A burnup tracking calculation method, system and medium for multi-cycle fuel management

Abstract

The present invention discloses a burnup tracking calculation method, system and medium for multi-cycle fuel management; it relates to the technical field of reactor burnup calculation; after the first-cycle core modeling, geometric grid division is performed on each burnup zone unit in the full-core model. During the cycle of the full-core model, the replacement of all reactor internal components in the full-core model is achieved by exchanging the positions of the corresponding spatial numbers in the repeated geometric grid. Combining with the multi-cycle burnup tracking calculation process, the dynamic changes of fuel burnup, control rods and beryllium followers during reactor operation and their coupling relationship with the particle transport process are accurately considered, and the simulation of the actual refueling process of the research reactor based on the Monte Carlo method is completed, realizing high-precision and high-efficiency core calculation and analysis for high-flux research reactors, and providing theoretical support for aspects such as high-quality testing of nuclear fuels and materials, optimization of core loading and irradiation resources of research reactors, and improvement of the operation safety of research reactor reactors.

Description

Technical Field

[0001] The present invention relates to the technical field of reactor burnup calculation, and in particular to a burnup tracking calculation method, system and medium for multi-cycle fuel management. Background Technique

[0002] The complex and variable core composition and loading arrangement of research reactors pose severe challenges to high-precision core physical calculations. The problem of insufficient calculation accuracy of the power and its distribution of test pieces exposed during the implementation of irradiation test tasks by existing calculation and analysis systems restricts the overall optimization of irradiation resources.

[0003] The Monte Carlo method is a method that solves complex calculation problems through random simulation and sampling based on statistical principles and has been widely used in reactor physics calculations, especially in nuclear reactor design and core fuel management. Compared with the traditional "two-step method" determinism, the Monte Carlo method has unique advantages for research reactors with characteristics such as flexible geometric structure, complex neutron energy spectrum, diverse material components, and strong non-uniformity, including fine modeling of complex geometries, continuous energy point cross-section processing, and fine nuclide fuel chain simulation. Monte Carlo transport-burnup coupling calculation is the mutual coupling of Monte Carlo transport calculation and burnup calculation. Currently, a large number of Monte Carlo programs already have the function of transport-burnup coupling calculation. Through the coupled burnup solver, the change in the nucleon density of burnable materials during the fuel burnup process can be obtained. Data such as neutron flux and single-group reaction cross-section are obtained through critical calculation, and the new nucleon density obtained by completing the burnup calculation is transmitted to the critical calculation module.

[0004] Based on the Monte Carlo transport-burnup coupling calculation, for the core loading characteristics of research reactors, an accurate description of the geometric space is required. The fuel / poison that is often mixed in the approximate grid must be considered separately, and the movement of control rods is no longer a change in the grid material, but the real movement of the geometric body. For multiple types of fuel / poison contained in the reactor, different burnup zone grid divisions need to be used. For the characteristics of dynamic and complex changes in the burnup zone grid, if the burnup zone grid is divided too finely, it will lead to excessive calculation costs and increase the difficulty of refueling.

[0005] The operation of a research reactor is a long-term process. At the end of each cycle, refueling is required due to insufficient reactivity. The refueling process is an actual operation process of a research reactor engineering, mainly including the removal of old fuel elements from the reactor, the insertion of new fuel elements into the reactor, and the rearrangement of old fuel elements. Compared with commercial pressurized water reactors, research reactors have the characteristics of complex and variable core loading, frequent refueling and reactor startup and shutdown, and multiple test loops. A batch of fuel elements often need to go through multiple cycles in a research reactor before being discharged, and the irradiation tests of fuels and materials in a research reactor often need to go through more than a dozen cycles. During the process of core fuel management calculation in a research reactor, it is necessary to perform modeling calculations and refueling operations for each cycle. In order to realize the multi-cycle burnup tracking calculation of a research reactor, the Monte Carlo method can be used to process this engineering operation process. Summary of the Invention

[0006] The technical problem to be solved by the present invention is that in the process of multi-cycle fuel management of a reactor, due to the large difference in full-core refueling compared with commercial pressurized water reactors, there are differences in the Monte Carlo core refueling process and burnup calculation methods, and the burnup calculation methods of traditional commercial pressurized water reactors are difficult to directly match and apply. The purpose of the present invention is to provide a burnup tracking calculation method, system and medium for multi-cycle fuel management. After the first-cycle core modeling, geometric grid division is performed on each burnup zone unit in the full-core model. During the cycle process of the full-core model, the rearrangement of all reactor internal components in the full-core model is realized by exchanging the positions of the corresponding spatial numbers in the repeated geometric grids. Combining the multi-cycle burnup tracking calculation process, accurately consider the dynamic changes of fuel burnup, control rods and beryllium followers during the reactor operation process and their coupling relationship with the particle transport process, complete the simulation of the actual refueling process of a research reactor based on the Monte Carlo method, and realize high-precision and high-efficiency core calculation and analysis for high-flux research reactors, providing theoretical support for aspects such as high-quality tests of nuclear fuels and materials, optimization of core loading and irradiation resources of research reactors, and improvement of the operation safety of research reactor reactors.

[0007] The present invention is realized through the following technical solutions:

[0008] This solution provides a burnup tracking calculation method for multi-cycle fuel management, including:

[0009] First-cycle core modeling: Divide the burnup zone units and assign spatial numbers to the reactor internal components to construct a full-core model;

[0010] Burnup zone grid division: Set the burnup zones for the full-core model and perform geometric grid division on each burnup zone unit, and cycle the full-core model;

[0011] Monte Carlo full-core refueling: During the cycle process of the full-core model, the rearrangement of all reactor internal components in the full-core model is realized by exchanging the positions of the corresponding spatial numbers in the repeated geometric grids;

[0012] Multi-cycle fuel consumption tracking calculation: The fuel consumption tracking calculation of each cycle is carried out by taking into account the control rod fuel consumption and beryllium fuel consumption, and the accumulation of poisons during the shutdown decay process is taken into account. After the end of each cycle, the full-core fuel consumption is calculated at the lowest reactor power and with all control rods inserted to calculate the distribution of poisons in the next cycle. After the Monte Carlo full core material is replaced, the fuel consumption tracking calculation of the next cycle is carried out.

