advancement in predictive modeling of mild steel … in...advancement in predictive modeling of mild...

Advancement in Predictive Modeling of MildSteel Corrosion in CO2- and H2S-ContainingEnvironments

Yougui Zheng,* Jing Ning,* Bruce Brown,* and Srdjan Nešic‡,*

ABSTRACT

Over the past decade, the knowledge related to predictinginternal pipeline corrosion for sweet and particularly sourenvironments has dramatically improved. Advancement inunderstanding of the corrosion mechanisms related to H2Scorrosion environments enabled the development of an inte-grated electrochemical model for CO2/H2S uniform corrosion,including the effect of H2S on the protective corrosion productformation on mild steel. The latest model of uniform CO2/H2Scorrosion of carbon steel accounts for the key processesunderlying of corrosion: chemical reactions in the bulk solution,electrochemical reactions at the steel surface, the masstransport between the bulk solution to the steel surface, and thecorrosion product formation and growth (iron carbonate andiron sulfide). The model is able to predict the corrosion rate, aswell as the surface water chemistry, as related to all of thekey species involved. The model has been successfully cali-brated against experimental data in conditions where cor-rosion product layers do not form and in environments wherethey do, and compared to other similar models.

KEY WORDS: carbon dioxide, carbon steel, corrosion model,corrosion rate, hydrogen sulfide, uniform corrosion

INTRODUCTION

Corrosion predictive models are very useful tools thatcan be used to determine corrosion allowances, make

predictions of facilities’ remaining life, and provideguidance in corrosion management. When it comes tointernal corrosion of mild steel in the oil and gasindustry, the mechanism of CO2 corrosion is well un-derstood through laboratory investigations.1-2 Hence,models for CO2 corrosion developed in the past rangefrom those based on empirical correlations to mech-anisticmodels describing the different processes involvedin CO2 corrosion of carbon steel. In 2002, Nyborg3

published a performance-based review of several CO2

corrosion models focusing on the ability to account foreffects of pH, protective iron carbonate layers, oil wetting,fluid flow, H2S, top-of-the-line corrosion, and aceticacid. Some five years later, Nešic published a compre-hensive review of the understanding and modelingpractices for internal corrosion of oil and gas pipelines.4

In the case of H2S corrosion, there are numerousexperimental studies; however, the mechanism of H2Scorrosion is still unclear and only a few models havebeen developed and published in the open literature forpure H2S or mixed CO2/H2S corrosion. It has beenwidely observed that the uniform corrosion rate is re-duced in the presence of very small concentrations ofH2S (1 mbar [0.1 kPa] or even smaller) at room tem-perature and higher. To account for this effect, oneapproach is to use a factor related to H2S concentrationand correct the predicted sweet (CO2) corrosion rate.For example, in 1999 Anderko, et al.,5 developed amechanistic model to predict the corrosion rates ofcarbon steel in both CO2- and H2S-containing envir-onments, which included a thermodynamic calcula-tion to predict corrosion product composition and anelectrochemical corrosion model to simulate the

Submitted for publication: February 10, 2015. Revised and accepted:January 20, 2016. Preprint available online: January 21, 2016,http://dx.doi.org/10.5006/1667.

‡ Corresponding author. E-mail: [email protected].* Institute for Corrosion and Multiphase Technology, Departmentof Chemical and Biomolecular Engineering, Ohio University,342 W. State St., Athens, OH 45701.

CORROSION—Vol. 72, No. 5ISSN 0010-9312 (print), 1938-159X (online)

16/000099/$5.00+$0.50/0 © 2016, NACE International 679

CORROSION SCIENCE SECTION

processes of cathodic and anodic reactions on the steelsurface. To get the desired performance, the predic-tions of the electrochemical model were simplycorrelated to the final steady state corrosion rateexperimental data by using a surface coverage factor ofiron sulfide and iron carbonate. Mechanistic verifi-cation of this approach using electrochemical kineticsdata was not performed, and the water chemistry atthe steel surface and in the bulk solution was notdistinguished in their model. In 2009, Sun andNešic2,6 modeled CO2/H2S corrosion based on an as-sumption that in the presence of H2S, the corrosionrate is always mass transfer controlled as a result of theubiquitous presence of iron sulfide layers. A widerange of experimental results were collected to calibratethis model, making it a useful tool for the prediction oftransient corrosion rates arising from the growth of ironsulfide layers. However, the model consisted of anumber of assumptions that were not explicitly verified.In particular, it was universally assumed that the rateof corrosion in the presence of H2S is always undermasstransfer control; hence, the electrochemical reactionswere not defined nor included in the model. This made itharder to integrate this model with mechanistic(electrochemical) models of CO2 corrosion.

In earlier papers published by the presentauthors, an electrochemical corrosion model7-8 of H2Scorrosion without iron sulfide layer growth has beendeveloped to describe the corrosion process on a baresteel surface, thereby avoiding the complex issuesassociated with formation and growth of an iron sulfidecorrosion product layer. The model in the presentpaper is mainly focused on the growth and the effect ofprotective corrosion product layers (iron carbonate oriron sulfide) on the corrosion by taking a mechanisticapproach. The model is able to predict the corrosionrate and also the concentration at the metal surface ofall of the species involved in the corrosion process.

PHYSICOCHEMICAL PROCESSESUNDERLYING CO2/H2S CORROSION

CO2/H2S corrosion is a complex process involv-ing multiple physicochemical processes occurring si-multaneously. These are: chemical reactions in thebulk solution, mass transport of aqueous speciesthrough the liquid boundary layer and the poroussurface layer, electrochemical reactions at the steel

surface, and porous corrosion product layer forma-tion which may or may not be protective. All of theseprocesses must be taken into account in a predictivemodel to provide a realistic estimation of the corrosionrate. For CO2 corrosion, an electrochemical mecha-nistic model9-10 based on the key physicochemicalprocesses has been developed and implemented intoa software package that is well known and freelyavailable.11 For H2S corrosion, Sun and Nešic’s masstransfer model6 is also publically available and widelyimplemented.2,11 Based on the recent experimentalfindings,12 and the more thorough understanding thathas emerged in the meantime, a more comprehensiveuniform aqueous H2S corrosion model can now beformulated and is described next.

