JP3100069B2 - Reactor operation planning method and apparatus, and reactor core characteristic monitoring apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for estimating and predicting power distribution and reactivity in a reactor core by numerical calculation and making a reactor operation plan. The present invention relates to a reactor operation planning method and a planning device thereof suitable for accurately determining the number.

[0002]

2. Description of the Related Art In order to accurately evaluate and predict core characteristics such as power distribution and reactivity in a reactor core, it is important to accurately grasp the material composition of nuclear fuel in each region in the core. is there. However, this material composition changes with the operation of the reactor due to the neutron nuclear reaction. Therefore, when calculating the core characteristics of a boiling water reactor, a detailed calculation (hereinafter, referred to as a single fuel assembly) assuming an infinite lattice system in which the fuel assemblies are arranged infinitely is described.
Aggregate calculation) is performed, and the neutron distribution of the aggregate is evaluated and the material composition in each fuel rod is tracked to obtain the aggregate characteristics at each time point. Usually, for one type of aggregate, aggregate calculations for several cases with different moderator densities are performed, and characteristic quantities such as the average nuclear reaction cross section and neutron infinite multiplication factor (hereinafter referred to as aggregate nuclei Is calculated, and the calculated values are arranged by values such as burnup, moderator density, and average combustion moderator density. In an actual core, different types of aggregates are mixed, and the moderator density and the burnup value differ depending on the arrangement position in the furnace. In the core calculation for obtaining the neutron distribution over the entire core and the reactivity of the entire core, the result of the assembly calculation is extrapolated to calculate the assembly nuclear constant according to the state in each region in the reactor. Such a calculation method is
For example, Nuclear Technology 33 (1977)
Page 18 (Nuclear Technology, 33 (1977),
p. 18).

A problem in the above calculation method is that an error occurs in the nuclear constant of the assembly because the situation around the assembly assumed in the assembly calculation is different from the situation around the actual core. That is, even when burning under the same moderator density, the reaction rate differs depending on the neutrons from the adjacent aggregate, and the composition change is shifted. For example, if a fuel assembly with high enrichment and a hard spectrum (low thermal neutrons) is adjacent to a fuel assembly with a low enrichment and soft spectrum (high thermal neutrons), the fuel assemblies adjacent to each other Due to body effects, the spectrum is softer in a highly enriched fuel assembly and conversely harder in a less enriched fuel assembly. As described above, since the spectrum of the fuel assembly is affected by the adjacent fuel, an error occurs in the nuclear constant obtained by the assembly calculation assuming the infinite lattice system. A method to reduce such errors is described in the proceedings of the 1988 International Reactor Physics Conference (198
8) Pages III-23 to III-25 (Proceedings of the
1988 International Reactor Physics Conference, p
p. III-23 to III-25, 1988). This method focuses on the distribution of the macrofission cross section value in the assembly, and calculates the parameter SH defined by the following equation (2).
Corrects the shift of the macrofission cross section distribution due to the influence of neighboring assemblies.

[0004]

(Equation 2)

As a method not relying on such correction,
There is a method described in Journal of the Atomic Energy Society of Japan 12, 1970, pp. 412 to 413, which tracks the material composition in each fuel rod in core calculation.

[0006]

SUMMARY OF THE INVENTION Among the above prior arts,
The method of tracking the material composition in the fuel rod by the core calculation has a problem that the amount of data necessary for the core calculation increases and the calculation time becomes enormous. Further, the method using the parameter SH focuses only on correcting the distribution of the macronuclear reaction cross section in the aggregate, and has a problem in that calculation of various nuclear constants of the aggregate average is not considered.

SUMMARY OF THE INVENTION An object of the present invention is to provide a new parameter for organizing the aggregate calculation results without greatly increasing the data amount, and for accurately determining the aggregate nuclear constant of each part in the reactor in the core calculation. An object of the present invention is to provide an operation planning method and a device thereof for a nuclear reactor used.

[0008]

The object of the present invention is to provide a new rearranging parameter << S >>

[0009]

(Equation 3)

This is achieved by introducing

Here, E represents the average burnup of the region of interest in the furnace. Further, φi and φj are a region-average neutron flux of a certain group i and a region-average neutron flux of another group j in a multi-group model in which neutrons are grouped in terms of their energy into several groups.