[0013] Working principle of this scheme: In the multi-cycle fuel management process of the reactor, due to the great difference between the full core refueling and the commercial pressurized water reactor, there are differences in the Monte Carlo core refueling process and the burnup calculation method, and the burnup calculation method of the traditional commercial pressurized water reactor is difficult to directly match and apply; the purpose of the present invention is to provide a burnup tracking calculation method, system and medium for multi-cycle fuel management. After the first cycle core model is built, the geometric grid division is performed on each burnup area unit in the full core model. During the cycle of the full core model, the position transposition of all reactor internal components in the full core model is achieved by exchanging the positions of the corresponding space numbers in the repeated geometric grid. Combined with the multi-cycle burnup tracking calculation process, the dynamic changes of fuel burnup, control rods and beryllium followers during the operation of the reactor and their coupling relationship with the particle transport process are accurately considered, and the simulation of the real refueling process of the research reactor based on the Monte Carlo method is completed, and high-precision and high-efficiency core calculation and analysis based on high-throughput research reactors are realized, providing theoretical support for high-quality testing of nuclear fuels and materials, optimization of research reactor core loading and irradiation resources, and improvement of research reactor reactor operation safety.

[0014] A further optimization scheme is that the division and numbering of the burnup zone units of the reactor internal components includes the following method:

[0015] Divide reactor internals into consumable units and non-consumable units;

[0016] Space division and space numbering for combustible units and non-combustible units:

[0017] Each component in the combustible unit is expanded into an independent combustible area, and all independent combustible areas are assigned different space numbers;

[0018] After each component in the non-combustible unit is expanded into a space, all spaces are assigned the same space number.

[0019] A further optimized solution is that the burnable unit includes: fuel elements, burnable poisons, reflective layer beryllium blocks, aluminum blocks, stainless steel blocks and control rod beryllium followers.

[0020] A further optimization scheme is that the geometric mesh division of each burnup zone unit includes the following method:

[0021] Geometric grid division is performed on each burnup zone unit based on the properties of each core, the properties of the components themselves, and the distance between the components and the core:

[0022] For the fuel irradiation test channels, they are divided based on the first-level three-dimensional burnup zone grid division method;

[0023] For the components in core a, and when the size of core a exceeds threshold A, they are divided based on the second-level three-dimensional burnup zone grid division method;

[0024] For the components inside the reactor with a distance from the core greater than threshold A, a self-screening effect less than threshold B, and a neutron absorption rate less than threshold C, they are divided based on the third-level three-dimensional burnup zone grid division method;

[0025] For the burnable poisons with a distance from the core greater than threshold B and a self-screening effect greater than threshold D, they are divided based on the second-level three-dimensional burnup zone grid division method;

[0026] Among them, the grid sparsity level divided by the first-level three-dimensional burnup zone grid division method is less than that of the second-level three-dimensional burnup zone grid division method, and the grid sparsity level divided by the second-level three-dimensional burnup zone grid division method is less than that of the third-level three-dimensional burnup zone grid division method.

[0027] A further optimization scheme is that during the full-core model cycle process, the transposition of all reactor internal components in the full-core model is achieved by exchanging their positions in the repeated geometric grid corresponding to the spatial numbers, including the method:

[0028] (1) For all burnable zones in the core, a unique spatial number and a unique lattice cell number are defined. For the fuel elements, each time a fuel element moves, its position in the core grid changes. In the case where the total number of fuel elements in the reactor remains unchanged, at this time, the number of spent fuel elements leaving the reactor is the same as the number of new fuel elements entering the reactor. First, delete the material information corresponding to the lattice cells of the spent fuel elements leaving the reactor, then assign the same initial material of the new fuel to the lattice cells corresponding to the spent fuel elements leaving the reactor, and then move the spatial number corresponding to this fuel element to a specific position in the repeated geometric grid. If the number of fuel elements in the reactor changes, if the number of fuel elements decreases, then delete the corresponding space and the lattice cells and material information in the space in the repeated geometric grid. If the number of fuel elements increases, then add the corresponding space and the lattice cells and initial new fuel material information in the space in the repeated geometric grid. During the refueling process, the lattice cells and material information corresponding to the spent fuel elements in the space are stored separately, and the spent fuel elements that left the reactor in the previous cycle can be reused later. For the burnable poisons and beryllium blocks with burnup, if the quantity increases, the corresponding space and material are increased, and vice versa. Their refueling method is the same as that of the fuel elements.

[0029] (2) For other in-core components such as non-consumable stainless steel blocks and aluminum blocks, the same in-core component is defined with the same spatial number, and the corresponding lattice cell numbers and material information in the space are also the same. First, exchange the positions of the spatial numbers within the core repetitive geometric grid to complete the refueling of the in-core components. If the number of in-core components increases, modify the corresponding positions in the core repetitive geometric grid to the corresponding spatial numbers of the in-core components. If the number of in-core components decreases, delete the corresponding spatial numbers of the in-core components at the corresponding positions in the core repetitive geometric grid.

[0030] A further optimization scheme is that the multi-cycle burnup tracking calculation includes the method: The burnup equation is the conservation equation of the quantities of various nuclides. The change in the nuclide concentration in the reactor materials is generally described by the Bateman equation, which belongs to a system of first-order ordinary differential equations. The nuclide burnup equation is shown in Formula 1.1, where, N i is the content of nuclide i, b j,i is the branching ratio from nuclide i to nuclide j, λ j is the decay constant of nuclide j, φ is the neutron flux, σ j,k is the microscopic cross-section of the k reaction channel of nuclide j, γ j,i,k is the fraction of nuclide i generated after nuclide j passes through the k reaction channel, including fission reactions and non-fission reactions.