The outline of the new physicochemical modelcan be started by picturing aqueous H2S diffusing to asteel surface, where it reacts rapidly to form a verythin adsorbed sulfide layer, as suggested by Marcus,et al.13 Following the mechanism proposed by Smithand Wright,14 it can be written as:

FeðsÞ þH2SðaqÞ → FeSðadÞ þ 2HðadÞ (1)

The work of Marcus, et al.,13 indicates that sulfuradsorbs very strongly to a steel surface and can displaceadsorbed H2O and OH−. This action results in slowingdown the kinetics of electrochemical reactions such asFe dissolution, H2O reduction, and carbonic acidreduction, apparently by affecting the double layer. Theelectrochemical reactions (both anodic and cathodic)continue to go forward despite an existing adsorbedsulfide layer, albeit at a slower rate.

When the surface concentrations of Fe2+ and S2−

ions exceed the solubility limit of iron sulfide (initiallymackinawite), solid iron sulfide is thermodynamicallystable, and it will precipitate on the steel surface:

Fe2þðaqÞ þ S2−ðaqÞ ⇋ FeSðsÞ (2)

This iron sulfide layer can grow and retard thecorrosion rate via a surface coverage effect and a masstransfer effect (acting as diffusion barrier). Thepresent transient corrosion model is somewhat similar,but also quite different from the model proposed bySun and Nešic6 in some key elements. A comparisonbetween the key differences for the two models islisted in Table 1.

TABLE 1Differences Between Sun-Nešic Model6 and the Present Model

Sun-Nešic Model (2009)6 Present Model

A thin inner mackinawite film formed by direct chemical reactionacting as a solid state diffusion barrier.

A thin adsorbed iron sulfide film affecting directly the kinetics ofdifferent electrochemical reactions (retardation effect).

A porous outer iron sulfide layer formed by spalling of the inner layer. An outer iron sulfide layer formed via a precipitation mechanism.Corrosion rate is always under mass-transfer control because of theporous outer iron sulfide layer and inner mackinawite film.

Corrosion rate is not always under mass-transfer control dependingon the kinetics of mass transfer and electrochemical reactions.

680 CORROSION—MAY 2016


MODEL DESCRIPTION

The present model describes H2S/CO2 corrosionin terms of two main processes: an electrochemicalcorrosion process including effect of mass transportfrom bulk to the surface, and corrosion product for-mation and growth process for iron carbonate andiron sulfide.

Electrochemical Corrosion ModelThe concentration of the species can be very

different in the bulk solution and at the corroding steelsurface because of corrosion, mass transfer effects,and chemical reactions. One usually knows (or canreadily calculate) the bulk species concentration;however, the electrochemical corrosion process dependson the surface concentrations. Therefore, the surfaceconcentrations need to be estimated by calculation. Inthe present model, two calculation “nodes” were usedin the computational domain: one for the species con-centrations in the bulk solution and the other for thespecies concentrations in the thin water layer adjacentto the corroding steel surface. The concentrations ofchemical species in the bulk solution can be calculatedusing a standard water chemistry equilibrium model.The concentrations of species at the corroding steelsurface need to be calculated in a way that ensuresthat all of the key physicochemical processes that affectthe surface concentrations are accounted for (seeFigure 1). These are:

(1) Homogenous chemical reactions close to thesteel surface.

(2) Electrochemical reactions at the steel surface.(3) Transport of species between the steel surface

and the bulk, including convection and diffu-sion through the boundary layer, as well aselectromigration resulting from establishmentof electrical potential gradients.

These three physicochemical processes are intercon-nected and can be expressed by writing a materialbalance ormass conservation reaction for a thin surfacewater layer.

∂csurface,j∂t

=Ne,j − Nw,j

Δxþ Rj (3)

where csurface,j is the concentration of species j, Ne,j isthe flux of species j on the east boundary resultingfrom mass transfer from the bulk solution to thesurface, Nw,j is the flux of species j on the westboundary resulting from electrochemical reactions atthe steel surface, and Rj is the source/sink termresulting from homogeneous chemical reactions in-volving species j.

Homogenous Chemical Reactions — The homoge-nous reactions considered in the presentmodel are wellknown and readily available in the open literature.1-2,9

The reactions describe the interaction between variousspecies (H2S, HS−, S2−, CO2, H2CO3, HCO3

−, CO32−, OH−,

and H+).It should be noted that chemical reactions are

often very rapid when compared to other processesinvolved in corrosion, such as species transport andelectrochemical reactions, thus preserving chemicalequilibria throughout the solution. On the otherhand, in the case of slow chemical reactions (such as theCO2 hydration reaction), other faster processes canlead to local non-equilibrium conditions at the corrod-ing steel surface. Therefore, chemical reactions cansignificantly affect the rates of electrochemical pro-cesses at the steel surface and then ultimately, thecorrosion rate.

In order to better understand how the rates ofhomogenous chemical reactions are calculated inthe present model, one is referred to papers byNešic, et al.1-2,9

Concentration of different speciesat the steel surface

Flux due toelectrochemicalreactions at thesteel surface

Ne,j, Mass transfer flux frombulk to steel surface

Nw,j =nj F

ij

Csurface,jCbulk,j

Concentration of different species in the bulk solution

Bulk solutionBoundary layer, δm

Thin surface water layer, Δx

±

FIGURE 1. Illustration of computation domain and governing reactions for mass transport simulation.

