A method, apparatus, electronic device, and storage medium for calculating fuel sphere fuel consumption.

Abstract

This application discloses a method, apparatus, electronic device, and storage medium for calculating fuel sphere burnup, relating to the field of nuclear reactor physics and thermal calculation technology. The method includes: dividing fuel spheres into multiple batches based on their distribution; establishing neutron transport equations for each batch of fuel spheres; calculating the self-shielding factor of each batch of fuel spheres; calculating the neutron flux density of each region of the reactor core using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector layer region; calculating the power density of each region of the pebble bed based on the neutron flux density of each region of the reactor core; calculating the neutron flux density and power density of each batch of fuel spheres at the current reactor core power level based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel spheres; and calculating the burnup depth of the corresponding batch of fuel spheres based on the power density of each batch of fuel spheres at the current reactor core power level, thereby improving the technical accuracy of fuel sphere burnup calculation in non-uniformly packed pebble bed reactors.

Description

Technical Field

[0001] This application relates to the field of nuclear reactor physics and thermal calculation technology, and in particular to a method, apparatus, electronic device and storage medium for calculating fuel sphere burnup. Background Technology

[0002] Pebble bed high-temperature gas-cooled reactors feature a "continuous refueling, multiple-pass" fuel cycle. Their core employs a hybrid pebble bed structure with randomly distributed fuel spheres. In some scenarios, a hybrid fuel sphere cycle, such as thorium-uranium or thorium-plutonium, is also used. Burnup depth is a core parameter for reactor physics design, fuel management, and safety assessment. Accurate calculation of fuel sphere burnup depth is crucial for ensuring the safety and economic efficiency of reactor operation.

[0003] In related technologies, fuel sphere burnup calculations primarily rely on traditional core physics calculation programs, typically employing whole-core homogenization or average sphere models. These methods generally treat the fuel spheres within the sphere bed region as a homogeneous whole, failing to differentiate batches based on distribution characteristics and cycle counts. This results in an inability to distinguish neutron flux density and energy spectrum differences between batches, forcing the approximation of uniform neutron flux and microscopic single-group cross-sections for burnup calculations, which fails to reflect the actual irradiation state of different batches. Furthermore, as strong neutron absorbers, fuel spheres exhibit significant spatial self-shielding effects, with the outer fuel cores shielding the inner ones, causing uneven neutron flux density distribution between the inner and outer layers. Related technologies often ignore this effect, directly using uniform neutron flux parameters for calculations, leading to significant deviations between the actual neutron flux density and reality.

[0004] In the core neutron transport and diffusion calculation phase, while related technologies employ homogenized cross-sections in the pebble bed and reflector regions for whole-core diffusion calculations, they fail to effectively bridge the gap between overall core homogenization calculations and local fuel sphere calculations. Due to the lack of consideration for individual differences among batches of fuel spheres, the neutron flux density across different core regions is difficult to accurately allocate to individual batches, leading to inaccurate power density calculations in the pebble bed region and ultimately affecting the accuracy of burnup depth calculations. This is particularly problematic in mixed-fuel pebble bed scenarios, where different types of fuel spheres may employ different loading strategies. The inability to specifically address these differences further exacerbates errors in burnup calculations. Summary of the Invention

[0005] This application provides a method, apparatus, electronic device, and storage medium for calculating fuel pellet burnup. It addresses the problem in related technologies where the distribution differences and self-shielding effects of different fuel pellets in the mixed pellet bed region are not considered, and the reactor core is treated as a homogeneous medium or the fuel pellets are roughly partitioned, resulting in insufficient accuracy in distinguishing the power density differences between batches of fuel pellets and thus insufficient burnup calculation precision.

[0006] According to a first aspect of this application, a method for calculating the fuel consumption of a fuel sphere is provided, comprising: In the mixed sphere bed region, the fuel spheres are divided into multiple batches according to their distribution. Neutron transport equations are established for each batch of fuel spheres, and the self-shielding factor of each batch of fuel spheres is calculated. The neutron diffusion in the reactor core is calculated using the homogenized cross sections of the pebble bed region and the reflector region to obtain the neutron flux density in each region of the reactor core. The power density in each region of the pebble bed is then calculated based on the neutron flux density in each region of the reactor core. Based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel spheres, calculate the neutron flux density and power density of each batch of fuel spheres at the current core power level. Based on the power density of each batch of fuel pellets at the current core power level, calculate the burn-up depth of the corresponding batch of fuel pellets.

[0007] According to a second aspect of this application, a fuel pellet fuel consumption calculation device is provided, comprising: The first calculation module is configured to divide the fuel balls into multiple batches according to the distribution of the fuel balls in the mixed sphere bed region, establish neutron transport equations for each batch of fuel balls, and calculate the self-shielding factor of each batch of fuel balls. The second calculation module is configured to perform core neutron diffusion calculations using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to obtain the neutron flux density of each region of the core, and calculate the power density of each region of the pebble bed based on the neutron flux density of each region of the core. The third calculation module is configured to calculate the neutron flux density and power density of each batch of fuel balls at the current core power level, based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel balls. The fourth calculation module is configured to calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls at the current core power level.

[0008] According to a third aspect of this application, an electronic device is provided, comprising: At least one processor; and memory that is communicatively connected to at least one processor; The memory stores instructions that can be executed by at least one processor, which are executed by at least one processor to enable the at least one processor to perform the fuel ball fuel consumption calculation method of the first aspect described above.

[0009] According to a fourth aspect of this application, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to cause a computer to execute the fuel ball fuel consumption calculation method of the first aspect described above.

[0010] According to a fifth aspect of this application, a computer program product is provided, including a computer program that, when executed by a processor, implements the fuel ball fuel consumption calculation method as described in the first aspect above.