[0031]

[0032] The burnup calculation method selects the Chebyshev rational approximation method (CRAM). The advantage of CRAM is good numerical stability, accurate calculation results and high calculation efficiency. The calculation accuracy only depends on the order k of the CRAM coefficients. There is a linear relationship between the calculation time and the accuracy. It is a very good method for solving large burnup equations. CRAM avoids problems such as the appearance of cyclic chains in the burnup chain that the linear sub-chain method (TTA) will encounter, directly performs numerical solutions, and reduces the introduction of truncation errors.

[0033] The burnup step strategy selects the predictor-corrector method. In the first step (prediction step), perform the full-step burnup calculation to obtain the predicted nuclide density, and perform the transport calculation to obtain corresponding parameters such as the flux and cross-section. In the second step (correction step), use the new flux and cross-section and other parameters to recalculate the entire burnup step length to obtain the corrected nuclide density. Finally, take the average of the predicted value and the corrected value of the nuclide density..

[0034] A further optimization scheme is that the multi-cycle burnup tracking calculation also includes the method: Use the actual rod positions during the real operation of the reactor for different burnup steps, and divide the actual operating power by the total initial fuel mass to obtain the total power density (W / gU) of each burnup step. To calculate the total initial fuel mass and power distribution, the correct volume needs to be specified for the burnup lattice cells.

[0035] A further optimization solution is that the poisons include: 135 Xe, 149 Sm, and 3 He.

[0036] This solution also provides a burnup tracking calculation system for multi-cycle fuel management, which is used to implement the burnup tracking calculation method for multi-cycle fuel management described above, and includes:

[0037] The first-cycle core modeling module is used to divide the burnup zone units and number the spaces of the reactor internal components, and construct a full-core model;

[0038] The burnup zone grid division module is used to set the burnup zones for the full-core model, and perform geometric grid division on each burnup zone unit, and cycle the full-core model;

[0039] The Monte Carlo full-core refueling module is used to make all the reactor internal components in the full-core model change positions during the cycle of the full-core model, which is achieved by exchanging the positions of the corresponding space numbers in the repeated geometric grids;

[0040] The multi-cycle burnup tracking calculation module is used to perform burnup tracking calculations for each cycle considering the burnup of control rods and beryllium, take into account the accumulation of poisons during the shutdown decay process, calculate the poison distribution for the next cycle with the lowest reactor power and all control rods fully inserted at the end of each cycle, and perform burnup tracking calculations for the next cycle after the Monte Carlo full-core refueling.

[0041] This solution also provides a computer-readable medium with a computer program stored thereon, and the computer program can be implemented by a processor to achieve the burnup tracking calculation method, system, and medium for multi-cycle fuel management described above.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] The present invention provides a burnup tracking calculation method, system, and medium for multi-cycle fuel management; after the first-cycle core modeling, geometric grid division is performed on each burnup zone unit in the full-core model. During the cycle of the full-core model, all the reactor internal components in the full-core model change positions by exchanging the positions of the corresponding space numbers in the repeated geometric grids. Combining with the multi-cycle burnup tracking calculation process, accurately consider the dynamic changes of fuel burnup, control rods, and beryllium followers during reactor operation and their coupling relationship with the particle transport process, complete the simulation of the actual refueling process of the research reactor based on the Monte Carlo method, and achieve high-precision and high-efficiency core calculation and analysis for high-flux research reactors, providing theoretical support for aspects such as high-quality testing of nuclear fuels and materials, optimization of core loading and irradiation resources of research reactors, and improvement of reactor operation safety of research reactors. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts. In the drawings:

[0045] Figure 1 Schematic flow chart of the burnup tracking calculation method for multi - cycle fuel management;

[0046] Figure 2 Schematic diagram of the principle of the burnup tracking calculation method for multi - cycle fuel management in Example 4;

[0047] Figure 3 Schematic diagram of the Monte Carlo full - core refueling process in Example 4. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the embodiments and the drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0049] Due to its high neutron flux density, the high - flux research reactor is an important platform for accelerating the irradiation tests of various new nuclear fuels and materials. The complex and variable core composition and loading arrangement pose a severe challenge to the high - precision physical calculation of the core. For a high - flux research reactor with multiple fuels / poisonous burnable materials, a complex and variable core loading, flexible and diverse irradiation samples, and strong non - uniformity, through the following embodiments, the present invention considers the dynamic changes of fuel burnup, control rods, and beryllium followers during the reactor operation and their coupling relationship with the particle transport process, completes the simulation of the actual refueling process of the research reactor based on the Monte Carlo method, realizes high - precision and high - efficiency core calculation and analysis for the high - flux research reactor, and provides theoretical support for aspects such as high - quality testing of nuclear fuels and materials, optimization of the core loading and irradiation resources of the research reactor, and improvement of the reactor operation safety of the research reactor.

[0050] Example 1

[0051] This example provides a burnup tracking calculation method for multi - cycle fuel management, as Figure 1 shown, including:

[0052] I. First - cycle core modeling: Divide the in - reactor components into burnup zone units and number them spatially to construct a full - core model;

[0053] The method for dividing and numbering the burnup zones of the reactor internals includes the following steps:

[0054] Divide the reactor internals into burnable units and non-burnable units;

[0055] Conduct spatial division and spatial numbering for the burnable units and non-burnable units:

[0056] For each component in the burnable units, expand it into an independent burnup zone, and assign different spatial numbers to all the independent burnup zones;

[0057] After expanding each component in the non-burnable units into space, assign the same spatial number to all the spaces.

[0058] The burnable units include: fuel elements, burnable poisons, reflector beryllium blocks, aluminum blocks, stainless steel blocks, and control rod beryllium followers.

