Method of determining the radioactivity concentration in a container

Abstract

Examples of the present application relate to a method of determining the radioactivity concentration inside a container. The present application is applicable to a container storing nuclear fuel assemblies or spent fuel assemblies, by modeling the fuel assemblies and the storage container, determining the location of the breach in the container model, and determining the radioactivity concentration level inside the container according to the spatial location of the breach and the source strength, thereby providing an alarm threshold for the instrumentation, discovering the leakage of radioactive gas in time, and preventing further radioactive contamination.

Description

TECHNICAL FIELD

[0001] The present application is suitable for a method for determining the radioactivity concentration in a container. BACKGROUND

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

[0003] There are various containers for storing nuclear fuel assemblies or spent fuel assemblies in nuclear facilities, and these containers are generally cylindrical. When there is a break in the nuclear fuel or spent fuel in the container, radioactive substances can begin to diffuse from the damaged part into the container, and if the fuel break is not discovered in time, radioactive contamination will result. There is a difficulty here, i.e. how to determine whether a fuel assembly is broken. Generally, when a fuel assembly is broken, it will release radioactive gases such as Kr, 85 Kr, 133 Xe, etc. 85 Kr, 133 Xe as a beta emitter can be monitored by inert gas monitoring devices, so as long as the content of Kr, 85 Kr, 133 Xe around the fuel assembly can be monitored, it can be determined whether the fuel assembly is broken. However, at the same time, the surrounding air contains natural radioactive nuclides, and these nuclides also emit beta rays, which will produce counts in the inert gas monitoring device, causing interference with the monitoring of Kr, 85 Kr, 133 Xe. Considering these interferences, the background activity concentration of natural radioactivity can be set as B0, 85 Kr, 133 Xe, and when the monitoring value X≥B0+u+ε, it can be considered that the spent fuel assembly is broken. At this time, the problem is reduced to how to obtain the activity concentration u of Kr, 85 Kr, 133 Xe. SUMMARY

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

[0005] The present application provides a method for determining the radioactivity concentration in a container, which is suitable for storing nuclear fuel assemblies or spent fuel assemblies. It comprises the following steps: S10: establishing a model of the container; S20: determining the radial position and axial position of the break in the damaged nuclear fuel assembly or spent fuel assembly in the model according to the model in step S10; S30: determining the radioactivity concentration at 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 breakage detection instrument. By using the above method to calculate the airborne radioactivity concentration in the container, an accurate alarm threshold can be obtained, so that the alarm response can be made quickly when fuel breakage occurs in the container, and pollution caused by radioactive gas can be prevented. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0009] Figure 2 is the airborne radioactivity concentration calculated by the method of the present application 85 Kr activity concentration changes with time image.

[0010] BRIEF DESCRIPTION OF DRAWINGS

[0011] 1, container; 2, breakage opening. DETAILED DESCRIPTION

[0012] The exemplary examples of the present application will be described below in conjunction with the accompanying drawings. For the sake of brevity, not all features of an implementation are described in the specification. Developers of the implementation may have specific goals in mind, for example, compliance with system- and business-related constraints, which can vary from one implementation to another.

[0013] In order to avoid obscuring the present application due to unnecessary details, only the equipment structure or processing steps closely related to the scheme of the present application are shown in the drawings, and other details not closely related to the present application are omitted.

[0014] The specific examples will be described below. Of course, they are only examples and the purpose is not to limit the present application.

[0015] Generally, a fuel assembly breakage monitoring system is provided in a nuclear facility to monitor the radioactive gas in the container to determine whether the fuel assembly is broken. When the activity concentration of the radioactive gas exceeds the alarm threshold, the monitoring system will start the alarm. Here, to set the alarm threshold, the airborne radioactivity concentration in the container needs to be calculated in advance.

[0016] The inventors of the present application find that the prior art still has the following problems in calculating the activity concentration: 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 is required to have high selection of grid size and difference format, improper operation can easily lead to divergence of the solution, and error control is too dependent on the selection of grid size and difference format, and the error convergence speed is slow. In view of the problems in the above technology, the present application provides a calculation method without grid division of the container space.

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

[0018] The container determined in the S10 step is cylindrical, and a cylindrical coordinate system is used for solving.

