Subcriticality evaluation device, subcriticality evaluation method and mox fuel assembly

Abstract

To rationally evaluate subcriticality of a fuel assembly stored in a fuel storage rack.SOLUTION: A subcriticality evaluation method includes the steps of: reading a maximum infinite multiplication factor, the maximum value of infinite multiplication factors throughout an entire combustion period in each of a plurality of sections consisting of an uppermost section, a lowermost section, and at least one section therebetween divided in a longitudinal direction in a basic fuel assembly; setting a reference infinite multiplication factor enveloping the maximum infinite multiplication factor in each section; deriving a model infinite multiplication factor for a model bundle having the plurality of sections by adjusting a nuclear fuel material concentration of the model bundle so that the model infinite multiplication factor in each section is larger than the reference infinite multiplication factor; and deriving an effective multiplication factor, with the model bundle stored in a fuel storage rack.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] Embodiments of the present invention relate to a subcriticality evaluation device, a subcriticality evaluation method, and a MOX fuel assembly.

Background Art

[0002] In order to optimize the output distribution within a fuel assembly loaded in a boiling water reactor, the fuel assembly has a plurality of types of fuel rods with different uranium enrichment degrees, plutonium enrichment degrees, or both (hereinafter referred to as nuclear fuel material concentrations) contained therein. A fuel rod has a region filled with fuel pellets and a region not filled with fuel pellets, and the length of the former in the longitudinal direction is called the fuel effective length. In the case of a boiling water reactor, the fuel effective length is about 3.7 m. The fuel rod is divided into nodes obtained by equally dividing the fuel effective length in the longitudinal direction (usually 24 divisions), and the nuclear fuel material concentration contained in the fuel rod is designed to vary depending on the node position. For this reason, the nuclide composition of the nuclear fuel material constituting the fuel assembly varies depending on the horizontal and longitudinal directions of the fuel assembly.

[0003] In the core of a 1.1 million kWe-class boiling water reactor, 764 fuel assemblies are loaded. Since these have different burnup histories depending on the core loading position and the residence period in the reactor, the nuclide composition after combustion and the reactivity differ for each fuel assembly.

[0004] In the subcriticality evaluation of a fuel storage pool that houses a fuel assembly, it is cumbersome and involves a great deal of labor to individually handle all the nuclide compositions of the fuel assembly after combustion. For this reason, it is reasonable to set a nuclide composition that represents a nuclide composition having an infinite multiplication factor (hereinafter referred to as the infinite multiplication factor: k ∞ ) higher than the infinite multiplication factor in the cold temperature infinite multiplication factor in the core loading state of fuel assemblies with all burnup histories (including fresh fuel), and perform the subcriticality evaluation using this nuclide composition. A virtual fuel assembly having this representative nuclide composition is called a model bundle.

[0005] In the case of a boiling water type light water reactor, the fuel assembly generally has fuel rods containing gadolinia in the fuel pellets as a burnable poison. Hereinafter, gadolinia will be taken as an example of the burnable poison for explanation. Since gadolinia has a large thermal neutron capture cross section and suppresses the nuclear fission reaction by capturing neutrons, it has a negative reactivity. When performing the subcriticality evaluation of a fuel assembly containing gadolinia, such negative reactivity of gadolinia can be analytically considered, which is called gadolinia credit.

[0006] The gadolinia contained in the fuel assembly decreases as the fuel assembly burns. For this reason, the maximum value of the infinite multiplication factor (k ∞R ) of the fuel assembly containing gadolinia occurs when the gadolinia has disappeared during the burning of the fuel assembly. In the subcriticality evaluation using gadolinia credit, a value that envelopes the maximum value of the infinite multiplication factor (k ∞R ) occurring during burning is set as the infinite multiplication factor (k ∞M ) of the model bundle, and the evaluation is performed conservatively. Note that although the burning characteristics of the fuel assembly vary depending on the node, at any node during the operation period, the maximum value of the infinite multiplication factor (k ∞R ) is designed to be less than 1.3 for uranium fuel and 1.23 for MOX fuel (mixed oxide fuel obtained by mixing uranium and plutonium, which is a solid oxide fuel). For this reason, in setting the model bundle, the reference value (k ∞M ) when setting the infinite multiplication factor (k ∞S ) of the model bundle is set to 1.3 for uranium fuel and 1.23 for MOX fuel, and the infinite multiplication factor (k ∞M ) of the model bundle is made larger than the reference value (k ∞S ). Note that the nuclide composition of the model bundle is set by first removing gadolinia based on the nuclide composition of the unburned fuel assembly and then adjusting the concentration of the nuclear fuel material so that a predetermined infinite multiplication factor is achieved.

[0007] FIG. 22 is a conceptual distribution diagram showing a conventional example of the composition distribution of a model bundle. Thus, in the conventional model bundle, in order to simplify the analysis model, the nuclide composition is set uniformly in the longitudinal direction. Also, the infinite multiplication factor (k ∞M ) of the model bundle becomes larger than 1.3 for uranium fuel and 1.23 for MOX fuel regardless of the node position, and in order to envelop the maximum value (k ∞R ) of the infinite multiplication factor of the actual fuel over the entire length of the fuel effective length, it is a conservative setting.

[0008] In the design of a fuel assembly, in order to ensure the critical safety in nuclear facilities such as a fuel storage rack, the maximum value of the infinite multiplication factor throughout the entire burnup period of the fuel assembly is restricted to be less than 1.30 for uranium fuel and 1.23 for MOX fuel. In other words, it has been difficult to design a fuel assembly in which the maximum value of the infinite multiplication factor throughout the entire burnup period of the fuel assembly exceeds the above limit value from the viewpoint of ensuring the critical safety of nuclear facilities such as a fuel storage rack.

Prior Art Documents

Patent Documents

[0009]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0010] As the above factors, there are the longitudinal composition distribution and the setting of the infinite multiplication factor of the conventional model bundle. In the conventional model bundle, since the infinite multiplication factor is constant regardless of the node position, depending on the node position, the infinite multiplication factor of the model bundle becomes excessively high compared to the infinite multiplication factor of the actual fuel assembly, and there is a tendency to overestimate the evaluation value (for example, the effective multiplication factor) in the subcriticality evaluation of the fuel storage rack. As a result, the number of fuel assemblies that can be stored in the fuel storage rack has been overly underestimated.

