A recently developed framework for predicting localized corrosion and stress corrosion cracking of corrosion-resistant alloys (CRAs) in oil and gas production environments relies on the computation of the repassivation potential and corrosion potential. While the repassivation potential defines the threshold condition for the existence of stable pits or crevice corrosion, the corrosion potential quantifies the driving force for localized corrosion. Localized corrosion can occur if the corrosion potential exceeds the repassivation potential. In a previous study, a model was developed for predicting the repassivation potential of CRAs in H2S-containing environments. In this work, a mixed potential model has been developed for calculating the corrosion potential of passive alloys in wide ranges of temperature, pressure, salinity, and H2S concentration. The model simulates passive dissolution of CRAs and incorporates the main cathodic reactions including the reduction of water and H2S molecules. The mixed potential model is integrated with a speciation-based thermodynamic model for calculating phase and chemical equilibria in the environment. The model has been parameterized using long-term corrosion potential measurements for Alloys 2535 (UNS N08535) and S13Cr (UNS S41425). The measurements have been performed at temperatures ranging from 20°C to 232°C with NaCl concentrations of ∼0.3 molal and 5.7 molal in the liquid phase and in the presence of N2, H2S, and N2−H2S mixtures in the gas phase. The model accurately represents the experimental corrosion potential data and can be used to elucidate the environmental conditions at which CRAs are susceptible to localized corrosion.
Corrosion-resistant alloys (CRAs) are widely used in the oil and gas industry to satisfy material performance requirements for deep wells involving high temperatures and pressures, to facilitate enhanced recovery techniques such as steam or CO2 injection or flooding with seawater, and to address weight reduction considerations. The performance of CRAs is affected by various environmental factors including temperature, chlorides, hydrogen sulfide, carbon dioxide, and elemental sulfur. Although the generally accepted methodology for selecting CRAs relies on standards (e.g., NACE MR0175/ISO 151561 ), guidance documents, and company specifications, there is a need for the development of mechanistic models that offer the possibility of rationalizing and predicting localized corrosion as a function of environmental conditions. Prediction of localized corrosion is of particular importance in oil and gas production because localized corrosion can be a precursor to stress corrosion cracking.2 Experimental evidence indicates that the propensity of CRAs for stress corrosion cracking correlates with their susceptibility to localized corrosion.3-4
In recent studies,5-6 a modeling approach was proposed to predict the tendency of CRAs to undergo localized corrosion in oil and gas environments. This approach relies on the computation of two characteristic potentials as functions of solution chemistry, i.e., the corrosion potential, Ecorr, and the repassivation potential, Erp. Erp is the potential below which stable pitting or crevice corrosion does not occur7-9 and thus provides a threshold condition for localized corrosion. An alloy is predicted to be susceptible to localized corrosion if the corrosion potential exceeds the repassivation potential in a given environment.7-8 This approach is valid in the initial stages of localized corrosion as long as the corrosion potential is not affected by the growth of pits and the interaction between pits can be ignored. For both the repassivation and corrosion potentials, mechanistic models need to be established and their parameters need to be calibrated based on a limited set of laboratory data at representative conditions. Then, the models can be used to extrapolate from laboratory tests to field conditions. The predictive character of this approach was previously validated for alloys in chloride-dominated solutions using standard critical crevice temperature measurements10 and multi-electrode array sensor data from chemical plant environments.11
For the repassivation potential of alloys in Cl−+H2S environments, a general model has been recently developed.5-6 This model is based on an earlier theoretical framework for alloys in the presence of aggressive and inhibitive species7 and accounts for specific H2S-induced phenomena including H2S adsorption and concomitant enhancement of anodic dissolution as well as the formation of metal sulfides.12-17 It elucidates the conditions at which H2S increases the propensity for localized corrosion and those at which it does not. Based on an extensive set of measurements, the repassivation potential model was established for S13Cr (UNS S41425(1))5 and S15Cr (UNS S42625)6 supermartensitic stainless steels, duplex stainless steel 2507 (UNS S32750), and three nickel-based alloys, i.e., 2535 (UNS N08535), 28 (UNS N08028), and 29 (UNS N08029).6
In this study, the focus is on the corrosion potential. New experimental long-term measurements are reported for Alloys S41425 and N08535 over a wide range of temperatures (from 20°C to 232°C) and for varying chloride concentrations and H2S partial pressures. Then, a previously developed mixed potential model18-20 is extended to H2S-containing systems and parameterized using the new data. Finally, the prediction methodology is verified using selected literature data.