[0059] Currently, deterministic programs are usually used for the core fuel management of existing research reactors and commercial pressurized water reactors. There are significant differences in the fuel management calculations between high-flux research reactors and commercial pressurized water reactors. Firstly, the core loading is complex and variable. Secondly, the core refueling is frequent. Thirdly, the irradiation samples in the reactor are flexible and diverse. The Monte Carlo method has unique advantages for high-flux research reactors with flexible geometric structures, complex neutron energy spectra, diverse material compositions, anisotropy, and strong leakage characteristics. Firstly, conduct refined Monte Carlo modeling for various types of reactor internals in the reactor (including various fuel elements, burnable poisons, beryllium blocks, aluminum blocks, stainless steel blocks, control rods, etc.). First, divide the reactor internals into burnable units and non-burnable units. The non-burnable units use the same spatial number, and the burnable units use different spatial numbers. In the initial state, all burnable units in the reactor are in the unburned state. Expand the burnable reactor internals (various fuel elements, burnable poisons, reflector beryllium blocks, control rod beryllium followers) into independent burnup zones, assign independent lattice cell numbers to all burnup zones, and expand different lattice cells to the corresponding spaces based on the repeated geometric structure, and assign independent numbers to different spaces. Since the fuel and material irradiation test channels in the reactor need to be opened and closed flexibly, the sample layout is complex and variable, and it may be necessary to enter, exit, or turn the surface midway, the repeated geometric structure used in large reactors is not used. Instead, a modeling strategy of separating the modeling from the large reactor and then filling it into the corresponding positions is adopted. Such a modeling strategy ensures that the subsequent refueling operation of the high-flux reactor based on the Monte Carlo method can be realized.

[0060] II. Burnup zone grid division: Set the burnup zones for the full-core model, conduct geometric grid division for each burnup zone unit, and run the full-core model in a loop;

[0061] The method for conducting geometric grid division for each burnup zone unit includes the following steps:

[0062] Geometric grid division is carried out for each burnup zone unit based on the properties of each core, the properties of the component itself, and the distance between the component and the core:

[0063] For the fuel irradiation test channels, they are divided based on the first-level three-dimensional burnup zone grid division method;

[0064] For the components in core a and when the size of core a exceeds threshold A, they are divided based on the second-level three-dimensional burnup zone grid division method;

[0065] For the components inside the reactor with a distance from the core greater than threshold A, a self-screening effect less than threshold B, and a neutron absorption rate less than threshold C, they are divided based on the third-level three-dimensional burnup zone grid division method;

[0066] For the burnable poisons with a distance from the core greater than threshold B and a self-screening effect greater than threshold D, they are divided based on the second-level three-dimensional burnup zone grid division method;

[0067] Among them, the grid sparsity level divided by the first-level three-dimensional burnup zone grid division method is less than that of the second-level three-dimensional burnup zone grid division method, and the grid sparsity level divided by the second-level three-dimensional burnup zone grid division method is less than that of the third-level three-dimensional burnup zone grid division method.

[0068] First, burnup zones are set for the entire core. Different granularities are used for burnup grid division in different burnable zones within the reactor. A three-dimensional heterogeneous burnup zone grid division method based on the neutron physics characteristics of materials is adopted according to the strength of the self-shielding effect of burnable materials. For the fuel irradiation test channels, the most refined three-dimensional burnup grid division is used to identify the position of the maximum burnup. For the fuel elements in the large reactor core, a relatively refined three-dimensional burnup grid division is used to obtain a more refined fuel burnup distribution. For the in-core burnable poisons, a relatively sparse three-dimensional burnup grid division is used for the in-core components far from the core with weak self-shielding effect and small neutron absorption, while a relatively refined three-dimensional burnup grid division is used for the burnable poisons close to the core or with strong self-shielding effect, which can improve the calculation efficiency on the premise of ensuring that the calculation accuracy meets the requirements. The traditional burnup zone grid division only targets the fuel and burnable poisons, without considering the burnup of the reflector beryllium blocks and the follower beryllium blocks. An axial burnup grid dynamic following method is adopted for the beryllium followers, and the burnup grid division is relatively refined. Since its position in the core is axially dynamically changing throughout the cycle, the movement of the control rod position is simulated based on the real movement of the geometry at different burnup steps. During this process, the number and size of the burnup grids remain unchanged, and the grid positions and materials change with the movement of the geometry. The above considerations are beneficial to improving the accuracy of burnup calculations. The traditional commercial pressurized water reactors usually use the same axial and radial burnup grid divisions for the same burnable materials. Since the irradiation test needs to distinguish the position of the maximum burnup, the sampling area for burnup measurement is usually small. Therefore, different burnup grid divisions need to be used for the areas with larger burnup for the same burnable materials to match the burnup measurement area.

[0069] III. Monte Carlo full-core refueling: During the cycle of the full-core model, the replacement of all in-core components in the full-core model is achieved by exchanging the positions of the corresponding spatial numbers in the repeated geometric grid;

[0070] During the cycle of the full-core model, the replacement of all in-core components in the full-core model is achieved by exchanging the positions of the corresponding spatial numbers in the repeated geometric grid, including the method:

[0071] (1) A unique spatial number and a unique lattice cell number are defined for all burnable regions in the core. For fuel elements, each time a fuel element moves, its position in the core grid changes. When the total number of fuel elements in the core remains unchanged, the number of spent fuel elements leaving the core is the same as the number of new fuel elements entering the core. First, delete the material information corresponding to the lattice cells of the spent fuel elements leaving the core, then assign the same initial material of the new fuel to the lattice cells corresponding to the spent fuel elements leaving the core, and then move the spatial number corresponding to the fuel element to a specific position in the repeating geometric grid. If the number of fuel elements in the core changes, if the number of fuel elements decreases, delete the corresponding space, lattice cells, and material information in the repeating geometric grid; if the number of fuel elements increases, add the corresponding space, lattice cells, and initial material information of the new fuel in the repeating geometric grid. During the refueling process, the lattice cells and material information corresponding to the spent fuel elements are stored separately, and the spent fuel elements discharged in the previous cycle can be reused later. For burnable burnable poisons and beryllium blocks, if the quantity increases, the corresponding space and material are increased; conversely, if it decreases, the refueling method is the same as that of fuel elements.