[0011] Embodiments of the present invention aim to provide a subcriticality evaluation device, a subcriticality evaluation method, and a MOX fuel assembly that can reasonably evaluate the subcriticality of a fuel assembly stored in a fuel storage rack.

Means for Solving the Problems

[0012] To achieve the above object, the subcriticality evaluation method according to the present embodiment is a subcriticality evaluation method for evaluating the subcriticality of a basic fuel assembly to be evaluated, which is stored in a fuel storage rack immersed in light water. The method includes: reading a maximum infinite multiplication factor, which is the maximum value of the infinite multiplication factor throughout the entire burnup period, in each of a plurality of sections including the uppermost section, the lowermost section, and at least one intermediate section obtained by dividing the basic fuel assembly in the longitudinal direction; setting a reference infinite multiplication factor, which is a reference value of the infinite multiplication factor that envelopes the maximum infinite multiplication factor, in each of the plurality of sections; adjusting the nuclear fuel material concentration of a model bundle, which is an analysis model for evaluating the subcriticality and has the plurality of sections, such that a model infinite multiplication factor, which is the infinite multiplication factor in each of the plurality of sections, is greater than the reference infinite multiplication factor; and deriving an effective multiplication factor in a state where the model bundle with the adjusted nuclear fuel material concentration is stored in the fuel storage rack.

Effects of the Invention

[0013] According to the embodiments of the present invention, it is possible to provide a subcriticality evaluation method, a subcriticality evaluation device, and a MOX fuel assembly that can reasonably evaluate the subcriticality of a fuel assembly managed by a fuel storage rack.

Brief Description of the Drawings

[0014]

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[0015] Hereinafter, with reference to the drawings, a subcriticality evaluation method, a subcriticality evaluation device, and a MOX fuel assembly according to an embodiment of the present invention will be described. Here, the same or similar parts are denoted by common reference numerals, and overlapping explanations are omitted.

[0016] [First Embodiment] First, the basic fuel assembly 10 that is the object of the subcriticality evaluation method will be described. Here, the basic fuel assembly 10 is a group of fuel assemblies that are the objects of subcriticality confirmation when a model bundle is created and stored in a fuel storage rack. Among them, the representative fuel assembly is the unburned fuel assembly that is the basis for creating the model bundle, that is, the fuel assembly used as the starting point and the foundation when adjusting the specifications of the model bundle. In addition, as a group of fuel assemblies, for example, types such as 9×9 type MOX fuel assemblies or 10×10 type uranium fuel assemblies can be considered.

[0017] Figure 1 is a plan sectional view showing the configuration of a basic fuel assembly 10 which is the object of the subcriticality evaluation method according to the first embodiment. In Figure 1, the case of a 9×9 array is shown as an example, but other arrays may also be applicable.

[0018] The basic fuel assembly 10 has a plurality of enriched fuel rods 11, a plurality of poison fuel rods 12, a water channel 13, and a channel box 14 that surrounds these from the radially outer side.

[0019] The enriched fuel rod 11 is a fuel rod containing at least one of enriched uranium and fissile plutonium as a fissile material. Also, the poison fuel rod 12 is a uranium fuel rod that does not contain fissile plutonium and contains enriched uranium and a burnable poison. The enriched uranium of the enriched fuel rod 11 and the enriched uranium of the poison fuel rod 12 may have different uranium enrichment levels. Hereinafter, the basic fuel assembly in the case where the enriched fuel rod 11 contains enriched uranium is referred to as a uranium fuel assembly. Also, the basic fuel assembly in the case where the enriched fuel rod 11 contains fissile plutonium is referred to as a MOX fuel assembly.

[0020] In Figure 1, the enriched fuel rods 11 are numbered from 1 to 4 according to the concentration of the fissile material, from the first type with the highest fissile material concentration to the fourth type with the lowest fissile material concentration, according to the enrichment level of the enriched uranium or the enrichment level of the fissile plutonium (hereinafter collectively referred to as the "fissile material concentration").

[0021] Also, in Figure 1, the poison fuel rods 12 are marked with the symbols G1 and G2 for the G1 type with a high uranium enrichment level and a high burnable poison concentration and the G2 type with a low uranium enrichment level and a low burnable poison concentration, according to the enrichment level of the enriched uranium and the concentration of the burnable poison. Here, the burnable poison is a nuclide with a large neutron absorption cross-section particularly in the thermal neutron region, for example, gadolinium.

[0022] The enriched fuel rods 11 and the poison fuel rods 12 are arranged in a 9×9 lattice within the channel box 14, but in the central 3×3 region, a water channel 13 is arranged.

[0023] FIG. 2 is a conceptual distribution diagram showing the distribution of the composition of the basic fuel assembly 10 targeted by the subcriticality evaluation method according to the first embodiment.

[0024] FIG. 2 shows the composition for each node obtained by equally dividing in the longitudinal direction the height of the region filled with fuel pellets, i.e., the effective fuel length, in each type of fuel rod. Here, taking the case where the number of nodes is 24 as an example, the nodes are numbered from 1 to 24 from the bottom upward. In the vertical direction of FIG. 2, the node number is shown, and in the horizontal direction, as the types of fuel rods, the first type to the fourth type of the enriched fuel rods 11, and the G1 type and G2 type as the poison fuel rods 12 are shown. Also, the respective numbers in the arrangement shown in FIG. 1 are shown in parentheses.

[0025] As shown in FIG. 2, except for the first type, natural uranium (NU) is arranged in the lowermost first node and the uppermost 24th node. Hereinafter, the nodes other than the first node and the 24th node for types other than the first type, that is, the second node to the 23rd node, shall be referred to as intermediate nodes.

[0026] In the case of the first type, fuel pellets with a uniform fissile material concentration A1 are filled from the first node to the 23rd node.

[0027] The intermediate nodes of the enriched fuel rods 11 of the second type to the fourth type have fissile material concentrations A2 to A4, respectively. That is, the intermediate nodes constitute one region. Therefore, the enriched fuel rods 11 of the second type to the fourth type have three regions including the top and bottom.

[0028] For the intermediate nodes of the G1 type of the poison fuel rod 12, uniformly, the enriched uranium has a nuclear fissionable material concentration B1 and the burnable poison has a concentration β. That is, the intermediate nodes constitute one region. Therefore, the G1 type of the poison fuel rod 12 has three regions including the top and bottom.

