A model has been developed for predicting the localized corrosion repassivation potential (Erp) for alloys in environments containing chloride ions and hydrogen sulfide. The model has been combined with Erp measurements for a 13-Cr supermartensitic stainless steel (UNS S41425) at various concentrations of Cl− and H2S. The model accounts for competitive adsorption at the interface between the metal and the occluded site environment, the effect of adsorbed species on anodic dissolution, and the formation of solid phases in the process of repassivation. The effect of H2S is complex, as it may give rise to a strong enhancement of anodic dissolution in the occluded environment and may lead to the formation of solid metal sulfide phases, which compete with the formation of metal oxides. H2S can substantially reduce the repassivation potential, thus indicating a strongly enhanced tendency for localized corrosion and stress corrosion cracking. However, exceptions exist at lower H2S and Cl− concentrations, at which H2S may lead to the inhibition of localized corrosion. The model accurately reproduces the measured repassivation potentials for Alloy S41425 and the limited literature data for Alloy CA6NM (UNS J91574), thus elucidating the conditions at which H2S increases the propensity for localized corrosion and those at which it does not. Because the repassivation potential defines the threshold condition for the existence of stable pits or crevice corrosion, the model provides the foundation for predicting localized corrosion and stress corrosion cracking in environments that are relevant to oil and gas production.
Corrosion behavior of corrosion-resistant alloys (CRAs) in the oil and gas industry has been attracting significant attention over the past two decades as a result of a marked trend toward increasing severity of corrosive environments in terms of temperature, pressure, and aggressive species. This trend, coupled with increasing scrutiny of production systems by regulators and the public, is expected to continue in the future and provides impetus to a reexamination of approaches to materials selection.
At present, materials specification is based on a combination of standard tests (e.g., NACE TM-01-771), fit-for-purpose testing, and experience. The empirical knowledge is embodied in standards, such as ISO 15156,2 guidance documents, and company specifications. The boundaries of acceptable performance of CRAs are often specified in terms of empirically determined ranges of H2S and CO2 partial pressures. However, such approaches may not be satisfactory because the performance of CRAs depends on many other factors such as temperature, acidity, chloride concentration, elemental sulfur, etc., which in turn may depend on complex chemical and phase equilibria in downhole environments. Furthermore, the relationship between accelerated laboratory tests and the actual field environment is often not quantified. Essentially, the performance of a given material needs to be understood in terms of its reliability in a given set of environmental conditions. Therefore, it is of interest to develop a predictive approach that covers a broad range of alloy-environment combinations using a limited set of experimental data coupled with a physical model that is capable of generalizing the experimental database and extrapolating from laboratory tests to field conditions.
From the point of view of CRAs in severe well environments, stress corrosion cracking (SCC) is of great interest because it can occur over wide ranges of conditions, including the moderate to high temperatures that are critical to downhole applications. For mapping the environmental ranges of SCC, it is crucial to identify a critical potential above which SCC can occur. SCC can be triggered if the corrosion potential of the metal (Ecorr) exceeds the critical potential. It is generally recognized that localized corrosion can be a precursor to SCC. This principle has been established and extensively investigated in chloride environments by Tsujikawa and coworkers.3–7 This is a result of the fact that the conditions that lead to localized corrosion (i.e., those that sustain a critical chemistry in an occluded environment inside a pit or crevice) are similar to the conditions that are needed to sustain SCC. The role of localized corrosion in the initiation of SCC has also been identified for sulfur-bearing environments, including those containing thiosulfates8 and hydrogen sulfide.9 In particular, experimental evidence exists that SCC in chloride-thiosulfate solutions occurs at potentials above the repassivation potential (Erp) for localized corrosion, thus indicating that localized corrosion leads to the initiation of SCC.8 Also, it has been shown through fracture mechanics testing that measurable crack growth occurs only at potentials more positive to Erp.8 This indicates that a reliable methodology for the prediction of SCC should be closely linked to the prediction of localized corrosion. Therefore, a project has been undertaken to:
Develop an electrochemical model for predicting the repassivation potential using a set of new Erp measurements that capture the effects of key electrochemically active species such as Cl− and H2S;
Develop a model for predicting the corrosion potential of CRAs in oil and gas production environments; a combination of the Ecorr and Erp models will make it possible to predict the occurrence of localized corrosion;10 and
Experimentally verify the hypothesis that the repassivation potential for localized corrosion is the appropriate critical potential above which SCC occurs. It should be noted that this is limited to the forms of environmentally assisted cracking for which localized corrosion is a precursor to cracking. Other forms of cracking such as sulfide stress cracking and hydrogen stress cracking occur according to different mechanisms and cannot be rationalized based on the approach described here. However, from the point of view of the performance of CRAs in severe oil and gas environments, SCC occurring at anodic potentials is of greater interest because it can occur over a wider range of environmental conditions, particularly at elevated temperatures.
This work focuses on part (1). Parts (2) and (3) will be the subject of separate studies.
To develop a model for predicting the repassivation potential in oil and gas environments, a previously developed model11–12 for calculating Erp in environments containing chlorides and various inhibitive oxyanions was extended. An especially useful feature of this model is its generalization in terms of the composition of Fe-Ni-Cr-Mo-W-N alloys,13 which makes it possible to predict Erp as a function of not only the environment chemistry but also the composition of the alloy. In particular, this generalization made it possible to predict the effect of chromium and molybdenum depletion on the repassivation potential of heat-treated alloys.14–16 However, in its original form, the model is not applicable to systems containing H2S or other aggressive sulfur species, thus making it necessary to develop a reformulated and extended version that incorporates the electrochemical effects of H2S.
