Method of determining radioactive activity concentration within container

Abstract

Examples of the present application relate to a method of determining a radioactivity concentration within a container. The method is suitable for a container for storing a nuclear fuel assembly or a spent fuel assembly, the fuel assembly and the storage container are modeled, the position of a damaged opening in a container model is determined, the radioactive activity concentration level in the container is determined according to the space position and the source intensity of the damaged opening, and therefore the alarm threshold value of an instrument is provided; radioactive gas leakage can be found in time, and further radioactive contamination is prevented.

Description

Technical Field

[0001] The present application is applicable to a method for determining the concentration of radioactivity in a container. Background Art

[0002] The statements herein provide background information relevant to the present application.

[0003] There are various containers for storing nuclear fuel assemblies or spent fuel assemblies in nuclear facilities. These containers are generally cylindrical. When the nuclear fuel or spent fuel in the container is damaged, radioactive substances may begin to spread from the damaged part to the container. If the fuel damage is not discovered in time, it will cause radioactive contamination. There is a difficulty here, that is, how to judge whether the fuel assembly is damaged. Generally speaking, when the fuel assembly is damaged, it will release 85 Kr, 133 Radioactive gases such as Xe, 85 Kr, 133 Xe, as a β emitter, can be detected by the inert gas monitoring device, so as long as the gas around the fuel assembly can be monitored 85 Kr, 133 The Xe content can be used to determine whether the fuel assembly is damaged. However, since the surrounding air contains natural radionuclides, these nuclides will also emit beta rays, which will generate counts in the inert gas monitoring device. 85 Kr, 133 Considering these interferences, the natural radioactive background activity concentration can be set as B 0 , 85 Kr, 133 The activity concentration of Xe is set to u. When the monitoring value X ≥ B 0 +u+ε, it can be considered that the spent fuel assembly is damaged. At this point, the problem comes down to how to find 85 Kr, 133 The activity concentration u of Xe. Summary of the invention

[0004] A brief summary of the present application is given below. It is not intended to identify the key or important parts of the present application, nor is it intended to limit the scope of the present application. Its purpose is only to simply give some concepts to facilitate a more detailed description later.

[0005] The present application provides a method for determining the radioactivity concentration in a container, wherein the container is suitable for storing nuclear fuel assemblies or spent fuel assemblies. The method comprises the following steps: S10: establishing a model of the container; S20: determining the radial position and axial position of the damaged opening of the damaged nuclear fuel assembly or spent fuel assembly in the model according to the model in step S10; S30: determining the radioactivity concentration of any point in the container according to the radial position and axial position determined in step S20.

[0006] The method of the present application can improve the working efficiency of radiation monitoring and fuel damage detection instruments. By using the above method to calculate the airborne radioactive activity concentration in the container, an accurate alarm threshold can be obtained, so that an alarm response can be made quickly when fuel damage occurs in the container to prevent contamination caused by radioactive gases. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] These drawings depict only typical examples of the present application and should not be considered as limiting the scope of the present application.

[0008] Figure 1 It is a schematic diagram of the method for constructing a container for storing nuclear fuel, and the coordinate system is a cylindrical coordinate system;

[0009] Figure 2 This is calculated from an example of this method. 85 Kr activity concentration changes over time.

[0010] Description of reference numerals:

[0011] 1. Container; 2. Damaged opening. DETAILED DESCRIPTION

[0012] The following will describe the exemplary embodiments of the present application in conjunction with the accompanying drawings. For the sake of brevity, not all features of the implementation are described in the specification. During the development process, the specific goals of the developer, such as compliance with those constraints related to the system and business, may change depending on the implementation.

[0013] In order to avoid obscuring the present application due to unnecessary details, only the device structure or processing steps closely related to the present application scheme are shown in the accompanying drawings, while other details that are not very relevant to the present application are omitted.

[0014] Specific examples are described below. Of course, they are only examples and are not intended to limit the present application.

[0015] Generally speaking, a nuclear facility will have a fuel assembly damage monitoring system to monitor the radioactive gas in the container to determine whether the fuel assembly is damaged. When the activity concentration of the radioactive gas exceeds the alarm threshold, the monitoring system will trigger an alarm. To set the alarm threshold here, the airborne radioactivity concentration in the container needs to be calculated in advance.