[0011] This application provides a method, apparatus, electronic device, and storage medium for calculating fuel pellet burnup, comprising: dividing fuel pellets into multiple batches according to their distribution in a mixed pellet bed region; establishing neutron transport equations for each batch of fuel pellets; calculating the self-shielding factor of each batch of fuel pellets; performing core neutron diffusion calculations using the homogenized cross section of the pellet bed region and the homogenized cross section of the reflector layer region to obtain the neutron flux density of each region of the core; calculating the power density of each region of the pellet bed based on the neutron flux density of each region of the core; calculating the neutron flux density and power density of each batch of fuel pellets at the current core power level based on the neutron flux density of the pellet bed region and the self-shielding factor of each batch of fuel pellets; and calculating the burnup depth of the corresponding batch of fuel pellets based on the power density of each batch of fuel pellets at the current core power level. This application addresses the problem in related technologies where the fuel spheres are divided into multiple batches based on their distribution. Neutron transport equations are established for each batch to calculate the self-shielding factor. The homogenization cross-section of the pebble bed region and the reflector region is combined to perform core neutron diffusion calculations, obtaining the neutron flux density in each core region and the power density in each pebble bed region. Based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel spheres, the neutron flux density and power density of each batch of fuel spheres at the current core power level are obtained. Finally, the burnup depth is calculated based on the power density of each batch of fuel spheres. Therefore, this approach solves the problem of insufficient burnup calculation accuracy in related technologies where the distribution differences and self-shielding effects of different fuel spheres in the mixed pebble bed region are not considered. The core is treated as a homogeneous medium, or the fuel spheres are roughly partitioned, resulting in an inability to accurately distinguish the power density differences between batches of fuel spheres. This achieves the technical effect of improving the burnup calculation accuracy of fuel spheres in non-uniformly packed pebble bed reactors.

[0012] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent from the following description. Attached Figure Description

[0013] To more clearly illustrate the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1A flowchart illustrating a fuel ball fuel consumption calculation method provided in an embodiment of this application; Figure 2 This is a flowchart illustrating another method for calculating fuel ball fuel consumption provided in an embodiment of this application; Figure 3 This is a flowchart illustrating another method for calculating fuel ball fuel consumption provided in an embodiment of this application; Figure 4 This is a schematic diagram of the structure of a fuel ball fuel consumption calculation device provided in an embodiment of this application. Detailed Implementation

[0015] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0016] The following description, with reference to the accompanying drawings, describes a fuel ball fuel consumption calculation method, apparatus, electronic device, and storage medium according to embodiments of this application.

[0017] Figure 1 This is a flowchart illustrating a method for calculating fuel consumption of a fuel ball, as provided in an embodiment of this application.

[0018] like Figure 1 As shown, the method includes the following steps: Step 101: In the mixed sphere bed region, the fuel spheres are divided into multiple batches according to their distribution. Neutron transport equations are established for each batch of fuel spheres, and the self-shielding factor of each batch of fuel spheres is calculated.

[0019] In some embodiments, during the burnup calculation of a non-uniformly packed pebble bed reactor, the mixed pebble bed region is the core region where fuel spheres are concentrated and nuclear reactions occur. Fuel spheres within this region exhibit different physical properties and reaction potentials due to differences in enrichment during production and the number of times they pass through the reactor core. To accurately distinguish the differences in nuclear reactions among different fuel spheres, it is necessary to group fuel spheres with the same or similar enrichment and the same number of times they pass through the reactor core into the same batch, ensuring that each batch of fuel spheres possesses unified core physical characteristics, laying the foundation for subsequent targeted calculations. For each batch of fuel spheres after division, a neutron transport equation is established. This equation comprehensively describes a series of physical processes within the fuel spheres, including neutron generation, movement, collision, absorption, and leakage. Solving this equation accurately yields the neutron flux density of each batch of fuel spheres under different neutron energy groups, intuitively reflecting the distribution and movement patterns of neutrons in each batch of fuel spheres. Based on the neutron flux density of each batch of fuel spheres obtained from the solution, and combined with key parameters such as the bed filling rate, the volume fraction of each batch of fuel spheres in the region, and the neutron flux density in the voids of the bed region, the self-shielding factor of each batch of fuel spheres under the corresponding neutron energy group is further calculated. This factor can quantify the shielding effect of the fuel sphere itself on neutrons, reflecting the neutron shielding effect of the outer nuclides of the fuel sphere on the inner nuclides. This process accurately captures the individual differences between different batches of fuel spheres, providing accurate basic data for subsequent burnup calculations, effectively avoiding calculation deviations caused by ignoring fuel sphere differences, and improving the accuracy of burnup calculations.

[0020] Step 102: Calculate the neutron diffusion in the core using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to obtain the neutron flux density in each region of the core, and calculate the power density in each region of the pebble bed based on the neutron flux density in each region of the core.

[0021] In some embodiments, in fuel sphere burnup calculations, a precise characterization of the overall physical properties of the reactor core is fundamental for subsequent targeted calculations of batches of fuel spheres, while the homogenization cross-section is a core parameter describing the neutron transport characteristics of different regions within the reactor core. The homogenization cross-section of the pebble bed region is calculated by integrating key information such as the neutron flux density and volume fraction of each batch of fuel spheres and voids within this region. It comprehensively reflects the absorption, scattering, and fission effects of neutrons on the mixed pebble bed region. The homogenization cross-section of the reflector region corresponds to the neutron physical properties of the reactor core's reflector layer. Its function is to capture the reflection and confinement effects of the reflector layer on leaked neutrons within the reactor core, ensuring the integrity of the overall neutron transport calculation. By combining the homogenization cross-sections of these two regions, neutron diffusion calculations are performed within the reactor core. This calculation process can simulate the complete physical processes of neutron generation, movement, interaction, and leakage throughout the entire reactor core, thereby accurately obtaining the neutron flux density of each region of the reactor core—a parameter that directly reflects the intensity of neutron movement within each region and is a core indicator for quantifying the intensity of nuclear reactions. Based on the obtained neutron flux density in each region of the reactor core, combined with the fission energy production cross-section of each neutron energy group in the pebble bed region, and by comprehensively considering the efficiency differences in energy production from nuclear fission induced by neutrons in different energy groups, the power density in each region of the pebble bed can be accurately calculated. This power density directly reflects the power level generated by nuclear reactions per unit volume in different regions of the pebble bed. This process, by integrating the physical parameters of key regions of the reactor core, achieves precise coupling between the overall neutron transport law of the reactor core and the regional power distribution, providing reliable overall data support for subsequent detailed calculations focusing on each batch of fuel spheres. It effectively avoids subsequent calculation deviations caused by inaccurate characterization of the overall physical properties of the reactor core, laying a solid foundation for improving the accuracy of burnup calculations.

