A method for calculating corrosion behavior of zirconium alloys

Abstract

The application discloses a kind of zirconium alloy corrosion behavior calculation method, and the application belongs to the technical field of zirconium alloy corrosion kinetics, method includes constructing zirconium alloy corrosion kinetics mechanism model;Based on the zirconium alloy corrosion kinetics model and relevant test parameters, the variation law of zirconium alloy oxide film thickness with corrosion time is calculated, and the long-term corrosion behavior of zirconium alloy is simulated and predicted.The application starts from the corrosion mechanism of zirconium alloy, uses the key factor that influences the long-term corrosion behavior of zirconium alloy in the reactor, constructs the zirconium alloy corrosion kinetics mechanism model, simulates and predicts the long-term corrosion behavior of zirconium alloy in the reactor, shortens the evaluation period of long-term corrosion performance of zirconium alloy, and fills the blank of the corrosion behavior of zirconium alloy under long-term service condition at present.

Description

Technical Field

[0001] This invention belongs to the technical field of zirconium alloy corrosion kinetics, and specifically relates to a method for calculating the corrosion behavior of zirconium alloys. Background Technology

[0002] Fuel cladding operates under the most demanding conditions in a reactor, facing nuclear fuel and enduring high temperatures, high pressures, and intense neutron radiation. Simultaneously, the inner wall of the cladding is susceptible to damage from fission gas pressure and nuclear fuel swelling, while the outer wall is threatened by coolant erosion, vibration, corrosion, and hydrogen embrittlement. These risks increase with increased burnup or power output. Zirconium alloys, due to their low thermal neutron absorption cross-section and the excellent resistance to high-temperature, high-pressure water corrosion, good overall mechanical properties, and high thermal conductivity of zirconium and its alloys, have long been used as the matrix and cladding materials for reactor fuel elements. As advanced fuel elements evolve towards higher burnup, longer lifespans, and higher safety and reliability, even higher requirements are placed on the service performance of zirconium alloys.

[0003] Corrosion resistance is a core indicator for zirconium alloys used as cladding materials in nuclear reactors. Extensive research has been conducted both domestically and internationally, including the development of models to depict the corrosion behavior of zirconium alloys. However, these models are largely based on empirical or semi-empirical relationships and are developed to meet the needs of nuclear power plants, making it difficult to evaluate the long-term corrosion behavior of fuel elements or predict their corrosion under long-term service conditions. Furthermore, due to limitations in irradiation testing conditions, current research on zirconium alloy corrosion behavior primarily employs external autoclaves or loops to simulate fuel elements operating at full power for 1 to 2 years. Long-term corrosion testing (20-30 years) results are lacking to evaluate whether new zirconium alloys meet predetermined performance requirements. Moreover, conducting long-term corrosion tests is time-consuming and costly, making it difficult to meet current research and development requirements in terms of both research progress and cost. Summary of the Invention

[0004] To address the shortcomings of existing zirconium alloy corrosion behavior analysis techniques in evaluating the long-term corrosion behavior of fuel elements and predicting the corrosion behavior of zirconium alloys under long-term service conditions, this invention provides a computational method for zirconium alloy corrosion behavior. Starting from the corrosion mechanism of zirconium alloys, this invention utilizes key factors influencing the long-term corrosion behavior within zirconium alloy stacks to construct a zirconium alloy corrosion kinetic mechanism model based on the oxide film growth equation, simulating and predicting the long-term corrosion behavior within zirconium alloy stacks.

[0005] This invention is achieved through the following technical solution:

[0006] A method for calculating the corrosion behavior of zirconium alloys, comprising:

[0007] Constructing a corrosion kinetics model for zirconium alloys;

[0008] Based on the corrosion kinetics model of the zirconium alloy and related experimental parameters, the variation law of the zirconium alloy oxide film thickness with corrosion time was calculated, and the long-term corrosion behavior of the zirconium alloy was simulated and predicted.

[0009] As a preferred embodiment, the process of constructing the zirconium alloy corrosion kinetic mechanism model of the present invention is as follows:

[0010] From Fick's first law:

[0011]

[0012] In the formula, H e and D e Here, Δw and Δt represent the equivalent diffusion thickness and equivalent diffusion coefficient of the oxide film, respectively, and Δw is the corrosion weight gain per unit area within time Δt. e / dx) e This represents the equivalent concentration gradient.