[0016] The inventor of the present application has found that the calculation of activity concentration in the prior art still has the following problems: the modeling process of the traditional CFD method is relatively cumbersome, it is relatively difficult to determine the boundary conditions and initial conditions, and it has high requirements for the selection of grid size and differential format. Improper operation can easily lead to divergent solutions. At the same time, error control is too dependent on the selection of grid size and differential format, and the error convergence speed is slow. In view of the problems existing in the above technology, the present application provides a calculation method that does not require gridding of the container space.

[0017] The present application provides a method for determining the radioactivity concentration in a container, which is applicable to containers storing nuclear fuel assemblies or spent fuel assemblies. Figure 1 As shown, it includes the following steps: S10: establishing a model of the container 1; S20: determining the radial position and axial position of the damaged opening 2 of the damaged nuclear fuel assembly in the model according to the model in step S10; S30: determining the radioactivity concentration at any point in the container 1 according to the radial position and axial position determined in step S20.

[0018] The container determined in step S10 is cylindrical and is solved using a cylindrical coordinate system.

[0019] In step S30, according to the radial position and axial position of the damage opening 2, it can be determined that the diffusion behavior of the radioactive gas in the container 1 conforms to the following expression:

[0020]

[0021] Where r represents the radial position of any point in the container 1, z represents the axial position of any point in the container 1, u represents the activity concentration, t represents the time, and r 1 represents the radial position of the damage opening 2, z 1 represents the axial position of the damage opening 2, θ represents the azimuth angle of the predetermined point in the container 1, and n 0 represents the source intensity of the damage opening 2, D represents the diffusion coefficient, and q is related to the size of the damage opening.

[0022] The right side of the equation is a function of the spatial position, which describes a source, which is a damage hole 2 on the nuclear fuel assembly. The damage hole 2 is at a predetermined position, such as (0, 3), and its source strength is n 0 , which is expressed as follows:

[0023] This function shows that for any given ε>0, there exists a positive number N such that when q>N, r≠0, z≠3, |f(r,z)-0|<ε. In other words, at other locations in container 1, the function value of f(r,z) approaches 0 infinitely.

[0024] Let q = 1000000, for the source point (0, 3), f(0, 3) = n 0 For any point around the source point, for example (0.001, 3.001), f(0.001, 3.001) = 0.0000000001n 0 , which is equivalent to the intensity of any point around the source point decaying to almost disappear. Therefore, the above expression shows that the damage port 2 can be regarded as a point source.

[0025] In step S10, a cylindrical coordinate system is constructed for the container 1, so that the position of each point in the container 1 can be represented by a spatial coordinate (r, z), where r represents a radial position and z represents an axial position.

[0026] In step S20, the damaged opening 2 of the nuclear fuel assembly can be represented by the spatial coordinates (r 1 , z 1 ) is used to represent the source strength n of the damaged port 2. 0 Also constant.

[0027] The radioactive activity concentration at the damage opening 2 is a finite value; at the initial moment, the core fuel assembly or spent fuel assembly in the container 1 is not damaged, and the radioactive activity concentration at any point in the container 1 is the background value; the radioactive gas in the container 1 will not diffuse out of the container.

[0028] When the origin of the coordinate system is set at the bottom center of the cylindrical container 1, in the above expression, when r = r 1 hour, It means that when any point is selected on the side wall of the container 1, the diffusion rate of the radioactive gas is 0, indicating that the side wall of the cylindrical container 1 is closed; when z = z 1 Or when z=0, It means that when any point is selected on the outer surface of the upper and lower bottom of the container 1, the diffusion rate of the radioactive gas is 0, which means that the upper and lower bottoms of the cylindrical container 1 are also closed, that is, the container 1 is a closed container.

[0029] like Figure 1 As shown, when the origin of the coordinate system is set at the axis of the cylindrical container 1, when r = 0, the value of the radioactivity concentration u is a finite value, which is a judgment condition that can exclude divergent solutions in subsequent calculations.