Various experimental studies have revealed that H2S and, in general, adsorbed sulfur, have a strong effect on the mechanism of the dissolution of individual metals17–26 and alloys.27–28 This effect has a profound influence on the behavior of alloys in occluded environments associated with localized corrosion.29–33 Moreover, alloy dissolution and localized corrosion are strongly affected by the formation of metal sulfides.34–38 Insights from these studies are utilized in the present work to develop an electrochemical model for the repassivation potential of CRAs in environments containing Cl− and H2S.
In general, there is a very limited amount of experimental repassivation potential data in the literature.9,39 Therefore, a comprehensive set of new Erp data has been obtained in this study for a 13-Cr supermartensitic stainless steel (UNS S41425,(1) commonly referred to as S13Cr) to elucidate the interplay of Cl− and H2S in localized corrosion. These data cover a wide range of Cl− and H2S concentrations and were used to parameterize and verify the model. After verifying the model using the new Erp measurements, the model was additionally tested using a limited amount of literature data.
Materials and Specimens
Specimens made out of Alloy S41425 supermartensitic stainless steel were used in the experiments. The chemical composition of this material is 12.10% Cr, 5.90% Ni, 1.90% Mo, 0.010% C, and balance Fe. Specimens in the form of a cylinder (for measurements on boldly exposed surfaces) and crevice samples were both used, with the dimensions shown in Figure 1. The crevice samples were prepared according to ASTM G192.40 The sample surface was abraded with 600 grit SiC sandpaper, cleaned in an ultrasonic bath with isopropanol, and dried by blowing nitrogen. The creviced specimens were assembled using ceramic multiple-crevice formers wrapped with Teflon† tape. Bolts, nuts, and washers were made out of Ti alloy. Seventy in·lbf (7.91 N·m) torque was applied on the assembly to ensure the formation of critical crevice geometry.
Electrochemical experiments were performed in NaCl solutions at various concentrations ranging from 3 molal to 0.0003 molal. All tests were performed at 85°C and ambient pressure. The experiments were conducted with and without the presence of H2S. Premixed gases with different concentrations of H2S in nitrogen were used to study the effect of H2S. A multi-neck round-bottom flask described in ASTM G541 was used, which included a working electrode, a saturated calomel electrode (SCE) as the reference in a water-cooled Luggin probe, and a Pt/Nb loop as the counter electrode. The electrochemical cell held approximately 800 mL of solution in all tests. The Luggin probe was also filled with the test solution. In all of the tests, research-grade nitrogen was purged through the solution and testing cell while the entire setup was heated up to 85°C. Nitrogen sparging was maintained for at least 2.5 h to remove oxygen. Water vapor was collected by a condenser and flowed back into the cell. The sample was mounted on the electrode holder as described in ASTM G5.41 The working electrode holder was quickly installed while maintaining nitrogen purging (with a positive pressure inside the glass cell). The sample was kept hanging over the solution surface in the nitrogen blanket for 10 min to 15 min to remove any introduced oxygen. Then, it was lowered and either partially immersed in the case of the cylindrical coupons (to avoid crevice corrosion for measurements on boldly exposed specimens) or fully immersed in the case of the crevice samples.
Electrochemical Experiments and Erp Determination
After immersing the sample, the open circuit potential (OCP) of the specimen was monitored overnight while the solution was deaerated with nitrogen. In experiments with hydrogen sulfide, a H2S gas mixture was introduced the next day and the solution was subsequently sparged with the gas mixture throughout the test. Electrochemical tests were started after OCP reached a steady state, which typically required 2 h. Following the OCP monitoring, dynamic potential scanning experiments were performed to obtain cyclic polarization curves. The dynamic potential scanning was started from −100 mVOCP to 1 VSCE or when the current density reached 1 mA/cm2, whichever came first. The scanning rate was 0.167 mV/s.
In typical electrochemical experiments, the repassivation potential (Erp) is selected as the crossover point of the reverse scan portion, with the forward scan portion on the polarization curve. In the present work, however, an inflection point often appeared on the reverse scan, indicating the change of passivation. When the anodic current density at the inflection point was within an order of magnitude of the passive current density in the forward scan, the potential at this point was selected to be the Erp. Otherwise, Erp was further confirmed by different electrochemical techniques, i.e., potentiostatic experiments without showing any localized attack for at least 24 h at a potential ~50 mV lower than the inflection point value, and the Tsujikawa-Hisamatsu Electrochemical (THE, also known as potentiodynamic-galvanostatic-potentiostatic) method40 showing a current transition from increasing to decreasing at potentiostatic holding steps.
The measurements were performed on both creviced and boldly exposed samples. Following the measurements, the tested specimens were removed from the solution and inspected under an optical microscope or a scanning electron microscope to confirm localized corrosion attack. Prior to the next cycle of measurements, the glass cell and accessories were soaked in 50% nitric acid to clean off corrosion products and subsequently cleaned with soap water, rinsed with deionized water, and dried.
The measured repassivation potentials are collected in Table 1. In order to be used for modeling, the Erp values have been converted to the standard hydrogen electrode (SHE) scale. This conversion includes a correction for the thermal junction potential and is described in detail in the Appendix. The Appendix also includes a table of corrections as a function of temperature and the NaCl concentration in the test solution. Table 1 lists both the Erp values that were directly measured with respect to the external SCE electrode and those converted to the SHE scale using the procedure described in the Appendix.
Repassivation Potential in Chloride Environments
The repassivation potential model for aqueous systems containing chlorides was described in detail in a previous study.11 In this section, the fundamentals of this model are described to create a foundation for a more general model that accounts for the effects of H2S.