Cylindrical specimens were cut out from pipe and machined with dimensions shown in Figure 1. The sample surface was abraded with 600 grit silicon carbide abrasive paper, cleaned in ultrasonic bath with isopropanol, and dried by blowing nitrogen. The cylindrical samples were mounted on an electrode holder with a polytetrafluoroethylene (PTFE) compression gasket. In order to avoid crevice corrosion underneath the PTFE compression gasket, cylindrical samples were partially submerged in the test solution.
Corrosion potential measurements were performed on two types of CRAs: N08535 and S41425. The chemical compositions of the two materials are listed in Table 1.
The development of the present model was focused on the effects of H2S and temperature on the corrosion potential. Therefore, various H2S concentrations and temperatures were tested, while the chloride concentration was fixed at 0.3 molal (m; 1.72 wt% NaCl) for S41425 and high, i.e., 5.7 m (25%), and low, i.e., 0.287 m (1.65%), concentrations were used for N08535, as shown in Table 2. For Alloy S41425, only a low Cl− concentration was used in conjunction with H2S because lower alloyed materials are generally used in less aggressive environments. Higher H2S contents (i.e., 75% or 62% H2S) were used in the tests for both alloys in order to determine the parameters of the model. The lower H2S content (i.e., 10%) was used only to test the predictions of the model and, therefore, only limited measurements were made for one alloy (i.e., N08535) in the presence of 10% H2S.
Tests at High Pressures and High Temperatures (HPHTs)
A conventional testing vessel made of Alloy C276 (UNS N10276) was used for high-pressure, high-temperature (HPHT) electrochemical tests in sour environments. Multiple threaded ports on the lid allow thermal well, electric wires, and gas tube to go through. The lid and body were bolted together and sealed with a PTFE O-ring. Wires ran through a Conax† sealing gland which was able to hold high pressure. The reference electrode was a custom-built external pressure balanced reference electrode (EPBRE) for HPHT conditions.21-23 It was based on an Ag/AgCl electrode, which operated in a saturated KCl solution at the testing pressure but at room temperature using a water-cooled jacket. In order to be compatible with H2S environments, the lower part of the reference assembly was packed with fine quartz sand, which served as an H2S diffusion barrier to prevent H2S contamination of the Ag/AgCl electrode. The reference assembly had a potential of 197 mV vs. standard hydrogen electrode (SHE) at room temperature. The potential of the reference assembly was checked before and after the tests to ensure its proper functionality. All of the potentials were measured with respect to this customized reference electrode at testing temperature, and then converted to the SHE scale at the same temperature as described in the Appendix.
On the first day, the cylindrical specimen was prepared and installed on the sample holder underneath the lid. The autoclave was then closed and sealed. It was subsequently deaerated to remove oxygen and was pressure tested overnight at the target temperature and pressure with research grade nitrogen. In the meantime, the test solution was deaerated overnight with research grade nitrogen in a separate pre-conditioning glass cell.
On the second day, if the pressure test passed, the autoclave was slowly cooled down to room temperature and released to ambient pressure. After the EPBRE assembly was installed, the autoclave was connected to the pre-conditioning glass cell and about 200 mL of the deaerated test solution was pressurized into the autoclave, leaving approximately one-quarter of the autoclave volume as overhead vapor space. The autoclave was continuously purged with research grade nitrogen to remove residual oxygen for about 2 h. Then pure H2S or an H2S-N2 mixture was introduced to the target pressure at room temperature. The solution was allowed to saturate with the gas phase for about 1 h, and was recharged to maintain the target pressure if the pressure dropped. The autoclave was finally ready to heat up to the test temperature. A single temperature or an ascending staircase temperature profile was adopted to measure the corrosion potential at 85°C or 100°C, 150°C, 200°C, and 232°C in a sequence. Corrosion potential at each temperature was measured for 3 d to 7 d, and the median value during the last 40% of the stable potential measuring period was reported. Also, the standard deviation of Ecorr was calculated during the same period. Figure 2 shows a representative example of the time evolution of the measured corrosion potential for triplicate specimens at a single temperature until steady-state is established. Figure 3 illustrates the evolution of the potential along a temperature staircase.