[0029] Also, for the intermediate nodes of the G2 type of the poison fuel rod 12, from the second node to the twelfth node, uniformly, the enriched uranium has a nuclear fissionable material concentration B3 and the burnable poison has a concentration γ. Also, for the intermediate nodes from the thirteenth node to the twenty-third node, uniformly, the enriched uranium has a nuclear fissionable material concentration B2 and the burnable poison has a concentration α. That is, the intermediate nodes constitute two regions. Therefore, the G2 type of the poison fuel rod 12 has four regions including the top and bottom.

[0030] FIG. 3 is a conceptual distribution diagram showing another example of the distribution of the composition of the basic fuel assembly targeted by the subcriticality evaluation method according to the first embodiment. The vertical and horizontal directions in FIG. 3 indicate the node number and the type of the fuel rod, respectively, in the same manner as in FIG. 2.

[0031] In the case of the first type, the fuel pellets with a uniform nuclear fissionable material concentration F1 are filled from the first node to the twelfth node, and the fuel pellets with a uniform nuclear fissionable material concentration E1 are filled from the thirteenth node to the twenty-third node.

[0032] For the enriched fuel rods 11 of the second to fourth types and the poison fuel rods 12 of the G1 to G2 types, from the second node to the twelfth node, they each have a uniform composition with nuclear fissionable material concentrations F2 to F6, and from the thirteenth node to the twenty-third node, they each have a uniform composition with nuclear fissionable material concentrations E2 to E6.

[0033] FIG. 4 is a conceptual plan view showing an example of a fuel storage rack 50 to which the subcriticality evaluation method according to the first embodiment is applied. Here, the fuel storage rack 50 is, for example, a fresh fuel storage rack in a power plant, or a spent fuel storage rack, a spent fuel storage rack in a reprocessing plant, or a spent fuel storage rack in an intermediate storage facility.

[0034] The fuel storage rack 50 has a lattice space 52 arranged in a lattice pattern of M×N. The lattice spaces 52 are partitioned from each other by lattice plates 51. The fuel storage rack 50 is installed, for example, in a pool and immersed in light water.

[0035] The lattice plate 51 is flat. Also, as the material of the lattice plate 51, for example, austenitic stainless steel, and it may also contain boron 10 ( 10 B) having a large neutron absorption cross section.

[0036] FIG. 5 is a block diagram showing the configuration of the subcriticality evaluation apparatus 100 according to the first embodiment.

[0037] Hereinafter, the subcriticality evaluation apparatus 100 will be described. However, the functions realized by the components of the subcriticality evaluation apparatus 100 may be implemented in circuitry or processing circuitry including a general-purpose processor, an application-specific processor, an integrated circuit, ASICs (Application Specific Integrated Circuits), a CPU (Central Processing Unit), a conventional circuit, and / or a combination thereof, which are programmed to realize the described functions. The processor includes transistors and other circuits and is regarded as circuitry or processing circuitry. The processor may be a programmed processor that executes a program stored in a memory.

[0038] Also, circuitry, units, and means are hardware programmed to implement the described functions, or hardware that executes. The hardware may be any hardware described below, or any hardware known to be programmed or execute to implement the described functions. When the hardware is a processor considered to be of the circuitry type, the circuitry, means, or unit is a combination of hardware and software used to configure the hardware and / or the processor.

[0039] As shown in FIG. 5, the subcriticality evaluation apparatus 100 includes an input unit 110, a storage unit 120, a calculation unit 130, and an output unit 140.

[0040] The input unit 110 receives, as external inputs, information regarding the specifications D1 of the basic fuel assembly 10, information regarding the arrangement conditions D2 such as the arrangement pitch of the basic fuel assemblies 10 in the fuel storage rack, information regarding the specifications D3 of the fuel storage rack, calculation conditions for setting the model bundle, necessary nuclear data, and the like. Here, examples of the calculation conditions for setting the model bundle include a predetermined value at the time of setting the reference infinite multiplication factor k ∞S (j), and the change width ΔF of the fissile material concentration in the iterative calculation.

[0041] The storage unit 120 includes a fuel assembly specifications storage unit 121, a fuel assembly arrangement condition storage unit 122, a fuel storage rack specifications storage unit 123, a model bundle specifications storage unit 124, a calculation condition storage unit 125, a nuclear data storage unit 126, and a calculation result storage unit 127.

[0042] The fuel assembly specifications storage unit 121 stores and remembers the information regarding the specifications D1 of the basic fuel assembly 10 received by the input unit 110.

[0043] The fuel assembly arrangement condition storage unit 122 stores and remembers the information regarding the arrangement conditions D2 in the fuel storage rack received by the input unit 110.

[0044] The fuel storage rack specification storage unit 123 stores and memorizes information regarding the specifications D3 of the fuel storage rack received by the input unit 110.

[0045] The model bundle specification storage unit 124 stores and memorizes information regarding the specifications of the model bundle.

[0046] The calculation condition storage unit 125 stores and memorizes calculation conditions for setting the model bundle received by the input unit 110, that is, for example, parameters such as a predetermined value at the time of setting the reference infinite multiplication factor k ∞S (j), and the change width ΔF of the fissile material concentration.

[0047] The nuclear data storage unit 126 stores and memorizes nuclear data such as neutron absorption cross sections and nuclear fission cross sections necessary for calculations for setting the model bundle and for calculating the effective multiplication factor.

[0048] The calculation result storage unit 127 stores and memorizes calculation results including the results in the calculation process of the calculations for setting the model bundle and for calculating the effective multiplication factor.

[0049] The calculation unit 130 includes a model bundle specification setting correction unit 131, an infinite multiplication factor calculation unit 132, an effective multiplication factor calculation unit 133, and a progress control unit 135.

[0050] The model bundle specification setting correction unit 131 performs setting of the specifications of the model bundle and correction calculations based on the change amount ΔF of the fissile material concentration.

[0051] The infinite multiplication factor calculation unit 132 calculates the infinite multiplication factor in each section.

[0052] The effective multiplication factor calculation unit 133 calculates the effective multiplication factor in a state where the model bundle is stored in the fuel storage rack.

[0053] The progress control unit 135 manages the progress of operations such as calculations in the calculation unit 130. For example, the progress control unit 135 performs determination and determines the process of processing based on the determination result.