CORROSION—Vol. 72, No. 5 681


Electrochemical Reactions at the Steel Surface —

Electrochemical reactions at the steel surface con-sidered in the present model include:

FeðsÞ → Fe2þðaqÞ þ 2e− (4)

2HþðaqÞ þ 2e− → H2ðgÞ (5)

2H2CO3ðaqÞ þ 2e− → H2ðgÞ þ 2HCO−3ðaqÞ

(6)

2H2SðaqÞ þ 2e− → H2ðgÞ þ 2HS−ðaqÞ (7)

2H2OðlÞ þ 2e− → H2ðgÞ þ 2OH−ðaqÞ (8)

The Tafel equation used to calculate the current den-sities (rate) of various electrochemical reactions listedabove is described in detail in previously publishedpapers on the electrochemical corrosion model:7,15

i= io10�E−Eob (9)

where i represents the reaction current density inA/m2, io represents a reference current density in A/m2,E represents the corrosion potential of the steel in V,Eo represents a reference potential in V, and b representsthe Tafel slope in V/decade. In this model, the currentdensity for each electrochemical reaction depends on thesurface concentration of species, which is not explicitlyknown and needs to be calculated, as explained below.For a spontaneous corrosion process, the unknowncorrosion potential of the steel, E, can be calculated fromthe charge balance reaction at the steel surface:

X

cathodic

i=X

anodic

i (10)

Details of this calculation have already been explainedelsewhere.7,15 Then, the flux at the steel surface can bedetermined from:

Nw,j = � ijnjF

(11)

where nj is the number of mol of electrons exchangedper mol of species j participating in a particular elec-trochemical reaction. For species j consumed byelectrochemical reactions at the steel surface, the posi-tive sign is applied. For species j produced by elec-trochemical reactions at the steel surface, the negativesign is applied. For those species j that are not involvedin the electrochemical reactions, ij = 0. Once the corro-sion potential (E) is found, the partial current (ij) for agiven species j is readily calculated from Reaction (9).

Species Surface Concentration and Mass Transfer—Tenminor species (H2S, HS−, S2−, CO2, H2CO3, HCO3

−,CO3

2−, OH−, H+, and Fe2+) and two major species(Na+ and Cl−) were accounted for by calculating their

mass transfer flux between the bulk solution and thesteel surface. The terms “major” and “minor” refer tothe magnitude of species concentration, with Na+ andCl− exceeding the concentration of other species byorders of magnitude. It should be noted that the con-centrations of species are not calculated throughoutthe mass transfer boundary layer, as is done in moreadvanced models presented by Nešic, et al.,9-10 be-cause of inherent complexities associated with thisapproach. Rather, only two calculation nodes areused, one in the bulk and the other at the steel surface,so the mass transfer flux between the bulk solution tothe steel surface can be calculated for each of thespecies using a mass transfer coefficient, km,j,approach:

Ne,j =km,jðcbulk,j − csurface,jÞ þ km,jzjF

RTcbulk,jΔΦ (12)

Here cbulk, j is the concentration of the species j inthe bulk solution, csurface,j is the concentration of thespecies j at the steel surface, and zj is the electriccharge of species j. The mass transfer coefficient ofspecies j, km,j, can be calculated from well-knowncorrelations such as the one for a rotating cylinderelectrode proposed by Eisenberg:16

Sh=km,jd

Dj=0.0791Re0.7Sc0.356 (13)

or for turbulent single phase pipe flow, the masstransfer coefficient can be calculated by a straightpipe correlation of Berger and Hau:17

Sh=km,jd

Dj=0.0165Re0.86 Sc0.33 (14)

where Sh is the Sherwood number, d is the cylinderelectrode diameter or pipe diameter (m), Dj is the dif-fusion coefficient of various species (m2/s), Re is theReynolds number = ρud/μ, and Sc is the Schmidtnumber = μ/ρDj.

The last term in the transport Reaction (11)represents electromigration resulting from a smallelectrical potential (ΔΦ) difference between the bulksolution and the surface water layer, which is significantonly for the transport of major species (Na+ and Cl−).

Substitution of flux density resulting from elec-trochemical reactions and mass transfer processes intomass conservation reaction of Reaction (3) yields thefinal transport reaction which can be written for eachspecies:

Δx∂Csurface,j

∂t= � ij

njFþ km,jðcbulk,j − csurface,jÞ

þ km,jzjF

RTcbulk,jΔΦþ Δx · Rj (15)



There are 13 unknowns (12 unknown surfaceconcentrations and the potential gradient, ΔΦ), and only12 transport reactions. Because the aqueous solutionis always charge neutral, the electroneutrality reactionmust be satisfied:

Xzjcsurface,j =0 (16)

The concentration for all of the consideredchemical species at the steel surface can now be cal-culated by solving these 13 reactions. At the sametime, the corrosion current and the corrosion potentialare calculated using Reactions (9) and (10).

Model of Corrosion Product Layer GrowthFrom the electrochemical corrosion model de-

scribed in the previous section, the surface waterchemistry (the concentration of different chemicalspecies at the steel surface) and the corrosion potentialof the steel are obtained. Using this information, athermodynamic model can be used to predict whichsolid corrosion product may form on the steel surface(solubility calculation).18-19 If this calculation suggeststhat solubility of a given salt is not exceeded, thecorrosion process at the bare steel surface proceedsunimpeded. If any given solubility is exceeded, acorrosion product layer forms on the steel surface. Theformation of the corrosion product layer may signif-icantly affect the corrosion process. Therefore, a cor-rosion product layer growth model, which focuses onkinetics of iron sulfide and iron carbonate formation,was developed to address this issue. In the currentmodel, the spalling of the corrosion product layerresulting from possible internal stress or flow was notconsidered, which can be addressed in future work.