[0012] Features of the present invention, the value of the conventional combustion average moderator density instead of the parameters, using the parameter "S" represented by Equation 3 that is newly introduced, and organize a collection calculation result The nuclear constant of the region is determined based on the << S >> value of each region obtained at the time of core calculation. Regarding the core division, the above procedure is common to the case where the assembly is divided into units and the case where the fuel rods are divided into units.

Since the parameter << S >> is a parameter representing the composition change in the fuel in combination with the burnup, it is effective to set the neutron flux having a large influence on the composition change to φi or φj. is there. Therefore, in the thermal neutron reactor, the parameter << S >> is defined by the ratio of the neutron flux of the thermal neutron group including the energy range of about 0.01 to 0.1 eV to the neutron flux of the other groups. desirable.

When the present invention is viewed as a calculation algorithm or a core characteristic calculating device, means for storing the value of << S >> of each region in the furnace, and << A means for updating the value of S >> is provided.

[0015]

The reduction of the number density Nx of the nuclide x by the neutron nuclear reaction follows the following differential equation 4.

[0016]

(Equation 4)

If the situation around the assembly in the actual core differs from the situation assumed at the time of assembly calculation, both σ and φ (both suffixes are omitted) in Equation 4 above change. However, according to the analysis of the inventors, it was found that the change in σ was relatively small, and the shift in φ greatly affected the change in composition. That is, the essential quantity that characterizes the composition change is the neutron spectrum.

In the present invention, since the aggregate calculation result is used using the parameter << S >> representing the burning history of the neutron spectrum as an intermediary, the neutron spectrum is one-to-one in the core.
It is possible to set a more accurate nuclear constant than in the related art that mediates the average combustion moderator density that does not correspond to the above.

[0019]

An embodiment of the present invention will be described below with reference to the drawings. In the first embodiment of the present invention, the whole core is divided into cells of about 15 cm3 along the assembly boundary. Assuming that the inside of each cell is homogeneous, the neutron distribution and the effective neutron multiplication factor in the reactor are obtained by neutron diffusion calculation of three energy groups, and further, the heat output distribution in the reactor is calculated.

FIG. 1 is a flowchart showing the flow of the core calculation according to this embodiment. In a boiling water reactor, the moderator density distribution changes depending on the power distribution inside the reactor.
A nuclear thermal-hydraulic coupling calculation consisting of an iteration of the neutron diffusion calculation process and the thermohydraulic calculation process obtains a state in which the power distribution and the void fraction distribution are consistent. In order to combine nuclear calculation and thermohydraulic calculation, in the nuclear constant calculation process, calculate the void fraction of each cell obtained by thermohydraulic calculation and the cell average multi-group nuclear constant according to the control rod insertion state etc. I do.

The nuclear constant of the cell average in the present embodiment includes a diffusion coefficient, a macro absorption cross section, a macro scattering cross section,
Macro fission cross section. For these nuclear constants, the values in some representative states are obtained in the aggregate calculation for the aggregate alone, and in the nuclear constant calculation process in the core calculation, the values in each cell are extrapolated and calculated. Determine. The macro cross-section required for neutron diffusion calculation depends greatly on the material composition in the cell, but a huge storage capacity is required to record the detailed composition of each cell in the core calculation,
It is common to cite the aggregate calculation results using a small number of other parameters as composition indices. The present embodiment provides a new parameter which is an index of the composition.

The structure of the neutron energy group in the three-group model of this embodiment is 10 MeV to 5.5 keV in the first group, 5.5 keV to 0.625 eV in the second group, and 0.625 eV or less in the third group. Here, the spectrum index S is defined by the ratio of the cell average third group neutron flux φ ₃ obtained by the core diffusion calculation in each cell to the cell average first group neutron flux φ ₁ (S≡φ ₃ / φ ₁ ). The spectrum index S of each cell changes with the operation of the nuclear reactor. The average of the spectrum index S from the initial combustion to the burnup E of the cell is defined as a history spectrum << S >>.

