A method and apparatus for predicting deposits on the surface of a pressurized water reactor fuel rod

Abstract

The application provides a kind of prediction method and device for pressurized water reactor fuel rod surface deposit, it is related to pressurized water reactor technical field, the prediction method for pressurized water reactor fuel rod surface deposit includes: the current PH value and the current boron element concentration of pressurized water reactor coolant are calculated;Determine the iron-nickel oxide in stable phase generated under the current operating condition based on the current PH value and the current boron element concentration of coolant, calculate the current concentration of iron-nickel oxide;The particle size of iron-nickel oxide and the dirt thickness of fuel rod surface under the condition of subcooled boiling of pressurized water reactor fuel rod surface are calculated based on the current concentration of iron-nickel oxide.The present application can accurately describe the deposition law and chemical composition of dirt on the pressurized water reactor fuel rod, can reflect the deposition law of iron-nickel oxide in the reactor core, and has an important role for carrying out precise scale-induced nuclear safety risk analysis.

Description

Technical Field

[0001] This invention relates to the field of pressurized water reactor technology, and in particular to a method and apparatus for predicting deposits on the surface of pressurized water reactor fuel rods. Background Technology

[0002] During pressurized water reactor (PWR) operation, corrosion products from the primary coolant, including soluble metal ions and insoluble metal or oxide particles, deposit on the surface of the fuel cladding in the upper part of the core, forming a thin scale layer. This oxidative corrosion deposit on the fuel cladding surface is called Chalk River Unidentified Deposit (CRUD). The porous structure of CRUD can enhance internal boiling, causing boron in the coolant to concentrate or even precipitate and be adsorbed by the porous morphology of the deposit layer, resulting in an uneven distribution of boron on the axial surface of the fuel rods. The strong neutron absorption effect of boron can induce a core power shift phenomenon known as foul-induced axial power shift (CIPS), which endangers the safety of the nuclear reactor. CIPS not only causes a reduction in reactor power or even an emergency shutdown, reducing the reactor's neutron economy, but also affects the core's remaining reactivity and shutdown margin, and may even cause cladding failure, threatening the integrity of the nuclear reactor safety barrier. However, due to the diversity of CRUD morphology and composition, the formation law, especially the composition law, of CRUD under pressurized water reactor operating conditions is not fully understood. Existing studies simulating corrosion product deposition mainly focus on the transport and metering distribution of corrosion products, while thermodynamic analysis calculations such as composition calculation and thickness calculation of deposited fouling on fuel rod surfaces are still relatively few. Therefore, there is an urgent need for a thermochemical analysis and prediction technique suitable for the deposition of oxidative corrosion products on fuel rod surfaces to reveal the impact of oxidative corrosion products on core safety. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method and apparatus for predicting deposits on the surface of pressurized water reactor fuel rods, which can accurately describe the deposition patterns and chemical composition of fouling on pressurized water reactor fuel rods, and reflect the deposition patterns of iron-nickel oxides in the reactor core, playing an important role in conducting accurate fouling-induced nuclear safety risk analysis.

[0004] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0005] In a first aspect, embodiments of the present invention provide a method for predicting deposits on the surface of pressurized water reactor fuel rods, comprising: calculating the current pH value and current boron concentration of the pressurized water reactor coolant; determining, based on the current pH value and current boron concentration of the coolant, the iron-nickel oxides in the stable phase generated under the current operating conditions, and calculating the current concentration of the iron-nickel oxides; and calculating, based on the current concentration of the iron-nickel oxides, the particle size of the iron-nickel oxides and the fouling thickness on the surface of the fuel rods under supercooled boiling conditions.

[0006] Furthermore, the present invention provides a first possible implementation of the first aspect, wherein the step of calculating the current pH value and current boron concentration of the pressurized water reactor coolant includes: calculating the chemical reaction equilibrium constant when boric acid interacts with water in the coolant; calculating the current dissolved hydrogen concentration and current boron concentration in the coolant based on the chemical reaction equilibrium constant and the mass and charge conservation of the chemical reaction formula between boric acid and water; and determining the current pH value of the coolant based on the current dissolved hydrogen concentration in the coolant.

[0007] Furthermore, the present invention provides a second possible implementation of the first aspect, wherein the step of calculating the chemical reaction equilibrium constant when boric acid interacts with water in the coolant includes: calculating the standard partial molar Gibbs free energy of formation of each reactant and product when boric acid interacts with water in the coolant, and the chemical reaction equilibrium constant determined by the change in the Gibbs free energy of formation.

[0008] Furthermore, this embodiment of the invention provides a third possible implementation of the first aspect, wherein the step of determining the iron-nickel oxide in a stable phase generated under the current operating conditions based on the current pH value and current boron concentration of the coolant, and calculating the current concentration of the iron-nickel oxide, includes: obtaining a stable phase diagram of the iron-nickel oxide of the pressurized water reactor under the current operating conditions; determining the target iron-nickel oxide in a stable phase precipitated by the coolant under the current pH value and current boron concentration based on the stable phase diagram of the iron-nickel oxide; and performing mass conservation and charge conservation calculations based on the chemical reaction formula corresponding to the target iron-nickel oxide to obtain the concentration of the target iron-nickel oxide in a stable phase in the coolant.