[0072] (2) For other in-core components such as non-burnable stainless steel blocks and aluminum blocks, the same in-core components are assigned the same spatial number, and the corresponding lattice cell numbers and material information in the space are also the same. First, exchange the positions of the spatial numbers in the repeating geometric grid of the core to complete the refueling of the in-core components. If the number of in-core components increases, modify the corresponding position in the repeating geometric grid of the core to the spatial number corresponding to the in-core component; if the number of in-core components decreases, delete the spatial number corresponding to the in-core component at the corresponding position in the repeating geometric grid of the core.

[0073] The multi-cycle burnup tracking calculation includes the following method: The burnup equation is the conservation equation of the quantity of various nuclides. The change in the nuclide concentration in the reactor material is generally described by the Bateman equation, which belongs to a system of first-order ordinary differential equations. The nuclide burnup equation is shown in Formula 1.1, where N i is the content of nuclide i, b j,i is the branching ratio from nuclide i to nuclide j, λ j is the decay constant of nuclide j, φ is the neutron flux, σ j,k is the microscopic cross-section of the k reaction channel of nuclide j, γ j,i,k is the fraction of nuclide i generated after nuclide j passes through the k reaction channel, including fission reactions and non-fission reactions.

[0074]

[0075] The Chebyshev Rational Approximation Method (CRAM) is selected for the burnup calculation. The advantages of CRAM are good numerical stability, accurate calculation results, high calculation efficiency. The calculation accuracy is only related to the order k of the CRAM coefficients. There is a linear relationship between the calculation time and the accuracy. It is a very good method for solving large burnup equations. CRAM avoids problems such as cyclic chains in the burnup chain that the linear sub-chain method (TTA) may encounter, and directly performs numerical solution, reducing the introduction of truncation errors.

[0076] The predictor-corrector method is selected for the burnup step strategy. In the first step (prediction step), a full-step burnup calculation is performed to obtain the predicted nuclide density, and a transport calculation is performed to obtain corresponding parameters such as flux and cross-section. In the second step (correction step), the entire burnup step length is recalculated using the new flux and cross-section and other parameters to obtain the corrected nuclide density. Finally, the average value of the predicted value and the corrected value of the nuclide density is taken.

[0077] The multi-cycle burnup tracking calculation also includes the method: the actual rod positions during the real operation of the reactor are used in different burnup steps, and the total power density (W / gU) of each burnup step is obtained by dividing the actual operating power by the total initial fuel mass. To calculate the total initial fuel mass and power distribution, the correct volume needs to be specified for the burnup lattice cell.

[0078] The poisons include: 135 Xe, 149 Sm and 3 He.

[0079] The full-core refueling of a research reactor is quite different from that of a commercial pressurized water reactor. Firstly, the core loading is complex and variable. There are many types of in-core components, and different types of in-core components can be flexibly placed at any position in the core. Secondly, the core is frequently started and stopped, and the refueling cycle is about 1 month, which is significantly shorter than that of a commercial pressurized water reactor. Thirdly, the irradiated samples in the core change flexibly, and some irradiated samples in the channels can enter and exit online. Fourthly, the steps of a single refueling are cumbersome (hundreds of steps). At present, there is no Monte Carlo refueling method for high-flux research reactors in China. This study adopted a refueling method that only adjusts the spatial numbers and corresponding materials, and for the first time in China, realized the Monte Carlo simulation of the actual refueling process of a high-flux research reactor, which is the basis for achieving high-precision Monte Carlo multi-cycle calculations. Due to insufficient reactivity at the end of the research reactor cycle, refueling operations are required. A batch of fuel elements often need to go through multiple cycles in the research reactor before being discharged, and the fuel and material irradiation tests in the research reactor often need to go through more than a dozen cycles. The refueling process includes the removal of old elements from the core, the insertion of new elements into the core, and the rearrangement of in-core components. For all burnable zones in the core, a unique spatial number and a unique lattice cell number are defined. Taking the entry and exit of fuel elements from the core as an example, when a fuel element moves once, its position in the core grid changes once. Since the total number of fuel elements in the core remains basically unchanged, the number of old fuel elements removed from the core is the same as the number of new fuel elements inserted into the core. First, the materials corresponding to the old fuel elements are deleted, then the materials corresponding to the new fuel elements are replaced, and then the new fuel elements are moved to specific positions. For the burnable poisons in the core, since the quantity is not fixed, when the quantity of burnable poisons increases, the corresponding space and materials are increased, and vice versa. All rearrangements of in-core components are achieved by exchanging the positions of the corresponding spatial numbers in the repeated geometric grid, realizing the built-in refueling based on the one-to-one mapping relationship of "core - space - lattice cell - burnup - material".

[0080] IV. Multi-cycle burnup tracking calculation: Consider the burnup of control rods and beryllium to perform the burnup tracking calculation for each cycle. Consider the accumulation of poisons during the shutdown decay process. After each cycle ends, calculate the poison distribution in the next cycle with the lowest reactor power and all control rods fully inserted. After the Monte Carlo full-core refueling, perform the burnup tracking calculation for the next cycle.

[0081] Based on the actual power and critical rod position history at different burnup steps of a high-flux research reactor, specify all burnable lattice cells (in traditional calculations, the burnup of control rods and beryllium is not considered. In this study, for control rods: the structure is absorber (Ag-In-Cd / Co) + transition section (stainless steel) + follower (Be / Al), considering the burnup of control rods and beryllium. And input the time step (days), total power density (W / gHM), and actual critical rod position at each burnup step to perform the single-cycle burnup tracking calculation. Consider the 135 Xe 149 Sm 3For the accumulation of poisons such as He, at the end of each cycle, the full-core burnup calculation is carried out with extremely low power and all control rods fully inserted to obtain the poison distribution at the beginning of the next cycle. Then, the full-core refueling operation based on the Monte Carlo method is carried out, and the burnup calculation of the next cycle is carried out. Based on the above steps, the multi-cycle burnup tracking calculation of the research reactor is realized.