[0054] The output unit 140 outputs, as necessary, the information received by the input unit 110 and stored in the storage unit 120, the information calculated by the calculation unit 130 and stored in the storage unit 120, or the determination information performed by the calculation unit. The output includes, for example, display on a display device or output to an electronic medium.

[0055] Note that the input unit 110 and the output unit 140 may be, for example, an HMI (Human Machine Interface) that has a display and includes an interface that can be directly input to the display.

[0056] FIG. 6 is a flowchart showing the overall procedure of the subcriticality evaluation method according to the first embodiment.

[0057] First, set the fuel storage facility (step S10).

[0058] Next, select the basic fuel assembly 10 (step S20). That is, identify whether the basic fuel assembly 10 is, for example, a 9×9 type MOX fuel assembly or a 10×10 type uranium fuel assembly.

[0059] Next, perform a burnup calculation of the basic fuel assembly 10 (step 30). The burnup calculation is performed for each node that bundles all the fuel rods of the enriched fuel rod 11 and the poison fuel rod 12 when viewing the fuel assembly in the horizontal direction. Specifically, for example, in the case of the composition distribution example shown in FIG. 3, for the four regions of the first node, the second node to the twelfth node, the thirteenth node to the twenty-third node, and the twenty-fourth node, the infinite multiplication factor k∞ with respect to the burnup is calculated respectively.

[0060] FIG. 7 is a graph showing an example of the dependence characteristics of the infinite multiplication factor on the cross-sectional average burnup at each node of the basic fuel assembly 10 targeted by the subcriticality evaluation method according to the first embodiment. The horizontal axis is the cross-sectional average burnup (GWd / t) related to the volume integral of (cross-section × node height) at each node of the basic fuel assembly 10. The vertical axis is the infinite multiplication factor k related to the volume integral of (cross-section × node height) at each node ∞ is. The one-dot chain line represents the first node, the two-dot chain line represents the second to twelfth nodes, the solid line represents the thirteenth to twenty-third nodes, and the broken line represents the infinite multiplication factor k ∞ at the 24th node. From these results, the maximum value of the infinite multiplication factor k ∞ is obtained at each node.

[0061] Next to step S30, a model bundle related to the basic fuel assembly is set (step S40). Details of step 40 will be described later with reference to FIG. 8.

[0062] Next, the subcriticality is confirmed when the model bundle is stored (step S50). Details of step S50 will be described later with reference to FIG. 13.

[0063] FIG. 8 is a flowchart showing the detailed procedure of the model bundle setting step S40 of the subcriticality evaluation method according to the first embodiment.

[0064] First, the initial specifications and arrangement conditions of the model bundle are set (step S41). That is, the model bundle specification setting correction unit 131 sets the initial values of the specifications of the model bundle based on the specifications D1 of the basic fuel assembly 10 received by the input unit 110 and stored in the fuel assembly specification storage unit 121, and sets the arrangement conditions such as the installation interval of the model bundle based on the arrangement conditions D2 such as the array pitch of the basic fuel assembly 10 stored in the fuel assembly arrangement condition storage unit 122.

[0065] Next, the section number j is set to 1 (step S42).

[0066] Here, the term "compartment" used in the procedure of this step S40 will be explained. "Compartment" may mean "node" in FIGS. 2 and 3, or may mean "region" described with reference to FIGS. 2 and 3. That is, "compartment" means "node" or "region". Therefore, when "compartment" means "node", the compartment number j ranges from 1 to 24, and the maximum value J of the compartment number j is 24. Also, when the number of regions is, for example, 4 and "compartment" means "region", the compartment number j ranges from 1 to 4, and the maximum value J of the compartment number j is 4.

[0067] Next, the reference infinite multiplication factor k ∞S (j) is set (step S43). That is, the model bundle specification setting correction unit 131 sets the reference infinite multiplication factor k ∞S (j) based on the maximum value of the infinite multiplication factor of each compartment throughout the entire combustion period obtained in step S30 and a predetermined value received by the input unit 110 and stored in the calculation condition storage unit 125. Here, the predetermined value is, for example, 1.30 for uranium fuel and 1.23 for MOX fuel.

[0068] Next, the model infinite multiplication factor k ∞M (j) is calculated (step S44). That is, based on the specifications of the model bundle in the corresponding compartment, the infinite multiplication factor calculation unit 132 calculates the model infinite multiplication factor k ∞M (j). Here, the calculation of the model infinite multiplication factor k ∞M (j) may be considered as an operation under the condition that the model bundles 20 are infinitely arranged in two-dimensional directions at a predetermined interval.

[0069] Next, the progress control unit 135 determines whether the model infinite multiplication factor k ∞M (j) exceeds the reference infinite multiplication factor k ∞S (j) (step S45).

[0070] When the progress control unit 135 determines that the model infinite multiplication factor k ∞M (j) exceeds the reference infinite multiplication factor k ∞SIf it is determined that it has not exceeded (j) (step S45 NO), the change in the fissile material concentration ΔF is added to the fissile material concentration F(j) of the section to obtain a new fissile material concentration F(j) (step S46). The change in the fissile material concentration ΔF may be a positive value or a negative value. Here, the fissile material F(j) is the uranium enrichment in the uranium fuel in the j-th section or the enrichment of fissile plutonium in the MOX fuel. The new fissile material concentration F(j) is stored and memorized in the calculation result storage unit 127. After step S46, steps S44 and S45 are repeated.

[0071] The progress control unit 135 determines the multiplication factor k of the model infinite ∞M (j) exceeds the reference infinite multiplication factor k ∞S If it is determined that (j) has been exceeded (step S45 YES), the progress control unit 135 determines whether the section number j is less than the maximum value J (step S47).

[0072] If the progress control unit 135 determines that the section number j is less than the maximum value J (step S47 YES), 1 is added to the section number j to obtain a new section number j (step S48), and steps S43 to S47 are repeated.

[0073] If the progress control unit 135 does not determine that the section number j is less than the maximum value J (step S47 NO), that is, if it is determined that the process has ended up to the maximum value, step S40 is terminated.

[0074] By the above procedure, the multiplication factor k of the model infinite of each j-th node of the model bundle 20 ∞M (j) does not fall below the reference infinite multiplication factor k ∞S (j) and is approximately close to the reference infinite multiplication factor k ∞S (j). The smaller the value of the change in the fissile material concentration ΔF, the closer the multiplication factor k of the model infinite ∞M (j) is to the reference infinite multiplication factor k ∞S (j). Therefore, in this way, since the change in the fissile material concentration ΔF is sufficiently small, the multiplication factor k of the model infinite∞M (j) is the reference infinite multiplication factor k ∞S When it is a value sufficiently close to (j), the model infinite multiplication factor k ∞M (j) is the reference infinite multiplication factor k ∞S It is to be said that it is substantially equal to the value of (j).