[0009] Furthermore, this embodiment of the invention provides a fourth possible implementation of the first aspect, wherein the horizontal axis of the stable phase diagram of the iron-nickel oxide is the boron concentration and the vertical axis is the pH value. The step of determining the target iron-nickel oxide of the stable phase precipitated by the coolant at the current pH value and the current boron concentration based on the stable phase diagram of the iron-nickel oxide includes: finding the target point corresponding to the current pH value and the current boron concentration in the stable phase diagram, and taking the stable phase iron-nickel oxide corresponding to the region where the target point is located as the target iron-nickel oxide.

[0010] Furthermore, this embodiment of the invention provides a fifth possible implementation of the first aspect, wherein the step of finding the target point corresponding to the current pH value and the current boron concentration in the stable phase diagram, and taking the stable phase iron-nickel oxide corresponding to the region where the target point is located as the target iron-nickel oxide, includes:

[0011] When the current boron concentration is greater than 0 and less than x1, and the current pH value is greater than p1 and less than p2, the target iron-nickel oxide in the stable phase is determined to be NiFe2O4.

[0012] When the current boron concentration is greater than 0 and less than x1 and the current pH value is greater than p2 and less than p3, or when the current boron concentration is greater than x1 and less than x2 and the current pH value is greater than k1*m B When +b1, the target iron-nickel oxide in the stable phase is determined to be NiO; where m B Where is the boron concentration, and k1 and b1 are constants;

[0013] When the current boron concentration is greater than x1 and less than x2 and the current pH value is less than k2*m B When +b2, the target iron-nickel oxide in the stable phase is determined to be Ni2FeBO5; where k2 and b2 are constants;

[0014] When the current boron concentration is greater than x1 and less than x2 and the current pH value is greater than k2*m B +b2 is less than k1*m B When +b1, the target iron-nickel oxides in the stable phase are determined to be NiO and Ni2FeBO5.

[0015] Furthermore, the present invention provides a sixth possible implementation of the first aspect, wherein the step of calculating the particle size of the iron-nickel oxide and the fouling thickness on the surface of the pressurized water reactor fuel rod under supercooled boiling conditions based on the concentration of the iron-nickel oxide includes: calculating the critical particle radius of the iron-nickel oxide at the current concentration based on the supersaturation ratio of the iron-nickel oxide, and using the critical particle radius as the particle size of the iron-nickel oxide during the deposition process; and calculating the fouling thickness on the surface of the fuel rod when the deposition and erosion of the fouling reach equilibrium based on the current concentration of the iron-nickel oxide.

[0016] Furthermore, this embodiment of the invention provides a seventh possible implementation of the first aspect, wherein the formula for calculating the critical particle radius at the current concentration is:

[0017]

[0018] Where, r * γ is the critical particle radius at the current concentration, γ is the solid-liquid surface free energy between the newly formed crystal and the solution, Q is the molecular volume of the crystal, k is the Boltzmann constant, T is the temperature of the coolant solution, and α is the supersaturation ratio of the iron-nickel oxide.

[0019] Furthermore, this embodiment of the invention provides an eighth possible implementation of the first aspect, wherein the formula for calculating the fouling thickness on the surface of the fuel rod is:

[0020]

[0021]

[0022] Where d is the thickness of the dirt, ρ CRUD For dirt density, Let t be the rate of change of mass. end k represents the deposition time at which deposition and erosion reach equilibrium. nonboiling K represents the deposition coefficient under non-boiling conditions. boiling q is the deposition coefficient of the fuel rod under supercooled boiling conditions. SNB m is the supercooled boiling heat flux density. coolant m is the current concentration of the iron-nickel oxide. erosion This represents the dirt erosion rate.

[0023] Secondly, embodiments of the present invention also provide a device for predicting deposits on the surface of pressurized water reactor fuel rods, comprising: a first calculation module for calculating the current pH value and current boron concentration of the pressurized water reactor coolant; a second calculation module for determining, based on the current pH value and current boron concentration of the coolant, the iron-nickel oxides generated under current operating conditions in a stable phase, and calculating the current concentration of the iron-nickel oxides; and a third calculation module for calculating, based on the current concentration of the iron-nickel oxides, the particle size of the iron-nickel oxides and the fouling thickness on the surface of the fuel rods under supercooled boiling conditions.