[0013] In a preferred embodiment, the thickness H of the oxide film at time t can be obtained by equation (2):

[0014]

[0015] In the formula, M o and M ox These are the molar masses of oxygen and ZrO2, respectively, where ρ is the porosity of the oxide film, and d is the molar mass of oxygen and ZrO2. ox Here, C(x,t) represents the theoretical density of ZrO2, and C(x,t) is the oxygen concentration distribution in the zirconium alloy matrix.

[0016] Wherein, C(x,t) satisfies the following equation:

[0017]

[0018]

[0019]

[0020] In the formula, D is the diffusion coefficient of oxygen in the zirconium alloy matrix during in-pile irradiation; x is the distance from a point in the zirconium cladding to the inner surface of the zirconium cladding; and L is the distance from the point in the zirconium cladding to the inner surface of the zirconium cladding. z To maintain the length of the α-Zr matrix in zirconium alloys, C z The oxygen concentration at the O / M interface of the zirconium alloy.

[0021] In a preferred embodiment of the present invention, the change in corrosion weight gain of zirconium alloy with time t at different temperatures is expressed as follows:

[0022] Δw(t)=K·t n (6)

[0023] In the formula, K is called the corrosion rate coefficient;

[0024] Taking the derivative of both sides of equation (6) with respect to t, we can obtain f e The relationship is:

[0025]

[0026] In the formula, Q is the activation energy, R is the universal gas constant, and A is the corrosion rate constant;

[0027] Equations (1) to (7) constitute a corrosion kinetic mechanism model for zirconium alloys.

[0028] As a preferred embodiment, the present invention calculates the variation law of zirconium alloy oxide film thickness with corrosion time based on the zirconium alloy corrosion kinetic model and related experimental parameters, specifically including:

[0029] Obtain relevant experimental data, including in-pile and out-of-pile corrosion weight gain curves at different temperatures, fuel plate structural parameters, thermal parameters, and material properties.

[0030] Based on the corrosion weight gain curves inside and outside the pile, determine f e ;

[0031] Determine the oxygen diffusion coefficient in the zirconium alloy matrix during in-pile irradiation;

[0032] Determine the oxygen concentration at the O / M interface of the zirconium alloy;

[0033] Based on f e The diffusion coefficient of oxygen in the zirconium alloy matrix and the oxygen concentration at the O / M interface of the zirconium alloy during in-pile irradiation were used to iteratively calculate the variation law of zirconium alloy oxide film thickness with corrosion time using the zirconium alloy corrosion kinetic mechanism model.

[0034] In a preferred embodiment, the present invention determines f based on the internal and external corrosion weight gain curves. e Specifically:

[0035] The K value of the aforementioned in-pile and out-of-pile corrosion weight gain curves is calculated according to the Arrhenius relation K(T) = Ae -Q / RT By fitting the data, the activation energy Q and the corrosion rate constant A are obtained.

[0036] Based on the obtained activation energy Q and corrosion rate constant A, f is calculated. e .

[0037] In a preferred embodiment, the oxygen diffusion coefficient in the zirconium alloy matrix during in-pile irradiation of the present invention is:

[0038] D irr =10D;

[0039] Where D represents the oxygen diffusion coefficient in an unirradiated environment outside the reactor; and

[0040] D = 0.0661e -183920 / RT .

[0041] In a preferred embodiment, the oxygen concentration at the O / M interface of the zirconium alloy of the present invention is: C z =0.25.

[0042] As a preferred embodiment, the present invention uses the differential iteration method to iteratively calculate the variation law of zirconium alloy oxide film thickness with corrosion time.

[0043] In a preferred embodiment, the differential iteration process of the present invention specifically includes:

[0044] Let W be the cumulative weight gain due to corrosion at the current time t, C(x,t) be the oxygen concentration distribution in the zirconium matrix, T(x,t) be the temperature field of the fuel plate, H be the oxide film thickness, and P be the surface power density of the element.

[0045] Iterative calculations are performed, and after each time step Δt, the stress and porosity in the oxide film, the temperature field T(x,t+Δt) of the fuel plate, and f are calculated sequentially. e The corrosion weight gain W+ΔW, oxygen concentration distribution C(x,t+Δt), and oxide film thickness H+ΔH calculated from equation (2) until t is greater than t L , t L The test period is [number].

[0046] The present invention has the following advantages and beneficial effects:

[0047] 1. Starting from the corrosion mechanism of zirconium alloys, this invention establishes a corrosion kinetic mechanism model of zirconium alloys by utilizing the key factors affecting the long-term corrosion behavior in zirconium alloy piles. This model simulates and predicts the long-term corrosion behavior in zirconium alloy piles, shortens the evaluation cycle of the long-term corrosion performance of zirconium alloys, and fills the current gap in the corrosion behavior of zirconium alloys under long-term service conditions.