[0075] FIG. 9 is a plan sectional view showing a configuration example of the model bundle 20 obtained by the subcriticality evaluation method according to the first embodiment.

[0076] FIG. 10 is a conceptual distribution diagram showing an example of the distribution of the composition of the model bundle by the subcriticality evaluation method according to the first embodiment.

[0077] The model bundle 20 is a 9×9 type fuel assembly and has enriched fuel rods 21, poison fuel rods 22, water channels 13, and channel boxes 14. The first a type to the fourth a type of the enriched fuel rods 21 correspond to the first type to the fourth type of the basic fuel assembly 10, and the fissile material concentration is adjusted from these. The G1a type and the G2a type of the poison fuel rods 22 correspond to the G1 type and the G2 type of the basic fuel assembly 10 respectively, and the combustible poison is removed from these and the fissile material concentration is adjusted. The respective adjusted concentrations are indicated by attaching "a" to the signs of the respective concentrations of the basic fuel assembly 10. Regarding "NUa", although the same notation is used for each type, it may be different between between node 1 and node 24 or between types.

[0078] For each of the first a type to the fourth a type of the enriched fuel rods 21, there may be those having the same fissile material concentration as each of the first type to the fourth type.

[0079] As described above, except for the individual compositions, the model bundle 20 has the same basic configuration as the basic fuel assembly 10.

[0080] FIG. 11 is a graph showing the distribution characteristics of the infinite multiplication factor of the model bundle by the subcriticality evaluation method according to the first embodiment.

[0081] The vertical axis indicates the node positions from the first node to the 24th node in the longitudinal direction. The horizontal axis is the maximum value of the infinite multiplication factor k ∞ throughout the entire combustion period. The broken line L U1 showing the infinite multiplication factor indicates the maximum value k ∞ of the infinite multiplication factor k ∞R of the basic fuel assembly 10 at each node position. Hereinafter, a straight line or a broken line showing the infinite multiplication factor is referred to as an infinite multiplication factor distribution line. The infinite multiplication factor distribution line M1 shown by the broken line indicates the model infinite multiplication factor k ∞M obtained by this embodiment. The infinite multiplication factor distribution line M C1 shown by the broken line indicates the model infinite multiplication factor k ∞MC1 obtained by the conventional method.

[0082] Hereinafter, when one infinite multiplication factor k ∞ is greater than or equal to the other infinite multiplication factor k ∞ at a part of each node position, it may be expressed that one infinite multiplication factor distribution line envelopes the other infinite multiplication factor distribution line.

[0083] Conventionally, since the model bundle is set so that various compositions are uniform for all nodes in the longitudinal direction, the model infinite multiplication factor k ∞MC1 is uniform in the longitudinal direction. This model infinite multiplication factor k ∞MC1 is the reference value k ∞R of the infinite multiplication factor that envelopes the maximum value k ∞S of the infinite multiplication factor throughout the entire combustion period of the basic fuel assembly 10 over all nodes, and a value larger than the reference value (k ∞S ) of the infinite multiplication factor is set. As the reference infinite multiplication factor k ∞S which is the reference value of the infinite multiplication factor, there is an example of 1.30 for uranium fuel and 1.23 for MOX fuel.

[0084] On the other hand, the model bundle 20 of this embodiment is the infinite multiplication factor distribution line L of the infinite multiplication factor of the basic fuel assembly 10U1 Set the values that envelope U1 individually for each longitudinal section. For example, when the model bundle is divided into three sections: the first node, the second to twenty-third nodes, and the twenty-fourth node as shown in FIG. 2, as shown in the infinite multiplication factor distribution line M1, the infinite multiplication factor k of the model bundle is set for each section. ∞M1 As a result, the infinite multiplication factor k of this embodiment ∞M1 is set to a value lower than the infinite multiplication factor distribution line M of the conventional model bundle in the range where the infinite multiplication factor is greater than the infinite multiplication factor distribution line L U1 to be enveloped. C1 can be made lower than that of the conventional model bundle.

[0085] FIG. 12 is a graph showing a modified example of the distribution characteristics of the infinite multiplication factor of the model bundle by the subcriticality evaluation method according to the first embodiment. FIG. 12 shows an example in the case where the composition distribution of the basic fuel assembly 10 is divided into four sections: the first node, the second to twelfth nodes, the thirteenth to twenty-third nodes, and the twenty-fourth node as shown in FIG. 3. At this time, the maximum value k of the infinite multiplication factor of the basic fuel assembly 10 indicated by the infinite multiplication factor distribution line L U2 takes four values for each section. Also, FIG. 12 shows a case where the model bundle 20 has four corresponding sections and takes four values. ∞R

[0086] In this case, as a result of changing the number of sections from three to four, the infinite multiplication factor distribution line M2 showing the infinite multiplication factor k of the model bundle has a further widened reduction compared to the infinite multiplication factor distribution line M ∞M2 showing the conventional infinite multiplication factor k ∞M2C and the effect of having a plurality of sections is further manifested. 2C

[0087] FIG. 13 is a flowchart showing the detailed procedure of the subcriticality confirmation step S50 of the subcriticality evaluation method according to the first embodiment.

[0088] First, read the specifications D3 of the fuel storage rack (step S51). That is, the effective multiplication factor calculation unit 133 reads the specifications D3 of the fuel storage rack stored in the fuel storage rack specifications storage unit 123.

[0089] Next, the effective multiplication factor k eff is calculated (step S52). That is, the effective multiplication factor calculation unit 133 calculates the effective multiplication factor k eff for the system in which the model bundle 20 is stored in the installation location (all lattices) of the fuel storage rack 50 (FIG. 4).

[0090] In addition, when the value of the effective multiplication factor k eff calculated in step S52 has little margin as a subcritical condition, that is, even if it is less than 1.0, for example, close to 0.95, it is conceivable to take measures such as restricting the number of fuel assemblies stored in the fuel storage rack 50.