[0082] Since the neutron energy spectrum of the high-flux research reactor changes frequently with the dynamic changes of control rods and fuel burnup, and the reaction rates, single-group neutron fluxes in individual burnup zones, and single-group equivalent cross-sections of various nuclides statistically calculated in the burnup calculation also change frequently, the predictor-corrector method is selected as the burnup step strategy in the burnup calculation process, which has the characteristics of good accuracy and strong inclusiveness of burnup step sizes; the Chebyshev rational approximation method is selected as the solution method for the burnup equation, which has the advantages of fast calculation speed and high accuracy because it does not need to separately process short-lived nuclides. And for the operation characteristics of the high-flux research reactor, that is, one furnace section operates for about one month, the burnup calculation is divided into 8 - 10 burnup steps, and for the characteristics of its pure rod-controlled core, the dynamic changes of the control rod positions during operation are finely simulated. Finally, based on the above calculation strategy, the high-precision calculation of multi-cycle burnup is realized, and the subsequent calculation results are compared with the measured values, and the results show good agreement.

[0083] Example 2

[0084] This example provides a burnup tracking calculation system for multi-cycle fuel management to implement the above method, including:

[0085] The first-cycle core modeling module is used to divide the burnup zone units and number the spaces of the reactor internal components to construct a full-core model;

[0086] The burnup zone grid division module is used to set the burnup zones for the full-core model, perform geometric grid division on each burnup zone unit, and cycle through the full-core model;

[0087] The Monte Carlo full-core refueling module is used to make all the reactor internal components in the full-core model change positions during the cycle of the full-core model by exchanging their positions in the repeated geometric grids corresponding to the space numbers;

[0088] The multi-cycle burnup tracking calculation module is used to perform burnup tracking calculations for each cycle considering control rod burnup and beryllium burnup, consider the accumulation of poisons during the shutdown decay process, calculate the poison distribution of the next cycle with the lowest power of the reactor and all control rods fully inserted at the end of each cycle, and perform the burnup tracking calculation of the next cycle after the Monte Carlo full-core refueling.

[0089] Example 3

[0090] This embodiment provides a computer-readable medium with a computer program stored thereon. When the computer program is executed by a processor, it can implement a burnup tracking calculation method for multi-cycle fuel management as described in Embodiment 1.

[0091] Embodiment 4

[0092] Specific examples are given in this embodiment:

[0093] As Figure 2 shown, the multi-cycle burnup tracking calculation process of a research reactor includes four main modules: initial cycle core modeling, initial cycle burnup tracking calculation, full-core refueling, and multi-cycle burnup tracking calculation. The following takes the multi-cycle burnup tracking calculation of the High Flux Engineering Test Reactor (HFETR) as an example application object for description:

[0094] Initial cycle core modeling (Step A):

[0095] Step A01: According to the example embodiment, based on the Monte Carlo three-dimensional particle transport-burnup coupling program (such as: RMC software package, not limited to this, as long as it is a program method that meets the requirements), a refined Monte Carlo model (including geometry and materials) of new in-core components (including but not limited to fuel elements, burnable poison targets, control rods, beryllium blocks, aluminum blocks, stainless steel blocks) is established using hierarchical modeling.

[0096] Step A02: According to the example embodiment, the spatial numbers of different in-core components are filled into the corresponding positions of the hexagonal repeating structure grid according to the initial cycle core loading. For burnable fuel elements, burnable poison targets, control rods, and beryllium blocks: The spatial number range of fuel elements is 20-99 (for example, 80 boxes of fuel elements, and the quantity can be modified according to the actual core loading). The spatial number range of burnable poison targets is 100-150 (for example, 50 boxes of burnable poison targets, and the quantity can be modified according to the actual core loading). Since the position of the control rod in the reactor remains unchanged, the control rod spatial numbers are defined as 6 (manual rods 3, 6 rod groups), 7 (safety rods 1, 2 rod groups), 8 (manual rods 1, 2 rod groups), 10 (manual rods 4, 7 rod groups), 11 (manual rods 5, 8 rod groups), 15 (automatic rod 1), 12 (automatic rod 2), 13 (manual rods 10, 11 rod groups), 13 (manual rods 13, 14 rod groups), 16 (manual rods 9, 12 rod groups), and filled into the corresponding positions in the core loading grid. The absorber material is Ag-In-Cd / Co, the transition section material is stainless steel, and the follower material is Be / Al. The position and material of the control rod can be modified according to the actual core loading. The spatial number of beryllium blocks is defined as 150-230 (for example, 80 boxes of beryllium blocks, and the quantity can be modified according to the actual core loading). For non-burnable aluminum blocks and stainless steel blocks: The same spatial numbers are defined in the actual core loading (aluminum block: 4, stainless steel block: 9), and the quantity can be modified according to the actual core loading.

[0097] Step A03: According to the exemplary embodiment, for the fuel and material irradiation channels in the reactor core, since their geometric sizes do not match the hexagonal repetitive structure grid, during the first cycle core loading, they are separated from the bottom grid elements according to their positions and sizes in the hexagonal repetitive structure grid, and Monte Carlo refined modeling (including geometry and materials) of the fuel and material irradiation test device is carried out. After filling the corresponding spaces (space numbers are 6, 7, 8, 9), they are backfilled into the bottom grid elements.