In the corrosion model described above, twonodes were considered in the computational domain forspecies concentration calculation: one in the bulksolution and the other at the steel surface. When acorrosion product layer forms, one more node needsto be added to account for this, as shown in Figure 2.

Formation of an iron sulfide and/or iron carbonatecorrosion product layer affects the fluxes and therebythe concentrations of species at the steel surface, whichin turn changes the kinetics of the electrochemicalprocesses and corrosion. To reflect this, the massconservation reaction, Reaction (3), needs to beslightly modified to read:

∂εcsurface,j∂t

=Ne,j − Nw,j

Δxþ Rj (17)

Here, ε is the porosity of the corrosion productlayer. The rate of reaction Rj (source or sink of species j)now includes both homogeneous chemical reactionsand heterogeneous chemical reactions such as ironsulfide and/or iron carbonate precipitation. The fluxof species between the bulk and the steel surface Ne,j isalso different as it is affected by the diffusion throughthe porous corrosion product layer. The flux of speciesas a result of electrochemical reactions at the steelsurface Nw,j is also changed because of the partialcoverage of the surface by the corrosion product layer.How these three terms, Rj, Ne,j, and Nw,j are calculatedexactly, when a corrosion product layer forms, isaddressed next.

Heterogeneous Chemical Reactions — Homogenousreactions have been discussed in the previous sec-tion. The focus here is on two new heterogeneouschemical reactions: iron carbonate and iron sulfideformation.

Csurface,j: concentration of different species at the steel surface.

Cscale,j: concentration of different species at the scale surface

Cbulk,j: concentration of different species in the bulk solution

Flux due toelectrochemicalreaction at thesteel surface

Ne,j, flux from bulk to the steel surfaceNw,j =

nj F

ij±

Boundary layer, δmCorrosion product layer, δs

Bulk solutionSteel

FIGURE 2. Sketch of corrosion process with corrosion product layer.



• Iron Carbonate Formation: Iron carbonate formswhen the product of the concentrations of Fe2+ andCO3

2− ions exceeds the solubility limit according to:

Fe2þðaqÞ þ CO2−3ðaqÞ ⇋ FeCO3ðsÞ (18)

This reaction acts as a sink for Fe2+ and CO32−

species, and the kinetics can be calculated usingReaction (19), proposed by Sun, et al.:20

RFeCO3ðsÞ = e28.20 − 64.85RT

SVKspFeCO3

ðSFeCO3− 1Þ (19)

where RFeCO3ðsÞ is the precipitation rate in mol/(m3·s); SV is

the surface to volume ratio of the iron carbonate in1/m; SFeCO3

is the saturation value of iron carbonate(considering only super saturation, i.e., whenSFeCO3

>1), and KspFeCO3is the solubility limit of iron

carbonate in (mol/L)2, which is given byReaction (20).21

log KspFeCO3= −59.3498 − 0.041377T −

2.1963T

þ 24.5724 log T þ 2.518I0.5 − 0.657I (20)

where T is the temperature in K and I is the ionic strengthin mol/L.

• Iron Sulfide Formation: The iron sulfide layerforms when the product of the concentrations ofFe2+ and S2− ions exceeds the solubility limit accordingto Reaction (2), Fe2þðaqÞ þ S2−

ðaqÞ⇋FeSðsÞ.The precipitation kinetics aremuch faster for iron

sulfide than for iron carbonate and the solubility limit islower. Therefore, in the present model, when an ironsulfide layer can precipitate (SFeS > 1), iron carbonateprecipitation is not considered. Although some pre-vious researchers22-23 have addressed the precipitationkinetics of iron sulfide, a reliable expression for theprecipitation kinetics is still elusive. A new expression issuggested here, which is similar in essence to the onefor iron carbonate precipitation kinetics:

RFeSðsÞ = e48 − 40,000RT

SVKsp,S2−ðSFeS − 1Þ (21)

In this expression, the constants were calibratedwith the experimental results from the present study(shown later) and by using Harmandas, et al.22 Thesaturation value for iron sulfide is denoted by SFeS,and Ksp,S2− is the solubility limit of iron sulfide in(mol/L)2, which can be calculated from Benning, et al.:24

Ksp,S2− =102,848.779

T −6.347KhsKbs (22)

Here, Khs and Kbs are the equilibrium constants for theH2S first dissociation and second dissociation, which areobtained from the open literature.25-26

Effect of Corrosion Product Layer on ElectrochemicalReactions — The electrochemical reactions are mainlyaffected by the surface coverage effect where thecorrosion product layer makes parts of the steel surfaceunavailable for corrosion. Assuming the surfacecoverage is equal to the volumetric porosity of the cor-rosion product layer,(1) the current density of eachelectrochemical reaction (Reaction [9]) now becomes:

i= εio10�E−Eob (23)

Based on the change in the current density, the fluxNe,j at the steel surface can be calculated usingReaction (11). The rate of the electrochemical reac-tions is also affected by the changes in surface con-centrations of various species resulting from retardedmass transfer through the porous corrosion productlayer, as described next.