[0024] This invention provides a method and apparatus for predicting deposits on the surface of pressurized water reactor (PWR) fuel rods. The method includes: calculating the current pH value and current boron concentration of the PWR coolant; determining the iron-nickel oxides in the stable phase generated under current operating conditions based on the current pH value and current boron concentration, and calculating the current concentration of the iron-nickel oxides; and calculating the particle size of the iron-nickel oxides and the fouling thickness on the fuel rod surface under supercooled boiling conditions based on the current concentration of the iron-nickel oxides. This invention, by determining the iron-nickel oxides in the corresponding stable phase according to the dissolved hydrogen concentration and pH value of the PWR coolant, and calculating the particle size and fouling thickness of the iron-nickel oxides when deposition and erosion reach equilibrium under supercooled boiling, can accurately describe the deposition patterns and chemical composition of fouling on PWR fuel rods. It can reflect the deposition patterns of iron-nickel oxides within the reactor core and plays an important role in conducting accurate fouling-induced nuclear safety risk analysis.

[0025] Other features and advantages of the embodiments of the present invention will be set forth in the following description, or some features and advantages may be inferred from the description or determined without doubt, or may be learned by practicing the techniques described above in the embodiments of the present invention.

[0026] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0027] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0028] Figure 1 A flowchart of a method for predicting deposits on the surface of pressurized water reactor fuel rods provided in an embodiment of the present invention is shown.

[0029] Figure 2 The diagram illustrates the variation of soluble nickel (Ni) solubility with pH according to an embodiment of the present invention.

[0030] Figure 3 The diagram illustrates the variation of soluble iron (Fe) solubility with pH according to an embodiment of the present invention.

[0031] Figure 4 The diagram shows a stable phase diagram of an iron-nickel oxide generated at saturation temperature in a pressurized water reactor, as provided in an embodiment of the present invention.

[0032] Figure 5 A schematic diagram of a device for predicting deposits on the surface of pressurized water reactor fuel rods, provided in an embodiment of the present invention, is shown. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0034] Currently, existing studies on simulated corrosion product deposition mainly focus on the transport and metering distribution of corrosion products. There are still relatively few thermodynamic analysis calculations, including component calculations and concentration balance calculations, for oxidative corrosion product deposition. To improve this problem, this invention provides a method and apparatus for predicting deposits on the surface of pressurized water reactor fuel rods. The following is a detailed description of this invention.

[0035] This embodiment provides a method for predicting deposits on the surface of fuel rods in a pressurized water reactor. This method can be applied to electronic devices such as computers. See [link / reference]. Figure 1 The flowchart shown illustrates a method for predicting deposits on the surface of pressurized water reactor fuel rods. This method mainly includes the following steps:

[0036] Step S102: Calculate the current pH value and current boron concentration of the pressurized water reactor coolant;

[0037] Under the scouring and corrosion of the high-temperature, high-pressure subcooled coolant, localized oxidation occurs on the surface of the steam generator heat transfer tubes, causing the iron-nickel oxides on their surface to dissolve or erode and enter the pressurized water reactor coolant. The iron-nickel-containing coolant is affected by subcooled boiling in the reactor core, resulting in localized concentration and precipitation, forming thermodynamically stable iron-nickel oxide particles that deposit on the surface of the fuel rods.

[0038] To obtain the operating temperature, pressure, and water chemical concentration of the pressurized water reactor (PWR), thermodynamic calculations were first performed on the boron-lithium-water (B-Li-H₂O) system to determine the forms of boron and lithium in the coolant, the dissolved hydrogen concentration, and the solution pH. The Helgeson-Kirkham-Flowers (HKF) model was used to determine the thermochemical data of the boric acid system under PWR operating conditions. The equilibrium constants of the chemical reactions in the B-Li-H₂O system were calculated using the HKF model and the Pitzer equation. Based on the definition of the equilibrium constant, mass conservation, charge conservation, and chemical equilibrium equations were established to calculate the concentrations of each substance and the current pH of the coolant.

[0039] Step S104: Determine the iron-nickel oxide in the stable phase generated under the current operating conditions based on the current pH value of the coolant and the current boron concentration, and calculate the current concentration of the iron-nickel oxide.

[0040] Based on the calculated current pH value and boron concentration of the coolant, the existing forms of nickel (Ni) and iron (Fe) in the coolant are determined, specifically the stable nickel-iron oxide forms at the current pH value and boron concentration. These nickel-iron oxide forms include NiFe₂O₄, NiO, and Ni₂FeBO₅. The corresponding nickel-iron oxide forms differ at different pH values ​​and boron concentrations.

[0041] Step S106: Calculate the particle size of iron-nickel oxides and the fouling thickness on the surface of the pressurized water reactor fuel rods under supercooled boiling conditions based on the current concentration of iron-nickel oxides.