[0098] Burnup zone grid division (Step B):

[0099] Step B01: According to the exemplary embodiment, burnup grids are divided for the burnable fuel elements, burnable poison targets, control rods, and beryllium blocks. The fuel element is geometrically divided into 10 layers axially and 6 layers radially (a total of 4800 burnup zones). The burnable poison target near the reactor core is geometrically divided into 5 layers axially and 4 layers radially, and the burnable poison target far from the reactor core is geometrically divided into 5 layers axially and 2 layers radially (a total of 750 burnup zones). The control rod absorber is geometrically divided into 5 layers axially and 2 layers radially (a total of 180 burnup zones), the control rod follower is geometrically divided into 5 layers axially and 4 layers radially (a total of 360 burnup zones), and the beryllium block is geometrically divided into 5 layers axially and 2 layers radially (a total of 180 burnup zones). Taking a certain fuel irradiation test piece as an example, its burnable zone is geometrically divided into 20 layers axially and 4 layers radially (a total of 1600 burnup zones). Then, the corresponding grid numbers of all burnup zones are classified and filled into the burnup calculation module.

[0100] Full core refueling (Step C):

[0101] Step C01: According to the exemplary embodiment, first, prepare the continuous calculation file at the end of the first cycle life. Then, extract the number and position information of the reactor and in-core components from the loading scheme. Table 1 shows the operation table of fuel element in and out of the reactor. Among them, D06 represents the position of the fuel element in the hexagonal repetitive structure grid of the first cycle core (X direction is 1 - 21, Y direction is A - V). If the number of in-core elements is equal to the number of out-core elements, first delete the corresponding materials of the old fuel elements (such as D06) in the core repetitive structure grid, then replace the corresponding materials of the new fuel elements, and then move the new fuel elements to a specific position in the core repetitive structure grid (such as F08). If the number of in-core elements is greater than the number of out-core elements, increase the space number (such as 231) and corresponding geometry and materials of the fuel element, and add them to a specific position in the core repetitive structure grid. If the number of in-core elements is less than the number of out-core elements, delete the space number and corresponding geometry and materials of the fuel element in the core repetitive structure grid. The in and out of the reactor operations of other burnable in-core components such as burnable poison targets and beryllium blocks are the same as those of fuel elements.

[0102] Table 1 Operation table of fuel element in and out of the reactor

[0103]

[0104] Step C02: According to the exemplary embodiment, as shown in Table 2 (partial) of the in-pile transposition operation table, first classify the initial positions of the in-pile components that have not been taken out of the pile according to different in-pile components, extract and organize the first-cycle position, the second-cycle position, and the spatial number of the in-pile component in the first cycle respectively. Taking D06→P16 as an example, move the spatial number at the D06 position of the core repetitive structure grid to P16 for replacement, that is, the transposition of all in-pile components is realized by moving the position of the spatial number in the core repetitive structure grid.

[0105] Table 2 (partial) In-pile transposition operation table

[0106] First cycle position Second cycle position First cycle space number First cycle position Second cycle position First cycle space number D06 P16 75 E07 L12 50 D07 P11 64 E09 D07 41 D08 S14 85 F04 M08 86 E05 F07 93 F05 L09 97 E06 F09 33 F06 E09 81

[0107] Step C03: According to the exemplary embodiment, for the parts separated from the core repetitive structure grid in the pile, such as the fuel and material irradiation test pieces in the pile, restore them from the bottom grid elements according to the position and size of the out-of-pile irradiation test pieces in the hexagonal repetitive structure grid, and no longer correspond to the grid elements of the non-irradiation test pieces, that is, realize the out-of-pile of the irradiation test pieces.

[0108] Multi-cycle burnup tracking calculation (Step D):

[0109] Step D01: According to the exemplary embodiment, divide the steady-state operation power (80 MW) of the first cycle by the total mass of the fuel (125.81 Kg) to obtain the power density (W / gHM) of different burnup steps. Based on the burnup step division situation (which can be flexibly changed), divide the segmented integrated power of different burnup steps by the steady-state operation power to obtain the time step (days) of each burnup step, and then fill in the corresponding inputs into the burnup calculation module.

[0110] Step D02: According to the exemplary embodiment, before each burnup step calculation, change the position of the control rod by modifying the relevant surfaces of different control rod group geometries, input the actual critical rod positions corresponding to different burnup steps into the burnup calculation module of the input file, and complete the change of the control rod position at the end of each burnup calculation. The burnup step strategy uses the predictor-corrector method, and the ignition burnup equation solving method uses the Chebyshev rational approximation method.

[0111] As shown in Table 3, the core k of the HFETR (High Flux Engineering Test Reactor) in the first cycle using the actual operating rod positions in different burnup steps eff Calculation results show that the reactivity calculation deviation is less than 700 pcm, verifying the accuracy of the first-cycle core modeling and burnup tracking calculation.

[0112] Table 3 Core k of the HFETR in the first cycle using the actual operating rod positions in different burnup steps eff Calculation results

[0113]

[0114] Step D03: According to the exemplary embodiment, after completing the full-core refueling module, all control rods are inserted into the core and then the shutdown decay calculation is carried out according to the actual decay time (e.g., 7 days). At this time, the power density (W / gHM) is set to extremely low (set to 0.01 in this example, which can be modified according to the shutdown decay power of different cores), and then the single-cycle tracking calculation for the next cycle is carried out. This cycle repeats, and a total of ten cycles are calculated. As shown in Table 4, the core k of HFETR (High Flux Engineering Test Reactor) for multi-cycle different burnup steps using the actual operating rod positions eff Calculation results show that the reactivity calculation deviations are all less than 1000 pcm, verifying the accuracy of the full-core refueling method and the multi-cycle burnup tracking calculation.

[0115] Step D04: According to the exemplary embodiment, as shown in Table 5, the comparison results of the multi-cycle burnup tracking calculation values and the measured values of a certain fuel irradiation test piece show that the relative deviations between the burnup calculation values and the measured values of different burnup measurement points are all less than 4%.