Figure 2 schematically depicts the phases that are considered in an occluded localized corrosion environment. The metal M undergoes an anodic dissolution process below a layer of a nonprotective hydrous halide MX with a thickness of l. The hydrous halide further dissolves in a solution with a boundary layer thickness Δ. In general, the existence of a solid phase MX is not necessary as long as a solution phase with a halide concentration close to saturation is present at the metal interface. The process of repassivation entails the formation of a protective layer of metal oxide (MO), which is assumed to cover a certain fraction of the metal surface at a given time. The original Erp model was derived11 by considering the measurable potential drop across the interface as a sum of four contributions, i.e.,
where the numbers in parentheses denote the interfaces shown in Figure 2: ΔΦM/MX(1,2) is the potential difference at the metal/hydrous halide interface, ΔΦMX(2,3) is the potential drop across the hydrous halide layer, ΔΦMX/S(3,4) is the potential difference across the halide/solution interface, and ΔΦS(4,5) is the potential drop across the solution boundary layer. The last three terms in Equation (1) can be evaluated in terms of fluxes and activities of metal and chloride ions using the methods of nonequilibrium thermodynamics introduced by Okada.42 As derived previously,11 the model is fully determined by the following equations:
- An equation that relates the measurable potential, E, to the current density, i, and the activities of metal ions in the bulk solution (aM(5)) and at the metal interface (aM(2)), i.e.,
- A relationship between the activities of chloride ions or other solution species (aj) and their fluxes in the hydrous halide (Jj′) and the boundary layer (Jj″), i.e., and are the average concentrations in the hydrous halide and the boundary layer, respectively, and and are the corresponding average mobilities in these phases.
Equations (3) and (4) can be simplified in the limit of repassivation when the current density reaches a certain small value, i = irp (typically, irp = 10−2 A/m2) and, simultaneously, the fluxes of active species and metal ions become small and comparable to those resulting from passive dissolution. Then, it can be shown that in the limiting case of E = Erp, Equations (3) and (4) simplify to:11
where K1 and K2 are constants. To obtain a working equation for Erp, a detailed expression needs to be established for i(ΔΦM/MX(1,2)) (Equation ), which reflects the mechanism of active dissolution and oxide formation. Such an expression was developed in the previous study11 for environments containing chlorides and inhibitive oxyanions. However, the previously established expression for i(ΔΦM/MX(1,2)) is not suitable for H2S-containing systems because it does not take into account the electrochemical behavior of metal interfaces with an adsorbed sulfur layer.
An expression that satisfies this requirement will be derived in the next section. While a new expression for i(ΔΦM/MX(1,2)) is necessary for systems containing H2S, Equations (1) through (6) still apply. For simplicity, the derivation will be limited to Cl− and H2S as electrochemically active species. An extension to multicomponent systems will be presented in a future study.
Repassivation Potential in Environments Containing Cl− and H2S
To extend the model to systems containing H2S, competitive adsorption of H2S, Cl− ions, and water were considered. The coverage fractions of H2S, Cl−, and H2O on a surface corroding in the active state are denoted by θs, θc, and θo, respectively. The reactions at the metal surface may further lead to the formation of a metal oxide (MO) and metal sulfide (MS). The surface coverage fractions of MO and MS are denoted by ΨMO and ΨMS, respectively. In systems that do not contain other electrochemically active species, the surface fractions satisfy the balance equation:
Adsorption of Cl− ions can be considered as a replacement of H2O on the metal surface (M) with Cl−, i.e.,
where and are the adsorption and desorption rate constants, respectively, and the adsorption coverage fractions θo and θc are placed below the adsorbed species to indicate the correspondence between the surface species and their coverage fractions. M is a metal whose properties are an appropriate average of those of the alloy components. In accordance with the previous studies,11,13 the adsorption is followed by the dissolution of the adsorbed complex, i.e.,
where ic is the c urrent density associated with the dissolution of the complex and z is the average charge. The process of repassivation is associated with the formation of a metal oxide layer according to the reaction:
where iMO is the current density that is associated with the formation of the oxide. It is important to consider the presence of adsorbed H2O in Equations (8) and (10) because water is the necessary precursor for the formation of oxide.42 The surface oxide MOz/2 can be further dissolved through a chemical dissolution process, i.e.,
where kMO is a chemical dissolution rate constant.
The presence of H2S gives rise to electrochemical reactions that may lead to a very significant enhancement of the anodic dissolution process and may result in the formation of a sulfide phase. The mechanisms of the H2S-induced acceleration of anodic dissolution were extensively studied in the literature for Fe,17–18,20–21,23–24 Ni,18–19,22,26 Cr,25 and Fe-Ni-Cr-Mo alloys.27–28 In this study, a simplified version of a previously proposed mechanism was adopted.17,20,23,26 The mechanism needs to be simplified because, in view of the available data, it is not possible to separate the reactions of the individual alloy components and it is necessary to limit the number of parameters that can be numerically evaluated to characterize the mechanism. Lumping the alloy components together prevents taking into account the different dissolution tendencies of individual alloy components (i.e., Fe, Ni, Cr, and Mo). Also, it excludes the detailed chemical characterization of the solid phases that form in the process of repassivation. These phases are primarily chromium oxides, which may form in the absence or presence of H2S, and nickel34,37 and iron sulfides, which may result from reactions involving H2S. The oxide and sulfide phases will be denoted by MOz/2 and MSz/2, respectively. While forgoing the detailed characterization of the behavior of alloy components, this approach makes it possible to characterize the repassivation process of the alloy with a minimum number of parameters. Although it is recognized that the individual alloy elements contribute differently to the formation of the oxide and sulfide phases, as well as to the dissolution in the active state, the overall electrochemical parameters are defined for the alloy rather than its components.