After the electrochemical test was completed, the autoclave was cooled down to room temperature and pressure was slowly released through a 12% NaOH scrubber. Nitrogen was kept purging through the regulator and autoclave to clean the residual H2S overnight.
MIXED POTENTIAL MODEL
In previous studies,18-20 an electrochemical model was developed for calculating the corrosion potential and general corrosion rates of various metals in aqueous environments. The model considers individual partial electrochemical reactions on the surface of the metal and incorporates transport processes for the species that participate in the reactions. Further, the electrochemical model is coupled with a thermodynamic speciation model for multicomponent aqueous systems, thus linking the interfacial processes with the solution chemistry of bulk environments. In this study, the model is generalized to systems containing hydrogen sulfide.
The model is constructed by establishing expressions for partial anodic and cathodic processes in accordance with generally accepted views on the mechanisms of electrochemical processes. Once the partial processes are related to the potential and solution chemistry, the corrosion potential can be obtained by using the mixed potential theory, i.e., by equating the total anodic and cathodic current densities on the metal surface:
where ia,j and ic,k are the j-th anodic and k-th cathodic current densities, respectively. In this section, expressions for the partial processes that are relevant to passive alloys in aqueous brines containing H2S are developed.
In previous studies,18-20 a model of passive dissolution and active-passive transition was constructed by assuming that, at any instant, a certain fraction of the surface, θMO, is covered by a passive oxide layer. At a fixed potential, E, and for fixed activities of solution species, ai, the coverage fraction changes with time according to:
where iMO is the current density that contributes to the formation of the passive layer and c and K are constants. In Equation (2), iMO is constant with time, whereas θMO varies with time until a steady state is reached. The first term on the right-hand side reflects the formation of the passive layer and the second term represents its dissolution. The parameter K is proportional to the rate of the dissolution of the passive layer. The solution of this equation in the steady-state limit gives an expression for the total anodic dissolution current:
where iM is the metal dissolution current density in the active state and ip is the passive current density, i.e.,
As shown in previous studies,18-19 the total current density reduces to ip at potentials above the Flade potential. In this study, the focus is exclusively on alloys in the passive state, in which iM,TOT → ip. At such conditions, the dependence of the passive current density on the chemistry of the environment is essential for modeling the corrosion potential. Here, a framework is developed for relating ip to the solution pH and the effect of H2S.
In the absence of H2S and other reactive solution species, the passive current density depends on the pH and temperature of the environment. To develop an expression for ip, the oxide film dissolution reactions are considered. In aqueous environments that are neither strongly acidic nor alkaline, such a reaction can be written as:
Analogous reactions in predominantly acidic and alkaline environments are given by:
In Reactions (4) through (6), the symbol “≡” denotes surface species and the overall oxide formula is given as MOz/2. Reactions (4) through (6) represent oxide dissolution without a change in the valence of the metal ion. Oxidative dissolution is not taken into account as it is not expected to be significant in the environments considered here. The oxide dissolution rate depends on the activities of the predominant aqueous species. Thus, the rates of dissolution that correspond to Reactions (4), (5), and (6) can be expressed as:
where No is the number of oxide dissolution sites per surface area, , , and are the activities of H2O, H+, and OH−, respectively, at the surface, and , κo,H, and κo,OH are the corresponding rate constants. The total rate of dissolution is:
Considering that the passive current density is given by Equation (3a) and the parameter K in Equation (2) is proportional to the rate of dissolution of the oxide r, i.e., K = dr, the passive current density can be calculated as:
where , ip,H, and ip,OH are the contributions to the passive current density in predominantly neutral, acidic, and alkaline solutions, respectively, and are expressed as:
In order to model the behavior of alloys in H2S-containing environments, the effect of H2S on passive dissolution needs to be taken into account. Various experimental studies indicate a profound effect of H2S on the structure of passive films on stainless steels and nickel-based alloys. As discussed in the reviews by Rhodes2 and Ueda24 (and papers cited therein), inner chromium oxide-dominated passive layers and outer layers composed primarily of nickel and molybdenum sulfides exist on CRAs in H2S environments. This structure is consistent with an H2S diffusion gradient from the environment to the metal. Also, the formation of layered films (i.e., Cr-O-rich layers adjacent to the metal and NiS-rich layers adjacent to the solution) is consistent with a strong thermodynamic driving force for the formation of nickel and molybdenum sulfides as a result of reactions with dissolved H2S.24 As a result of such interactions, the passive current density may increase25 which entails an increase in general corrosion rate as a function of dissolved H2S.26 At the same time, the depassivation pH of CRAs increases in the presence of H2S,16 thus indicating a weakening of the passive film in the presence of H2S. To account for the effect of H2S on passive dissolution, the above scheme (Equations  through ) needs to be modified in accordance with these observations.