[0022] Step 103: Calculate the neutron flux density and power density of each batch of fuel balls at the current core power level based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel balls.

[0023] In some embodiments, the neutron flux density of the pebble bed region is a core parameter reflecting the overall intensity of neutron motion within that region. It is precisely obtained through core neutron diffusion calculations, providing an overall benchmark for subsequent detailed calculations of each batch of fuel spheres. The self-shielding factor of each batch of fuel spheres is a unique characteristic parameter specific to different batches, accurately quantifying the neutron shielding effect of each batch. This reflects the differences in neutron absorption and shielding capabilities among different batches due to variations in enrichment levels, number of times they pass through the core, and other factors. When calculating the neutron flux density of each batch of fuel spheres at the current core power level, the overall neutron flux density of the pebble bed region is used as a basis, combined with the self-shielding factor corresponding to each batch of fuel spheres for targeted correction. A larger self-shielding factor indicates a stronger neutron shielding effect of that batch of fuel spheres, resulting in a relatively lower actual neutron flux density participating in the nuclear reaction within it. This correction method overcomes the limitation of traditional methods that treat the neutron flux density of all fuel spheres in the region as uniform, accurately obtaining the actual neutron flux density of each batch of fuel spheres at the current power state. Based on this, and considering the fission energy production cross-section of each batch of fuel spheres (which is determined by core characteristics such as the enrichment of the fuel spheres, and naturally varies between batches), the power density of each batch of fuel spheres can be accurately calculated by integrating the neutron flux density under each neutron energy group with the corresponding fission energy production cross-section. This power density truly reflects the energy intensity produced by the core reaction per unit volume of each batch of fuel spheres at the current core power level. This process achieves a precise conversion from the overall physical parameters of the core region to the individual parameters of each batch of fuel spheres, effectively capturing the differences in nuclear reactions between different batches of fuel spheres. This provides crucial data support for the subsequent accurate calculation of burnup depth and significantly reduces calculation errors caused by neglecting batch differences.

[0024] Step 104: Calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls at the current core power level.

[0025] In some embodiments, burnup depth is a core indicator for measuring the degree of nuclear fuel consumption of fuel spheres during nuclear reactions. Its accurate calculation directly impacts reactor fuel cycle optimization, operational safety, and economic assessment. The power density of each batch of fuel spheres at the current core power level accurately reflects the intensity of nuclear fission reaction per unit volume of each batch and is a key basis for calculating burnup depth. Differences in power density between different batches of fuel spheres due to variations in enrichment, number of times they pass through the core, etc., directly lead to different nuclear fuel consumption rates. During the calculation, the time step corresponding to each burnup step must be considered. This time step clarifies the duration of each calculation stage, ensuring that the burnup depth calculation accurately corresponds to the actual operating period of the core. Simultaneously, the fuel loading mass of each batch of fuel spheres must be introduced. This parameter is the basis for quantifying the degree of fuel consumption and determines the total amount of fuel within the batch that can participate in the nuclear reaction. By combining the power density of each batch of fuel pellets with the corresponding time step, the total energy output of that batch of fuel pellets within a specific time period can be obtained. Combined with its fuel loading mass, the burnup depth of each batch of fuel pellets can be accurately calculated at each burnup step, enabling precise differentiation of the consumption levels of different batches. This process avoids the drawback of traditional methods that uniformly average fuel pellets with different characteristics, allowing burnup depth calculations to closely reflect the actual reaction states of each batch of fuel pellets. The significant benefit lies in the improved accuracy of burnup depth calculations, providing reliable data support for reactor fuel replacement timing judgment, fuel inventory management, and operational safety assessment.

[0026] Compared with related technologies, in this embodiment, fuel balls are divided into multiple batches according to their distribution in the mixed pebble bed region. Neutron transport equations are established for each batch of fuel balls, and the self-shielding factor of each batch is calculated. Core neutron diffusion calculations are performed using the homogenized cross-sections of the pebble bed region and the reflector region to obtain the neutron flux density of each region of the core. The power density of each region of the pebble bed is calculated based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls. The neutron flux density and power density of each batch of fuel balls at the current core power level are calculated based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls. Finally, the burnup depth of the corresponding batch of fuel balls is calculated based on the power density of each batch of fuel balls at the current core power level. This solves the problem in related technologies where the distribution differences and self-shielding effects of different fuel balls in the mixed pebble bed region are not considered, and the core is only treated as a homogeneous medium or the fuel balls are roughly partitioned, resulting in insufficient accuracy in distinguishing the power density differences of each batch of fuel balls and thus insufficient burnup calculation accuracy. This achieves the technical effect of improving the burnup calculation accuracy of fuel balls in non-uniformly packed pebble bed reactors.

[0027] Figure 2 A flowchart illustrating another fuel pellet fuel consumption calculation method provided in this application embodiment includes the following steps: Step 201: Based on the differences in fuel sphere enrichment and the number of times they flow through the reactor core, the fuel spheres in the mixed sphere bed region are divided into multiple batches.

