Nuclide Transmutation Method Based on Time-Step Iteration

Abstract

The present invention relates to a nuclide transmutation method based on time-step iteration. The method obtains the nuclide conversion path and the conversion rate between nuclides based on time-step iteration, and then completes nuclide transmutation. Compared with the prior art, the method of the present invention does not need to modify the program multiple times for specific problems, can simultaneously complete the ignition burnup model analysis and nuclide transmutation analysis, and efficiently and accurately obtain physical parameters such as nuclide density, nuclide conversion path, and nuclide conversion rate in the entire time domain, thereby effectively supporting efficient and accurate nuclide transmutation. The method is accurate and universal, and has good application prospects in isotope production and complex nuclide transmutation.

Description

Technical Field

[0001] The present invention relates to the technical field of nuclide transmutation in the processes of nuclide burnup and activation, and more particularly to a nuclide transmutation method based on time-step iteration. Background Art

[0002] Traditional nuclide transmutation methods based on Monte Carlo-burnup calculations are difficult to determine the nuclide conversion path and the conversion rate between nuclides, and need to modify the program for specific problems, with low efficiency and no universality.

[0003] Therefore, there is an urgent need for a nuclide transmutation method that is efficient, accurate, universal and can determine the nuclide conversion path and the conversion rate between nuclides. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a nuclide transmutation method based on time-step iteration. By parsing the depletion burnup model through time-step iteration, while obtaining the nuclide density, the nuclide conversion path is determined and the conversion rate between nuclides is quantified, thereby realizing accurate nuclide transmutation. Aiming at the problems of traditional nuclide transmutation methods based on Monte Carlo-burnup calculations, which are difficult to determine the nuclide conversion path and the conversion rate between nuclides, and need to modify the program for specific problems, with low efficiency and no universality, a nuclide transmutation method based on time-step iteration is proposed. This method divides the total burnup time into multiple time steps, parses the depletion burnup model in each time step, obtains the nuclide conversion relationship within each time step, thereby determining the nuclide conversion path and quantifying the conversion rate between nuclides, and realizing nuclide transmutation. This method can simultaneously complete the parsing of the depletion burnup model and the nuclide transmutation analysis, efficiently and accurately complete nuclide transmutation, is accurate and universal, and has good application prospects in isotope production and complex nuclide transmutation.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The purpose of the present invention is to provide a nuclide transmutation method based on time-step iteration. The method divides the total burnup time into multiple time steps, parses the depletion burnup model in each time step, obtains the nuclide conversion relationship within each time step, thereby determining the nuclide conversion path and quantifying the nuclide conversion rate, and realizing nuclide transmutation.

[0007] Furthermore, the method includes the following steps:

[0008] Step 1: Model the problem according to the problem and perform Monte Carlo criticality calculation;

[0009] Step 2: Determine the neutronics environment of nuclide transmutation according to the Monte Carlo criticality calculation in Step 1;

[0010] Step 3: Under the neutronics environment in Step 2, based on the depletion model analysis with time-step iteration, obtain the final nuclide density, nuclide transformation path, and nuclide conversion rate;

[0011] Step 4: Output the nuclide density, nuclide transformation path, and nuclide conversion rate obtained in Step 3, and perform nuclide transmutation analysis based on time-step iteration;

[0012] Step 5: Achieve nuclide transmutation according to the nuclide transmutation analysis in Step 4.

[0013] Furthermore, in Step 1, the specific process of problem modeling and performing Monte Carlo criticality calculation is as follows:

[0014] Step 11: Conduct geometric and material modeling of the reactor, and determine the simulated particle type and total number of particles;

[0015] Step 12: Perform Monte Carlo criticality calculation to obtain the neutron flux density and average energy in the target area of the reactor.

[0016] Furthermore, in Step 3, the specific process of depletion model analysis based on time-step iteration is as follows:

[0017] Step 31: Identify the starting nuclide and target nuclide of nuclide transmutation. Use the nuclide density of the starting nuclide as the nuclide density of the initial nuclide for the first time step. Divide the total burnup time T evenly with the minimum half-life t of all nuclides involved in this nuclide transmutation process as the time step to obtain multiple time steps;

[0018] Step 32: Calculate the nuclide density of each initial nuclide after the current time step according to the exponential decay law (here the initial nuclide refers to the initial nuclide in the current iteration step, and as the iteration progresses, more and more nuclides will participate in the iteration), and calculate the nuclide density of each daughter nuclide according to the nuclear reaction transformation relationship. Use the nuclide density of the initial nuclide and each daughter nuclide as the initial nuclide density for the next time step;