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

[0020]

[0021] Wherein, 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, r1 represents the radial position of the breakage opening 2, z1 represents the axial position of the breakage opening 2, θ represents the azimuth angle of the predetermined point in the container 1, n0 represents the source strength of the breakage opening 2, D represents the diffusion coefficient, and q is related to the size of the breakage opening.

[0022] The right side of the equation is a function of the spatial position, which describes a source, which is the breakage opening 2 on the nuclear fuel assembly, the breakage opening 2 is at a predetermined position, for example, (0, 3), and the source strength is n0, and its expression is as follows:

[0023] The function shows that for any given ε>0, there is a positive number N, such that when q>N, and r≠0, z≠3, |f(r,z)-0|<ε. That is, the function value of f(r,z) at other positions in the container 1 tends to 0 infinitely.

[0024] Let q = 1000000, for the source point (0, 3), f(0, 3) = n0. For any point around the source point, for example (0.001, 3.001), f(0.001, 3.001) = 0.0000000001n0, which means that the intensity of any point around the source point is attenuated to almost zero. Therefore, the above expression shows that the breakage 2 can be regarded as a point source.

[0025] In the 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 the spatial coordinates (r, z), wherein r represents the radial position and z represents the axial position.

[0026] In the step S20, the breakage 2 of the nuclear fuel assembly can be represented by the spatial coordinates (r1, z1), and the source intensity n0 of the breakage 2 is constant.

[0027] The radioactivity concentration of the breakage 2 is a finite value; at the initial moment, the nuclear fuel assembly or spent fuel assembly in the container 1 has no breakage, and the radioactivity concentration of 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 center of the bottom of the cylindrical container 1, in the above expression, when r = r1, which means that when any point is selected on the side wall of the container 1, the diffusion speed of the radioactive gas is 0, which shows that the side wall of the cylindrical container 1 is closed; when z = z1 or z = 0, which means that when any point is selected on the upper and lower outer surfaces of the container 1, the diffusion speed of the radioactive gas is 0, which shows that the upper and lower bottoms of the cylindrical container 1 are also closed, that is, the container 1 is a sealed container.

[0029] As shown in Figure 1 When the origin of the coordinate system is set at the center of the bottom of the cylindrical container 1, in the above expression, when r = r1,

[0030] In the above expression, when the time t = 0, the radioactivity concentration u is a predetermined value, that is, since the container 1 is a sealed container, when the nuclear fuel assembly in the container 1 has no breakage, the background value of the radioactivity concentration in the container 1 is constant.

[0031] Therefore, the method for determining the radioactivity concentration in the container provided by the present application only needs to model the cylindrical container 1 in the calculation process, does not need to draw a grid on the space region, and the boundary conditions and initial conditions are easy to establish, so that the calculation process is more simple.

[0032] The diffusion coefficient is determined in the following manner:

[0033]

[0034] wherein: D is the diffusion coefficient; μ is the viscosity of air, μ = 1.853 Pa·S; p is the atmospheric pressure, p = 1.013 x 10 5 Pa; M is the relative molecular mass of air, in g / mol; B is the second Virial coefficient, B = -0.84671 x 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 x 10 -23 J / K; m is the mass of the radioactive gas molecule.

[0035] q is determined in the following way: the value of q is determined according to the size of the breach 2.

[0036] q and the size of the breach 2 are in accordance with the following expression:

[0037] δ represents the size of the breach 2, the breach being considered as a very small circle, the radius of the circle being δ, in m.

[0038] The activity concentration as a function of the radial position, the axial position and the time is in accordance with the following expression:

[0039]

[0040] wherein: z0 represents the height of the container; r0 represents the radius of the container; B0 represents the background value;

[0041] 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, r1 represents the radial position of the breach 2, z1 represents the axial position of the breach 2, n0 represents the source strength of the breach 2, D represents the diffusion coefficient, q is a constant determined by the size of the breach, J0 is the Bessel function, x n is the zero point of the Bessel function.

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

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

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

[0045] According to the established container model, the radial position and axial position (0, 3) of the breakage opening 2 in the model are determined; the source intensity of the breakage opening 2 is denoted as 2.605 x 10 13 Bq / m 3 .

[0046] According to the pressure, temperature, molecular weight and viscosity, the diffusion coefficient is determined:

[0047]

[0048] According to the size of the breakage opening 2, the value of q is determined, and the size of the breakage opening 2 is denoted as δ = 0.001 m, q = 1 / δ^2 = 1000000.