[0116] Table 4 Core k of HFETR for multi-cycle different burnup steps using the actual operating rod positions eff Calculation results

[0117]

[0118]

[0119] Table 5 Comparison of multi-cycle burnup tracking calculation values and measured values of a certain fuel irradiation test piece

[0120] Sampling position Relative deviation A -2.58％ B 2.49％ C -3.60％

[0121] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A burnup tracking calculation method for multi-cycle fuel management, characterized in that, Including: Initial cycle core modeling: Divide the in-core components into burnup zones and number them spatially to construct a full-core model; Burnup zone mesh generation: Set up burnup zones for the full-core model and perform geometric mesh generation for each burnup zone unit, and run the full-core model in a loop; Monte Carlo full-core refueling: During the loop process of the full-core model, the transposition of all in-core components in the full-core model is achieved by exchanging their positions corresponding to the spatial numbers in the repeated geometric mesh; specifically including: for fuel elements, each time it moves, the position of the spatial number in the core mesh is changed; If the total number of fuel elements in the reactor remains unchanged, at this time the number of spent fuel elements leaving the reactor is the same as the number of new fuel elements entering the reactor. First, delete the material information corresponding to the spent fuel element cells leaving the reactor, then assign the same initial material of the new fuel to the cells corresponding to the spent fuel elements leaving the reactor, and then move the spatial number corresponding to this fuel element to a specific position in the repeated geometric mesh; if the number of fuel elements in the reactor changes, if the number of fuel elements decreases, delete the corresponding spaces and the corresponding cells and material information in the spaces in the repeated geometric mesh, and if the number of fuel elements increases, add the corresponding spaces and the corresponding cells and initial new fuel material information in the spaces in the repeated geometric mesh Multi-cycle burnup tracking calculation: Consider the burnup of control rods and beryllium for burnup tracking calculation in each cycle, consider the accumulation of poisons during the shutdown decay process, and calculate the poison distribution in the next cycle with the lowest power of the reactor and all control rods fully inserted at the end of each cycle. After the Monte Carlo full-core refueling, perform the burnup tracking calculation for the next cycle.

2. The burnup tracking calculation method for multi-cycle fuel management according to claim 1, wherein, The method of dividing the in-core components into burnup zones and numbering them includes: Divide the in-core components into burnable units and non-burnable units; Perform spatial division and spatial numbering for the burnable units and non-burnable units: For each component in the burnable units, expand it into an independent burnup zone, and assign different spatial numbers to all independent burnup zones; After expanding each component in the non-burnable units into spaces, assign the same spatial number to all spaces.

3. A burnup tracking calculation method for multi-cycle fuel management according to claim 2, characterized in that, The burnable units include: fuel elements, burnable poisons, reflector beryllium blocks, aluminum blocks, stainless steel blocks, and control rod beryllium followers.

4. A burnup tracking calculation method for multi-cycle fuel management according to claim 3, characterized in that The method of performing geometric mesh generation for each burnup zone unit includes: Perform geometric mesh generation for each burnup zone unit based on the core properties, component self-properties, and the distance of the component from the core: For fuel irradiation test channels, divide them based on the first-level three-dimensional burnup zone mesh generation method; For components in core a, and when the size of core a exceeds threshold A, divide them based on the second-level three-dimensional burnup zone mesh generation method; For components in the reactor with a distance from the core greater than threshold A, and with a self-shielding effect less than threshold B and a neutron absorption rate less than threshold C, divide them based on the third-level three-dimensional burnup zone mesh generation method; For burnable poisons with a distance from the core greater than threshold B and a self-shielding effect greater than threshold D, divide them based on the second-level three-dimensional burnup zone mesh generation method; Among them, the grid sparsity level of the grid division method for the first-level three-dimensional burnup zone is less than that of the grid division method for the second-level three-dimensional burnup zone, and the grid sparsity level of the grid division method for the second-level three-dimensional burnup zone is less than that of the grid division method for the third-level three-dimensional burnup zone.

5. A burnup tracking calculation method for multi-cycle fuel management according to claim 1, characterized in that The multi-cycle burnup tracking calculation includes the following methods: There is a quantity conservation equation for nuclide i and nuclide j: Among them, N j is the content of nuclide j, N i is the content of nuclide i, b j，i is the branching ratio from nuclide i to nuclide j, is the decay constant of nuclide j, is the neutron flux, is the microscopic cross section of the k reaction channel of nuclide j, is the fraction of nuclide i generated after nuclide j passes through the k reaction channel.

6. A burnup tracking calculation method for multi-cycle fuel management according to claim 5, characterized in that The multi-cycle burnup tracking calculation also includes the following methods: During different burnup steps, the actual rod positions during the real operation of the reactor are used, and the total power density of each burnup step is obtained by dividing the actual operating power by the total initial fuel mass of the burnup step. To calculate the total initial fuel mass and power distribution, the correct volume needs to be specified for the burnup lattice cell.

7. A burnup tracking calculation method for multi-cycle fuel management according to claim 1, characterized in that The poisons include: 135 Xe, 149 Sm, and 3 He.

8. A burnup tracking calculation system for multi-cycle fuel management, characterized in that, A burnup tracking calculation method for multi-cycle fuel management according to any one of claims 1-7, includes: A first-cycle core modeling module, which is used to divide the burnup zone units and perform spatial numbering on the reactor internal components to construct a full-core model; A burnup zone grid division module, which is used to set the burnup zones for the full-core model and perform geometric grid division on each burnup zone unit, and cycle the full-core model; A Monte Carlo full-core refueling module, which is used to, during the cycle of the full-core model, make all the reactor internal components in the full-core model change positions by exchanging the positions of the corresponding spatial numbers in the repeated geometric grids; A multi-cycle burnup tracking calculation module, which is used to perform burnup tracking calculations for each cycle considering control rod burnup and beryllium burnup, consider the accumulation of poisons during the shutdown decay process, calculate the poison distribution for the next cycle with the lowest power of the reactor and all control rods fully inserted at the end of each cycle, and perform burnup tracking calculations for the next cycle after the Monte Carlo full-core refueling.

9. A computer-readable medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it can implement a burnup tracking calculation method for multi-cycle fuel management according to any one of claims 1-7.

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