[0019] Step 33: Statistically calculate the density conversion amounts of all nuclides and all daughter nuclides of all nuclides in the current time step;

[0020] Step 34: Repeat the process of Step 32 to Step 33 until all time-step iterations are completed to obtain the final nuclide density;

[0021] Step 35: Perform two depth-first searches, one with the starting nuclide as the search starting point and the target nuclide as the search target, and the other with the target nuclide as the search starting point and the starting nuclide as the search target. Retain the intersection nuclides in the results of the two searches, and determine the complete nuclide transformation path according to the parent-daughter nuclide relationship between the intersection nuclides;

[0022] Step 36: Normalize the conversion amounts of various nuclide densities in the nuclide conversion path to obtain the conversion rates between various nuclides.

[0023] Further, the exponential decay law means: N1 = N0e -λΔt , where N0 is the initial nuclide density, λ is the decay constant read directly from the nuclear database, and N1 is the nuclide density after a time of Δt.

[0024] Further, the nuclide conversion path refers to the nuclide conversion relationship formed via intermediate nuclides during the conversion from one nuclide to another.

[0025] Further, in step 4, the specific process of performing nuclide transmutation analysis based on time-step iteration is as follows: Determine the key nuclides by analyzing the nuclide conversion path and the nuclide conversion rates.

[0026] Further, the key nuclides refer to the nuclides for which the reactions occurring according to the path account for less than 50% of all reactions in the nuclide conversion path.

[0027] Further, in step 5, the specific process of realizing nuclide transmutation according to the nuclide transmutation analysis in step 4 is as follows: In the neutronics environment of step 2, make the nuclides undergo reactions such as fission, decay, and absorption to be converted into other nuclides.

[0028] Further, verify and confirm the results of the nuclide transmutation analysis in step 4.

[0029] Further, verify the obtained key nuclides by calculating the fission absorption ratio of the nuclides.

[0030] Further, after analyzing the calculation results obtained in step 3, verify the obtained final nuclide density using traditional burnup calculation.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The nuclide transmutation method based on time-step iteration provided by this technical solution solves the problems of the traditional nuclide transmutation method based on Monte Carlo-burnup calculation, which is difficult to determine the nuclide conversion path and the conversion rate between nuclides, and requires modifying the program for specific problems, with low efficiency and no universality. Compared with the traditional method, the present invention does not need to modify the program multiple times for specific problems, can simultaneously complete the analysis of the burnup model and nuclide transmutation analysis, and efficiently and accurately obtain physical parameters such as nuclide density, nuclide conversion path, and nuclide conversion rate in the entire time domain, thereby effectively supporting efficient and accurate nuclide transmutation. The method is accurate and has universality, and has good application prospects in isotope production and complex nuclide transmutation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the flow chart of the embodiment of the present invention;

[0034] Figure 2 is the X-Y cross-sectional sketch of the high-flux reactor model of the embodiment of the present invention;

[0035] Figure 3 is the X-Z cross-sectional sketch of the high-flux reactor model of the embodiment of the present invention;

[0036] Figure 4 is the schematic diagram of the nuclide transformation path from curium-244 to californium-252 of the embodiment of the present invention;

[0037] Figure 5 is the deviation diagram of nuclide density calculated by the time-step iteration method and the traditional burnup method of the embodiment of the present invention;

[0038] Figure 6 is the schematic diagram of the fission absorption ratio of some nuclides of the embodiment of the present invention;

[0039] Figure 7 is the schematic diagram of the proportion of nuclide reaction rates on the transformation path of the embodiment of the present invention. Specific Embodiments

[0040] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Features such as component models, material names, connection structures, control methods, etc. that are not clearly stated in the present technical solution are regarded as common technical features disclosed in the prior art.

[0041] The present invention relates to a nuclide transmutation method based on time-step iteration, including the following steps:

[0042] Step 1: Define the starting nuclide and the target nuclide of the nuclide transmutation, and use the nuclide density of the starting nuclide as the initial nuclide density of the first time step. Divide the total burnup time T evenly with the minimum half-life t of all nuclides involved in the nuclide transmutation process as the time step to obtain multiple time steps.

[0043] Step 2: Calculate the nuclide density of each initial nuclide after the current time step according to the exponential decay law, and calculate the nuclide density of each daughter nuclide according to the nuclear reaction transformation relationship. Use the nuclide density of the initial nuclide and each daughter nuclide as the initial nuclide density of the next time step.

[0044] The exponential decay law mentioned above refers to: N1 = N0e -λΔt , where N0 is the initial nuclide density, λ is the decay constant read directly from the nuclear database, and N1 is the nuclide density after Δt time.