[0028] In some embodiments, in the batch classification of fuel spheres in the mixed pebble bed region, enrichment and core passage number are the core key parameters determining the nuclear reaction characteristics of the fuel spheres. Enrichment refers to the mass percentage of fissile nuclides in the fuel sphere, directly affecting its ability and potential to participate in nuclear fission reactions. Fuel spheres with different enrichments exhibit significant differences in reaction intensity under the same irradiation conditions. Core passage number reflects the irradiation history of the fuel sphere; the more times a fuel sphere passes through the core, the higher the proportion of nuclear fuel consumed and the lower its remaining reaction potential. Based on these two key dimensions of difference, all fuel spheres in the mixed pebble bed region are classified and grouped. Fuel spheres with the same or similar enrichment and the same number of core passages are grouped into the same batch, ensuring that each batch of fuel spheres possesses uniform core physical characteristics and reaction basis. This classification method can accurately distinguish the essential differences between different fuel spheres, providing clear computational units for subsequent targeted neutron transport calculations and self-shielding factor solutions. It effectively avoids computational biases caused by the mixture of fuel sphere characteristics, laying a classification foundation for the accuracy of the entire burnup calculation.

[0029] Step 202: Establish a set of collision probability equations for each batch of fuel spheres based on the collision probability method, and solve the set of collision probability equations to obtain the neutron flux density of each batch of fuel spheres.

[0030] In some embodiments, the collision probability method is a mature approach suitable for neutron transport calculations in discrete media. Its core advantage lies in its ability to accurately describe the collision and migration patterns of neutrons between different media regions, perfectly suited to the physical scenario of alternating distribution of fuel spheres and voids in a hybrid pebble bed region. When establishing the collision probability equations for each batch of fuel spheres based on this method, it is necessary to fully consider the neutron migration paths and collision probabilities within each batch of fuel spheres, between different batches of fuel spheres, and between fuel spheres and pebble bed voids. The neutron flux density of each batch of fuel spheres and pebble bed voids under different neutron energy groups is used as the core solution variable of the equations. By quantifying the processes of neutron generation, collision, absorption, and leakage in each region, a complete system of equations is constructed. When simultaneously solving this collision probability equation system, it is necessary to combine the boundary conditions such as the geometry of the pebble bed and the physical parameters of the fuel spheres, and obtain the neutron flux density of each batch of fuel spheres under the corresponding neutron energy group through rigorous mathematical calculations. This process can accurately capture the distribution of neutrons in different batches of fuel spheres, providing accurate and reliable basic data for the subsequent calculation of the self-shielding factor, and avoiding the errors caused by the simplified processing of fuel sphere characteristics in traditional neutron transport calculations.

[0031] Step 203: Calculate the self-shielding factor of each batch of fuel balls based on the seed flux density.

[0032] In some embodiments, the self-shielding factor of each batch of fuel pellets is calculated based on the seed flux density. The formula for calculating the self-shielding factor is as follows:

[0033] Indicates the batch number of the fuel pellets. Indicates the neutron energy group number. This indicates the batch number of fuel pellets within the pellet bed area. This represents the self-shielding factor of the g-th energy group of the i-th batch of fuel spheres. Indicates the ball bed filling rate. This represents the volume fraction of the i-th batch of fuel pellets relative to all fuel pellets in the region. This represents the neutron flux density of the g-th energy group in the i-th batch of fuel spheres. This represents the neutron flux density of the g-th energy group in the spherical bed region void.

[0034] When calculating the self-shielding factor, the physical meaning and practical implications of each parameter are first clarified. The pebble bed filling rate characterizes the proportion of fuel spheres in the total volume within the pebble bed region, directly affecting the migration path of neutrons within the pebble bed. The volume fraction of the i-th batch of fuel spheres reflects the proportion of that batch of fuel spheres within the pebble bed region, serving as a key link between the overall characteristics of the region and the individual characteristics of the batch. The neutron flux density of the g-th energy group of the i-th batch of fuel spheres and the neutron flux density of the g-th energy group in the pebble bed region voids respectively reflect the intensity of neutron movement inside the fuel spheres and in the pebble bed voids. Combining these key parameters, an integrated calculation is performed using a specified formula. Essentially, the formula quantifies the neutron shielding effect of the outer nuclides of the fuel spheres on the inner nuclides by comparing the neutron flux densities of the batch of fuel spheres and the pebble bed voids, and then adjusting the weights of the filling rate and volume fraction, ultimately obtaining the self-shielding factor of the g-th energy group of the i-th batch of fuel spheres. The calculation process strictly follows the physical laws of neutron transport, ensuring that the self-shielding factor can accurately reflect the unique characteristics of each batch of fuel spheres. This provides a precise basis for subsequent correction of the actual neutron flux density of the fuel spheres and effectively avoids the calculation deviation of nuclear reaction intensity caused by ignoring the self-shielding effect.

[0035] Step 204: Calculate the homogenization cross section of the pebble bed region based on the neutron flux density and volume fraction of each component within the pebble bed region. Based on the homogenization cross section, and combined with the homogenization cross section of the reflector region calculated by the Monte Carlo particle transport calculation software NECP-MCX, complete the core neutron diffusion calculation to obtain the neutron flux density of each region of the core.