[0091] As described above, according to the subcriticality evaluation device 100 and the subcriticality evaluation method according to the present embodiment, by setting a plurality of sections of the model bundle 20, it is only necessary to ensure the enveloping property of the infinite multiplication factor of the basic fuel assembly 10 for each section. As a result, compared with the case of setting specifications uniformly in the longitudinal direction as in the prior art to ensure the enveloping property, it is not necessary to set an excessively large infinite multiplication factor, and it is possible to perform a reasonable setting while ensuring the enveloping property.

[0092] [Second Embodiment] This embodiment is a modification of the first embodiment. Specifically, when the basic fuel assembly 10 is a MOX fuel assembly, the handling of the infinite multiplication factor of the model bundle of the 24th node in the uppermost section or the 1st node in the lowermost section is changed. Otherwise, it is the same as the first embodiment.

[0093] In the case of a MOX fuel assembly, the first node may not contain a burnable poison. In this case, the maximum infinite multiplication factor k ∞L3 of the first node becomes significantly larger compared to other nodes.

[0094] FIG. 14 is a graph showing the distribution characteristics of the infinite multiplication factor of the model bundle 20 according to the subcriticality evaluation method according to the second embodiment. FIG. 14 is a graph corresponding to FIG. 12 described in the first embodiment.

[0095] In FIG. 14, the infinite multiplication factor distribution line L showing the distribution of the infinite multiplication factor of the MOX fuel assembly M1 For the infinite multiplication factor distribution line L that is uniformly set across all nodes M1 The infinite multiplication factor distribution line M showing the infinite multiplication factor of the conventional model bundle set to enclose it CM , and for each of the three regions of the first node, the second to 23rd nodes, and the 24th node, L M1 The infinite multiplication factor distribution line M showing the infinite multiplication factor of the model bundle of the present embodiment individually set to enclose it M1 is plotted. The infinite multiplication factor distribution line L of the MOX fuel assembly M1 is an example where no burnable poison is included in the first node, and the infinite multiplication factor of that node is higher than the infinite multiplication factors of the other nodes. Also, since the infinite multiplication factor distribution line M of the present embodiment M1 can set the infinite multiplication factor individually for each node, it is possible to reasonably set a smaller infinite multiplication factor than the infinite multiplication factor distribution line M CM of the conventional model bundle over the longitudinal direction.

[0096] FIG. 15 is a graph showing a comparison example between the effective multiplication factor k eff obtained by the subcriticality evaluation method according to the first embodiment and the conventional case. The horizontal axis shows the cases of the conventional example (infinite multiplication factor M CM ) and the present embodiment (infinite multiplication factor M M1 ). The vertical axis shows the effective multiplication factor k eff .

[0097] As shown in FIG. 15, the effective multiplication factor k CM in the case of the conventional example (infinite multiplication factor M eff ) is about 0.95, and the effective multiplication factor k M1 in the case of the present embodiment (infinite multiplication factor M eff ) is about 0.91. In the case of the present embodiment, compared with the conventional example, the effective multiplication factor k eff decreases by about 0.04, that is, by about 4% Δk.

[0098] In the examples shown in FIGS. 14 and 15, although MOX fuel is targeted, the same effect can be obtained when uranium fuel is targeted.

[0099] As described above, according to the present embodiment, in a MOX fuel assembly in which the maximum value of the infinite multiplication factor throughout the entire combustion period in a node containing no burnable poison tends to be significantly larger than that of other nodes, since the infinite multiplication factor of the model bundle is set with an appropriate margin for each node position in the longitudinal direction, the infinite multiplication factor of other nodes excluding the node containing no burnable poison does not become excessively large, and a great effect of rationalization can be obtained by the subcriticality evaluation method according to the present embodiment.

[0100] FIG. 16 is a graph showing the distribution characteristics of the infinite multiplication factor of a model bundle according to a modified example of the subcriticality evaluation method according to the second embodiment.

[0101] In this modified example, as shown in part A of FIG. 16, the infinite multiplication factor k of the first node (first section) of the model bundle 20 ∞M3 can be set independently. Further, in the present embodiment, without enclosing the infinite multiplication factor of the MOX fuel assembly indicated by the infinite multiplication factor distribution line L M1 , the infinite multiplication factor of the first node (first section) is substantially at the same level as the infinite multiplication factors of the second to twelfth nodes (second section), and it is substantially divided into two sections.

[0102] In this modified example, the reason why it is not necessary to enclose the infinite multiplication factor of the basic fuel assembly 10 only for the first node (first section) is as follows.

[0103] In the core of a nuclear reactor in a critical state, due to the leakage of neutrons out of the core, the neutron flux distribution is low at the periphery, and the degree to which neutrons contribute to future nuclear fissions is smaller in the peripheral part of the core than in the central part of the core. Similarly, in a system in which the fuel assembly is stored in the fuel storage rack 50, the degree to which neutrons contribute to future nuclear fissions is smaller in the peripheral part than in the central part.

[0104] That is, in the first node, the infinite multiplication factor k ∞ increases, but when considering a system in which fuel assemblies are stored in the fuel storage rack 50, the contribution to the effective multiplication factor k eff of that system is small compared to the intermediate region. Since the quantity that should be originally evaluated is the effective multiplication factor k eff , even if the value of the infinite multiplication factor k ∞ in the first node is lowered, there is almost no influence on the effective multiplication factor k eff .

[0105] Therefore, by adjusting the first node to the infinite multiplication factors of the second node to the twelfth node, a more reasonable setting can be made. For example, if the reference infinite multiplication factors of the second to twelfth nodes (second section) were set high considering the reference infinite multiplication factor of the first node (first section), by releasing this condition, the reference infinite multiplication factors of the second to twelfth nodes (second section) can also be set lower as shown in FIG. 16.

[0106] [Third Embodiment] This embodiment is a modification of the second embodiment, and is characterized in that the setting of the reference infinite multiplication factor k ∞S depends on the weight ratio of fissile plutonium isotopes in the plutonium contained in the MOX fuel assembly at the time of unburned.

[0107] FIG. 17 is a block diagram showing the configuration of the subcriticality evaluation device according to the third embodiment.

[0108] The arithmetic unit 130a in this embodiment further includes a reference infinite multiplication factor arithmetic unit 134.

[0109] The reference infinite multiplication factor arithmetic unit 134 sets the reference infinite multiplication factor k ∞S depending on the weight ratio of fissile plutonium isotopes in the plutonium contained in the MOX fuel assembly 30 (FIG. 21) at the time of unburned. Details will be described below.