[0048] 2. This invention can calculate the long-term variation of the thickness of the in-pile zirconium alloy oxide film with time and power history, and predict the thickness range of the oxide film under different full power days.

[0049] 3. This invention provides technical support for the study of the corrosion resistance of zirconium alloys, which is of great significance for improving the service life and safety reliability of nuclear fuel elements. Attached Figure Description

[0050] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0051] Figure 1 This is a schematic diagram of the iterative calculation process according to an embodiment of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0053] Example

[0054] Existing techniques for studying the corrosion resistance of zirconium alloys are insufficient to meet the requirements for evaluating the long-term corrosion behavior of fuel elements, and even more so, they cannot predict the corrosion behavior of zirconium alloys under long-term service conditions. Furthermore, limitations in irradiation testing conditions restrict the ability to conduct long-term corrosion tests, which are time-consuming and costly. Therefore, this embodiment proposes a method for calculating the corrosion behavior of zirconium alloys. This method provides a zirconium alloy corrosion kinetic mechanism model that can simulate and predict the long-term corrosion behavior of zirconium alloys.

[0055] The calculation method proposed in this embodiment specifically includes the following steps:

[0056] Step 1: Construct a corrosion kinetic model for zirconium alloy.

[0057] The specific process of constructing the corrosion kinetics model for zirconium alloys includes:

[0058] From Fick's first law:

[0059]

[0060] In the formula, H e and D e Here, denoted by , are the equivalent diffusion thickness and equivalent diffusion coefficient of the oxide film (ignoring details of the oxide film composition and variations in the oxygen diffusion coefficient with composition), and Δw is the corrosion weight gain per unit area within time Δt, (dH e / dx) e This represents the equivalent concentration gradient.

[0061] At time t, the thickness H of the oxide film can be obtained by solving the integral equation (2):

[0062]

[0063] In the formula, M o and M ox These are the molar masses of oxygen and ZrO2, respectively, where ρ is the porosity of the oxide film, and d is the molar mass of oxygen and ZrO2. ox denoted as ZrO2, and C(x,t) is the oxygen concentration distribution in the zirconium alloy matrix.

[0064] C(x,t) satisfies the following equation:

[0065]

[0066]

[0067]

[0068] In equation (3), D is the diffusion coefficient of oxygen in α-Zr, which can be obtained from literature or experiments. In equation (4), x is the distance from a point in the zirconium cladding to the inner surface of the zirconium cladding, and L... z To maintain the length of the α-Zr matrix in zirconium alloys, C z The oxygen concentration at the O / M interface of the zirconium alloy.

[0069] The corrosion weight gain of zirconium alloys at different temperatures can generally be described by the following formula:

[0070] Δw(t)=K·t n (6)

[0071] K is called the corrosion rate coefficient. Taking the derivative of both sides of equation (6) with respect to t and comparing it with equation (1), we can obtain f. e The relationship is shown in equation (7):

[0072]

[0073] In the formula, Q is the activation energy, R is the universal gas constant, and A is the corrosion rate constant.

[0074] This embodiment utilizes equation (7) to avoid the diffusion coefficient D at different thicknesses of the oxide film. e and concentration gradient (dH) e / dx) e It is difficult to find a value for it.

[0075] In the corrosion kinetic model composed of equations (1)-(7), the parameters directly related to corrosion kinetics are simplified to the corrosion rate coefficient K, the oxygen diffusion coefficient D in the zirconium matrix, and C. z .

[0076] It should be noted that:

[0077] (1) The corrosion rate coefficient K and the diffusion coefficient D are the input parameters required for the calculation of this model. This model itself cannot calculate the values ​​of these coefficients, and their values ​​are determined by experiments.

[0078] (2) Even for the same zirconium alloy and core environment, the diffusion coefficient D and rate coefficient K are closely related to the power. During in-core operation, the temperature of the fuel cladding changes due to fluctuations in operating power. The temperature of the fuel cladding at any given time is a prerequisite for corrosion calculation.

[0079] (3) In addition to thermal parameters, the temperature of the cladding is also affected by the thickness H of the oxide film and its porosity ρ, and H and ρ are themselves functions of the corrosion rate coefficient K.

[0080] Step 2: Based on the constructed zirconium alloy corrosion kinetic model, calculate the variation law of zirconium alloy oxide film thickness with corrosion time, and simulate and predict the long-term corrosion behavior of zirconium alloy.

