Analysis of oxide scale thickness and pores position of HCM12A steel in supercritical water

2.1 Summary of previous experimental results

Known from the literatures [2,3,4,5,6,7,8], a multilayer oxide scale is formed on ferritic–martensitic steels in supercritical water. The oxidation film growth follows parabolic oxidation kinetics, and the oxide film generally consists of three different layers, namely, a porous surface layer, a dense middle layer, and a bottom diffusion layer. The surface oxide is composed of dense columnar magnetite (Fe₃O₄) particles. The middle oxide consists of Cr-rich spinel oxide Fe_3−x Cr _x O₄ equiaxed crystal, in which x = 0.7–1 is related to the type of alloy [14]. The results of SEM show that the ratios of Cr and Fe are slightly different in each environment. However, a significant trend of the Fe:Cr ratios is observed in different alloys. The averaged Cr concentrations in the internal oxide of HCM12A are 11.8%. It is observed that the Cr concentrations in the inner layer are relatively close to those in the original alloy substrate, and slight enrichment was observed. Corresponding Fe:Cr:O ratios of inner oxide in HCM12A are 2.1:0.9:4 [14]. So the inner oxide is assumed as a stoichiometry of Fe₂CrO₄ in this study.

2.2 Proposed mechanism in other environments

The oxidation characteristics of different Fe–Cr steels are similar in different environments, such as evaluated temperature steam, CO₂, and liquid LBE. The “available space model” has become one of the most reliable models to explain the structure of double oxide scale [15]. In this model, Fe atom diffuses outward, and an external oxide film is formed at the oxide/oxidation medium interface, where a large number of vacancies are left. Vacancies condense into voids at the metal/oxide interface, where the oxides decompose and produce micro-channels in the oxide scale. The oxidant passes through micro-channels to metal/oxide interface and a new internal oxide layer is formed. In other words, the internal oxide layer grows inward. Although the oxygen transport is very fast through micro-channels, it is not the growth rate controlling step of internal oxide layer.

3.1 Assumptions

• Ferrite–martensitic steels form double oxide scale in supercritical water. The external layer is magnetite layer, whose growth is at the interface of supercritical water/magnetite. The internal layer is Cr-rich spinel layer, whose growth is at the interface of alloy/Cr-rich spinel layer. The iron flux through Cr-rich spinel is equal to that through magnetite.

• The oxide film is in a local thermodynamic equilibrium condition.

• The component concentration is fixed at the internal and external interfaces.

• The oxide thickness growth follows parabolic law.

• The deviation stoichiometric ratio of Cr-rich spinel layer composition is very small.

• The influence of cavity and crack is not considered.

• The dissolution of oxide is not considered.

3.2 Formulas

The thickness of growth of the two oxide layers shows a parabolic law over time, and the relations can be described as follows:

where h spinel and h mag are the thicknesses of the Cr-rich spinel layer and the magnetite layer (μm). k p,spinel and k p,mag are the oxidation proportionality constants of oxide layers (cm² s⁻¹). t is time (s).

Based on Wagner oxidation theory, the oxidation process of the alloy is controlled by the diffusion of iron in the oxide layer. The oxidation rate constants of the two layers obey the following expression [16]:

where a O 2 steel/spinel , a O 2 mag/spinel , and a O 2 mag/scw are the oxygen activities at steel/Cr-rich spinel layer interface, Cr-rich spinel layer/magnetite layer interface, and magnetite layer/SCW interface. f is the correlation coefficient of diffusion mechanism and is about 0.5 [16]. D Fe,mag and D Fe,spinel are the diffusion coefficients of Fe in Cr-rich spinel and magnetite. a O 2 = P O 2 / P O 2 0 , P O 2 is the oxygen partial pressure at the interface (atm), P O 2 0 = 1 atm .