[0042] Fouling growth on the surface of pressurized water reactor fuel rods is mainly determined by deposition and erosion, with boiling deposition having a greater impact in areas of strong supercooled boiling. According to thermodynamic principles, the stable crystal radius is related to the supersaturation ratio. Therefore, in the solution process, the critical radius can be used as the particle size of iron-nickel oxides during deposition, and the particle size of iron-nickel oxides can be calculated based on the relationship between the critical radius and the supersaturation ratio. The rate of change of fouling mass over time is calculated based on the current concentration of iron-nickel oxides. When the rate of change is 0, it indicates that fouling deposition and erosion have reached equilibrium, and the fouling thickness no longer changes. The fouling thickness at which deposition and erosion reach equilibrium is then calculated based on the fouling density.

[0043] The method for predicting deposits on the surface of pressurized water reactor fuel rods provided in this embodiment determines the iron-nickel oxides in the corresponding stable phase based on the dissolved hydrogen concentration and pH value of the pressurized water reactor coolant, and calculates the particle size and fouling thickness of the iron-nickel oxides when deposition and erosion reach equilibrium under subcooled boiling. This method can accurately describe the deposition pattern and chemical composition of fouling on pressurized water reactor fuel rods, and can reflect the deposition pattern of iron-nickel oxides in the reactor core. It plays an important role in conducting accurate fouling-induced nuclear safety risk analysis.

[0044] In the process of fouling deposition, the chemical reactions considered can be divided into three main categories: the interaction between boric acid and water (Equations (1)-(3)), the dissolution equilibrium of Fe(II) and Ni(II) (Equations (4)-(16)), and the ionization equilibrium of water (Equation (17)). The chemical reaction formulas involved include the following:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] In one embodiment, this embodiment provides a specific implementation method for calculating the current pH value and current boron concentration of the pressurized water reactor coolant: calculating the chemical reaction equilibrium constant when boric acid interacts with water in the coolant; calculating the current dissolved hydrogen concentration and current boron concentration in the coolant based on the chemical reaction equilibrium constant and the mass and charge conservation of the chemical reaction formula between boric acid and water; and determining the current pH value of the coolant based on the current dissolved hydrogen concentration in the coolant.

[0063] The chemical reaction equilibrium constant when boric acid interacts with water is calculated using the Helgeson-Kirkham-Flowers (HKF) model and the Pitzer formula. In one specific implementation, the standard partial molar Gibbs free energy of formation of each reactant and product when boric acid interacts with water in the coolant can be calculated first, and the chemical reaction equilibrium constant is determined by the change in Gibbs free energy of formation.

[0064] The standard partial molar Gibbs free energy of formation for each reactant and product in the above chemical reactions (1)-(3) can be calculated using the HKF model, as well as the equilibrium constant determined by the change in Gibbs free energy of formation. For details, please refer to the following formulas (18) and (19):

[0065]

[0066]

[0067] in, The standard partial molar Gibbs free energy of formation; T is temperature; P is pressure; p r The reference pressure is typically taken as 1 bar; T r The reference temperature is typically taken as 298.15 K; Ψ is the solvent pressure parameter, taken as 2600 bar; θ is the solvent temperature parameter, taken as 228 K. In the equation, each substance has nine independent parameters, namely: It is the Gibbs free energy of formation at reference temperature and reference pressure; It is the entropy at reference temperature and reference pressure; a1, a2, a3, and a4 are volume integral constants; c1 and c2 are specific heat capacity integral constants; ω is the Born constant; ∈ is the dielectric constant of water; Y usually takes the value of K is the chemical reaction equilibrium constant; R is the ideal gas constant.

[0068] The change in borate activity in the coolant solution due to the presence of lithium ions (Li+) can be calculated using the Pitzer formula, as shown in formula (20):

[0069]

[0070] Among them, G ex n is the excess Gibbs free energy due to the presence of lithium ions (Li+); w A is the amount of substance of water. φ Here, represents the Debye-Huckel parameter; I represents the ionic strength of the solution; b is a constant, which can take values ​​of 1.2 (kg / mol)¹ / ²; the second term on the right side of the equation is ∑ c ∑ a m c m a[B ca +(∑ c m c z c C ca [] represents the influence of ion interactions.

[0071] After calculating the equilibrium constants of the above chemical reactions (1)-(3) using the HKF model and Pitzer formula, the equations for mass conservation, charge conservation, and chemical equilibrium are listed according to the definition of equilibrium constant, as shown in the following formula (21) (m is the mol / kg mass concentration). Solving the equations in formula (21) simultaneously will yield the concentrations of each substance in the above chemical reactions (1)-(3) and the current pH value of the coolant solution.

[0072]

[0073] Where, m B The concentration of boron in the coolant solution. This refers to the concentration of H3BO3 in the coolant solution. B(OH)4 in the coolant solution - concentration, B2O(OH)5 in the coolant solution - concentration, B3O3(OH)4 in the coolant solution - concentration, H in the coolant solution + concentration, Li in the coolant solution + Concentration, K w Where is the equilibrium constant of water, and pH is the current pH value of the coolant. The concentration of OH- in the coolant solution. To determine the concentration of dissolved hydroxide ions, Let K be the dissolved hydrogen concentration and m be the chemical reaction equilibrium constant. For the chemical reaction aA + bB = eE + dD, A and B are reactants, E and D are products, a, b, e and d are the stoichiometric coefficients, and m is the mass concentration. The chemical reaction equilibrium constant K is calculated as the product of the mass concentrations of each product and the mass concentrations of each reactant.