Figure 4 shows a schematic of the surface layers and key reactions that are considered in the derivation of the model. In the presence of H2S, an overall reaction between the metal oxide surface and dissolved H2S can be assumed to reflect the experimentally observed sulfide layer formation:
where Ns is the number of sites per surface area occupied by the sulfide. Because sulfides are frequently non-stoichiometric, the value of z may be, in general, non-integer and may vary within a certain range. The derivation presented here is not sensitive to the exact value of z. While this simplified reaction does not explicitly deal with various possible mechanisms of sulfide formation, it limits the number of parameters that are needed to characterize the H2S effect. Assuming that Reaction (15) is in quasi-equilibrium, its equilibrium constant can be expressed as:
where is the activity of H2S at the surface. The dissolution of the surface sulfide sites, ≡MSz/2, in environments that are neither strongly acidic nor alkaline can be written as:
In strongly acidic and moderately alkaline environments, analogous reactions are:
Consequently, Equations (12) through (14) need to be modified to include contributions resulting from the dissolution of sulfide sites. By utilizing the proportionality between the dissolution rate of the surface layer and the passive current density (cf. Equations [3a],  through , and  through ), the following are obtained:
where , ks,H, and ks,OH are the corresponding rate constants for the sulfide dissolution reactions given by Equations (17) through (19). By calculating Ns from Equation (16), substituting the result into Equations (20) through (22), and then substituting the resulting equations for , ip,H, and ip,OH into Equation (11), an expression is obtained for the passive current density:
where the parameters of Equation (23) are obtained as products of the primary parameters, i.e.,
In oil and gas-related environments, the alkaline contribution (i.e., the third term in the numerator of Equation ) can be neglected. The acidic contribution (i.e., the second term in the numerator) becomes important when the pH is below or in the vicinity of the depassivation pH. For alloys that are in the passive state, the first term in the numerator is by far most important. Thus, under typical conditions, the passive dissolution is effectively characterized by three parameters, i.e., , , and Ks. The parameter reflects passive dissolution in the absence of H2S or other aggressive solution species, whereas the parameters and Ks represent the effect of H2S. Of these parameters, depends on temperature, which reflects the temperature dependence of the passive current density. In principle, the parameters Ks and can also depend on temperature because Ks is a pseudo-equilibrium constant and is a product of Ks and a ratio of two rate constants according to Equation (25). However, regression of these parameters based on experimental data revealed that they can be treated as independent of temperature. This is a desirable outcome because it simplifies the parameterization of the model.
The temperature dependence of is obtained on the assumption that the enthalpy of activation of passive dissolution (Equation ) is non-zero but independent of temperature. This assumption yields:
where is the enthalpy of activation and Tref is the reference temperature (Tref = 298.15 K). The parameters and are calculated on the basis of experimental general corrosion rate data, which reflect passive dissolution in H2S-free environments as a function of temperature. Then, the and Ks parameters are evaluated using general corrosion rate data in the presence of H2S.
In general, an expression for the current density associated with a given partial cathodic reaction can be given by a generalized Butler-Volmer expression:10
where is a rate constant, θk is the surface coverage fraction of the k-th electrochemically active species, xk is the reaction order, αj is the electrochemical transfer coefficient, E is the potential, is the reversible (equilibrium) potential calculated from the Nernst equation, T is the temperature, and F and R are the Faraday and gas constants, respectively.