[0110] FIG. 18 is a graph showing the dependence characteristics of the reference value of the infinite multiplication factor on the fissile plutonium isotope ratio by the subcriticality evaluation device 100 according to the third embodiment. The horizontal axis of the graph is the fissile plutonium isotope ratio [%], that is, the weight ratio [%] of the fissile plutonium isotope in all plutonium contained in the MOX fuel assembly 30 at the time of unburned. The fissile plutonium isotopes are plutonium 239 and plutonium 241. Also, the vertical axis of the graph is the infinite multiplication factor k of the MOX fuel assembly 30 ∞ is.

[0111] In the region shown by part B of the graph in FIG. 18, it is indicated by four points, but the maximum infinite multiplication factor k ∞R which is the maximum value of the infinite multiplication factor throughout the entire combustion period of the MOX fuel assembly 30, generally has a positive correlation with the fissile plutonium isotope weight ratio. That is, the larger the fissile plutonium isotope weight ratio, the maximum infinite multiplication factor k ∞R tends to be larger. This is because although the weight of the fissile plutonium isotope does not increase, the fact that the weight ratio in the total amount of plutonium increases means that, conversely, the neutron absorption by non-fissile Pu-240 etc. contained in the MOX fuel assembly 30 decreases, and as a result, the number of neutrons increases.

[0112] In the model bundle of the conventional MOX fuel assembly, regardless of the fissile plutonium isotope weight ratio of the plutonium contained in the MOX fuel assembly, as a value enclosing the maximum value (k ∞R ) of the infinite multiplication factor throughout the entire combustion period, the reference infinite multiplication factor k ∞S which is the reference value of the infinite multiplication factor, is set to a constant value of 1.23 without depending on the fissile plutonium isotope ratio [%].

[0113] On the other hand, in this embodiment, the reference infinite multiplication factor k ∞S depends on the weight ratio of the fissile plutonium isotope in the plutonium contained in the MOX fuel assembly at the time of unburned, and the details will be described below.

[0114] In this embodiment, the reference infinite multiplication factor k ∞S is not a constant value, but a linear function of the weight fraction of fissile plutonium isotopes in plutonium. This linear function is such that, in the range where the effective multiplication factor (k eff ) of a system in which model bundles are stored in a fuel storage rack is equal to or less than the subcritical limit value of the effective multiplication factor (k limit ), the reference value of the infinite multiplication factor (k ∞S ) is set as large as possible.

[0115] When the reference infinite multiplication factor k ∞S is set to be larger than the maximum value (k ∞R ) of the infinite multiplication factor throughout the entire burnup period of the fuel assembly and smaller than the upper limit S1 of the value of the reference infinite multiplication factor k ∞S shown in FIG. 18, the reference infinite multiplication factor k ∞S can be expressed as follows.

[0116] That is, the upper limit value of the reference infinite multiplication factor k ∞S is a linear function of the weight fraction of fissile plutonium isotopes in plutonium. Specifically, the function is given by the following formulas (1) to (3) using the weight fraction (x) of fissile plutonium isotopes.

[0117] k ∞R <k ∞S <A × x + B ···(1)

[0118] 0 < A ≦ 0.002 ···(2)

[0119] 0 < B ≦ 1.126 ···(3)

[0120] Here, formulas (2) and (3) regarding coefficients and the like are examples, and may be appropriately reviewed based on the creation of the model bundle and the actual performance of using the model bundle when storing the actual fuel assembly.

[0121] FIG. 19 is a graph showing the distribution characteristics of the infinite multiplication factor of the model bundle by the subcriticality evaluation method according to the third embodiment. FIG. 20 is a graph obtained by enlarging a part of FIG. 19.

[0122] In this way, the reference value (k ∞S ) of the infinite multiplication factor at some nodes of the model bundle is set to be larger than the conventional 1.23 and smaller than the upper limit S1 of the reference value of the infinite multiplication factor in FIG. 13. In this case, an example where the effective multiplication factor (k eff ) of the system in which the model bundle is accommodated in the fuel storage rack 50 is equal to or less than the subcritical limit value (k limit ) of the effective multiplication factor will be described with reference to FIGS. 19 and 20.

[0123] FIG. 19 shows the infinite multiplication factor distribution line L M2 of the MOX fuel assembly with the fissile plutonium isotope weight ratio of 67% and the infinite multiplication factor distribution line M M3 of the model bundle. FIG. 20 is a graph obtained by enlarging the range of the 1st to 23rd nodes in FIG. 19.

[0124] When the fissile plutonium isotope weight ratio is 67%, as shown in FIG. 20, the upper limit S1 of the reference infinite multiplication factor is 1.26. In the case shown in FIGS. 19 and 20, the infinite multiplication factor M M3 of the model bundle is set to be larger than the conventional 1.23 at the 1st node and the 2nd to 23rd nodes and smaller than 1.26.

[0125] At this time, the effective multiplication factor (k eff ) of the system in which the model bundle of the reference infinite multiplication factor shown in FIGS. 19 and 20 is accommodated in the fuel storage rack is 0.93, which is equal to or less than 0.95, which is the subcritical limit value (k limit ) of the effective multiplication factor generally used in boiling water reactors. Therefore, even when the reference value (k ∞S ) of the infinite multiplication factor of the model bundle is larger than the conventional 1.23 and smaller than the upper limit S1 of the reference value of the reference infinite multiplication factor in FIG. 18, subcriticality is established.

[0126] FIG. 21 is a plan sectional view showing a configuration example of the MOX fuel assembly 30 obtained by the subcriticality evaluation method according to the third embodiment. In FIG. 21, the case of a 9×9 array is shown as an example, but other arrays may also be applicable.

[0127] The MOX fuel assembly 30 has a plurality of MOX fuel rods 31, a plurality of poison fuel rods 32, a water channel 13, and a channel box 14 that surrounds these from the radially outer side.

[0128] The MOX fuel rod 31 is a fuel rod containing fissile plutonium such as plutonium 239 and plutonium 241 as fissile materials. Further, the poison fuel rod 32 is a uranium fuel rod containing enriched uranium and a burnable poison.

[0129] In FIG. 20, the MOX fuel rods 31 are numbered from 1b to 4b according to the enrichment of fissile plutonium, which is the fissile material concentration, from the first type with the highest fissile material concentration to the fourth type with the lowest fissile material concentration.