The iron diffusion coefficient in magnetite and Cr-rich spinel can be showed as a function of oxygen activity by the following formula [17,14]:

where A = D V K V / 12 , B = 4 D I K I / 3 , D V and D I are self-diffusion coefficients of vacancies and interstitials, and K V and K I are the equilibrium constants for the formation of vacancies and interstitials in magnetite. They are functions of temperature [17]. In equation (5), the two terms represent vacancy diffusion and interstitial diffusion of iron, respectively. Both terms are functions of temperature and oxygen activity. Interstitial diffusion of Fe occurs preferentially for low oxygen activity, while iron diffuses through vacancies for high oxygen activity

It is assumed that the diffusion of iron in magnetite and Cr-rich spinel has the same temperature dependence, R V and R I are the ratios between D V and D I in Cr-rich spinel and those in magnetite by Töpfer’s data [18]. D mag,V topfer and D mag,I topfer are the partial cation vacancy and interstitial diffusion coefficients in Fe₃O₄. D spinel,V topfer and D spinel,I topfer are the partial cation vacancy and interstitial diffusion coefficients in Cr-rich spinel oxide layer.

It is generally believed that the thickness of the consumed alloy is the same as the thickness of the generated Cr-rich spinel layer. The thickness relationship between the two oxide scales can be expressed as follows [14]:

where C Fe(magnetite) , C Fe(spinel) , and C Fe(steel) are the concentration of Fe in magnetite, spinel, and steel (mol/cm³), respectively.

3.3 Estimation of iron diffusion coefficients in Fe–Cr spinel and magnetite

Accurate estimation of iron diffusion coefficients in Cr-rich spinel and magnetite is important to the simulation results. The diffusion coefficients of iron in magnetite were given by Töpfer et al. [18] for temperatures at 900 and 1,400°C. The iron diffusion coefficients were proposed by Backhaus-Ricoult and Dieckmann [17], but the coefficients were only for higher temperature conditions. Atkinson et al. [16] confirmed that the iron diffusion coefficients can be estimated to 500°C. The iron diffusion coefficients in Fe₃O₄ and Fe₂CrO₄ were measured at 1,200°C by Töpfer et al. [18], and the iron self-diffusion coefficients at low temperatures can be calculated from the Töpfer’s data. The experimental values of diffusion coefficients of iron in Fe₃O₄ and Fe₂CrO₄ at 1,200°C are listed in Table 2.

Linear regression was carried out with data points in Table 2 and the calculation expressions are listed in Table 3. The relation between the expression of R V and R I and oxygen activity are derived as:

3.4 Estimation of oxygen activities at interfaces

The oxidation growth rate is connected with the oxygen activities at three interfaces. Furukawa considered that the oxidation growth kinetics do not depend on the properties of the oxidizing medium, but on the oxygen activity in the oxidizing medium [19]. During the oxidation process of T91 in LBE, magnetite and chromium trioxide are formed at first, and then they react together to form iron-chromium spinel layer [9]. Considering the T91/magnetite equilibrium for oxygen activity, the calculated growth rate is close to experimental data. So equilibrium oxygen activity of Fe/magnetite is used as the oxygen activity at steel/Cr-rich spinel interface in this study. The reaction between Fe and H₂O is as follows:

According to Gaskell’s data [20], the standard free energy of reaction (10) is listed in the following formula:

At 600°C, Δ G T = − 25,391 J , and the equilibrium P H 2 O / P H 2 ratio is 0.03. From dissociation equation, water dissociation reaction rate, Gibbs free energy, and the equivalent oxygen pressure at steel/Cr-rich spinel interface can be evaluated. The equivalent oxygen partial pressure at steel/Cr-rich spinel interface at 500 and 600°C is shown in Table 4.

Cory and Herrington [21] suggested that the steam partial pressure is independent of corrosion rate. The oxygen activity at the interface of magnetite/external layer is not that of oxidizing medium, but that of magnetite/hematite equilibrium. The hematite layer is very thin and will change the oxygen activity at the magnetite/hematite interface.

Fe₂O₃ is formed at the grain boundary of magnetite by reaction (12) at the magnetite/supercritical water interface. Oxygen transports through short-circuit channels and grain boundary, and the oxide layers become thicker. The equivalent oxygen partial pressure at the magnetite/supercritical water interface is not the dissolved oxygen partial pressure, but satisfies the pressure at equilibrium of reaction (12).