[0030] In the above expression, when time t=0, the radioactivity concentration u is a predetermined value, that is, since container 1 is a closed container, when the nuclear fuel assembly in container 1 is not damaged, the background value of the radioactivity concentration in container 1 is constant.

[0031] Therefore, the method for determining the radioactivity concentration in the container provided in the present application only needs to model the cylindrical container 1 during the calculation process, and does not need to draw a grid for the spatial area. In addition, the boundary conditions and initial conditions are easy to establish, making the calculation process simpler.

[0032] The diffusion coefficient is determined as follows:

[0033]

[0034] Where: D is the diffusion coefficient; μ is the air viscosity, μ = 1.853 Pa·S; p is the atmospheric pressure, p = 1.013×10 5 Pa; M is the relative molecular mass of air, in g / mol; B is the second Virial coefficient, B = -0.84671×10 -5 m 3 / mol; R is the gas constant, R = 8.314 J / (mol·K); T is the air temperature, T = 300.15 K; k is the Boltzmann constant, k = 1.380649×10 -23 J / K; m is the molecular mass of the radioactive gas.

[0035] q is determined in the following manner: the value of q is determined according to the size of the damaged opening 2 .

[0036] q and the size of the damage opening 2 conform to the following expression:

[0037] δ represents the size of the damage opening 2. The damage opening is regarded as a very small circle with a radius of δ in m.

[0038] The activity concentration with respect to radial position, axial position and time conforms to the following expressions:

[0039]

[0040] Among them, z 0 Indicates the height of the container; r 0 Indicates the radius of the container; B 0 Indicates background value;

[0041] r represents the radial position of any point in container 1, z represents the axial position of any point in container 1, u represents the activity concentration, t represents the time, r 1 represents the radial position of the damage opening 2, z1 Indicates the axial position of the damage opening 2, n 0 represents the source intensity of the damage opening 2, D represents the diffusion coefficient, q is a constant determined by the size of the damage opening, and J 0 is the Bessel function, x n are the zeros of the Bessel function.

[0042] The method of the present application can improve the working efficiency of radiation monitoring and fuel damage detection instruments. By using the above method to calculate the airborne radioactive activity concentration in the container 1, an accurate alarm threshold can be obtained, so that an alarm response can be quickly made when fuel damage occurs in the container 1.

[0043] The following is a specific embodiment of the method for determining the radioactivity concentration in a container provided in the present application.

[0044] The container for storing spent fuel assemblies is a cylinder with a radius of 0.225m and a height of 9m, and a cylindrical coordinate system is established at the same time.

[0045] According to the constructed container model, the radial position and axial position (0, 3) of the damage opening 2 in the model are determined; the source strength of the damage opening 2 is recorded as 2.605×10 13 Bq / m 3 .

[0046] Determine the diffusion coefficient based on pressure, temperature, molecular weight, and viscosity:

[0047]

[0048] The value of q is determined according to the size of the damaged opening 2. The size of the damaged opening 2 is represented by δ, δ=0.001m, and q=1 / δ^2=1000000.

[0049] According to the above data, the relationship between the position (0, 3) of the damage opening 2 and the radioactivity concentration u at any point (r, z) in the container is listed as follows:

[0050]

[0051] Among them, n 0 =2.605×10 13 Bq / m 3 , B 0 =3.7×10 3 Bq / m 3 , r represents the radial position of any point in container 1, z represents the axial position of any point in container 1, u represents the activity concentration, t represents the time, D represents the diffusion coefficient, J 0 is the Bessel function, x n is the zero of the Bessel function, r * is the complex conjugate of r, z* is the complex conjugate of z.

[0052] In order to verify the radioactivity concentration obtained by the above method, the calculated 85 Kr, 131m Xe, 133 Xe and 133m The trend of Xe activity concentration over time is compared with the actual situation. The following examples are selected 85 Kr, 131 XE m , 133 Xe and 133 XE m As a representative gas for monitoring fuel damage, the airborne activity concentration in the container 1 is calculated and reflected.