In accordance with the previous studies,17,20,23,26 a key step in the H2S-mediated dissolution is the adsorption of H2S on the surface. The adsorption can be written as a displacement of hydration water on the metal surface by hydrogen sulfide:
where and are the H2S adsorption and desorption rate constants, respectively. The adsorption is followed by an electrochemical step:
Equation (13) can be then followed by a dissolution reaction, which is responsible for the acceleration of the anodic process, i.e.,
or it can be followed by the formation of a solid metal sulfide phase:
In Equation (15), it can be assumed in practice that the effective formula of the metal sulfide is MS because NiS and mixed Ni-Fe sulfides are the predominant sulfides that may form on Fe-Ni-Cr alloys in aqueous solutions.34,37 By adding Equations (13) and (14), the following equation is obtained:
where iMS is the current density for the formation of the metal sulfide. Thus, the mechanism reflects the competitive formation of metal oxide (Equation ) and metal sulfide (Equation ). This is illustrated schematically in Figure 2 and is in agreement with the experiments of Marcus and Grimal,35 who observed the formation of islands of chromium oxide and nickel sulfide on a surface. The sulfur islands were found to persist even in a passivated system.
The metal sulfide may undergo chemical dissolution according to the reactions:
where the second reaction recognizes the possibility of formation of complex aqueous species such as Fe(HS)20 or Ni(HS)20, whose existence has been postulated in thermodynamic studies.43
After defining the reactions that may occur in the system in the process of repassivation, the change of coverage fractions with time can be related to the current densities and rate constants defined above. Based on Equations (8) and (9), the change of the Cl− coverage fraction is:
where ac(2) is the activity of Cl− at the metal surface and cc is a constant. The first and second terms on the right-hand side of Equation (20) represent the physical adsorption and desorption according to Equation (8), whereas the last term reflects the electrochemical desorption as a result of Equation (9). The current density ic is related to θc in accordance with Equation (9):
where the symbol is introduced to simplify further notation and is given by:
where the first term on the right-hand side is a result of the electrochemical reaction of oxide formation (Equation ) and the second term is a result of the chemical dissolution of the oxide (Equation ). The coefficient cMO relates the increase in the oxide coverage factor, ΨMO, to the current density that leads to the formation of the oxide (iMO), and kMO is the dissolution rate of the oxide. Both the cMO and kMO coefficients will be related in further derivation to parameters that can be determined from experimental data. The current density iMO is related to θo according to Equation (10):
where as(2) is the activity of H2S at the metal surface and cMS and cs are constants. The first and second terms on the right-hand side of Equation (26) represent the physical adsorption and desorption (Equation ), the third term reflects the electrochemical Equation (17) that leads to the formation of the metal sulfide, and the fourth term corresponds with the electrochemical desorption resulting from Equation (16). The current density iMS, which is responsible for the formation of the metal sulfide according to Equation (17), is given by:
and the current density that accounts for H2S-accelerated dissolution is:
where the factor is given by
where the first term on the right-hand side of Equation (31) is a consequence of Equation (17) and the second and third terms result from the chemical dissolution of the sulfide, i.e., Equations (18) and (19), respectively. The coefficient cMS relates the increase in the metal sulfide coverage factor, YMS, to the current density that leads to the formation of the sulfide, iMS. The coefficients kMS and uMS′ are the rate constants for the dissolution of the sulfide according to Equations (18) and (19), respectively.
The total anodic current density is a sum of those for the individual processes, i.e.,
In the steady state, which corresponds to the limit of repassivation, the surface coverage fractions no longer undergo a change. Hence,
The condition (33), together with Equations (20), (23), (26), and (31), gives four equations that depend on θc, θo, ΨMO, θs, and ΨMS. By substituting θo from the surface coverage balance Equation (7), the five variables θc, θo, ΨMO, θs, and ΨMS can be obtained analytically. Then, these variables are substituted into the defining equations for ic, iMO, iMS, and is (Equations  and ,  and ,  and , and  and , respectively) and the resulting expressions for current densities are summed according to Equation (32). The resulting expression for the total current density is:
Equation (34) can be solved in the limit of repassivation, i.e., when E = Erp and i = irp. For this purpose, Equations (5) and (6) are utilized, which are valid in the repassivation limit. Then, Equation (34) becomes:
where and are rescaled adsorption equilibrium constants for Cl− and H2S, respectively, ac = ac(5) and as = as(5) are the activities of Cl− and H2S, respectively, in the bulk environment, and
In the limit of repassivation, the expressions for , , , and take the form:
where fc, fMO, fMS, and fs are rescaled pre-exponential factors, which incorporate the unknown value of K1.
Practical Implementation of the Model
To make the model manageable with respect to the number of parameters, it was observed that the coefficients and could be neglected. This is because, at the low current densities at repassivation, the electrochemical desorption terms in Equations (20) and (26), which result from the existence of the current densities ic and is, can be expected to be less significant than the physical desorption terms. Thus, the coefficients cc and cs can be expected to be much smaller than the desorption rate constants and in Equations (20) and (26). Also, preliminary numerical tests have revealed that the terms that contain the ec and es coefficients can be neglected in Equation (35). On the other hand, the coefficient eMS (Equation [35c]) cannot be neglected, although it can be expected to be small. Then, Equation (35) reduces to:
The repassivation potential is then obtained numerically by solving a single nonlinear equation with respect to Erp, i.e., Equation (40) with ic, iMO, iMS, and is defined by Equations (36) through (39). Following previous work,11,13 the activities ac and as are calculated from an electrolyte thermodynamic model.44–47 The thermodynamic model provides the activities of all aqueous species that are in equilibrium with an H2S-containing gas phase. At the conditions investigated here, H2S exists in the aqueous phase predominantly in the form of a neutral species H2S(aq) and, therefore, there is no need to include other sulfur-bearing species in the Erp model.