[0081] Specifically, such as Figure 1 As shown, the simulation and prediction process for the long-term corrosion behavior of zirconium alloys specifically includes:

[0082] Step 21: Obtain relevant experimental parameters, including the in-core and out-of-core corrosion weight gain (oxide film thickness) curves at different temperatures; fuel plate structural parameters, such as plate width, plate spacing, cladding thickness, etc.; thermal parameters, such as cooling water temperature, water flow rate and viscosity, etc.; material properties, such as thermal conductivity, elastic modulus, oxygen diffusion coefficient, etc.

[0083] Step 22, calculate f based on the corrosion weight gain curves inside and outside the reactor core. e .

[0084] During in-core operation, the temperature of the zirconium alloy cladding mainly varies between 280℃ and 350℃, while the corrosion weight gain curves inside and outside the in-core show only a few fixed temperature values, such as 360℃ or 400℃. To calculate f at different temperatures (e.g., 320℃)... e The K value of the weight gain curve needs to be calculated according to the Arrhenius relation K(T) = Ae -Q / RT By fitting the data, the activation energy Q and the corrosion rate constant A are obtained, and f is calculated according to equation (7). e .

[0085] If the weight gain curve has many temperature values, K can be used for interval fitting to reduce bias. Different A values ​​are used for different temperature intervals. i and Q i Calculate f e .

[0086] Step 23: Determine the oxygen diffusion coefficient in the zirconium alloy matrix during in-pile irradiation.

[0087] Based on literature and experimental data, the diffusion coefficient of oxygen with temperature under non-irradiated external environment is shown in Equation (8):

[0088] D = 0.0661e -183920 / RT (8)

[0089] In principle, oxygen diffusion should be accelerated under in-reactor neutron irradiation, but no data has been reported in this regard. Studies have shown that neutron irradiation does not significantly accelerate hydrogen diffusion in zirconium alloys. This may be because hydrogen has a very small atomic radius, requiring less diffusion barrier, and its migration rate in zirconium is inherently fast. The literature reports an oxygen diffusion coefficient of 3.34 × 10⁻⁶ in ZrO₂ without irradiation. -14 cm 2 / sec, with a diffusion coefficient of 1.33 × 10⁻⁶ under neutron irradiation. -13 cm 2 / sec, approximately four times that of no irradiation. Based on this result, this embodiment uses the oxygen diffusion coefficient D during in-pile irradiation. irr =10D.

[0090] Step 24: Determine the oxygen concentration C at the O / M interface of the zirconium alloy. z .

[0091] It is generally believed that a stable oxide phase is formed only when the oxygen solubility in α-Zr reaches 30% or more. In fact, Zr3O is a stable phase in the Zr-O system, exhibiting both hexagonal and trigonal crystal structures, with a density of approximately 6.6 g / cm³. 3 Some metastable oxides (such as ZrO and Zr2O) decompose into Zr3O + ZrO2. Therefore, the solid solubility of oxygen in α-Zr should be below 25%. Recent studies have also found that a stable Zr4O phase appears to exist in the Zr-O system, with a six-coordinate triclinic crystal structure and a density of approximately 6.54 g / cm³. 3 In the COSIC program, the highest oxygen concentration in α-Zr is taken as 25%, i.e., C0. z =0.25.

[0092] Step 25: Using the zirconium alloy corrosion kinetic model, the variation of oxide film thickness with time during the test period is iteratively calculated according to a preset time step. During the corrosion process, the oxide film continuously thickens, L... z As the number of particles decreases, equations (3) to (5) constitute a moving boundary problem, which is solved using the differential iteration method. Specifically, let the cumulative weight gain due to corrosion at time t be W, the oxygen concentration distribution in the zirconium matrix be C(x,t), the temperature field of the fuel plate be T(x,t), the oxide film thickness be H, and the surface power density of the element be P. After a time step Δt, the stress and porosity in the oxide film, the temperature field of the fuel plate T(x,t+Δt), and f are calculated sequentially. e The corrosion weight gain is W+ΔW, the oxygen concentration distribution is C(x,t+Δt), and the oxide film thickness H+ΔH is calculated from equation (2). This continues until t>t L , t L The test period is [number].

[0093] The calculation method proposed in this embodiment is based on the corrosion kinetic mechanism model of zirconium alloy, and the model is used to calculate the variation law of zirconium alloy oxide film thickness with corrosion time, which improves the experimental efficiency and saves costs.