[0036] In some embodiments, the homogenization cross section of the pebble bed region is a key parameter comprehensively reflecting the neutron transport characteristics of the region, and its calculation relies on the core physical data of each component within the region. The components of the pebble bed region encompass the previously divided batches of fuel pellets and the voids within the region. The neutron flux density of each component is accurately obtained through previous neutron transport calculations, reflecting the intensity of neutron movement within different components. The volume fraction of each component clarifies the proportion of different components in the total volume of the pebble bed region, serving as an important weighting parameter for integrating the overall characteristics of the region. By combining the neutron flux density of each component with its corresponding volume fraction and performing weighted integration calculations, the homogenization cross section of the pebble bed region can be obtained. This cross section comprehensively characterizes the combined effects of neutron absorption, scattering, and fission on the pebble bed region. The homogenization cross section of the reflector layer region is obtained using Monte Carlo particle transport calculation software. The Monte Carlo method excels at simulating particle transport processes under complex geometries, accurately capturing the reflection and confinement characteristics of the reflector layer on leaked neutrons in the reactor core, ensuring the accuracy of the reflector layer homogenization cross section. By synergistically applying the homogenized cross sections of the pebble bed region and the reflector region, neutron diffusion calculations were performed on the reactor core. This calculation process fully considered the overall geometry of the core, the neutron physics characteristics of each region, and the generation, movement, collision, and leakage patterns of neutrons throughout the entire core, ultimately enabling the accurate acquisition of the neutron flux density in each region of the core. This process effectively fused the physical parameters of key regions of the core, providing reliable foundational data for subsequent calculations of the power density in the pebble bed region and ensuring the accuracy of the overall physical characteristics of the core.

[0037] Step 205: Calculate the power density of each region of the pebble bed based on the neutron flux density of each region of the reactor core.

[0038] In some embodiments, the power density of each region of the pebble bed is calculated based on the neutron flux density of each region of the reactor core, and the calculation formula is as follows:

[0039] Where P represents the power density of the spherical bed region, and G represents the number of neutron energy groups. This represents the cross section where the fission energy of the g-th energy group in the spherical bed region is generated. Let represent the neutron flux density of the g-th energy group in the sphere bed region.

[0040] The homogenization cross section of the pebble bed region is a key parameter comprehensively reflecting the neutron transport characteristics of this region, and its calculation relies on the core physical data of each component within the region. The components of the pebble bed region encompass the previously divided batches of fuel pellets and the voids within the region. The neutron flux density of each component is accurately obtained through previous neutron transport calculations, reflecting the intensity of neutron movement within different components. The volume fraction of each component clarifies the proportion of each component in the total volume of the pebble bed region, serving as an important weighting parameter for integrating the overall characteristics of the region. By combining the neutron flux density of each component with its corresponding volume fraction and performing weighted integration calculations, the homogenization cross section of the pebble bed region can be obtained. This cross section comprehensively characterizes the combined effects of neutron absorption, scattering, and fission on the pebble bed region. The homogenization cross section of the reflector layer region is obtained using Monte Carlo particle transport calculation software. The Monte Carlo method excels at simulating particle transport processes under complex geometries, accurately capturing the reflection and confinement characteristics of the reflector layer on leaked neutrons in the reactor core, ensuring the accuracy of the reflector layer homogenization cross section. By synergistically applying the homogenized cross sections of the pebble bed region and the reflector region, neutron diffusion calculations were performed on the reactor core. This calculation process fully considered the overall geometry of the core, the neutron physics characteristics of each region, and the generation, movement, collision, and leakage patterns of neutrons throughout the entire core, ultimately enabling the accurate acquisition of the neutron flux density in each region of the core. This process effectively fused the physical parameters of key regions of the core, providing reliable foundational data for subsequent calculations of the power density in the pebble bed region and ensuring the accuracy of the overall physical characteristics of the core.

[0041] Step 206: Calculate the neutron flux density of each batch of fuel balls at the current core power level based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls in the pebble bed region.

[0042] In some embodiments, the neutron flux density of each batch of fuel pellets at the current core power level is calculated based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel pellets in the pebble bed region. The formula for calculating the neutron flux density is as follows:

[0043] in, This represents the neutron flux density of the g-th energy group of the i-th batch of fuel spheres in the pebble bed region at the current core power level. This represents the neutron flux density of the g-th energy group in the sphere bed region. This represents the self-shielding factor of the g-th energy group of the i-th batch of fuel spheres. Indicates the ball bed filling rate. This represents the volume share of the i-th batch of fuel balls among all fuel balls in the region.

[0044] The calculation of neutron flux density for each batch of fuel pellets at the current core power level requires a precise correction based on the overall neutron flux density of the pebble bed region, combined with the specific characteristic parameters of each batch of fuel pellets. The neutron flux density of the g-th energy group in the pebble bed region is the baseline data reflecting the overall motion intensity of neutrons in that energy group within the region, accurately obtained from previous core neutron diffusion calculations. The self-shielding factor of the g-th energy group of the i-th batch of fuel pellets quantifies the shielding effect of that batch of fuel pellets on neutrons in that energy group, directly affecting the actual distribution of neutrons within the fuel pellets. The pebble bed fill rate reflects the density of fuel pellets within the pebble bed region, determining the path length and collision probability of neutrons within the region. The volume fraction of the i-th batch of fuel pellets clarifies the proportion of that batch of fuel pellets among all fuel pellets in the region, serving as a key weighting parameter connecting the overall region and individual batches. By using a specified formula, the neutron flux density of the g-th energy group in the sphere bed region is multiplied by the self-shielding factor of the corresponding batch of fuel spheres. This is then combined with the sphere bed fill rate and the volume fraction of the batch of fuel spheres for comprehensive adjustment, ultimately yielding the neutron flux density of the g-th energy group of the i-th batch of fuel spheres at the current core power level. This calculation process fully considers the coupling relationship between the overall neutron environment of the region and the individual characteristics of each batch of fuel spheres, avoiding the coarse estimation of fuel sphere neutron flux density used in traditional methods. This ensures the accuracy of the neutron flux density calculation for different energy groups in each batch of fuel spheres, providing core data support for the subsequent precise solution of power density.