where j = c, MO, s, or MS. An analogous equation expresses the dissolution rate constant uMS in terms of the corresponding Gibbs energy of activation, , i.e.,
The Gibbs energy of activation may be temperature-dependent according to the relation:
where Tref is a reference temperature (Tref = 298.15 K). The adsorption equilibrium constants are expressed using the Gibbs energy of adsorption, i.e.,
where j = c and s. For the coefficient fs in Equation (39), a first-order dependence on the activity of chlorides is assumed, i.e.,
where fs′ is expressed by Equations (41) and (43). This reflects the synergistic effect of H2S and Cl− on anodic dissolution. The remaining coefficients fj (j = c, MO, and MS) depend only on temperature according to Equations (41) and (43). For simplicity, the electrochemical transfer coefficients in Equations (36) and (39) are assumed to be 1, i.e.,
On the other hand, the electrochemical transfer coefficient ξMO in Equation (37) needs to have a value that is lower than 1, which is necessary for accurately determining the slope of Erp versus chloride concentration in the low-chloride, high-slope region.11,13 The coefficient ξMO can be assigned the same value for various alloys as determined previously.13 The electrochemical transfer coefficient for metal sulfide formation, ξMS, can be assumed to be the same as that for oxide formation, i.e.,
The constants ip and iq in Equation (40) are assigned the value 10−4 A/m2. This results from the fact that ip is equal to the passive current density,11 for which 10−4 A/m2 is a reasonable approximation for CRAs. The constant iq, which is an analog of ip for a metal surface covered with the sulfide rather than the oxide (cf. Equations [35d] and [35e]), can be expected to have a comparable value and is also assumed to be equal to 10−4 A/m2.
RESULTS AND DISCUSSION
First, the model has been applied to Alloy S41425 in chloride-only environments because such environments provide a baseline for analyzing the effect of H2S. In addition to the new Erp data reported in Table 1, a substantial number of experimental measurements is available from a previous study13 for Alloy S41425 in Cl− solutions at 23°C, 60°C, and 95°C. In Cl− systems, the model is completely defined when six parameters are specified: the Gibbs energy and enthalpy of activation for the anodic dissolution mediated by the adsorption of Cl− ions (Equations , , and ), the Gibbs energy and enthalpy of activation for the formation of the oxide (Equations , , and ), the electrochemical transfer coefficient for the formation of the oxide ξMO (Equation ), and the Gibbs energy of adsorption of Cl− ions Δgads,c (Equation ). These parameters have been determined as follows:
The parameters ξMO and Δgads,c have been assigned their generalized values, which have been established in a previous study13 on the basis of experimental data for 13 stainless steels and Ni-based alloys.
The remaining four parameters (i.e., , , , and ) have been determined by simultaneously regressing the combined experimental Erp data from this study (Table 1 for 0% H2S) and from a previous study.13 In principle, these parameters could also be calculated from the generalized correlation,13 but determining them directly from the experimental data for Alloy S41425 maximizes the accuracy of the model.
Among the regressed parameters, and determine the Gibbs energy of activation for Cl−-mediated alloy dissolution as a function of temperature according to Equation (43). These parameters primarily influence the Erp vs. Cl− dependence at higher Cl− concentrations, i.e., for Cl− molalities above approximately 0.003. This corresponds to the low-slope segment of the Erp vs. Cl− curves. On the other hand, the parameters and determine the Erp values at lower Cl− concentrations, at which the Erp vs. Cl− curves show a higher slope, as demonstrated in previous studies.11,13 The fact that the low-slope and high-slope sections of the Erp vs. Cl− curves are sensitive to different parameters facilitates the determination of the parameters.
The model parameters are listed in Table 2. With these parameters, the model can accurately reproduce the experimental Erp data as a function of chloride concentration and temperature. This is illustrated in Figure 3, which compares the calculated results with the data. It should be noted that it is convenient to plot Erp as a function of chloride activity rather than concentration because the model is expressed in terms of activities and, most importantly, various chloride-containing solutions (not necessarily only binary NaCl solutions) can be uniformly characterized using the chloride activity. Thus, the Erp vs. Cl− activity plot has a more general character than a plot against Cl− concentration.
As shown in Figure 3, the Erp vs. chloride activity plot shows a typical pattern of a lower slope at higher Cl− concentrations and a higher slope at lower concentrations. The temperature dependence of Erp is strong only at low chloride concentrations and diminishes at high concentrations.
It should be noted that the model described here represents an improvement over the original version of the model,11,13 even in the absence of H2S. In the original version, a simplifying assumption was made that the water coverage fraction θo was always equal to one, which was reasonable if the adsorption of all other species was fairly weak. Also, an empirical reaction order with respect to chloride ions was introduced, which was greater than 1. In the present model, the coverage fractions of all species including H2O are rigorously interrelated (cf. Equation ) and there is no need to introduce empirical fractional reaction orders. Consequently, the reaction order with respect to Cl− and other electrochemically active species is equal to 1 (cf. Equation ) and the parameterization of the model is simplified without a loss in accuracy.