[0053] Figure 2 Shows the calculated 85 Schematic diagram of Kr activity concentration changing with time, such as Figure 2 As shown, for 85 Kr, as time goes by, the growth of activity concentration gradually slows down. For the diffusion process, at the initial moment, the concentration of radioactive gas nuclides in various places in the space is low, while the concentration at the source point is large, and the diffusion speed is proportional to the concentration difference between each point, so the diffusion is faster at the initial moment, and the corresponding curve has a large rising slope; after a period of diffusion, the concentration of radioactive gas nuclides in various places in the space becomes higher, and the concentration difference with the source point decreases, so after a period of time, the diffusion slows down, and the corresponding curve has a decreasing rising slope; the above phenomenon is consistent with the laws of physics, which verifies the formal correctness of the solution.

[0054] Table 1 Calculated values ​​of activity concentration at different positions when t = 60 seconds

[0055]

[0056] Table 2 Calculated values ​​of activity concentration at different positions when t = 120 seconds

[0057]

[0058] For the examples of the present application, in the absence of conflict, the features in the examples of the present application can be combined with each other to obtain new examples.

[0059] The above are only specific implementation methods of the present application, but the protection scope of the present application is not limited thereto. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for determining the concentration of radioactivity in a container, applicable to a container for storing nuclear fuel assemblies or spent fuel assemblies, characterized by the following steps: S10: Building a container model; S20: According to the model in step S10, the radial position and the axial position of the damaged opening on the damaged nuclear fuel assembly or the spent fuel assembly are determined in the model; S30: Determine the radioactivity concentration at any point in the container according to the radial position and the axial position in step S20.

2. The method according to claim 1, characterized in that In step S30, according to the radial position and axial position of the damage opening, it can be determined that the diffusion behavior of the radioactive gas in the container conforms to the following expression: Among them, r represents the radial position of any point in the container, z represents the axial position of any point in the container, u represents the activity concentration, t represents the time, r1 represents the radial position of the damage opening, z1 represents the axial position of the damage opening, θ represents the azimuth angle of the predetermined point in the container, n0 represents the source intensity of the damage opening, D represents the diffusion coefficient, and q is a constant determined by the size of the damage opening.

3. The method according to claim 2, characterized in that: The activity concentration of radioactive gas released from the damage opening is a limited value; At the initial moment, the nuclear fuel or spent fuel in the container is not damaged, the radioactive gas has not yet begun to diffuse, and the radioactivity concentration at any point in the container is the predetermined value; The radioactive gas in the container will not diffuse outside the container.

4. The method according to claim 1, characterized in that The model determined in step S10 is set as a cylinder, and the solution coordinate system is a cylindrical coordinate system.

5. The method according to claim 2, characterized in that: The diffusion coefficient is determined based on the pressure, temperature, molecular weight of the gas molecules, and the viscosity of the gas in the container.

6. The method according to claim 5, characterized in that The diffusion coefficient conforms to the following expression: Where: D is the diffusion coefficient; μ is the air viscosity, μ = 1.853 Pa·S; p is the atmospheric pressure, p = 1.013×10 5 Pa; M is the relative molecular mass of air, in g / mol; B is the second Virial coefficient, B = -0.84671×10 -5 m 3 / mol; R is the gas constant, R = 8.314 J / (mol·K); T is the air temperature, T = 300.15 K; k is the Boltzmann constant, k = 1.380649×10 -23 J / K; m is the molecular mass of the radioactive gas.

7. The method according to claim 2, characterized in that: q is determined as follows: Determine the size of the damage opening and determine the value of q based on the size of the damage opening.

8. The method according to claim 7, characterized in that q and the size of the broken opening conform to the following expression: δ represents the size of the damage opening. The damage opening is a circle with a radius of δ, and the diameter of the circle is small enough.

9. The method according to claim 1, characterized in that: The activity concentration with respect to radial position, axial position and time conforms to the following expressions: Among them, z0 represents the height of the container; r0 represents the radius of the container; B0 represents the background value; r represents the radial position of any point in the container, z represents the axial position of any point in the container, u represents the activity concentration, t represents the time, r1 represents the radial position of the damage opening, z1 represents the axial position of the damage opening, n0 represents the source intensity of the damage opening, D represents the diffusion coefficient, q is a constant determined by the size of the damage opening, J0 is the Bessel function, x n are the zeros of the Bessel function.

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