In the H2S–N2–brine environments, the key cathodic reactions are the reduction of water molecules and dissolved H2S. The water reduction reaction is the most common cathodic process in aqueous systems and can be written as:
Because the environment is dominated by water, the surface coverage for water molecules, , in Equation (27) can be replaced with the activity of water, . Thus, the current density for the water reduction becomes:
Equation (29) includes a reaction order with respect to water, , which is not necessarily equal to one. Reaction orders greater than one with respect to water were previously identified in brine environments.27
The reduction of H2S molecules can be written as:
In contrast to the water molecules, the availability of H2S molecules at the interface is limited by the solubility of H2S in brines and by the transport of H2S from the bulk solution to the interface. To relate the surface coverage to bulk concentration, it is convenient to assume the Langmuir isotherm as in previous studies:19
where is a Langmuir adsorption constant for H2S and is the activity of H2S at the interface. In Equation (31), the reaction order with respect to H2S is assumed to be 1. In Equations (29) and (31), the equilibrium potential is the same because Reactions (28) and (30) are thermodynamically equivalent to the proton reduction reaction. The quantity is calculated from the Nernst equation for the proton reduction reaction. The electrochemical transfer coefficients and in Equations (29) and (31) are assumed to be 0.5.
The activity of solute species at the interface can be related to that in the bulk solution by the mass transfer equation:
where km,j is the mass transfer coefficient for species j, aj is the activity of species j in the bulk solution, and is the activity of species at the interface. The mass transfer coefficient can be predicted as a function of the flow regime as described previously10 and the activities of species in the bulk environment are obtained from a comprehensive thermodynamic model28-29 as a function of temperature, pressure, and overall system composition. Then, the surface activity of solute species is substituted into the current density expressions (Equations , , and ). Because the corrosive environment is dominated by water, it is assumed that the surface activity of water is equal to that in the bulk solution, i.e., .
The temperature dependence of the rate parameters (where j denotes H2O in Equation  and H2S in Equation ) is calculated on the assumption that the activation enthalpy, , is independent of temperature, i.e.,
With this assumption, both cathodic processes are characterized by three electrochemical parameters: , , and in the case of the reduction of H2O and , , and in the case of the reduction of H2S. The parameters , , and are determined on the basis of experimental corrosion potential data on passive alloys in the absence of H2S. Then, the parameters , , and are evaluated based on the corrosion potential data in the presence of H2S. It is assumed that the electrochemical parameters are the same for the reduction reactions that proceed on the sites occupied by the sulfide and on the unoccupied sites. This simplifying assumption is reasonable in view of the experimental evidence that the sulfide corrosion products are essentially metallic (i.e., have appreciable electronic conductivity) and, therefore, do not slow down electron transfer reactions on the surface.30
In general, the direct proton reduction reaction, i.e.,
RESULTS AND DISCUSSION
The corrosion potentials and their standard deviations, which were obtained during the last 40% of the stable measuring period, are listed in Table 3. In order to utilize the data for modeling, they have been converted to the SHE scale using a procedure described in the Appendix. The converted potentials are given in the last column of Table 3. The long-term Ecorr data obtained for Alloys N08535 and S41425 in H2S-free solutions and in the presence of higher H2S contents have been used in the determination of the parameters of the mixed potential model. The data for lower H2S contents (i.e., 10%) have been used for verifying the predictions of the model.
The parameters for calculating the passive current density have been constrained to match experimental long-term corrosion rates of passive alloys.26,31-33 Then, the parameters for the cathodic processes have been determined on the basis of the long-term corrosion potential data assembled in Table 3. The relevant model parameters are summarized in Table 4.