After establishing the model for chloride-only systems, parameters have been determined for mixed Cl−-H2S systems. These parameters include the Gibbs energy of adsorption of H2S (Δgads,s), the Gibbs energies of activation for H2S-accelerated dissolution, metal sulfide formation, and sulfide chemical dissolution , , and , respectively), and the parameter eMS, which couples the sulfide formation with the desorption constant (). The H2S-related parameters have been determined as follows:
iv. The enthalpies of activation for H2S-accelerated dissolution and metal sulfide formation (i.e., and in Equation ) have been assumed to be zero for simplicity. These two parameters determine the temperature dependence of the H2S-related phenomena, and will be investigated in future studies on the basis of experimental data measured over a wide range of temperatures.
v. The parameters Δgads,s and have been determined from the Erp data at high Cl− concentrations, at which the accelerating effect of H2S on anodic dissolution is well established. The Gibbs energy of adsorption Δgads,s determines the strength of adsorption and, therefore, influences by how much the H2S effect differs for different H2S concentrations at high Cl− concentrations. The obtained value of Δgads,s is more negative than the Gibbs energy of adsorption of Cl− (i.e., Δg ads,c), which indicates that the adsorption of H2S is, as expected, stronger than that of Cl−. The decrease in Erp in the presence of H2S is determined by the value of .
vi. The parameters and reflect the effect of metal sulfide formation on Erp. Therefore, they have been determined based on the Erp data at low Cl− concentrations and 1% H2S, at which the metal sulfide formation manifests itself in an increase in the repassivation potential (see further discussion later). The elevation of the Erp beyond the baseline that would exist in the absence of metal sulfide formation is controlled by the value. The parameter reflects how readily the metal sulfide dissolves and, hence, it influences the threshold concentrations at which the effect of the metal sulfide appears.
vii. Finally, the parameter eMS has been set equal to 10−3. This parameter dampens the metal sulfide-induced elevation of Erp at low chloride concentrations. An accurate determination of this parameter is not possible with the currently available data and, therefore, an approximate low value needs to be assumed. Numerical testing revealed that the results are not sensitive to this parameters as long as it remains of the order of 10−3.
The obtained parameters are included in Table 2. In the analysis of Erp data, preference has been given to measurements obtained on creviced samples whenever data obtained on creviced and boldly exposed samples were not in quantitative agreement. In general, measurements on creviced samples give more reproducible results at less aggressive conditions when the alloy is less prone to localized corrosion. The differences between the measurements on creviced and boldly exposed samples are significant only at 1% H2S and lower chloride concentrations (cf. Table 1). In more aggressive environments, the results obtained on both kinds of samples are quantitatively consistent.
The results of calculations are shown in Figure 4 in comparison with those for H2S-free environments at 358.15 K. Figure 4 indicates that the effect of H2S on the repassivation potential is very complex. At high H2S concentrations (100 wt%), the Erp vs. Cl− curve is almost parallel to that in the absence of H2S, but is shifted toward lower potentials by approximately 0.2 V. This is a manifestation of the acceleration of anodic dissolution in the localized environment by the presence of H2S. As a result, H2S strongly increases the tendency of the alloy to undergo localized corrosion at Cl− concentrations ranging from 0.0003 m to 3 m provided that the H2S concentration is sufficiently high (cf. the lowest line and the diamond symbols in Figure 4). On the other hand, the effect of H2S at lower H2S concentrations (i.e., 1 wt%) strongly depends on the chloride concentration. At high chloride concentrations, the behavior of the alloy in environments with 1% and 100% H2S is similar, with the Erp depression in 1% H2S being, as expected, weaker. This results from the fact that the adsorption of H2S is strong48–50 and, therefore, 1% H2S in the gas phase is sufficient to obtain a substantial H2S coverage on the metal surface. Thus, as long as the mechanism of H2S-accelerated anodic dissolution remains the same (which appears to be the case at high chloride concentrations), the difference between the Erp values at 1% and 100% H2S is not large.
However, a drastically different behavior is observed at low chloride concentrations, which indicates a change in mechanism. In the low-Cl− range, there is no reduction in Erp because of H2S and, instead, Erp increases even above its level in Cl−-only solutions. It should be noted that this phenomenon was previously observed by Hinds, et al.,27 in environments with low H2S concentrations in the gas phase. This effect is a result of the formation of solid metal sulfide in competition with metal oxide. The presence of metal sulfide has a strong inhibitive effect. The net behavior of the system is a result of the competition between the acceleration of anodic dissolution from the adsorption of H2S and the inhibition from the formation of a solid sulfide phase. At chloride activities below approximately 0.03, the effect of metal sulfide formation is predominant and leads to an increase in the repassivation potential by as much as 200 mV. Thus, under such low-H2S and low-Cl− conditions, H2S effectively inhibits localized corrosion. The transition between the enhancement and inhibition of localized corrosion is predicted to occur over a narrow range of Cl− activities (between approximately 0.01 and 0.05), which is in agreement with the experimental data. Thus, the model correctly represents the complex dependence of Erp on both Cl− and H2S concentration.
At very low chloride concentrations, the Erp lines for 0% H2S and 1% H2S converge (c.f., Figure 4). In this region, the potential becomes too high for the metal sulfides to persist. At such potentials, metal sulfides should not be stable because they should oxidize to higher oxidation states of sulfur.51 Also, Marcus and Protopopoff48–49 showed a similar limit of the stability field of adsorbed sulfur at higher potentials. Because the Erp enhancement is attributed to the effect of metal sulfides, it should disappear at high potentials.
While the results of calculations for Alloy S41425 prove that the model can accurately reproduce the repassivation potential as a function of Cl− and H2S, they do not prove by themselves that the model has a predictive character. To verify whether the model is truly predictive, it is necessary to apply it to other metals and/or other conditions. Such calculations are shown in Figure 5 for Alloy CA6NM (UNS J91574) and compared with the approximate Erp data of Rhodes.9 The data of Rhodes9 were obtained at 298 K, which is 60 K lower than the temperature used for the measurements reported here. For Alloy J91574 in H2S-free environments, the model parameters have been calculated on the basis of the predictions from the previously developed generalized correlation.13 The parameters that reflect the effect of H2S have been simply assumed to be the same as those for Alloy S41425 (cf. Table 2). Thus, the model was used in a purely predictive manner for Alloy J91574, i.e., no parameters were adjusted based on the data that are specific to this alloy. As shown in Figure 5, the predicted results are in a good agreement with the data. Additionally, these results indicate that the H2S effect on Erp is not appreciably influenced by temperature, at least in the 298 K to 358 K range.