According to Gaskell’s data [20], the standard free energy of reaction (12) is listed in the following formula:

Using the methods above, water dissociation reaction rate, Gibbs free energy, and the equivalent oxygen pressure at magnetite/supercritical water interface can be evaluated. These values at 500 and 600°C are shown in Table 4.

3.5 Thickness of oxide layer and weight gain of the oxide scale

Weight gain of the oxide scales is linear with oxide scale thickness due to the absorption of oxygen. With the increase of exposure time, the internal and external thickness of oxide scale gradually thickens. The thickness relationship between the two oxide layers and weight gain is estimated by the following formula [22]:

where Δ w is the amount of absorbed oxygen per unit area in mg cm⁻², ρ outer and ρ inner are the external and internal layer density (g cm⁻³), respectively, h outer and h inner are the external and internal layer thickness, respectively, M o-outer and M o-inner are the mole mass of oxygen in external and internal layer, respectively, M Fe 3 O 4 and M Fe 3 O 4 − FeCr 2 O 4 are the mole mass of external and internal layer, respectively.

3.6 Illustration of iron diffusion coefficient, oxygen activity, flux of ion and its divergence as a function of the location (x/X) in the oxide scale

Figure 1 shows a schematic diagram of iron and oxygen diffusion in magnetite layer and Cr-rich spinel layer. During the formation of double oxide scale, iron diffuses inward and oxygen diffuses outward.

Figure 1

Schematic diagram of iron and oxygen diffusion in magnetite layer and spinel layer

The flux of iron in the Cr-rich spinel layer of HCM12A is expressed as [23]:

The above formula is integrated through the Cr-rich spinel layer.

The equation (15) is integrated from 0 to x,

a, b, and X are the thickness of Cr-rich spinel layer, magnetite layer, and whole oxide scale layer, respectively. The oxygen activity and the position (x/X) in the Cr-rich spinel layer have the following relationship:

According to the above derivation process, the oxygen activity and the position (x/X) in the magnetite layer have the following relationship:

According to Millot’s research [24], the diffusion coefficient of oxygen in Fe₃O₄ at 1,073 and 1,423 K follows an equation of the form:

where C and F are the fitting parameters, respectively.

With the data given by Millot, the oxygen diffusion coefficient in magnetite can be estimated to the temperature applied in this study. Because the data of oxygen diffusion coefficient in Cr-rich spinel is not reported, the oxygen diffusion coefficient is assumed to be the same as that in magnetite. The results of extrapolation are in Table 5.

The flux of oxygen in the Cr-rich spinel layer of HCM12A is expressed as [23]:

where C o(spinel) is the concentration of oxygen ion (mol m⁻³), D o,spinel the oxygen diffusion coefficient in Fe–Cr spinel layer (m² s⁻¹), and μ O 2 the chemical potential of oxygen (J mol⁻¹).

The relation between oxygen chemical potential and oxygen partial pressure is given as:

where μ O 2 0 is the standard chemical potential of oxygen (J mol⁻¹), R gas constant (J mol⁻¹ K⁻¹).

With equations (18), (21), and (22), the flux of oxygen in the Cr-rich spinel layer is derived as follows:

First order derivative of the variable J O,spinel with respect to the independent variable x, i.e., the divergence of oxygen flux, is derived as:

In the same way, the flux of oxygen in the magnetite layer is derived as:

The divergence of oxygen flux in magnetite layer is expressed:

4.1 Iron diffusion coefficient in oxide scale

Using equations (4), (5), (6), and (9), iron diffusion coefficients in Fe₃O₄ and Fe₂CrO₄ are available at 500 and 600°C. The iron diffusion coefficients are presented over oxygen activity at 500 and 600°C, as shown in Figure 2. The vacancy diffusion and interstitial diffusion regions of iron in magnetite at 600°C are shown in the Figure 2.

Figure 2

Iron diffusion coefficient in magnetite and Cr-rich spinel over oxygen activity at 500 and 600°C.