First, the model has been applied to the alloys in NaCl brine environments saturated with N2 in the absence of H2S. In such environments, the only significant cathodic reaction is the reduction of water molecules. Because the reduction of H2O is ubiquitous in aqueous systems, such systems provide a baseline for modeling the corrosion potential. In systems where other cathodic processes are important, the corrosion potential can be expected to be higher at a fixed temperature, pressure, and pH. For Alloy N08535, detailed Ecorr data are available at two NaCl concentrations (0.287 m and 5.7 m) and at temperatures ranging from 100°C to 232°C (cf. Table 3). Additionally, relevant literature data exist for other Ni-based alloys at room temperature in other salt solutions.34 It is noteworthy that the concentration of NaCl has a significant effect on the corrosion potential. In 5.7 m NaCl brines, Ecorr is lower by 40 mV to 65 mV (depending on temperature) than in 0.287 m NaCl. This is explained by the dependence of the water reduction reaction on the activity of water (cf. Equation ). This phenomenon was first identified by Smart and Bockris27 and can be quantitatively accounted for by the reaction order, . In highly saline environments, the water activity becomes significantly lower than 1, which reduces the partial current density for water reduction (Equation ) and, consequently, reduces the corrosion potential. Although the effect of chloride ion concentration on the passive current density can also contribute to the lowering of Ecorr, this effect is less significant than the effect of water activity. The dependence of Ecorr on both temperature and NaCl concentration is accurately reproduced by the model as shown in Figure 5 for Alloy N08535 (cf. the dark blue lines and hollow triangles for 0.287 m Cl solutions and light blue lines and solid squares for 5.7 m Cl solutions).
For Alloy S41425, the experimental Ecorr data in N2-saturated brines are available for only one NaCl concentration (i.e., 0.3 m) and show a somewhat larger scattering (cf. the dark blue triangles in Figure 6). The corrosion potential of Alloy S41425 is somewhat lower than that of Alloy N08535 (by 22 mV to 42 mV depending on temperature). This is a result of the higher passive current density for Alloy S41425. As discussed by Kirchheim, et al.,35 the passive current density depends primarily on the chromium content in the alloy. Because Alloy S41425 contains 12.1% Cr and Alloy N08535 contains 24.7% (cf. Table 1), a fairly significant difference in the passive current density is to be expected. The observed difference in the corrosion potential is consistent with the passive current density of Alloy S41425 being greater by a factor of ∼1.62 than that of Alloy N08535. Because it is reasonable to assume that the kinetic parameters for the reduction of H2O (Equation ) on both alloys are the same, the difference in the corrosion potential is attributed to the higher passive current density for Alloy S41425.
After establishing the baseline for the corrosion potential in H2S-free environments, the model has been applied to systems containing H2S. Figure 5 shows the experimental and calculated results for Alloy N08535 in systems in which the H2S content in the gas phase is effectively equal to 75 wt% and 10 wt%. For the higher H2S content, the data are available for two NaCl concentrations, i.e., 0.287 m (cf. the dark green triangles in Figure 5) and 5.7 m (cf. the light green squares). For the lower H2S content, only limited data are available (cf. the red squares in Figure 5), which were used to verify the model predictions after establishing the parameters on the basis of the high-H2S data. The presence of H2S results in a large elevation of the corrosion potential, ranging from ca. 380 mV at room temperature to ca. 180 mV at 232°C in 5.7 m solutions. The cathodic effect of H2S on the corrosion potential is twofold, i.e., it encompasses the influence of pH on the water reduction reaction and the effect of the direct reduction of dissolved H2S molecules. Both effects are partially counteracted by the effect of the dissolution of the sulfide layer on the passive current density. In the H2S-containing systems, pH reaches a value as low as 3.15 at room temperature. The reduction of water (Equation ) depends on pH because the equilibrium potential is a logarithmic function of the activity of protons according to the Nernst equation. Thus, the corrosion potential of passive alloys in deaerated solutions was observed to follow the pH dependence of the equilibrium potential for proton reduction.34 To analyze the relative importance of the two effects, the corrosion potential has also been calculated by excluding the H2S reduction reaction (i.e., Equation ). These hypothetical calculations are shown as the dotted lines in Figure 5 and illustrate the pH effect on Ecorr alone. As expected, the lower pH in H2S environments results in a substantial elevation of the corrosion potential but the pH effect alone accounts for only about 30% to 60% of the total elevation of Ecorr, depending on the temperature (cf. the dotted and solid dark green lines for systems with 75% H2S/0.287 m Cl and light green lines for systems with 75% H2S/5.7 m Cl in Figure 5). The rest of the elevation is a result of the reduction of H2S molecules.