[0074] In one embodiment, this embodiment provides an implementation method for determining the iron-nickel oxide in the stable phase generated under current operating conditions based on the current pH value and current boron concentration of the coolant, and calculating the current concentration of the iron-nickel oxide. The specific steps are as follows:

[0075] Step (1): Obtain the stable phase diagram of iron-nickel oxides in the pressurized water reactor under the current operating conditions;

[0076] The stable phase diagram of the aforementioned iron-nickel oxide can be generated based on the current operating conditions of the pressurized water reactor, which may include the operating temperature, pressure, and water chemical concentration of the pressurized water reactor.

[0077] The solution of the thermochemical parameters of iron-nickel is similar to that of the above-mentioned solution of the thermochemical parameters of boron-lithium. After obtaining the thermochemical parameters using the HKF model and the Pitzer formula, they can be solved by mass conservation, charge conservation, and chemical equilibrium equations. Meanwhile, since the thermodynamic properties of Ni2FeBO5 solid oxide are unknown, it is necessary to estimate them from the thermodynamic properties of NiFe2O4 solid oxide, which is similar to it. Using the reported density functional theory (DFT) method, combined with entropy and heat capacity estimation methods, the enthalpy of formation of Ni2FeBO5 solid oxide can be predicted. Studies have shown that the presence of two nearest-neighbor tetrahedral interstitial positions of boron defects in spinel structures is advantageous. The enthalpy of formation of boron interstitial atoms at 298.15 K is shown in Equation (22). The heat capacity can be estimated using the Neumann-Kopp superposition rule, while the entropy value can be estimated using the Latimer method, as shown in Equation (23).

[0078]

[0079] C P (Ni2FeBO5)=2C P (NiO) + 0.5C P (Fe2O3)+0.5C P (B2O3) (23)

[0080] in, The difference in total energy calculated by DFT for boron-defect-free and boron-containing solids; q represents the charge state of the boron interstitium; E F Fermi energy serves as a reference for the energy at the top of the valence band; The reference chemical potential for boron can be -6.20 eV.

[0081] Because the solubility of iron-nickel oxides is extremely low, a saturation concentration needs to be introduced as a constraint. After obtaining the equilibrium constants of each reaction involving iron and nickel through thermochemical parameter calculation, taking the dissolution equilibrium of Ni(OH)₂ as an example, taking the logarithm of the equilibrium constant expression for the reaction involving Ni(OH)₂ and plotting it, an equilibrium relationship with other forms of nickel oxide can be obtained, as shown in the figure. Figure 2 The graph showing the solubility of soluble nickel (Ni) as a function of pH is shown below. Figure 3 The graph shown illustrates the variation of soluble iron (Fe) solubility with pH. Figure 2 The figure shows the relationship between the solubility of soluble nickel oxides and the total concentration of Ni(II) under different pH conditions. Figure 3 The figure shows the relationship between the solubility of soluble iron oxides and the total iron concentration under different pH conditions.

[0082] After obtaining the solubility, thermochemical parameters, and equilibrium parameters of iron and nickel in solution, the chemical equilibrium that minimizes the Gibbs free energy of the entire pressurized water reactor under current operating conditions is solved using the Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) method. This yields the stable phase diagram of the precipitated iron-nickel oxide under current operating conditions. (See figure...) Figure 4 The diagram shows the stable phase diagram of iron-nickel oxides generated at the saturation temperature of a pressurized water reactor. Figure 4 The image shows an example of a stable phase of iron-nickel oxide generated by a pressurized water reactor under certain operating conditions. The types of stable phase iron-nickel oxides differ depending on the coolant pH and boron concentration.

[0083] Step (2): Determine the target iron-nickel oxide that will precipitate as a stable phase in the coolant at the current pH and current boron concentration based on the stable phase diagram of the iron-nickel oxide;

[0084] The horizontal axis of the stable phase diagram of the aforementioned iron-nickel oxides represents boron concentration, and the vertical axis represents pH value. The target point in the stable phase diagram corresponding to the current pH value and current boron concentration is located, and the stable phase iron-nickel oxide corresponding to the region where the target point is located is taken as the target iron-nickel oxide. For example, using... Figure 4 Taking the stable phase diagram of the iron-nickel oxide shown as an example, when the target point corresponding to the current pH value and the current boron concentration is in the stable phase NiFe2O4 region, the target iron-nickel oxide is NiFe2O4.

[0085] In one specific implementation, when the current boron concentration is greater than 0 and less than x1, and the current pH value is greater than p1 and less than p2, the target iron-nickel oxide in the stable phase is determined to be NiFe2O4; p1 is the minimum pH value of the coolant, such as 6; p2 is the critical pH value when the form of the iron-nickel oxide changes; and x1 is the critical boron concentration when the form of the iron-nickel oxide changes.