[0130] Also, in FIG. 21, the poison fuel rods 32 are denoted by symbols G1b and G2b for the G1 type with high uranium enrichment and burnable poison concentration and the G2 type with low uranium enrichment and burnable poison concentration, respectively, according to the uranium enrichment and the concentration of the burnable poison. Here, the burnable poison is a nuclide having a large neutron absorption cross section particularly in the thermal neutron region, for example, gadolinium.

[0131] The MOX fuel rods 31 and the poison fuel rods 32 are arranged in a 9×9 lattice within the channel box 14, but the water channel 13 is arranged in the central 3×3 region.

[0132] The infinite multiplication factor k ∞R (j) in each section j in the longitudinal direction of the MOX fuel assembly 30 satisfies the above-mentioned formulas (1) to (3) depending on the weight ratio of fissile plutonium isotopes, and the reference infinite multiplication factor k ∞SIf it is smaller than (j), there is no limit to the magnitude of the infinite multiplication factor.

[0133] As described above, according to the present embodiment, corresponding to the weight ratio of the fissile plutonium isotope of plutonium contained in the MOX fuel assembly during unburned, the reference value (k ∞S ) of the infinite multiplication factor can be set reasonably higher than the conventional 1.23.

[0134] As described above, according to the embodiment, it is possible to provide a subcriticality evaluation method, a subcriticality evaluation device, and a MOX fuel assembly that can reasonably evaluate the subcriticality of the fuel assembly stored in the fuel storage rack 50.

[0135] [Other Embodiments] Although the embodiments of the present invention have been described above, the embodiments are presented as examples and are not intended to limit the scope of the invention. Also, the features of each embodiment may be combined. Furthermore, the embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the gist of the invention. The embodiments and their modifications are included in the scope and gist of the invention, and are also included in the invention described in the claims and the equivalent scope thereof.

Description of Reference Numerals

[0136] 10…Basic fuel assembly, 11…Enriched fuel rod, 12…Poison fuel rod, 13…Water channel, 14…Channel box, 20…Model bundle, 21…Enriched fuel rod, 22…Poison fuel rod, 30…MOX fuel assembly, 31…MOX fuel rod, 50…Fuel storage rack, 51…Lattice plate, 52…Lattice space, 100…Subcriticality evaluation device, 110…Input unit, 120…Memory unit, 121…Fuel assembly specifications memory unit, 122…Fuel assembly arrangement condition memory unit, 123…Fuel storage rack specifications memory unit, 124…Model bundle specifications memory unit, 125…Calculation condition memory unit, 126…Each data memory unit, 127…Calculation result memory unit, 130…Calculation unit, 131…Model bundle specifications setting and modification unit, 132…Infinite multiplication factor calculation unit, 133…Effective multiplication factor calculation unit, 135…Progress control unit, 140…Output unit

Claims

1. A subcriticality evaluation method for evaluating the subcriticality of a target fuel assembly to be evaluated, which is stored in a fuel storage rack immersed in light water, comprising: selecting a basic fuel assembly as a basis in the target fuel assembly, and reading a maximum infinite multiplication factor, which is the maximum value of the infinite multiplication factor throughout the entire burnup period, in each of a plurality of sections including the uppermost section, the lowermost section, and at least one intermediate section divided in the longitudinal direction in the basic fuel assembly; setting a reference infinite multiplication factor, which is a reference value of the infinite multiplication factor enveloping the maximum infinite multiplication factor, in each of the plurality of sections; for a model bundle, which is an analysis model for the evaluation of the subcriticality and has a plurality of the sections, adjusting the nuclear fuel material concentration of the model bundle so that a model infinite multiplication factor, which is the infinite multiplication factor in each of the plurality of sections, becomes larger than the reference infinite multiplication factor, and deriving the model infinite multiplication factor; deriving an effective multiplication factor in a state where the model bundle with the adjusted nuclear fuel material concentration is stored in the fuel storage rack; A subcriticality evaluation method characterized by comprising the above steps.

2. The subcriticality evaluation method according to claim 1, wherein the nuclear fuel material concentration is at least one of a uranium enrichment degree and a fissile plutonium enrichment degree.

3. The subcriticality evaluation method according to claim 1, wherein the target fuel assembly has a uranium fuel rod containing first enriched uranium and a uranium fuel rod with a burnable poison containing second enriched uranium and a burnable poison.

4. The subcriticality evaluation method according to claim 1, wherein the target fuel assembly is a MOX fuel assembly having a MOX fuel rod containing uranium and plutonium and a uranium fuel rod with a burnable poison containing enriched uranium and a burnable poison.

5. The subcriticality evaluation method according to claim 1, wherein in at least one of the uppermost section and the lowermost section, which does not contain a burnable poison, the reference infinite multiplication factor is set to be smaller than the maximum infinite multiplication factor.

6. The subcriticality evaluation method according to claim 4, characterized in that in the section, the larger the weight ratio of the fissile plutonium isotope of the MOX fuel assembly at the time of unburned, the larger the reference infinite multiplication factor is set.

7. The benchmark infinite multiplication factor satisfies the following formulas (1) to (3) when the weight ratio of the fissile plutonium isotope contained in the MOX fuel assembly is x, and is characterized in that the subcriticality evaluation method according to claim 6. k ∞Ｓ (i) < Ax + B …(1) 0 < A ≤ 0.002... (2) 0 < B ≤ 1.126... (3)

8. The fuel storage rack has a structure in which first metal plates are arranged in a square lattice so as to accommodate the target fuel assembly in the longitudinal direction, and the entire periphery of the lattice is covered with a second metal plate, and is characterized in that the subcriticality evaluation method according to claim 1.

9. A plurality of MOX fuel rods containing MOX fuel, A plurality of poison fuel rods containing burnable poison, A cylindrical water channel, A channel box that surrounds the plurality of MOX fuel rods, the plurality of poison fuel rods, and the water channel from the radially outer side, A MOX fuel assembly comprising: The infinite multiplication factor of each node divided in the longitudinal direction satisfies the following formulas (1) to (3) with respect to the weight ratio (x) of the fissile plutonium isotope contained in the MOX fuel assembly, and is characterized in that the MOX fuel assembly. k ∞Ｓ (i) <Ax + B...(1) 0 < A ≤ 0.002... (2) 0 < B ≤ 1.126... (3)

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