It is noteworthy that the corrosion potential in H2S-containing environments is less strongly dependent on salinity than in H2S-free systems, especially at lower temperatures. This is primarily a result of a different effect of salinity on the H2S reduction reaction. While the H2O reduction reaction depends on salinity through the activity of water (cf. Equation ), H2S reduction depends on salinity through the solubility of H2S in aqueous environments, which determines the availability of H2S at the interface (cf. Equation ). The solubility of H2S is reduced by the presence of salts36 and the salt effect is significantly affected by temperature. The H2S concentration effect is mitigated by the effect of adsorption of H2S (as indicated by the denominator in Equation ). It is interesting to note that both the experimental and calculated corrosion potentials for the two salinities (i.e., 0.287 m and 5.7 m) show a weak crossover as a function of temperature (cf. the dark green line for 0.287 m Cl and light green line for 5.7 m Cl in Figure 5). Whereas the corrosion potential in 5.7 m NaCl solutions is slightly higher than that in 0.287 m NaCl at low temperatures, it becomes somewhat lower at higher temperatures. The latter behavior is in line with that observed for H2S-free systems. This behavior results from the different temperature dependencies of the H2S solubility, which shows a minimum with respect to temperature, and the rate parameter , which shows a monotonic temperature dependence according to Equation (33). Although the difference in Ecorr between the two Cl− concentrations is small, it is larger than the standard deviation of Ecorr measurements (cf. Table 3), especially at higher temperatures. However, the location of the apparent crossover of the Ecorr vs. T curves for the two Cl− concentrations is very uncertain because the differences between the calculated lines in this region are close to the experimental uncertainty. The model reproduces the experimental data with very good accuracy with the exception of one point at 150°C, which deviates from the expected temperature trend.
For Alloy S41425, the experimental data are available for only one NaCl concentration, i.e., 0.3 m (cf. Table 3 and the dark green triangles in Figure 6). Nevertheless, it is clear that the qualitative trends are similar to those for Alloy N08535. The corrosion potential of Alloy S41425 in H2S-containing systems is substantially lower than that of Alloy N08535. At high H2S and low Cl− conditions, the difference ranges from ca. 165 mV at room temperature to 110 mV at 232°C. This difference is larger than that in H2S-free environments and results from a lesser contribution of the H2S reduction reaction. Although the lower value of the corrosion potential reduces the driving force for localized corrosion, this effect is more than compensated by the much lower value of the repassivation potential for Alloy S41425,6 which indicates a lower threshold potential for localized corrosion.
It is also of interest to examine the consistency of the predictions of the mixed potential model with previously published corrosion potential and corrosion rate data in similar environments. Figure 7 shows a comparison with the data of Miyuki, et al.,26 and Onoyama, et al.,31 for Alloy S32750. Because the Cr and Mo contents of Alloys S32750 and N08535 are fairly similar, it has been assumed that the parameters of the mixed potential model are the same for these alloys. Figure 7(a) shows that the corrosion potential in H2S-free, CO2-containing systems is accurately predicted by the model. There is no dependence of Ecorr on the partial pressure of CO2, thus indicating that the reduction of water is responsible for the observed Ecorr and the reduction of carbonic acid is not significant at the corrosion potential. Figure 7(b) compares the calculated and experimental rates of general corrosion in H2S-free systems. The model provides an upper bound for the observed rates. No effect of NaCl is observed in accordance with the data, which indicates that the passive current density is not affected by chloride concentration. Figure 7(c) illustrates the effect of partial pressure of H2S in NaCl + CO2 + H2S solutions. A weak increase in the passive dissolution rate is observed, which is consistent with the proposed anodic dissolution model (Equation ).