[0045] Step 207: Calculate the power density of each batch of fuel pellets at the current core power level based on the neutron flux density of each batch of fuel pellets at the current core power level.

[0046] In some embodiments, the power density of each batch of fuel spheres at the current core power level is calculated based on the neutron flux density of each batch of fuel spheres at the current core power level. The power density calculation formula is as follows:

[0047] in, This represents the power density of the i-th batch of fuel pellets within the pellet bed region. This represents the interface at which the fission energy of the g-th energy group of the i-th batch of fuel pellets is generated within the pellet bed region. denoted as neutron flux density of the g-th energy group of the i-th batch of fuel pellets in the pebble bed region at the current core power level, and N represents the number of batches of fuel pellets in the pebble bed region.

[0048] The power density of each batch of fuel pellets is a key indicator reflecting the intensity of its nuclear reaction. Its calculation requires consideration of the neutron flux density of each batch of fuel pellets at the current core power level and their own fission energy production characteristics. The fission energy production cross-section of the g-th energy group of the i-th batch of fuel pellets is determined by the core physical characteristics of that batch of fuel pellets, such as enrichment, directly reflecting the ability of neutrons in that energy group to undergo fission reactions with the fuel pellets and release energy. The neutron flux density of the g-th energy group of the i-th batch of fuel pellets at the current core power level reflects the probability of neutrons in that energy group initiating fission reactions within the fuel pellets. The product of these two values ​​can accurately quantify the contribution of neutrons in that energy group to the power output of that batch of fuel pellets. The number of batches of fuel pellets within the pellet bed region clarifies the calculation coverage. By summing the contribution values ​​for all energy groups, the total power density of the i-th batch of fuel pellets can be obtained. This calculation process comprehensively integrates the fission contribution of neutrons with different energies, fully respects the differences in physical properties of each batch of fuel pellets, avoids the drawbacks of averaging the power density of different batches of fuel pellets, and accurately captures the actual energy output level of each batch of fuel pellets. Its beneficial effect is that it provides a direct basis for the accurate calculation of subsequent burnup depth, and further improves the accuracy and reliability of the entire burnup calculation process.

[0049] Step 208: Calculate the burnup depth of the corresponding batch of fuel pellets based on the power density of each batch of fuel pellets in the pebble bed region under the current core power level.

[0050] In some embodiments, the burn-down depth of the corresponding batch of fuel pellets is calculated based on the power density of each batch of fuel pellets in the pebble bed region at the current core power level. The formula for calculating the burn-down depth is as follows:

[0051] Where n represents the number of fuel consumption steps, This represents the burn-out depth of the i-th batch of fuel balls in the ball bed region at the n-th burn-out step. This represents the time step size of the nth fuel consumption step. This represents the fuel loading mass of the i-th batch of fuel balls.

[0052] The calculation of burnup depth relies on the power density of each batch of fuel pellets at the current core power level, combined with the time dimension parameters of the burnup process and the basic parameters of the fuel itself, to achieve precise quantification. The burnup step number n divides the entire irradiation cycle of the fuel pellets into several consecutive calculation stages, each stage corresponding to a fixed time step Δt. n This time step specifies the exact duration of each burnup step, providing a time reference for calculating fuel consumption at each stage and ensuring that the burnup depth calculation closely matches the actual operating sequence of the reactor core. The fuel loading mass m of the i-th batch of fuel pellets... iThis is a core parameter for measuring the total amount of fuel in a batch that can participate in a nuclear reaction. It directly determines the maximum consumable potential of the fuel within a batch and is a key basis for distinguishing the burnup limits of fuel spheres from different batches. In the calculation, the energy production rate per unit time of the i-th batch of fuel spheres is first obtained through the power density, and then multiplied by the time step size Δt of the nth burnup step. n The total energy release of this batch of fuel pellets during this burnup step is obtained, and the total energy release is related to the fuel loading mass m. i There exists a fixed physical correlation—energy release originates from the fission consumption of nuclear fuel. This correlation allows for the precise deduction of the fuel consumption ratio, ultimately yielding the burnup depth BU of the i-th batch of fuel pellets at the n-th burnup step. i (n) This calculation process strictly follows the energy release and fuel consumption laws of nuclear reactions, fully combining the actual power output and basic characteristics of each batch of fuel pellets. It avoids the neglect of consumption differences between different batches of fuel pellets in traditional averaging calculations. The beneficial effect is that it enables accurate step-by-step calculation of the burnup depth of each batch of fuel pellets, providing reliable data support for reactor fuel cycle optimization and replacement timing judgment.

[0053] Figure 3 A flowchart illustrating another fuel pellet fuel consumption calculation method provided in this application embodiment includes the following steps: Step 301: In the mixed sphere bed region, the fuel spheres are divided into multiple batches according to their distribution. Neutron transport equations are established for each batch of fuel spheres, and the self-shielding factor of each batch of fuel spheres is calculated.

[0054] In some embodiments, Step 302: Use the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to perform neutron diffusion calculations in the reactor core to obtain the neutron flux density in each region of the reactor core, and calculate the power density in each region of the pebble bed based on the neutron flux density in each region of the reactor core.

[0055] In some embodiments, Step 303: Calculate the neutron flux density and power density of each batch of fuel balls at the current core power level based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel balls.

[0056] In some embodiments, Step 304: Calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls at the current core power level.

[0057] For a description of steps 301-304, please refer to the description of steps 101-104 in the embodiment. This embodiment will not repeat them in detail.

[0058] Step 305: Based on the neutron flux density of each batch of fuel pellets in the pebble bed region at the current core power level, solve the burnup equation to obtain the nuclide concentration of each batch of fuel pellets at different burnup steps.