To verify the model further, it is necessary to analyze the behavior of additional alloys, especially those that are more corrosion-resistant than Alloy S41425. Experimental and modeling work is currently in progress for selected nickel-based and duplex alloys and will be reported in a forthcoming study.
It is of interest to compare the effect of H2S on localized corrosion with the effect of thiosulfate ions, which was investigated by Newman, Garner, Laycock, and coworkers.29–33 A considerable similarity exists between the effects of H2S and thiosulfate because thiosulfate ions lead to substantial acceleration of dissolution. As with the H2S-accelerated anodic dissolution mechanism proposed in this study, thiosulfate was demonstrated to activate anodic dissolution on the bare metal surface through the formation of a layer of adsorbed sulfur, which resulted from the electroreduction of the thiosulfate ion. However, the effect of thiosulfate appears to have its own complexity because inhibition of localized corrosion was found for increasing concentrations of thiosulfate, beyond a certain concentration. In view of the potential use of thiosulfate-containing systems as an alternative model environment for studying corrosion in sour environments, Tsujikawa, et al.,52 found that the concentration of H2S in thiosulfate-containing acidic solutions decreased with time and none was found in 316L stainless steel (UNS S31603) unless it was scratched. It has been speculated that H2S was created from thiosulfate through the disproportionation reaction to elemental sulfur, which was then either chemically or electrochemically reduced to H2S.52 While it is possible that such reactions may occur in active pits, it appears that the effect of thiosulfate is much more complex than that of H2S. Therefore, it was not considered viable to attempt a unified treatment of localized corrosion in H2S and thiosulfate environments in the current state of knowledge, and the methodology presented in this study is limited to H2S systems.
Finally, it is of interest to highlight the commonalities and differences of the present model and the reactive transport models that are available in the literature. A pioneering reactive transport model was developed by Galvele53–54 and extensively used to elucidate the pitting and, secondarily, repassivation potentials (cf. a review by Newman55). In common with the model presented here, the Galvele model relates the potential drop within the occluded space to the current density and the concentrations of various species (cf. Equation ). Therefore, some experimental observations can be explained by both models (in particular, the linear dependence of Erp on chloride activity at higher chloride concentrations). In Galvele’s model, it is assumed that the main triggering mechanism for pitting is the acidification of the pit and the attainment of a critical pH for depassivation. Further, the role of aggressive species such as chloride is mainly to affect the transport processes (and hence the conductivity) and, secondarily, the activity of protons (which is included qualitatively through a correction factor). Indeed, a key conclusion of the Galvele model is that the effect of aggressive species on pitting and protection potentials can all be accounted for through their effect on the transport processes. However, a correction factor is added for inhibiting species, which is not related to transport. Although the Galvele model laid an important milestone for thinking about localized corrosion, it has significant limitations in explaining experimental observations related to the effects of chloride and H2S. First, the fundamental assumption about the central role of transport cannot explain the double slope that is observed for the repassivation potential vs. chloride concentration. Therefore, other surface reactions (namely the effect of water on passivation) have to be invoked and are essential at low chloride concentrations.11 In the present model, the effect of chloride activity appears explicitly in the working equation that is solved for Erp (i.e., Equation ) and is a consequence of the contribution to the current density as a result of the adsorption of Cl− ions (cf. Equations  and ). At low chloride concentrations, the slope of the Erp vs. Cl− curve changes because of the additional contribution to the current density resulting from the oxide formation (cf. Equations  and ). Most importantly, in acidic H2S solutions, the predominant species is the neutral H2S molecule which will not affect conductivity through electromigration. Therefore, the role of H2S in repassivation potential cannot be easily explained by Galvele’s model. Instead, the complex effect of H2S is explained in the present model through interfacial reactions that lead either to the acceleration of anodic dissolution or its inhibition via metal sulfide formation. At the limit of repassivation, the surface reactions that occur at the pit bottom play a central role in the present model, whereas the transport processes, while important in general, play a subsidiary role because the current density is low in the limit of repassivation.
❖ A systematic study has been undertaken to provide the values of the repassivation potential of corrosion-resistant alloys as a criterion for predicting whether the alloys can undergo localized corrosion and stress corrosion cracking in oil and gas-related environments.
❖ A comprehensive set of Erp data has been obtained for Alloy S41425 in Cl− + H2S environments at 358.15 K.
❖ A model for calculating the repassivation potential as a function of solution chemistry and temperature has been developed. The model considers competitive adsorption, enhancement of anodic dissolution resulting from the adsorption of electrochemically active species, and competitive formation of metal oxide and sulfide in the process of repassivation.
❖ The presence of H2S can substantially reduce the repassivation potential, thus indicating a strongly enhanced tendency for localized corrosion and SCC. However, exceptions exist at lower H2S and Cl− concentrations, at which H2S may lead to the inhibition of localized corrosion. This complex behavior is accurately represented by the model.
The work reported here was supported by Chevron, ConocoPhillips, DNV GL, JFE, Nippon Steel & Sumitomo Metal, Petrobras, Sandvik, and Vallourec-Manesmann within the framework of the joint industry program “Performance Assessment of CRAs in Severe Well Environments.”
(1) UNS numbers are listed in Metals and Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.
