SINOPEC (China Petroleum), TOTAL,and Wood Group Kenny under a joint industrial research project.

Nomenclatures

A Surface area, m2

Ci Concentration of species i, MCbi Concentration of species i at bulk, M

Csi Concentration of species i at metal surface, M

Di Diffusion coefficient of species i, m2/sDi;ref Diffusion coefficient of species i at reference temperature,

m2/sE Electrode potential, VEa Activation energy, JE0j Standard potential of reaction j, VF Faradays constant, C/molDHj Enthalpy of reaction j, kJ/molij Current density of reaction j, A/m2

Kj Equilibrium constant of reaction jk0j Rate constant of electrochemical reaction jk0 j;ref Rate constant of electrochemical reaction j at reference

temperaturekf Forward reaction rate constantkb Backward reaction rate constantmi Reaction order with respect to species inj Number of transferred electrons in electrochemical

reaction jnr Number of reacting speciesnp Number of produced speciesNi Flux of species i, mol/m2 sr Temkin adsorption isotherm correlation coefficientR Universal gas constant, J/K molRi Reaction rate of species i, M/ssij Stoichiometric coefficient of species i in reaction jT temperature, KTref Reference temperature, Kt Time, sui Mobility of species i, m/svx Velocity along x axis, m/sx Distance from metal surface, mzi Charge of ion iaj Transfer coefficient of electrochemical reaction jd Diffusion layer thickness, mm Water viscosity, kg/s.mmref Water viscosity at reference temperature, kg/s.mq Surface coverage by acetic acidrw Density of water, kg/m3

y Kinematic viscosity, m2/sf Electric potential inside liquid, V

u Angular velocity, rad/s

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