[0086] When the current boron concentration is greater than 0 and less than x1 and the current pH value is greater than p2 and less than p3, or when the current boron concentration is greater than x1 and less than x2 and the current pH value is greater than k1*m B When +b1, the target iron-nickel oxide in the stable phase is determined to be NiO; where, m B Where is the boron concentration, k1 and b1 are constants; p3 is the maximum pH value of the coolant, such as 8.

[0087] The current boron concentration is greater than x1 and less than x2, and the current pH value is less than k2*m. B When +b2, the target iron-nickel oxide in the stable phase is determined to be Ni2FeBO5; where k2 and b2 are constants; x2 is the maximum boron concentration, such as 2500 ppm;

[0088] The current boron concentration is greater than x1 and less than x2, and the current pH value is greater than k2*m. B +b2 is less than k1*m B When +b1, the target iron-nickel oxides in the stable phase are determined to be NiO and Ni2FeBO5.

[0089] The thresholds x1~x2, p1~p3 and constants k1, k2, b1 and b2 mentioned above are related to the current operating conditions of the pressurized water reactor. When the operating conditions of the pressurized water reactor change, the values ​​of the above thresholds will also change.

[0090] In one specific implementation, with Figure 4 Taking the stable phase diagram of iron-nickel oxide shown as an example, Figure 4 The method for determining the target iron-nickel oxide corresponding to the stable phase is as follows:

[0091] When the pH value is greater than 6 and less than 7.30, and the boron concentration is greater than 0 and less than 1660 ppm, the stable phase is NiFe2O4.

[0092] When the pH value is greater than 7.30 and less than 8.0 and the boron concentration is greater than 0 and less than 1660 ppm, and when the boron concentration is greater than 1660 and less than 2500 ppm and the pH value is greater than [5.95 × 10^(-4) × m B At +6.31], the stable phase is NiO;

[0093] When the boron concentration is greater than 1660 and less than 2500 ppm and the pH value is less than [5.12×10^(-4)×m] B At +6.25%, the stable phase is Ni2FeBO5;

[0094] When the boron concentration is greater than 1660 and less than 2500 ppm and the pH value is greater than [5.12×10^(-4)×m] B +6.25] is less than [5.95×10^(-4)×m B At +6.31], the stable phase is NiO+Ni2FeBO5.

[0095] Step (3): Based on the chemical reaction formula corresponding to the target iron-nickel oxide, perform mass conservation and charge conservation calculations to obtain the concentration of the target iron-nickel oxide in the stable phase in the coolant.

[0096] When the stable phase is NiFe2O4, only the chemical reaction formulas shown in formulas (4) to (10) above are considered;

[0097] When the stable phase is NiO, only the chemical reaction formulas shown in formulas (4) to (9) and (12) above are considered;

[0098] When the stable phase is Ni2FeBO5, only the chemical reaction formulas shown in formulas (4) to (9) and (14) above are considered;

[0099] When the stable phases are NiO and Ni2FeBO5, only the chemical reaction formulas shown in the above formulas (4) to (9), (12) and (14) are considered.

[0100] The concentration of the target iron-nickel oxide in the stable phase is calculated based on the conservation of mass and charge. Taking NiFe2O4 as the stable phase as an example, the calculation formula is shown in formula (24):

[0101]

[0102] Where m is the molality (mol / kg), S is the solubility, and each subscript represents the corresponding chemical substance. By combining the formulas in the above formula (24), the concentration of the target iron-nickel oxide can be calculated.

[0103] In one embodiment, this embodiment provides an implementation method for calculating the particle size of iron-nickel oxides and the fouling thickness on the surface of pressurized water reactor fuel rods under supercooled boiling conditions based on the concentration of iron-nickel oxides. The specific steps are as follows:

[0104] Step 1): Calculate the critical particle radius of iron-nickel oxide at the current concentration based on the supersaturation ratio of iron-nickel oxide, and use the critical particle radius as the particle size of iron-nickel oxide during the deposition process.

[0105] According to thermodynamic principles, the stable crystal radius is related to the supersaturation ratio. Therefore, in the solution process, the critical radius is used as the particle size of the iron-nickel oxide during the deposition process, and the relationship between the particle size of the iron-nickel oxide and the supersaturation ratio is shown in formula (25).

[0106] The formula for calculating the critical particle radius at the current concentration is:

[0107]

[0108] Where, r * γ is the critical particle radius at the current concentration, γ is the solid-liquid surface free energy between the newly formed crystal and the solution, Q is the molecular volume of the crystal, k is the Boltzmann constant, T is the temperature of the coolant solution, and α is the supersaturation ratio of the iron-nickel oxide, i.e., the ratio of concentration C to saturation concentration C0.