[0045] Step 3: Calculate the density conversion amounts of all nuclides and their respective daughter nuclides within this time step.

[0046] Step 4: Repeat the process of Steps 2 to 3 until the iteration of all time steps is completed.

[0047] Step 5: Perform two depth - first searches. One search starts from the starting nuclide and targets the ending nuclide, and the other starts from the ending nuclide and targets the starting nuclide. Retain the intersecting nuclides from the two search results, and determine the complete nuclide conversion path based on the parent - nuclide and daughter - nuclide relationships among these nuclides.

[0048] Step 6: Normalize the density conversion amounts of various nuclides in the nuclide conversion path to obtain the conversion rates between various nuclides.

[0049] Step 7: Use the nuclide conversion path and the conversion rates between nuclides determined in Steps 5 and 6 as quantitative indicators to achieve precise nuclide transmutation.

[0050] Example

[0051] This example is implemented in Figure 2-3 the shown High - Flux Isotope Reactor (HFIR) in the United States. Taking the nuclide transmutation of a mixed target of curium - 244 and curium - 246 irradiated at a constant power as an example. As Figure 1 shown, it is a flowchart of the example implementation of the nuclide transmutation method based on time - step iteration involved in this example, specifically including:

[0052] Step 1: Conduct geometric modeling and material modeling of the United States High - Flux Reactor to determine the simulated particle type and the total number of particles.

[0053] In this example, the number of neutrons per generation N = 1×10 6 , and a total of 200 generations are simulated, that is, a total of 2×10 8 particles are simulated.

[0054] Step 2: Perform Monte Carlo criticality calculations to obtain a neutron flux density φ = 3.55×10 16 particles / (cm 2 ·s) in the target area, with an average energy of 0.1096 MeV.

[0055] Step 3: Set the mixture of curium - 244 and curium - 246 as the starting nuclide for nuclide transmutation, where curium - 244 and curium - 246 are mixed at an atomic density ratio of 1:3, and californium - 252 is set as the ending nuclide for nuclide transmutation. The initial nuclide density of curium - 244, N1 = 2.45×10 23 particles / cm 3 , and the initial nuclide density of curium - 246, N2 = 7.55×10 23 particles / cm3 The total irradiation time T = 90 days. The neutron flux density and average energy of the irradiation environment are based on the Monte Carlo critical calculation results, and the burnup depletion model analysis based on time-step iteration is performed.

[0056] The specific process of performing the burnup depletion calculation with time-step iteration is as follows:

[0057] Step 31: Identify the starting nuclide and target nuclide of nuclide transmutation. Use the nuclide density of the starting nuclide as the nuclide density of the initial nuclide for the first time step. Divide the total burnup time T evenly with the minimum half-life t of all nuclides involved in the nuclide transmutation process as the time step to obtain multiple time steps.

[0058] Step 32: Calculate the nuclide densities of each initial nuclide after the current time step according to the exponential decay law, and calculate the nuclide densities of each daughter nuclide according to the nuclear reaction transformation relationship. Use the nuclide densities of the initial nuclides and each daughter nuclide as the initial nuclide densities for the next time step.

[0059] Step 33: Statistically calculate the density conversion amounts of all nuclides and all daughter nuclides of all nuclides at the current time step.

[0060] Step 34: Repeat the process of steps 32 to 33 until all step iterations are completed to obtain the final nuclide density.

[0061] Step 35: Perform two depth-first searches. One search starts from the starting nuclide with the target nuclide as the search target, and the other search starts from the target nuclide with the starting nuclide as the search target. Retain the intersection nuclides in the results of the two searches, and determine the complete nuclide transformation path according to the relationship between the parent nuclide and daughter nuclide among the intersection nuclides.

[0062] Step 36: Normalize the density conversion amounts of various nuclides in the nuclide transformation path to obtain the conversion rates between various nuclides.

[0063] Step 4: Output the final nuclide density, nuclide transformation path, and nuclide conversion rate calculated in step 3, and perform the nuclide transmutation analysis based on time-step iteration to analyze the proportion of the reaction rates of nuclides on the transformation path. The nuclide transformation path is as Figure 4 shown.

[0064] Step 5: By analyzing the nuclide transformation path and nuclide conversion rate, determine that the three nuclides, curium-245, curium-247, and californium-251, are the key nuclides involved in this nuclide transmutation.

[0065] In this embodiment, the burnup depletion calculation using the Chebyshev rational approximation method to solve the Bateman equations is used to verify the nuclide density calculated by the present invention. The verification results are as Figure 5As shown. At the same time, the key nuclides determined by the present invention are verified by calculating the fission absorption ratio of the nuclides, and the verification results Figure 6 and Figure 7 as shown.