APPENDIX: CONVERSION OF POTENTIALS OBTAINED USING EXTERNAL SCE ELECTRODE TO THE SHE SCALE
This appendix describes the conversion of a potential measured with respect to an external saturated calomel electrode (SCE) at a temperature T0, Emeas, to the potential of the standard hydrogen electrode (SHE) at the temperature of observation, T, i.e., EH(T). The solutions in the working and reference vessels are different, i.e., the working vessel contains a NaCl solution of varying concentration, whereas the reference electrode is placed in a saturated KCl solution (4.82 m KCl). The salt bridge between the reference and working vessels contains a NaCl solution with the same concentration as in the working vessel. To make the conversion, it is necessary to estimate the quantity Ecorrection in the relation:
In order to calculate Ecorrection, it is convenient to convert the potential that is measured with respect to the external electrode (i.e., Emeas) to a potential relative to SHE at T = 25°C, Eext, i.e., Eext = Emeas + Eref,H(T0), where Eref,H(T0) is the potential of the external electrode relative to SHE under standard conditions. Thus, for SCE at T0 = 25°C, the authors have Eref,H(T0) = 0.2438 V. On the other hand:
where EWE(T) is the potential of working electrode. The correction ETherm = ESHE(T) − ESHE(T0) can be subdivided into two parts, i.e., = ETh,SHE + ETJ. The first term, ETh,SHE, is the difference between the potentials of two standard hydrogen electrodes at the temperatures T and T0 and can be evaluated from a thermodynamic analysis of the cell SHE(298K)SHE(T). Such analysis was performed by Macdonald56 and Bosch, et al.,57 and the results can be accurately approximated by:
where ΔT = T – 298.15 K and ETh,SHE is expressed in V.
The second term, ETJ, represents the potential drop in the salt bridge and can be determined experimentally or estimated by considering the mass transfer in the bridge. Such an estimate was developed by assuming that only the NaCl solution is present within the salt bridge and the temperature inside it increases from T0 to T. On the cold side of the bridge (i.e., near the reference electrode), a thin porous cap separates the saturated KCl and working (NaCl) solutions. The temperature of this cap is equal to that of the reference vessel, i.e., T0.
Accordingly, ETJ can be in turn subdivided into two parts, i.e., ETJ = ETLJP + EDIF, where ETLJP is the potential drop in the salt bridge and EDIF is the potential drop in the porous cap. The latter value can be estimated via the Henderson method.58 Accordingly, the ion fluxes for i-th species are written in the Nernst-Planck approximation as:
along with the condition of electroneutrality. In the absence of current, there is JK+ + JNa+ = JCl−. In addition, in accordance with the Henderson assumption, the concentrations or activities of all species inside the mass transport region (i.e., the porous cap) change linearly.58 After integration, Equation (A-5) is obtained:
For example, for T0 = 25°C, CKCl = 4.82 m, and CNaCl = 5.7 m (the latter concentration being considered constant across the bridge because the influence of thermodiffusion on concentration distribution is small), Equation (A-5) yields EDIF = 4.8 mV. It should be noted that this is the highest estimate of EDIF for this system. EDIF decreases for smaller NaCl concentrations and, for example, Equation (A-5) yields EDIF = −0.2 mV for T0 = 25°C, CKCl = 4.82 m, and CNaCl = 0.44 m.
The potential drop in the salt bridge ETLJP can be estimated on the basis of the following simplified system of mass transfer equations:59
where σi are the Soret coefficients. The system (A-6) combines the usual mass transfer equations in the Nernst-Planck approximation with additional thermodiffusional terms. In accordance with Agar, et al.,60 the Soret coefficient, σi, can be expressed as:
Here and are the ionic heat and entropy of transport, respectively, and ε is the dielectric permeability. In Equation (A-7), the parameter Ai depends on the hydrodynamic radius of the species, which is not well known for any real solution and, hence, should be considered an empirical parameter and derived from experimental data.60 It was assumed that the parameter Ai only slightly depends on T. When the species fluxes are equal to 0, integration between the points () and (CNaCl,T) yields the following estimate for the thermal liquid junction potential:
Because the concentration of NaCl inside the salt bridge is approximately constant (i.e., ), the first (diffusion) term can be neglected and, in accordance with Equation (A-7) the following is obtained after integration:
where the parameter P does not depend on temperature. Finally, Equation (A-10) is obtained:
Equations (A-9) and (A-11) yield very close results (with a deviation of no more than 1 mV to 3 mV) if ε(T) of pure water is used in Equation (9)62 and P = 5.7. However, experimental data63 show that the dielectric constant is reduced by a factor of ~1.7 in nearly saturated KCl solutions at 25°C even though it varies only slightly with concentration for CKCl ≤ 0.505 m. Although experimental data are not available for ε(T) in saturated KCl at different temperatures, it can be assumed that ε in saturated KCl solutions changes with temperature proportionally to ε in pure water. Then, the parameter P in Equation (9) needs to be changed from 5.7 to 9.9 in order to estimate ETLJP in a saturated KCl solution. It is also natural to observe that, in the case of a NaCl salt bridge, the parameter P must be proportional to the term () instead of the term () in the case of a KCl salt bridge (cf. Equation [A-8]). Hence, the parameter P will increase for a NaCl salt bridge by the additional factor , which is obtained using the entropies of transport at infinite dilution, S*, according to Agar, et al.60
Figure A-1 illustrates the calculated values of ETherm – ESHE(T) – ESHE(T0) as a function of the temperature drop and shows the contributions of each constituent term when the NaCl concentration in the test solution is 5.7 m NaCl. It should be noted that the dependence of ETherm on NaCl concentration is weak and the behavior shown in Figure A-1 remains valid for other NaCl concentrations.
Finally, the correction term in Equation (A-1) is calculated as:
To facilitate the practical use of Equations (A-1) through (A-12), the correction term can be fitted to the following equations as a function of NaCl concentration:
Presented in a preliminary form as paper 3744 at CORROSION 2014, March 9–13, 2014, San Antonio, Texas.
*OLI Systems Inc., 240 Cedar Knolls Road, Suite 301, Cedar Knolls, NJ 07927.
**DNV GL - Strategic Research and Innovation, 5777 Frantz Road, Dublin, OH 43017.