Effect of Porous Corrosion Product Layer on MassTransfer — The governing reactions used to quantify themass transfer process through the corrosion productlayer for different species are similar to those describedby Nešic, et al., in 2003.9 The retardation of masstransfer depends primarily on the properties of thecorrosion product layer, such as the thickness, po-rosity, and tortuosity. Considering the models availablein the open literature, the mass transfer coefficientks,j of species j through the porous corrosion productlayer is a function of the diffusion coefficient (Dj),porosity (ε), tortuosity (τ), and thickness (δs) of thecorrosion product layer.27-30

ks,j =ετDj

δs(24)

The tortuosity (τ) is taken to be proportional to thesquare root of porosity, in an analogy with the theory ofporous electrodes.31 The total mass transfer coefficientfrom the bulk solution to the steel surface is representedby kT,j, which is the function of km,j and ks,j:

1kT,j

=1ks,j

þ 1km,j

(25)

The corrosion product layer thickness Δδs changeover time is calculated as follows:

• When iron sulfide layer forms:

Δδs =ΔxRFeSðsÞMFeSΔt

ρFeSð1 − εÞ (26)

• When iron carbonate layer forms:

Δδs =ΔxRFeCO3ðsÞMFeCO3

Δt

ρFeCO3ð1 − εÞ (27)

(1) Porosity is a volumetric measure of how much open space there is inthe corrosion product layer. The surface coverage is a measure ofhow much open steel surface is available for electrochemical reac-tions (i.e., the surface not covered by the corrosion product layer),which can be thought of as a “superficial measure of porosity.” In theabsence of better data, the two measures of porosity (one volumetric,the other superficial) can be assumed to be the same.



Here MFeS and MFeCO3represent the molecular weight

of iron sulfide and iron carbonate (kg/mol), Δt is the timestep, and ρFeS and ρFeCO3

are the density of iron sulfideand iron carbonate (kg/m3).

The change in surface corrosion layer porosity ε iscalculated explicitly using a corrosion product layergrowth model developed by Nešic, et al.,10 as shownby mass balance reactions (28) and (29). The detailedderivation of these reactions is explained in theoriginal paper and will not be repeated here.

• For the iron carbonate layer:

∂ε

∂t= −

MFeCO3

ρFeCO3

RFeCO3− CR

∂ε

∂x(28)

• For the iron sulfide layer:

∂ε

∂t= −

MFeS

ρFeSRFeS − CR

∂ε

∂x(29)

At the interface between corrosion product layerand steel surface, ε is taken to be 1, as the corrosionprocess continuously creates voids underneath thecorrosion product layer. The initial porosity was also setas 1.

The procedure for the calculation of the corrosionrate over time is sought at discrete time steps. First, theinitial corrosion rate, including surface water chem-istry, is determined by the electrochemical corrosionmodel without the effect of any corrosion productlayer. Then, a corrosion product prediction model basedon thermodynamic framework is used to determinewhether a corrosion product layer forms or not on thesteel surface. If a corrosion product layer does notform, the calculation is over and a bare steel corrosionrate is the result. If a corrosion product layer doesform, a corrosion product layer growthmodel is invoked.The change in porosity for the corrosion product layeris calculated from Reactions (28) or (29), and the changein thickness of layer growth is obtained from Reac-tions (26) or (27), depending on which corrosion pro-ducts forms. Finally, the mass conservation reactions

for each species are solved. Therefore, the concentrationfor all of the chemical species at the steel surface canbe obtained. The corrosion current, corrosion potential,corrosion rate, potential gradient in solution, and therates (currents) for each of the cathodic reactions andthe anodic reaction are calculated.

MODEL VERIFICATION

Although the present model was primarily de-veloped to address H2S corrosion and combinedH2S/CO2 corrosion, it also has the capability ofpredicting pure CO2 corrosion. As the entire mathe-matical model was revised and simplified, this newmodel needs to be compared with other models andverified with experimental data.

Verification of Corrosion Model Without CorrosionProduct Layer

Comparison with Other Models — The comparisonwas done with two other advanced multi-node mod-els, i.e., model presented by Nešic, et al.9-10 (denoted asModel Nešic) and a corrosion model developed by Pots(denoted as Model Pots).32

For a pure CO2 environment, the predicted cor-rosion rate, surface pH, and CO3

2− concentrationat 25°C from these different models are shown inFigure 3. Reasonably good agreement is obtained. Allthree models predicted the increase of corrosion rateand the decrease of surface pHwith increasing flow rate.The deviation between these three models is within20%. Many other comparisons were made for variousconditions and it was concluded that the presentmodel is directly comparable in performance with theother two models, while being much simpler thaneither of them.

Comparison with Experimental Results — A modelcannot be used with confidence before its perfor-mance is compared with experimental results. Variouscomparisons with laboratory data are presented next.Figure 4 shows the comparison between the presentmodel and experimental data for an aqueous acidic

00

1

2

3

4

5

2 4 6Velocity (m/s)

Co

rro

sio

n R

ate

(mm

/y)

8

Model Pots

Model Nešic

Present model

Model PotsModel NešicPresent model

10 03

4

5

6

2 4 6Velocity (m/s)

Su

rfac

e p

H

8 10

FIGURE 3. Comparison between the present model and two other models (Model Nešic and Model Pots) for a pure CO2

environment using velocities up to 8 m/s at 25°C, [Fe2+] = 1 ppm, pH 4.0, 1 bar (100 kPa) CO2, pipeline diameter = 0.1 m, and1 wt% NaCl.



environment purged by N2 (without any CO2 or H2S) atpH 4.0 and various flow velocities. The predictionsmade by Model Nešic are also added to the plot, in orderto get a better sense how this well-established modelcompared with the same experimental data. One canconclude that for a pure acidic environment, thepredictionsmade by the presentmodel agree reasonablywell with experimental results within approximately a20% deviation, which is better than the predictionsmade by Model Nešic.

For an aqueous CO2 environment, the comparisonbetween the model predictions and experimentalresults for the corrosion rate obtained in glass cell and

flow systems are made by varying two importantparameters: pH and velocity, as shown in Figure 5.Many other comparisons were made for a CO2

aqueous environment with similar results: a reasonableagreement was obtained within a 50% deviation. Theperformance of the present model was as good as that ofModel Nešic. For an aqueous H2S environment,Figure 6 shows how the present model captures theeffect of H2S concentration, flow rate, and pH. Ex-cellent agreement is obtained. Mostly the predictionsare within a 10% deviation of the experimentalresults, except for the very acidic pH 2 condition.