[0059] In some embodiments, nuclide concentration is a core parameter reflecting changes in nuclide composition during nuclear reactions in fuel spheres. Accurate acquisition of this concentration is crucial for reactor reactivity control, fuel lifetime assessment, and radioactive waste management. In step 305, solving the burnup equation to obtain the nuclide concentration of each batch of fuel spheres at different burnup steps requires using the neutron flux density of each batch of fuel spheres at the current core power level as the core basis. Nuclide generation and consumption both depend on the interaction between neutrons and nuclides, and the neutron flux density of each batch of fuel spheres directly determines the rate of nuclear reactions. Differences in neutron flux density between different batches of fuel spheres lead to drastically different nuclide concentration changes. The burnup equation systematically describes the transformation of nuclides under neutron irradiation, covering various nuclear reaction processes such as fission, capture, and transmutation. Solving this equation requires combining the specific neutron flux density of each batch of fuel spheres with key physical parameters such as the reaction cross-section of the nuclides, while also considering the time step of each burnup step, to progressively calculate the amount of nuclides generated and consumed at each burnup stage. By specifically solving the burnup equations for each batch of fuel spheres, the dynamic changes in the internal nuclide composition of each batch of fuel spheres under different burnup steps can be accurately captured, avoiding the drawbacks of traditional methods that uniformly average the nuclide concentrations of different batches of fuel spheres. The beneficial effects of this process are that it not only improves the burnup calculation system and provides key data for a comprehensive understanding of the nuclear reaction process of fuel spheres, but also provides reliable support for reactivity regulation, fuel replacement strategy optimization, and radioactivity safety assessment during reactor operation, further enhancing the comprehensiveness and accuracy of the entire burnup calculation method.

[0060] Figure 4 This is a schematic diagram of the structure of a fuel pellet fuel consumption calculation device provided in an embodiment of this application, as shown below. Figure 4 As shown, it includes: a first calculation module 401, a second calculation module 402, a third calculation module 403, and a fourth calculation module 404.

[0061] The first calculation module 401 is configured to divide the fuel balls into multiple batches according to the distribution of the fuel balls in the mixed sphere bed region, establish neutron transport equations for each batch of fuel balls, and calculate the self-shielding factor of each batch of fuel balls. The second calculation module 402 is configured to perform core neutron diffusion calculations using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to obtain the neutron flux density of each region of the core, and to calculate the power density of each region of the pebble bed based on the neutron flux density of each region of the core. The third calculation module 403 is configured to calculate the neutron flux density and power density of each batch of fuel balls at the current core power level based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls. The fourth calculation module 404 is configured to calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls at the current core power level.

[0062] In some examples of this embodiment, the first calculation module 401 is specifically configured to divide the fuel balls in the mixed pebble bed region into multiple batches based on the difference in the enrichment degree of the fuel balls and the number of times they flow through the reactor core; establish a set of collision probability equations for each batch of fuel balls based on the collision probability method; solve the set of collision probability equations to obtain the neutron flux density of each batch of fuel balls; and calculate the self-shielding factor of each batch of fuel balls based on the seed flux density.

[0063] In some examples of this embodiment, the second calculation module 402 is specifically configured to calculate the homogenization cross section of the pebble bed region based on the neutron flux density and volume fraction of each component within the pebble bed region; based on the homogenization cross section, combined with the homogenization cross section of the reflector region calculated by the Monte Carlo particle transport calculation software NECP-MCX, complete the core neutron diffusion calculation to obtain the neutron flux density of each region of the core; and calculate the power density of each region of the pebble bed based on the neutron flux density of each region of the core.

[0064] In some examples of this embodiment, the third calculation module 403 is specifically configured to calculate the neutron flux density of each batch of fuel balls at the current core power level based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls in the pebble bed region; and to calculate the power density of each batch of fuel balls at the current core power level based on the neutron flux density of each batch of fuel balls at the current core power level.

[0065] In some examples of this embodiment, the fourth calculation module 404 is specifically configured to calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls in the pebble bed region under the current core power level.

[0066] It should be noted that other corresponding descriptions of the functional units involved in the fuel pellet fuel consumption calculation device provided in this embodiment can be found in [reference needed]. Figure 1 , Figure 2 and Figure 3 The corresponding description in [the document] will not be repeated here.

[0067] Based on the above, Figure 1 , Figure 2 and Figure 3The embodiment illustrates a method for calculating fuel consumption of a fuel sphere. Correspondingly, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method. Figure 1 , Figure 2 and Figure 3 This illustrates a method for calculating the fuel consumption of fuel pellets.

[0068] Based on the above, Figure 1 , Figure 2 and Figure 3 The embodiment illustrates a method for calculating fuel consumption of fuel pellets. Correspondingly, this embodiment also provides a computer program product storing a computer program that, when executed by a processor, implements the above-described method. Figure 1 , Figure 2 and Figure 3 This illustrates a method for calculating the fuel consumption of fuel pellets.

[0069] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.

[0070] Based on the above, Figure 1 , Figure 2 and Figure 3 A method for calculating the fuel consumption of a fuel pellet is shown, and Figure 4 To achieve the above objectives, the present application also provides an electronic device, such as a personal computer or a server, in the illustrated virtual device embodiment. This device includes a storage medium and a processor; the storage medium stores a computer program; the processor executes the computer program to implement the above-described virtual device. Figure 1 , Figure 2 and Figure 3 This illustrates a method for calculating the fuel consumption of fuel pellets.

[0071] In some embodiments, the aforementioned physical device may further include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, an input unit such as a keyboard, etc., and optionally, a USB interface, a card reader interface, etc. In some embodiments, the network interface may include a standard wired interface, a wireless interface (such as a Wi-Fi interface), etc.

[0072] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the aforementioned physical device, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software in the information processing physical device.