[0066] From Figure 5 it can be seen that for the nuclide densities on the nuclide conversion path, the deviation between the technology of the present invention and the calculation results of traditional ignition consumption is within 1%, so the technology of the present invention has high calculation accuracy.

[0067] From Figure 6 and Figure 7 it can be seen that the nuclides with a calculated fission absorption ratio greater than 1 are the three nuclides of curium-245, curium-247, and californium-251. In the nuclide reaction proportion calculated by the present invention, the reactions of curium-245, curium-247, and californium-251 occurring in the path conversion account for less than 50% of all reactions, and the two calculation results are in good agreement.

[0068] The above description of the embodiments is for the convenience of those of ordinary skill in the art to understand and use the invention. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and the improvements and modifications made by those skilled in the art without departing from the scope of the present invention according to the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A nuclide transmutation method based on time-step iteration, characterized in that the method comprises the following steps: Step 1: Model the problem and perform Monte Carlo criticality calculation; Step 2: Determine the neutronics environment of nuclide transmutation according to the Monte Carlo criticality calculation in Step 1; Step 3: In the neutronics environment of Step 2, based on the analysis of the burnup model by time-step iteration, divide the total burnup time into multiple time steps, analyze the burnup model in each time step, obtain the nuclide conversion relationship within each time step, and obtain the final nuclide density, nuclide conversion path, and nuclide conversion rate; Step 4: Output the final nuclide density, nuclide conversion path, and nuclide conversion rate obtained in Step 3, and perform nuclide transmutation analysis based on time-step iteration; Step 5: Verify and confirm the results of the nuclide transmutation analysis in Step 4, determine the key nuclides involved in nuclide transmutation, and verify the obtained key nuclides by calculating the fission absorption ratio of the nuclides; In Step 1, the specific process of modeling the problem and performing Monte Carlo criticality calculation is as follows: Step 11: Perform geometric and material modeling of the reactor, and determine the type of particles to be simulated and the total number of particles; Step 12: Perform Monte Carlo criticality calculation to obtain the neutron flux density and average energy in the target area of the reactor.

2. The nuclide transmutation method based on time-step iteration according to claim 1, wherein In Step 3, the specific process of analyzing the burnup model by time-step iteration is as follows: Step 31: Identify the starting nuclide and target nuclide of nuclide transmutation, use the nuclide density of the starting nuclide as the nuclide density of the initial nuclide in the first time step, and use the minimum half-life t of all nuclides involved in the nuclide transmutation process as the time step to evenly divide the total burnup time T to obtain multiple time steps; Step 32: Calculate the nuclide density of each initial nuclide after passing through the current time step according to the exponential decay law, and calculate the nuclide density of each daughter nuclide according to the nuclear reaction conversion relationship, and use the nuclide density of the initial nuclide and each daughter nuclide as the initial nuclide density in the next time step; Step 33: Statistically calculate the density conversion amount of all nuclides and all daughter nuclides of all nuclides at the current time step; Step 34: Repeat the process of Step 32 to 33 until all step iterations are completed to obtain the final nuclide density; Step 35: Perform two depth-first searches, one with the starting nuclide as the search starting point and the target nuclide as the search target, and the other with the target nuclide as the search starting point and the starting nuclide as the search target, retain the intersection nuclides in the results of the two searches, and determine the complete nuclide conversion path according to the relationship between the parent nuclide and daughter nuclide among the intersection nuclides; Step 36: Normalize the density conversion amounts of various nuclides in the nuclide conversion path to obtain the conversion rates between various nuclides.

3. The nuclide transmutation method based on time-step iteration according to claim 2, characterized in that The exponential decay law means that: , where is the initial nuclide density, is the decay constant, which is directly read from the nuclear database, is the nuclide density after a certain time.

4. The nuclide transmutation method based on time step iteration according to claim 2, wherein The nuclide conversion path refers to: in the process of converting from one nuclide to another nuclide, the nuclide conversion relationship formed via intermediate nuclides.

5. A nuclide transmutation method based on time-step iteration according to claim 1, characterized in that In Step 4, the specific process of performing nuclide transmutation analysis based on time-step iteration is as follows: Determine the key nuclides by analyzing the nuclide conversion path and nuclide conversion rate.

6. The nuclide transmutation method based on time step iteration according to claim 5, wherein The key nuclides refer to: In the nuclide transformation path, nuclides for which the reactions occurring according to the path account for less than 50% of all reactions.

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