The kinetics of oxide layer are generally bound up with many factors, such as defect properties, defect concentration, and oxide microstructure [25]. According to Wagner oxidation theory, the oxidation rate constant which depends on the property of the diffusing defect can vary with the oxygen partial pressure. With increasing temperature, the vacancy concentration at the external layer/supercritical water interface is higher than that at the steel/internal layer interface. The external oxygen partial pressure increases and the vacancy concentration increases too. The conversion between a vacancy and an interstitial mechanism depends on the temperature and external oxygen activity. There is a strong correlation between iron self-diffusion coefficient in oxide layer and oxygen activity, and different oxygen activities correspond to iron diffusion different mechanism in oxide. The iron diffusion under high oxygen activity follows the vacancy mechanism and the interstitial mechanism under low oxygen activity [9].

In fact, the oxygen activity is low at the steel/Cr-rich spinel interface, and iron diffuses via interstitial mechanism. The oxygen activity is high at the magnetite/supercritical water interface and iron diffuses via vacancies mechanism. The oxygen activity at the magnetite/Cr-rich spinel interface needs to be determined by calculation, so it is impossible to predict the diffusion mechanism of the interface. With the increase of temperature, the iron diffusion coefficient and the growth rate of oxide film increase.

4.2 Comparisons between simulation results and experiment results

According to equations (1)–(9) and (14), the simulation of HCM12A in supercritical water at 500 and 600°C under 25 MPa was carried out. The simulation results and experiment results of oxide weight gain are compared in Figure 3.

Figure 3

Simulation results and experiment results of oxidation weight gain of HCM12A in supercritical water at 500 and 600°C.

In ref. [5,13], oxidation tests of HCM12A exposed to SCW at 500 and 600°C, and 25 MPa are performed for oxidation time from 1 to 3,000 h. The dissolved oxygen concentration in supercritical water is less than 20 ppb.

The simulated values of oxidation weight gain of HCM12A at 500 and 600°C are lower than the experimental values. The maximum difference in weight gain at 600°C is 178 mg dm⁻², and the equivalent thickness is 12.7 µm according to the formula (14). The maximum difference in weight gain at 500°C is 49 mg dm⁻², and the equivalent thickness is 3.5 µm. The reason for the difference may be that the equilibrium oxygen partial pressure of the selected reaction (10) is higher than the actual oxygen partial pressure of the steel/Cr-rich spinel interface at this temperature, or the thermodynamic equilibrium oxygen partial pressure of the reaction (12) is lower than the actual oxygen partial pressure at the magnetite/supercritical water interface.

Over 3,000 h of oxidation, the relative errors between the predicted values and the experimental values of HCM12A oxidation weight gain in supercritical water at 500 and 600°C are shown in Figure 4.

Figure 4

Relative errors between the simulated values and the experimental values of HCM12A oxidation weight gain in supercritical water at 500 and 600°C.

The relative errors between the simulated values and the experimental values of HCM12A oxidation weight gain at 500 and 600°C are less than 20%, and the calculated values are consistent with the experimental values with increasing time.

Without considering the scale pores, bucking, and peeling, some errors between simulation and experiments of oxidation rate are present.

4.3 Comparison of oxidation rates

From the above relational expression, the oxidation rates of each layer and the overall oxidation rate are calculated and compared with the data in EPRI [26]. These values are shown in Table 6.

The oxidation rates of simulation for HCM12A at 500 and 600°C agree with that of the data in EPRI [26] in the same order. Because of the errors of diffusion coefficients which were estimated to be at low temperature, the oxidation rate of simulation is lower. The oxidation rate of simulation of HCM12A at 600°C is nearly 100 times higher than that at 500°C.

4.4 Analysis of oxygen activities and iron diffusion coefficients in oxide scale

The oxygen partial pressures at the oxide interfaces HCM12A at 500 and 600°C are shown in Table 6. When HCM12A is oxidized at 600°C, the oxygen activities on both sides of the Cr-rich layer are 3.36 × 10 − 25 and 1.12 × 10 − 16 , respectively. From Figure 2, there is a change diffusion of iron via from interstitials to vacancies. The oxygen activities on both sides of the magnetite layer are 1.12 × 10 − 16 and 2.57 × 10 − 16 , and iron diffusion follows the vacancy diffusion mechanism. At 500°C, the oxygen activities on both sides of Cr-rich spinel layer are 2.01 × 10 − 29 and 1.68 × 10 − 20 , and there is a change diffusion of iron via from interstitials to vacancies. The oxygen activities on both sides of the magnetite layer are 1.68 × 10 − 20 and 3.5 × 10 − 20 , and iron diffusion conforms to the vacancy diffusion mechanism.