[0109] Step 2): Calculate the fouling thickness on the fuel rod surface when the deposition and erosion reach equilibrium based on the current concentration of iron-nickel oxides.

[0110] Fouling growth on the surface of pressurized water reactor fuel rods is mainly determined by deposition and erosion, with boiling deposition having a greater impact in areas with strong supercooled boiling. Near the wall, formulas (26) to (27) can be used to calculate the fouling thickness and fouling mass change rate. When the value becomes 0, deposition and erosion reach equilibrium, and the thickness of the dirt no longer changes.

[0111] The formula for calculating the thickness of the fouling on the fuel rod surface is:

[0112]

[0113]

[0114] Where d is the dirt thickness, ρ CRUD For dirt density, Let t be the rate of change of mass. end k represents the deposition time at which deposition and erosion reach equilibrium. nonboiling K represents the deposition coefficient under non-boiling conditions. boiling q is the deposition coefficient of the fuel rod under supercooled boiling conditions. SNB m is the supercooled boiling heat flux density. coolant m represents the current concentration of iron-nickel oxide. erosion This represents the dirt erosion rate.

[0115] The method for predicting deposits on the surface of pressurized water reactor fuel rods provided in this embodiment can predict the thickness of fouling deposits on the surface of pressurized water reactor fuel rods, and can describe the deposition patterns and chemical composition of fouling on pressurized water reactor fuel rods. It plays an important role in conducting accurate fouling-induced nuclear safety risk analysis.

[0116] Corresponding to the method for predicting deposits on the surface of pressurized water reactor fuel rods provided in the above embodiments, this invention provides a device for predicting deposits on the surface of pressurized water reactor fuel rods, see [link to relevant documentation]. Figure 5 The diagram shows a structural schematic of a device for predicting deposits on the surface of pressurized water reactor fuel rods. The device includes the following modules:

[0117] The first calculation module 51 is used to calculate the current pH value and current boron concentration of the pressurized water reactor coolant;

[0118] The second calculation module 52 is used to determine the iron-nickel oxide in the stable phase generated under the current operating conditions based on the current pH value and current boron concentration of the coolant, and to calculate the current concentration of the iron-nickel oxide.

[0119] The third calculation module 53 is used to calculate the particle size of the iron-nickel oxide and the fouling thickness on the surface of the pressurized water reactor fuel rods under supercooled boiling conditions based on the current concentration of the iron-nickel oxide.

[0120] The device for predicting deposits on the surface of pressurized water reactor fuel rods provided in this embodiment determines the iron-nickel oxides in the corresponding stable phase based on the dissolved hydrogen concentration and pH value of the pressurized water reactor coolant, and calculates the particle size and fouling thickness of the iron-nickel oxides when deposition and erosion reach equilibrium under subcooled boiling. It can accurately describe the deposition pattern and chemical composition of fouling on pressurized water reactor fuel rods, and reflect the deposition pattern of iron-nickel oxides in the reactor core. It plays an important role in conducting accurate fouling-induced nuclear safety risk analysis.

[0121] The device provided in this embodiment has the same implementation principle and technical effect as the aforementioned embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0122] This invention provides an electronic device, which includes a processor and a memory. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the steps of the method provided in the above embodiments.

[0123] This invention provides a computer-readable medium storing computer-executable instructions. When these computer-executable instructions are invoked and executed by a processor, they cause the processor to implement the methods described in the above embodiments.

[0124] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0125] The computer program product of the method and apparatus for predicting deposits on the surface of pressurized water reactor fuel rods provided in the embodiments of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation, please refer to the method embodiments, which will not be repeated here.

[0126] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0127] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting deposits on the surface of pressurized water reactor fuel rods, characterized in that, include: Calculate the current pH value and current boron concentration of the pressurized water reactor coolant; Based on the current pH value and current boron concentration of the coolant, determine the iron-nickel oxide in the stable phase generated under the current operating conditions, and calculate the current concentration of the iron-nickel oxide; Calculate the particle size of the iron-nickel oxide and the fouling thickness on the surface of the pressurized water reactor fuel rods under supercooled boiling conditions based on the current concentration of the iron-nickel oxide. The step of calculating the particle size of the iron-nickel oxide and the fouling thickness on the surface of the pressurized water reactor fuel rod under supercooled boiling conditions based on the current concentration of the iron-nickel oxide includes: calculating the critical particle radius of the iron-nickel oxide at the current concentration based on the supersaturation ratio of the iron-nickel oxide, and using the critical particle radius as the particle size of the iron-nickel oxide during the deposition process; and calculating the fouling thickness on the surface of the fuel rod when the deposition and erosion of the fouling reach equilibrium based on the current concentration of the iron-nickel oxide.