Verification of Corrosion Model for Conditionswhen Iron Carbonate Corrosion Layer Forms

Figure 7 shows the comparison of the modelpredictions with results of experiments conducted in aCO2 aqueous solution under flowing conditions, forconditions when protective iron carbonate corrosionproduct layer forms. The corrosion rate was rapidlyreduced; however, these experiments are notoriouslydifficult to reproduce, as indicated by differences inresults from five repetitions of a nominally identicalexperiment. The model predictions are within therange of the variation of experimental data, and aresimilar to those made by Model Nešic. This indicatesthat the present model is capable of simulating the ironcarbonate layer growth kinetics and the effect on theCO2 corrosion rate.

0.000.000.200.40

0.600.801.00

1.201.401.60

1.80

0.50 1.00 1.50 2.00 2.50 3.00Velocity (m/s)

CR

(m

m/y

)

Model Nešic

Experimental

pH = 4

Present model

FIGURE 4.Comparisons betweenmodel predictions and experimentresults for N2 environment, 20°C, [Fe2+] < 1 ppm, pH 4.0, pipelinediameter = 0.01 m, and various velocities.

00

1

2

3

4

5

2 4 6 8 10 12 14Velocity (m/s)

Co

rro

sio

n R

ate

(mm

/y)

0

1

2

3

4

5

Co

rro

sio

n R

ate

(mm

/y)

0

1

2

3

4

5

Co

rro

sio

n R

ate

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Model NešicPresent model

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Model NešicPresent model

FIGURE 5. Comparisons between model predictions and experiment results at 1 bar (100 kPa) CO2, 20°C, various pH, andvarious velocities.



Verification of Corrosion Model for Conditionswhen Iron Sulfide Layer Forms

Effect of pH2S — The partial pressure of H2S isdirectly related to the aqueous H2S concentration inthe solution, and is an important factor as it plays dualroles. First, aqueous H2S is a corrosive species ac-celerating the corrosion rate by enhancing the cathodicreaction rate. Second, H2S also promotes the rate ofthe iron sulfide precipitation that decreases the generalcorrosion rate.

Figure 8 illustrates the predicted effect of pH2S onthe corrosion rate calculated by the present model. Theinitial corrosion rate increases with increasing pH2S;because no corrosion product layer protectiveness isaccounted for at the initial time (time zero), the sys-tem is overwhelmed by the accelerating role of H2Sreduction. However, during longer reaction times,such as 1 d, the formation of a protective iron sulfidelayer is promoted by pH2S. The best example of thedual roles of H2S is that at 10 bar (1,000 kPa) pH2S, theinitial corrosion rate is the highest, but the corrosionrate after 1 d is the lowest.

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FIGURE 6. Comparisons between model predictions and experiment results for 30°C, 1 bar (100 kPa) total pressure, andvarious H2S concentrations, velocities, and pH.

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FIGURE 7. Comparisons between the model predictions and theexperiment results for iron carbonate layer forming condition atpH 6.6, 80°C, 0.53 bar (53 kPa) CO2, and 1,000 rpm rotating speed,50 ppm bulk Fe2+. Data is taken from the ICMT (Institute for Corrosionand Multiphase Technology) database.

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FIGURE 8. The predicted effect of pH2S on the corrosion rate frompresent model for pH 5.0, T = 80°C, and V = 1 m/s.



The model by Sun-Nešic6 of H2S corrosion was aprecursor to the current work, as described earlier.Both models, the Model Sun-Nešic and the presentmodel, were compared with the experimental data, asshown below. First, the performance at low partialpressures of H2S was examined. The test was con-ducted by Sun6 at H2S gas partial pressures from 0.54mbar to 54 mbar (0.054 kPa to 5.4 kPa). Figure 9shows that both the present model and Model Sun-Nešic capture the corrosion rate change well.

Corrosion experiments at higher pH2S (pH2S =16.1 bar [1,610 kPa] in the mixed H2S/N2 environ-ment) were reported by Liu, et al.,33 and model pre-dictions are compared with the experimental resultsin Figure 10. The present model performs much betterthan Model Sun-Nešic at this condition.

A similar range of H2S partial pressures werereported by Bich, et al.,34 with the main differencebeing the presence of CO2. Figure 11 shows the com-parison between the model prediction and experi-mental results in a mixed H2S/CO2 environment. Thepresent model captures the corrosion rate change

with time, but Model Sun-Nešic tends to overpredict thecorrosion rate.

Effect of pH — The predicted effect of pH on thecorrosion rate for a pure H2S environment is dem-onstrated in Figure 12 and compared with experimentaldata. Corrosion rate increases with a decrease in pHas expected, as the corrosiveness of the solutionincreases and the solubility of iron increases as well.The decrease of corrosion rate with time is much fasterat pH 6.0 as a result of the formation of a denser ironsulfide layer. The present model captures the corrosionrate change much better than Model Sun-Nešic,which does not agree well with the corrosion rates at pHvalues less than 5. It is worth noting that the ex-perimental linear polarization resistance corrosionrates are much higher than the model prediction atpH 4.0. This is probably a result of the iron carbideremaining on the metal surface after corroding awaythe ferrite phase at pH 4.0, which can accelerate thecorrosion rate by providing a more cathodic reactionarea.35-36 This effect is not included in the pres-ent model.