The normalized position (x/X) is used to express the iron diffusion coefficient in oxide scale of HCM12A in supercritical water for 3,000 h. Figure 5 shows the relationship between the calculated oxygen activities and the normalized position (x/X) in the oxide scale on HCM12A at 600 and 500°C. Figure 6 shows the relationship between the iron diffusion coefficient and the normalized position (x/X) in the oxide scale on HCM12A. The oxygen activity in the oxide scale of HCM12A steel is continuous, but the iron diffusion coefficient at the interface between the internal and external layers is discontinuous.

Figure 5

Model predictions of oxygen activities in oxide scale on HCM12A as a function of normalized position.

Figure 6

Relationship between iron diffusion coefficient and normalized position (x/X) in oxide scale on HCM12A.

It can be seen from Figures 5 and 6 that the oxygen activity in the oxide scale suddenly increases at a certain position, and the iron diffusion coefficient reaches the minimum value. It is possible to form pores at the location of the minimum iron diffusion coefficient. Figure 6 shows relationship between iron diffusion coefficient and normalized position (x/X) in oxide scale on HCM12A at 600 and 500°C. When the normalized position is about 0.05 at 500°C, the iron diffusion coefficient of oxide scale formed on HCM12A reaches the minimum. The higher the experimental temperature, the closer the location of pores to the internal layer/external layer interface.

4.5 Flux of oxygen ion and its divergence in oxide scale

Figures 7–10 show the calculated results in oxide scale formed on HCM12A in supercritical water for 3,000 h at 600 and 500°C. Figure 7 shows the change of the flux of oxygen ion in oxide scale formed on HCM12A at 600 and 500°C over normalized position. The flux of oxygen ion in the double oxide scale is negative. In the case of oxidation of HCM12A at 600°C, the sudden change in the flux of oxygen ion occurs at the interface between the internal oxide and the external oxide. The flux of oxygen ion sharply increases at a certain position (x/X = 0.11) and the normalized position (x/X = 0.05) in the magnetite layer during oxidation at 600 and 500°C, respectively.

Figure 7

Calculated flux of oxygen ion in oxide scale on HCM12A at 500°C (left) and 600°C (right) over normalized position.

Figure 8

Logarithm of negative of the flux of oxygen ion in oxide scale on HCM12A at 500°C (left) and 600°C (right) over normalized position.

Figure 9

Divergence of flux of oxygen ion in oxide scale on HCM12A at 500°C (left) and 600°C (right) over normalized position.

Figure 10

Logarithm of the divergence of flux of oxygen ion in oxide scale formed on HCM12A at 500°C (left) and 600°C (right) over normalized position.

Figure 8 shows logarithm of negative of flux of oxygen ion in the double oxide scale of HCM12A at 500 and 600°C. The flux of oxygen ion in the double oxide scale is discontinuous at the Cr-rich spinel layer/magnetite layer interface.

Figure 9 shows divergence of oxygen ion flux in the double oxide scale. At 600°C, the divergence of flux of oxygen ion in oxide scale is negative at the range from the substrate/Cr-rich spinel layer interface to the normalized position (x/X = 0.11). The divergence of flux of oxygen ion at the Cr-rich spinel layer/magnetite layer interface is discontinuous. Then the divergence of flux of oxygen ion becomes positive from this position to the surface. The drastic change at the normalized position (x/X = 0.11) indicates pore formation. At 500°C, divergence of flux of oxygen ion in the double oxide scale is negative at the range from substrate/Cr-rich spinel layer interface to the normalized position (x/X = 0.05). The drastic change at the normalized position (x/X = 0.05) indicates pore formation. Then divergence of flux of oxygen ion becomes positive from this position to the surface.

Figure 10 shows logarithm of the divergence of flux of oxygen ion in oxide scale on HCM12A at 600 and 500°C over normalized position. Flux of oxygen ion and its divergence in oxide scale are discontinuous at the Cr-rich spinel layer/magnetite layer interface, which indicates pores probably form at this interface.