The corrosion potential model can be used in conjunction with the previously developed repassivation potential model5-6 to predict whether localized corrosion can be anticipated at given conditions. Although a comprehensive validation of the complete methodology is outside of the scope of this study, Figure 8 illustrates the application of the model to predict localized corrosion of Alloy S32750 at 200°C in an environment with 10 atm (1,013.25 kPa) H2S, 0.5 wt% acetic acid, and varying concentrations of NaCl. Because the Cr and Mo contents of Alloys S32750 and N08535 are fairly similar, the corrosion potential of Alloy S32750 can be closely approximated by that of Alloy N08535 as long as both alloys are in the passive state. For the repassivation potential, the previously developed model6 has been used. Both potentials are plotted as a function of NaCl concentration in Figure 8. While Ecorr is not as sensitive to NaCl concentration, Erp is a strong function of chloride activity. The two potentials intersect at the NaCl molality of ∼0.72, which is indicated by the vertical line in Figure 8. Thus, localized corrosion is predicted to be possible at NaCl molalities above ca. 0.72. Below this concentration, only general corrosion is expected. The mixed potential model developed here predicts the general corrosion rate in the passive state as well as the corrosion potential. The predictions are compared with the corrosion rate data from long-term exposure experiments of Miyuki, et al.26 At low NaCl concentrations, the data of Miyuki, et al.,26 indicate low corrosion rates and are in a very good agreement with the calculated general corrosion rates. At NaCl concentrations for which localized corrosion is predicted, the experimentally observed corrosion rates are substantially higher than the general corrosion rates for passive dissolution. Such elevated rates are consistent with the presence of localized corrosion at NaCl concentrations above ca. 0.72 m, thus providing an independent validation of the model. Localized corrosion was indeed observed in this environment in 5 wt% (0.9 m) NaCl solutions.26
A previously developed mixed potential model has been extended to environments containing hydrogen sulfide. The model represents the effects of environmental conditions on passive dissolution of CRAs and on the key cathodic reactions.
The model reproduces the experimental data for Alloys N08535 and S41425 in both H2S-free and H2S-containing environments. Also, it has been validated using previously published corrosion potential and corrosion rate data.
In H2S-free environments, increasing salinity appreciably reduces the corrosion potential. The model explains this observation as an effect of salinity on the water reduction reaction.
In H2S-containing environments, a large elevation of the corrosion potential is observed compared to the baseline H2S-free solutions. The model elucidates this elevation as a combination of the effect of the pH dependence of the water reduction reaction and the contribution of direct reduction of dissolved H2S molecules.
When combined with the previously developed repassivation potential model, the mixed potential model makes it possible to predict conditions that are conducive to localized corrosion.
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.
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.”
APPENDIX: CONVERSION OF POTENTIALS OBTAINED USING EXTERNAL Ag/AgCl ELECTRODE TO THE SHE SCALE
In a previous paper,5 a procedure was developed for converting potentials measured with respect to an external electrode to the SHE scale for experimental setups in which the salt bridge between the reference and working vessels contains an NaCl solution with the same concentration as that in the working vessel. This Appendix describes a modification of this procedure to convert potentials measured with respect to an external Ag/AgCl pressure-balanced reference electrode, which is placed in a saturated KCl solution and is connected to the working vessel by a non-isothermal salt bridge filled with saturated KCl. For conversion purposes, the difference from the experimental configuration described earlier5 lies in the salt bridge, which is filled with saturated KCl rather than the working solution.
To convert a potential measured with respect to an external electrode at a temperature T0, Emeas, to the potential of the SHE electrode at the temperature of observation, T, i.e., EH(T), it is necessary to calculate the quantity Ecorrection in the relation:
It has been shown previously1 that:
where Eref,H (T0) is the potential of the external electrode relative to SHE under standard conditions, ETh,SHE is the difference between the potentials of two standard hydrogen electrodes at the temperatures of T and 298.15 K, EDIF is the potential drop in the porous cap, and ETLJP is the potential drop in the salt bridge.
For the Ag/AgCl electrode in saturated KCl at T0 = 25°C, Eref,H(T0) = 0.1972 V. ETh,SHE does not depend on the solution composition and is calculated from the same equation as in the previous study,1 i.e.,
where CNaCl is the concentration of NaCl in the working vessel, CKCl is the concentration of saturated KCl, and DNa+, DK+, and DCl− are the diffusion coefficients of the ions. In the current case, it is assumed that only the KCl solution is present within the salt bridge and the temperature inside it increases from T0 to T., i.e., the temperature of the thin porous cap, T, in Equation (A4) coincides with the temperature of the working solution (NaCl).
The potential drop in the salt bridge, ETLJP, is estimated via the relation:5
where ε is the dielectric constant of water and the parameter P does not depend on temperature. The value of P was estimated in the previous study for saturated KCl solutions and found to be 9.9 V.
For practical applications, the correction term has been fitted using the following simple equations as a function of NaCl concentration:
Presented in an abridged form as paper no. 7708 at CORROSION 2016, March 2016, Vancouver, Canada.