[0023]

(Equation 5)

In this embodiment, the above-mentioned hysteresis spectrum << S >> and burn-up E
Is used. In addition, the nuclear constant of the cell is determined by the average moderator density U of each cell and the control rod insertion rate C. In the core burn-up calculation, the above-mentioned nuclear thermal-hydraulic coupling calculation is performed for each appropriate burn-up step. At this time, the burnup is updated and the history spectrum is also updated. When the cell burnup in the previous step is E ₀ , the new burnup is E, and the spectrum index of the cell from E ₀ to E is S, the history spectrum << S >> is updated by the following equation (6).

[0025]

(Equation 6)

In the aggregate calculation, a two-dimensional calculation is performed on a system in which aggregates of the same type and the same state are arranged infinitely. The nuclear constants obtained by the aggregate calculation for some states are stored in a table that can be extrapolated with the above parameters, and are quoted in the core calculation. The values set in the aggregate calculation are used for the moderator density, control rod insertion rate, and burnup. The history spectrum used for organizing nuclear constants is calculated based on the average neutron flux for combustion calculation for calculating the composition change in the aggregate calculation. In the burning calculation of the aggregate, the spectrum is set considering the neutron leakage effect from the aggregate.
It may not match the spectrum of a simple infinite system. However, since the history spectrum is an amount used as an index of the composition, it must be calculated based on the combustion calculation spectrum. The energy group structure is made to match the model of the core calculation described above. In order to evaluate the dependence on the history spectrum, the result of a plurality of aggregate combustion calculations with different moderator densities is used.

In the core calculation of the present embodiment, the spectrum itself in the combustion calculation of the assembly is used as a parameter serving as an index of the composition. This makes it possible to refer to a nuclear constant corresponding to a more appropriate composition as compared with the case where the conventional average combustion moderator density is used, thereby improving the core characteristic evaluation accuracy.

FIG. 2 is an infinite system composed of two types of aggregates assumed to show the quantitative effects of the present embodiment. The assembly 11 has an average enrichment of 1.75%, and the assembly 12 has an average enrichment of 3.50%. The void ratio in each assembly is 40%. The solid line in FIG. 3 shows the infinite multiplication factor change of the aggregate 11 when the combustion is advanced in the mixed system shown in FIG. 2, and the combustion is advanced assuming that the aggregate 11 is arranged infinitely (normal aggregate calculation). The change of the infinite multiplication factor of the (model) is shown by a broken line in FIG. At the early stage of combustion, φ ₃ / φ ₁ is 0.
In contrast, in a system in which the aggregates 12 are adjacent to each other, since high-energy neutrons flow into the aggregates 11, φ ₃ / φ ₁ of the aggregates 11 is 0.51. Under such low thermal neutron spectra, U-238 to Pu-
The transmutation rate to 239 is increased, and the fissile material is reduced or suppressed. Therefore, as combustion proceeds, the difference between the infinite multiplication factors increases as shown in FIG.

In the conventional core calculation method, the average combustion moderator density was used as a parameter indicating the combustion history. However, in the system shown in FIG. 2, since the void fraction is constant at 40%, the nuclear constant of the aggregate 11 of the mixed system In this case, an aggregate calculation result with a void ratio of 40% relating to a system including only the aggregate 11 is quoted.

On the other hand, in the calculation method of this embodiment, a combustion average value << S >> of S≡φ ₃ / φ ₁ is used as a combustion history parameter. The burnup of the aggregate 11 in a mixed system is 11 GWd / t
In this case, << S >> is 0.47. This value is the aggregate 1
This corresponds to the case of burning with a void ratio of about 48% in the system of only one.

FIG. 4 shows the infinite multiplication factor of the assembly 11 when calculating the nuclear constant with the conventional average combustion moderator density and the neutron spectrum history << S >> according to the present embodiment.
Shows the error when calculating the nuclear constant in. In the conventional method, an error of 0.6% occurs near the burnup of 11 GWd / t, whereas in the method of the present embodiment, the error is suppressed to 0.2%.

Next, a second embodiment of the present invention will be described. In this embodiment, the core is divided into rectangular parallelepiped cells each having a length of about 5 cm for each fuel pin. The inside of this cell is regarded as homogeneous, and the neutron flux distribution in the reactor is obtained by neutron diffusion calculation of a detailed mesh. The flow of the core calculation and the energy model in the neutron diffusion calculation are the same as in the first embodiment. The nuclear constant of the cell in this embodiment is the average macro cross-sectional area of the pin cell region including the fuel pin and the moderator around it. A nuclear constant table is prepared for each pin cell type in a format that can be interpolated with the same parameters as the first embodiment. In the present embodiment, the composition change is tracked for each fuel pin, so that a more accurate core characteristic analysis can be performed as compared with the first embodiment.