[0094] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the corrosion behavior of zirconium alloys, characterized in that, include: Constructing a corrosion kinetics model for zirconium alloys; Based on the corrosion kinetics mechanism model of zirconium alloy and related experimental parameters, the variation law of zirconium alloy oxide film thickness with corrosion time was calculated, and the long-term corrosion behavior of zirconium alloy was simulated and predicted. The specific process for constructing the zirconium alloy corrosion kinetic mechanism model is as follows: From Fick's first law: In the formula, H e and D e Here, Δw and Δt represent the equivalent diffusion thickness and equivalent diffusion coefficient of the oxide film, respectively, and Δw is the corrosion weight gain per unit area within time Δt. e / dx) e The equivalent concentration gradient; the thickness H of the oxide film can be obtained by equation (2): In the formula, M o and M ox These are the molar masses of oxygen and ZrO2, respectively, where ρ is the porosity of the oxide film, and d is the molar mass of oxygen and ZrO2. ox Here, C(x,t) represents the theoretical density of ZrO2, and C(x,t) is the oxygen concentration distribution in the zirconium alloy matrix. Wherein, C(x,t) satisfies the following equation: In the formula, D is the diffusion coefficient of oxygen in the zirconium alloy matrix during in-pile irradiation; x is the distance from a point in the zirconium cladding to the inner surface of the zirconium cladding; and L is the distance from the point in the zirconium cladding to the inner surface of the zirconium cladding. z To maintain the length of the α-Zr matrix in zirconium alloys, C z The oxygen concentration at the O / M interface of the zirconium alloy is given by: The change in corrosion weight gain of the zirconium alloy with time t is expressed as: Δw(t)=K·t n (6) In the formula, K is called the corrosion rate coefficient; Taking the derivative of both sides of equation (6) with respect to t, we can obtain f e The relationship is: In the formula, Q is the activation energy, R is the universal gas constant, and A is the corrosion rate constant; Equations (1) to (7) constitute a corrosion kinetic mechanism model for zirconium alloys. Based on the aforementioned corrosion kinetic mechanism model and relevant experimental parameters, the variation law of zirconium alloy oxide film thickness with corrosion time is calculated, specifically including: Obtain relevant experimental parameters, including in-pile and out-of-pile corrosion weight gain curves at different temperatures, fuel plate structural parameters, thermal parameters, and material properties. Based on the corrosion weight gain curves inside and outside the pile, determine f e ; Determine the oxygen diffusion coefficient in the zirconium alloy matrix during in-pile irradiation; Determine the oxygen concentration at the O / M interface of the zirconium alloy; Based on f e The diffusion coefficient of oxygen in the zirconium alloy matrix and the oxygen concentration at the O / M interface of the zirconium alloy during in-pile irradiation were used to iteratively calculate the variation law of zirconium alloy oxide film thickness with corrosion time using the zirconium alloy corrosion kinetic mechanism model.

2. The method for calculating the corrosion behavior of zirconium alloy according to claim 1, characterized in that, Based on the corrosion weight gain curves inside and outside the pile, determine f e Specifically: The K value of the aforementioned in-pile and out-of-pile corrosion weight gain curves is calculated according to the Arrhenius relation K(T) = Ae -Q / RT By fitting the data, the activation energy Q and the corrosion rate constant A are obtained. Based on the obtained activation energy Q and corrosion rate constant A, f is calculated. e .

3. The method for calculating the corrosion behavior of zirconium alloy according to claim 1, characterized in that, The diffusion coefficient of oxygen in the zirconium alloy matrix during in-pile irradiation is: D irr =10D; Where D represents the oxygen diffusion coefficient in an unirradiated environment outside the reactor; and D=0.0661e -183920 / RT 。 4. The method for calculating the corrosion behavior of zirconium alloy according to claim 1, characterized in that, The oxygen concentration at the O / M interface of the zirconium alloy is: C z =0.

25.

5. The method for calculating the corrosion behavior of zirconium alloy according to claim 1, characterized in that, The variation law of zirconium alloy oxide film thickness with corrosion time was obtained by iterative calculation using the differential iterative method.

6. The method for calculating the corrosion behavior of zirconium alloy according to claim 5, characterized in that, The differential iteration process specifically includes: Let W be the cumulative weight gain due to corrosion at the current time t, C(x,t) be the oxygen concentration distribution in the zirconium matrix, T(x,t) be the temperature field of the fuel plate, H be the oxide film thickness, and P be the surface power density of the element. Iterative calculations are performed, and after each time step Δt, the stress and porosity in the oxide film, the temperature field T(x,t+Δt) of the fuel plate, and f are calculated sequentially. e The corrosion weight gain W+ΔW, oxygen concentration distribution C(x,t+Δt), and oxide film thickness H+ΔH calculated from equation (2) until t is greater than t L , t L The test period is [number].

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