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Model Sun-Nešic, pH2S = 5.4 mbarModel Sun-Nešic, pH2S = 0.54 mbar

FIGURE 9. Corrosion rate changing with time at different H2S partial pressure from present model and Model Sun-Nešic.Points: experimental data, lines: model predictions. Conditions: total pressure = 1 bar (100 kPa), H2S gas partial pressurefrom 0.54 mbar to 54 mbar (0.054 kPa to 5.4 kPa), 80°C, experiment duration 1 h to 24 h, pH 5.0 to 5.5, stagnant.Experimental data taken from Sun.6

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FIGURE 10. Corrosion rate changing with time. Points: experimentaldata, lines: model predictions. Conditions: 16.1 bar (1,610 kPa) H2S,90°C, 2 L autoclave, stagnant. Experimental data taken fromLiu, et al.33

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FIGURE 11. Corrosion rate changing with time. Points: experimentaldata, lines: model predictions. Conditions: 12.2 bar (1,220 kPa)H2S, 3.5 bar (350 kPa) CO2, 65°C. Experimental data taken fromBich, et al.34



Effect of Flow — Fluid flow and turbulence play animportant role in the corrosion process. Higher flowcan increase the corrosion rate through enhancing themass transport process, especially when there is nocorrosion product layer formed. Flow can also affect theformation of a protective iron sulfide layer. Speciestransport in turbulent flow affects the surface concen-tration of species and, consequently, changes theprecipitation rate of iron sulfide.

Figure 13 shows the comparisons between modelpredictions and experimental results at differentflow conditions. The present model is generally ableto predict the change of the corrosion rate ratherwell.

Effect of Temperature — Increasing temperaturemakes the bare steel corrosion rate higher, as seen inthe beginning of the experiments shown in Figures 14and 15. However, the formation of a protective iron

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FIGURE 12. Corrosion rate changing with time. Points: experimental data, lines: model predictions. Conditions: 0.054 bar(5.4 kPa) pH2S, balance nitrogen, T = 80°C, stirring rate: 600 rpm for pH 4 and pH 5, and 400 rpm for pH 6.

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FIGURE 13. Corrosion rate vs. time. Points: experimental data, lines: model predictions. Conditions: pH2S = 0.054 bar(5.4 kPa), balance nitrogen, T = 80°C, pH 5.0.

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FIGURE 14. Corrosion rate vs. time. Points: experimental data, lines: model predictions. Conditions: total pressure = 1 bar(100 kPa), pH2S = 0.1 bar (10 kPa) at 25°C, pH2S = 0.054 bar (5.4 kPa) at 80°C, pH 6.0, 400 rpm stirring rate. Experimentaldata taken from Ning.37



sulfide layer is also promoted at high temperature, andtherefore, the corrosion rate decreases more rapidlywith temperature increase. Comparisons between thepresent model predictions and experimental resultsat different temperatures, shown in Figures 14and 15, faithfully capture this behavior. Model Sun-Nešic is not sensitive to temperature because masstransfer control of the corrosion process was assumedin the model, and the mass transfer process is not assensitive as the electrochemical and chemical reac-tion processes to temperature change. Therefore,Model Sun-Nešic cannot capture the higher initialcorrosion and lower final corrosion at the hightemperature.

CONCLUSIONS

v A relatively simple mechanistic transient model ofuniform CO2/H2S corrosion of carbon steel has beendeveloped, which accounts for the key processesunderlying corrosion:

• chemical reactions in the bulk solution,• electrochemical reactions and chemical reac-tions at the steel surface,

• mass transport between the bulk solution tothe steel surface, and

• corrosion product formation and growth (ironcarbonate and iron sulfide).

v The model is able to predict the corrosion rate, aswell as the surface concentration, of all key speciesinvolved in the corrosion process. The model has beensuccessfully calibrated against experimental data inconditions where corrosion product layers do notform and in those where they do. Parametric testing ofthe model in iron sulfide forming conditions has beenconducted in order to gain insight into the effect ofvarious environmental parameters on the H2S/CO2

corrosion process. Performance of the present modelwas favorably compared to the performance of othersimilar models that are publically available.

ACKNOWLEDGMENTS

The authors would like to express sincere appre-ciation to the following industrial sponsors for theirfinancial support and direction: BP, Champion Tech-nologies, Chevron, Clariant Oil Services, ConocoPhillips,ENI S. P. A., ExxonMobil, Inpex Corporation, NALCOEnergy Services, Occidental Petroleum Co., Petrobras,PETRONAS, PTT, Saudi Aramco, Total, TransCanada,MI-SWACO, HESS, and WGIM. The authors would alsolike to thank Dr. Bert Pots for his expert advice andproviding data for the model comparison.

REFERENCES

1. S. Nešic, “Carbon Dioxide Corrosion of Mild Steel,” in UhligsCorrosion Handbook, ed. R.W. Revie, 3rd ed. (Hoboken, NJ:John Wiley & Sons, Inc., 2011), p. 229-245.

2. S. Nešic, W. Sun, “Corrosion in Acid Gas Solutions,” in Shreir’sCorrosion, ed. T.J.A. Richardson, vol. 2 (Amsterdam, Netherlands:Elsevier, 2010), p. 1270-1298.

3. R. Nyborg, “Overview of CO2 Corrosion Models for Wells andPipelines,” CORROSION 2002, paper no. 233 (Houston, TX: NACEInternational, 2002).