[0073] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0074] The above are merely specific embodiments of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to these embodiments, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for calculating the fuel consumption of fuel pellets, characterized in that, include: In the mixed sphere bed region, the fuel spheres are divided into multiple batches according to their distribution. Neutron transport equations are established for each batch of fuel spheres, and the self-shielding factor of each batch of fuel spheres is calculated. The neutron diffusion of the reactor core is calculated using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to obtain the neutron flux density of each region of the reactor core. The power density of each region of the pebble bed is then calculated based on the neutron flux density of each region of the reactor core. Based on the neutron flux density in the pebble bed region and the self-shielding factor of each batch of fuel spheres, calculate the neutron flux density and power density of each batch of fuel spheres at the current core power level. Based on the power density of each batch of fuel pellets at the current core power level, calculate the burn-up depth of the corresponding batch of fuel pellets.

2. The fuel pellet fuel consumption calculation method according to claim 1, characterized in that, The above includes: Based on the differences in the enrichment degree and the number of times the fuel pellets flowed through the reactor core, the fuel pellets in the mixed pellet bed region were divided into multiple batches; The collision probability equations for each batch of fuel spheres are established based on the collision probability method, and the neutron flux density of each batch of fuel spheres is obtained by solving the collision probability equations. The self-shielding factor of each batch of fuel pellets is calculated based on the seed flux density. The formula for calculating the self-shielding factor is as follows: Indicates the batch number of the fuel pellets. Indicates the neutron energy group number. This indicates the batch number of fuel pellets within the pellet bed area. This represents the self-shielding factor of the g-th energy group of the i-th batch of fuel spheres. Indicates the ball bed filling rate. This represents the volume fraction of the i-th batch of fuel pellets relative to all fuel pellets in the region. This represents the neutron flux density of the g-th energy group in the i-th batch of fuel spheres. This represents the neutron flux density of the g-th energy group in the spherical bed region void.

3. The fuel pellet fuel consumption calculation method according to claim 1, characterized in that, The above includes: Based on the neutron flux density and volume fraction of each component in the pebble bed region, the homogenization cross section of the pebble bed region is calculated. Based on the homogenization cross section, combined with the homogenization cross section of the reflector region calculated by the Monte Carlo particle transport calculation software NECP-MCX, the neutron diffusion calculation of the reactor core is completed, and the neutron flux density of each region of the reactor core is obtained. The power density of each region of the pebble bed is calculated based on the neutron flux density of each region of the reactor core, and the calculation formula is as follows: Where P represents the power density of the spherical bed region, and G represents the number of neutron energy groups. This represents the cross section for the fission energy generation of the g-th energy group in the spherical bed region. This represents the neutron flux density of the g-th energy group in the sphere bed region.

4. The fuel pellet fuel consumption calculation method according to claim 1, characterized in that, The above includes: The neutron flux density of each batch of fuel pellets in the pebble bed region is calculated based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel pellets in the pebble bed region at the current core power level. The neutron flux density calculation formula is as follows: in, This represents the neutron flux density of the g-th energy group of the i-th batch of fuel spheres in the pebble bed region at the current core power level; This represents the neutron flux density of the g-th energy group in the spherical bed region. This represents the self-shielding factor of the g-th energy group of the i-th batch of fuel spheres. Indicates the ball bed filling rate. This represents the volume share of the i-th batch of fuel balls among all fuel balls in the region; The power density of each batch of fuel spheres at the current core power level is calculated based on the neutron flux density of each batch at the current core power level. The formula for calculating the power density is as follows: in, This represents the power density of the i-th batch of fuel pellets within the pellet bed region. This represents the interface where the fission energy of the g-th energy group of the i-th batch of fuel pellets is generated within the pellet bed region. N represents the neutron flux density of the g-th energy group of the i-th batch of fuel pellets in the pebble bed region at the current core power level, and N represents the number of batches of fuel pellets in the pebble bed region.

5. The fuel pellet fuel consumption calculation method according to claim 1, characterized in that, The calculation of the burnup depth for each batch of fuel pellets based on the power density of each batch at the current core power level includes: Based on the power density of each batch of fuel pellets in the pebble bed region at the current core power level, the burnup depth of the corresponding batch of fuel pellets is calculated. The formula for calculating the burnup depth is as follows: Where n represents the number of fuel consumption steps, This represents the burn-out depth of the i-th batch of fuel balls in the ball bed region at the n-th burn-out step. This represents the time step size of the nth fuel consumption step. This represents the fuel loading mass of the i-th batch of fuel balls.

6. The fuel pellet fuel consumption calculation method according to claim 1, characterized in that, Also includes: Based on the neutron flux density of each batch of fuel pellets in the pebble bed region at the current core power level, the burnup equation is solved to obtain the nuclide concentration of each batch of fuel pellets at different burnup steps.

7. A fuel pellet fuel consumption calculation device, characterized in that, include: The first calculation module is configured to divide the fuel balls into multiple batches according to the distribution of the fuel balls in the mixed sphere bed region, establish neutron transport equations for each batch of fuel balls, and calculate the self-shielding factor of each batch of fuel balls. The second calculation module is configured to perform core neutron diffusion calculations using the homogenized cross section of the pebble bed region and the homogenized cross section of the reflector region to obtain the neutron flux density of each region of the core, and to calculate the power density of each region of the pebble bed based on the neutron flux density of each region of the core. The third calculation module is configured to calculate the neutron flux density and power density of each batch of fuel balls at the current core power level based on the neutron flux density of the pebble bed region and the self-shielding factor of each batch of fuel balls. The fourth calculation module is configured to calculate the burn-up depth of the corresponding batch of fuel balls based on the power density of each batch of fuel balls at the current core power level.

8. An electronic device, characterized in that, include: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the fuel ball fuel consumption calculation method according to any one of claims 1-6.

9. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to execute the fuel ball fuel consumption calculation method according to any one of claims 1-6.

10. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the fuel ball fuel consumption calculation method according to any one of claims 1-6.

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