2. The method according to claim 1, characterized in that, The steps for calculating the current pH value and current boron concentration of the pressurized water reactor coolant include: Calculate the chemical equilibrium constant of the interaction between boric acid and water in the coolant; Based on the chemical reaction equilibrium constant and the mass and charge conservation of the chemical reaction formula between boric acid and water, the current dissolved hydrogen concentration and the current boron element concentration in the coolant are calculated. The current pH value of the coolant is determined based on the current dissolved hydrogen concentration in the coolant.

3. The method according to claim 2, characterized in that, The step of calculating the chemical reaction equilibrium constant when boric acid interacts with water in the coolant includes: Calculate the standard partial molar Gibbs free energy of formation of each reactant and product when boric acid in the coolant interacts with water, and determine the chemical reaction equilibrium constant based on the change in the Gibbs free energy of formation.

4. The method according to claim 1, characterized in that, The step of determining the iron-nickel oxide in a stable phase generated under current operating conditions based on the current pH value and current boron concentration of the coolant, and calculating the current concentration of the iron-nickel oxide, includes: Obtain the stable phase diagram of the iron-nickel oxide of the pressurized water reactor under the current operating conditions; Based on the stable phase diagram of the iron-nickel oxide, the target iron-nickel oxide of the stable phase precipitated by the coolant at the current pH value and current boron concentration is determined; Based on the chemical reaction formula corresponding to the target iron-nickel oxide, mass and charge conservation calculations are performed to obtain the concentration of the target iron-nickel oxide in the stable phase in the coolant.

5. The method according to claim 4, characterized in that, The horizontal axis of the stable phase diagram of the iron-nickel oxide is the boron concentration, and the vertical axis is the pH value. The step of determining the target iron-nickel oxide of the stable phase precipitated by the coolant at the current pH value and current boron concentration based on the stable phase diagram of the iron-nickel oxide includes: Locate the target point in the stable phase diagram corresponding to the current pH value and the current boron concentration, and take the stable phase iron-nickel oxide corresponding to the region where the target point is located as the target iron-nickel oxide.

6. The method according to claim 5, characterized in that, The step of finding the target point corresponding to the current pH value and the current boron concentration in the stable phase diagram, and taking the stable phase iron-nickel oxide corresponding to the region where the target point is located as the target iron-nickel oxide, includes: When the current boron concentration is greater than 0 and less than x1, and the current pH value is greater than p1 and less than p2, the target iron-nickel oxide in the stable phase is determined to be NiFe2O4. When the current boron concentration is greater than 0 and less than x1 and the current pH value is greater than p2 and less than p3, or when the current boron concentration is greater than x1 and less than x2 and the current pH value is greater than k1*m B When +b1, the target iron-nickel oxide in the stable phase is determined to be NiO; where m B Where is the boron concentration, and k1 and b1 are constants; When the current boron concentration is greater than x1 and less than x2 and the current pH value is less than k2*m B When +b2, the target iron-nickel oxide in the stable phase is determined to be Ni2FeBO5; where k2 and b2 are constants; When the current boron concentration is greater than x1 and less than x2 and the current pH value is greater than k2*m B +b2 is less than k1*m B When +b1, the target iron-nickel oxides in the stable phase are determined to be NiO and Ni2FeBO5.

7. The method according to claim 1, characterized in that, The formula for calculating the critical particle radius at the current concentration is: in, The critical particle radius at the current concentration is... This refers to the solid-liquid surface free energy between the newly formed crystal and the solution. The volume of the molecules in the crystal is denoted as . Boltzmann's constant, The temperature of the coolant solution. The supersaturation ratio of the iron-nickel oxide is denoted as .

8. The method according to claim 6, characterized in that, The formula for calculating the thickness of the fouling on the surface of the fuel rod is: in, The thickness of the dirt, For dirt density, For the rate of change in quality, This refers to the deposition time at which deposition and erosion reach equilibrium. The deposition coefficient under non-boiling conditions. The deposition coefficient of the fuel rod under supercooled boiling conditions. The supercooled boiling heat flux density, The current concentration of the iron-nickel oxide. This represents the dirt erosion rate.

9. A device for predicting deposits on the surface of pressurized water reactor fuel rods, characterized in that, include: The first calculation module is used to calculate the current pH value and current boron concentration of the pressurized water reactor coolant; The second calculation module is used to determine the iron-nickel oxide in the stable phase generated under the current operating conditions based on the current pH value and current boron concentration of the coolant, and to calculate the current concentration of the iron-nickel oxide. The third calculation module is used to calculate the particle size of the iron-nickel oxide and the fouling thickness on the surface of the pressurized water reactor fuel rod under supercooled boiling conditions based on the current concentration of the iron-nickel oxide. The third calculation module is also used to calculate the critical particle radius of the iron-nickel oxide at the current concentration based on the supersaturation ratio of the iron-nickel oxide, and use the critical particle radius as the particle size of the iron-nickel oxide during the deposition process; and to calculate the fouling thickness on the surface of the fuel rod when the deposition and erosion of the fouling reach equilibrium based on the current concentration of the iron-nickel oxide.

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