[0049] According to the above data, the relationship formula for determining the radioactivity concentration u of any point (r, z) in the container according to the position (0, 3) of the breakage opening 2 is listed:

[0050]

[0051] wherein n0 = 2.605 x 10 13 Bq / m 3 , B0 = 3.7 x 10 3 Bq / m 3 , 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 time, D represents the diffusion coefficient, J0 is the Bessel function, x n is the zero point 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 Xe activity concentration trends over time can be compared with the actual situation. The following examples select 85 Kr, 131 Xe m , 133 Xe and 133 Xe m as representative gases for monitoring fuel breakage, and the gas-borne activity concentration in the container 1 is calculated and reflected.

[0053] Figure 2 The calculated 85The activity concentration of Kr changes with time, as shown in the following figure: Figure 2 As shown in the following figure: 85 For Kr, the growth of activity concentration slows down gradually with time. For the diffusion process, at the initial moment, the concentration of the source point is large due to the low concentration of radioactive gas nuclides in the space. The diffusion speed is proportional to the concentration difference between points, so the diffusion is fast at the initial moment, corresponding to a large slope of the curve. After a period of time, the concentration of radioactive gas nuclides in the space is high, and the concentration difference with the source point is small, so the diffusion slows down after a period of time, corresponding to a small slope of the curve. The above phenomenon is consistent with the physical law, i.e., the correctness of the solution is verified in form.

[0054] Table 1: Calculated activity concentration at different positions at t = 60 seconds

[0055]

[0056] Table 2: Calculated activity concentration at different positions at t = 120 seconds

[0057]

[0058] For the examples of the present application, the features in the examples of the present application can be combined with each other to obtain new examples without conflict.

[0059] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for determining the radioactivity concentration in a container, suitable for a container storing nuclear fuel assemblies or spent fuel assemblies, characterized by the following steps: S10: establishing a model of the container; S20: determining the radial position and axial position of a breach in a broken nuclear fuel assembly or spent fuel assembly in the model according to the model in step S10; S30: determining the radioactivity concentration at any point in the container according to the radial position and axial position in step S20; the model determined in step S10 is set as a cylinder, and the coordinate system is a cylindrical coordinate system; in step S30, the diffusion behavior of the radioactive gas in the container according to the radial position and axial position of the breach conforms to the following expression: wherein 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 time, r1 represents the radial position of the breach, z1 represents the axial position of the breach, θ represents the azimuth angle of the predetermined point in the container, n0 represents the source strength of the breach, D represents the diffusion coefficient, and q is a constant determined by the size of the breach.

2. The method according to claim 1, characterized in that: the activity concentration of the radioactive gas released by the breach is a finite value; at the initial moment, the nuclear fuel or spent fuel in the container has no breach, and the radioactive gas has not yet begun to diffuse, and the radioactivity concentration at any point in the container is a predetermined value; and the radioactive gas in the container does not diffuse outside the container.

3. The method according to claim 1, characterized in that: the diffusion coefficient is determined according to the pressure, temperature, molecular weight of the gas molecules, and viscosity of the gas in the container.

4. The method according to claim 3, characterized in that: the diffusion coefficient conforms to the following expression:

5. The method according to claim 1, characterized in that: q is determined in the following manner: the size of the breach is determined, and the value of q is determined according to the size of the breach.

6. The method according to claim 5, characterized in that: q and the size of the breach conform to the following expression: wherein δ represents the size of the breach, the breach is a circle with a radius of δ, and the diameter of the circle is small enough. ； ​ ​ ； wherein z0represents the height of the container; represents the radius of the container; represents the background value; r denotes the radial position of any point in the vessel, z denotes the axial position of any point in the vessel, u denotes the activity concentration, t denotes time, r1 denotes the radial position of the breach, z1 denotes the axial position of the breach, n0 denotes the source strength of the breach, D denotes the diffusion coefficient, q is a constant determined by the size of the breach, J0 is the Bessel function, x n is the zero point of the Bessel function. ​ ​ ​ ​ ​ ​ ​ ​ ； where D is the diffusion coefficient; μ is the air viscosity, μ = 1.853 Pa-s; p is the atmospheric pressure, p = 1.013 x 10 5 Pa; M is the relative molecular mass of air, in g / mol; B is the second virial coefficient, B = -0.84671 x 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 x 10 -23 J / K; and m is the radioactive gas molecular mass. ​ ​ ​ ​ ​ ； ​

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