4. S. Nešic, Corros. Sci. 49 (2007): p. 4308-4338.5. A. Anderko, P. McKenzie, R.D. Young, Corrosion 57 (2001):

p. 202-213.6. W. Sun, S. Nešic, Corrosion 65 (2009): p. 291-307.7. Y. Zheng, B. Brown, S. Nešic, Corrosion 70 (2014): p. 351-365.8. Y. Zheng, J. Ning, B. Brown, S. Nešic, Corrosion 71 (2015):

p. 316-325.9. S. Nešic, A. Stangeland, M. Nordsveen, R. Nyborg, Corrosion 59

(2003): p. 489-497.10. S. Nešic, K.L.J. Lee, Corrosion 59 (2003): p. 616-628.11. “FREECORP - Corrosion Prediction Software,” Ohio University,

2008, http://www.corrosioncenter.ohiou.edu/software/freecorp/(Mar. 27, 2016).

12. Y. Zheng, J. Ning, B. Brown, D. Young, S. Nešic, “MechanisticStudy of the Effect of Iron Sulfide Layers on Hydrogen SulfideCorrosion of Carbon Steel,” CORROSION 2015, paper no. 5933(Houston, TX: NACE, 2015).

13. P. Marcus, E. Protopopoff, J. Electrochem. Soc. 137 (1990): p. 2709-2712.

14. S.N. Smith, E.J. Wright, “Prediction of Minimum H2S Levels Re-quired for Slightly Sour Corrosion,” CORROSION 1994, paper no.11 (Houston, TX: NACE, 1994).

15. Y. Zheng, J. Ning, B. Brown, S. Nešic, “Electrochemical Model ofMild Steel Corrosion in a Mixed H2S/CO2 Aqueous Environment,”CORROSION 2014, paper no. 3907 (Houston, TX: NACE, 2014).

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Experimental 90°C

Experimental 50°C

Experimental 90°C

Present model 50°C

Present model 90°C



FIGURE 15. Corrosion rate vs. time. Points: experimental data, lines: model predictions. Conditions: total pressure = 1 bar(100 kPa), pH2S = 0.3 bar (30 kPa) at 90°C, pH2S = 0.88 bar (88 kPa) at 50°C, pH 4.2 to 4.7, stirring condition. Experimentaldata taken from Abayarathna, et al.38



16. M. Eisenberg, C.W. Tobias, C.R. Wilke, J. Electrochem. Soc. 101(1954): p. 306-320.

17. F.P. Berger, K.-F.F.-L. Hau, Int. J. Heat Mass Transf. 20 (1977):p. 1185-1194.

18. J. Ning, Y. Zheng, D. Young, B. Brown, S. Nešic, Corrosion 70(2014): p. 375-389.

19. T. Tanupabrungsun, “Thermodynamics and Kinetics of CarbonDioxide Corrosion of Mild Steel at Elevated Temperatures” (Ph.D.diss., Ohio University, 2012).

20. W. Sun, “Kinetics of Iron Carbonate and Iron Sulfide Scale For-mation in Carbon Dioxide/Hydrogen Sulfide Corrosion” (Ph.D.diss., Ohio University, 2006).

21. W. Sun, S. Nešic, R.C. Woollam, Corros. Sci. 51 (2009):p. 1273-1276.

22. N.G. Harmandas, P.G. Koutsoukos, J. Cryst. Growth 167 (1996):p. 719-724.

23. D. Rickard, Geochim. Cosmochim. Acta 59 (1995): p. 4367-4379.24. L.G. Benning, R.T. Wilkin, H.L. Barnes, Chem. Geol. 167 (2000):

p. 25-51.25. O.M. Suleimenov, R.E. Krupp, Geochim. Cosmochim. Acta 58

(1994): p. 2433-2444.26. Y.K. Kharaka, W.D. Gunter, P.K. Aggarwal, E.H. Perkins,

J.D. Dedraal, “SOLMINEQ. 88: A Computer Program forGeochemical Modeling of Water - Rock Interactions,” U.S.Geological Survey, Water-Resources Investigations Report88-4227, 1988.

27. E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 2nd ed.(Cambridge, United Kingdom: Cambridge University Press,1997).

28. P. Grathwohl, Diffusion in Natural Porous Media: ContaminantTransport, Sorption/Desorption and Dissolution Kinetics (New York,NY: Springer, 1998).

29. M. Gopal, S. Rajappa, R. Zhang, “Modeling the Diffusion EffectsThrough the Iron Carbonate Layer in the Carbon Dioxide Corrosionof Carbon Steel,” CORROSION 1998, paper no. 026 (Houston, TX:NACE, 1998).

30. D. Mu, Z.-S. Liu, C. Huang, N. Djilali, Microfluidics Nanofluidics 4(2008): p. 257-260.

31. L. Pisani, Transp. Porous Media 88 (2011): p. 193-203.32. B.F.M. Pots, “Mechanistic Models for the Prediction of CO2 Cor-

rosion Rates Under Multi-Phase Flow Conditions,” CORROSION1995, paper no. 137 (Houston, TX: NACE, 1995).

33. M. Liu, J. Wang, W. Ke, E.-H. Han, J. Mater. Sci. Technol. 30 (2014):p. 504-510.

34. N.N. Bich, K.G. Goerz, “Caroline Pipeline Failure: Findings onCorrosion Mechanisms in Wet Sour Gas Systems ContainingSignificant CO2,” CORROSION 1996, paper no. 026 (Houston, TX:NACE, 1996).

35. J.L. Mora-Mendoza, S. Turgoose, Corros. Sci. 44 (2002):p. 1223-1246.

36. T. Berntsen, M. Seiersten, T. Hemmingsen, Corrosion 69 (2013):p. 601-613.

37. J. Ning, “Investigation of Polymorphous Iron Sulfide in H2S Cor-rosion of Mild Steel,” Ohio University Advisory Board Meeting, OhioUniversity, 2013.

38. D. Abayarathna, A.R. Naraghi, S. Wang, “The Effect of SurfaceFilms on Corrosion of Carbon Steel in a CO2-H2S-H2O System,”CORROSION 2005, paper no. 417 (Houston, TX: NACE, 2005).



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