Next, a third embodiment of the present invention will be described. In the present embodiment, the nuclear parameter reduction method of the present invention is applied to the diffusion calculation method for one neutron energy group. As in the first embodiment, the entire core is divided into cells of about 15 cm cubic along the boundary of the assembly, and the neutron diffusion calculation is performed with the inside of the cells being homogeneous. In this embodiment, the nuclear calculation is performed using a one-group diffusion model obtained by reducing the three-group model.

[0034]

(Equation 7)

In the first lens group model, since φ ₂ and φ ₃ cannot be directly obtained, the value of K is approximately evaluated as shown in the following equation 8.

[0036]

(Equation 8)

The nuclear constants of the cells in this calculation method are K (Ｋ), M ² , f, and R described above. In order to calculate these nuclear constant values in the core calculation, the moderator density U, the control rod insertion rate C, the burnup E, and the hysteresis spectrum << S >> are used. The history spectrum << S >> is the average burnup of the spectrum index S defined above. Then, as in the first embodiment, K (∞), M ² , f, R
Are arranged in a format that can be extrapolated by the above parameters U, C, E, << S >>. The history spectrum << S >> is arranged based on the spectrum used for the combustion calculation of the aggregate calculation.

In this embodiment, since the one-group diffusion calculation is performed by approximately evaluating K, the amount of necessary nuclear constant is small, and the time required for the diffusion calculation can be shortened.

Next, a fourth embodiment of the present invention will be described. The present embodiment is an example applied to a core characteristic analysis in a case where a soluble neutron absorbing material (soluble poison) is mixed into a moderator and a core is operated in a pressurized water reactor or the like. The fuel cell is divided for each fuel pin, and the nuclear characteristics are evaluated based on the two-group diffusion model. In this embodiment, the soluble poison concentration B, the burnup E, and the hysteresis spectrum << S >> are used as parameters for calculating the nuclear constant of the pinsel. Since the two-group diffusion model is used, the nuclear constant includes a diffusion coefficient, a macro absorption cross section, a macro scattering cross section, and a macro fission cross section. Using these, two-group diffusion calculation is performed to obtain the neutron effective multiplication factor and the neutron flux distribution of each group. Further, using the obtained neutron flux distribution, a detailed power distribution in the reactor is calculated.

In this calculation method, the first group is 10 MeV to 0.6 MeV.
25 eV and 0.625 eV or less in the second group. Define the spectral index S by 1 group neutron flux phi ₁ and 2 group neutron flux phi ₂ ratio, a value obtained by averaging in burnup E a historical spectrum "S".

[0041]

(Equation 9)

In order to evaluate the dependence of the nuclear constant on the history spectrum, the result of burning calculation of a plurality of aggregates having different soluble poison concentrations is used. In the first embodiment, the history spectrum is mainly introduced as a parameter that considers the difference in the composition change due to the difference in the moderator density. However, in the present embodiment, the difference in the composition change due to the difference in the soluble toxic substance concentration is considered. Parameter. In this way, by arranging the nuclear constants using the combustion spectrum itself closely adhering to the composition change as a parameter, it is possible to cite an appropriate nuclear constant regardless of the cause of the difference in the spectrum.

In the calculation methods of the first to third embodiments, the present invention can also be applied to the case where the nuclear constant table is arranged by the average combustion moderator density as in the conventional method. After calculating the hysteresis spectrum << S >> by the method described in the first embodiment or the third embodiment, an equivalent combustion average moderator is used such that the average value of the combustion spectrum in the aggregate calculation matches this value. Find the density Ueq. For this purpose, a correspondence table between the history spectrum << S >> and the average combustion moderator density is prepared for each type of assembly. Then, using the moderator density U, control rod insertion rate C, burnup E, and equivalent combustion average moderator density Ueq, the same nuclear constant table as in the conventional method is extrapolated to determine the nuclear constant of the cell. According to this method, the conventional nuclear constant table can be used as it is,
The present invention can be easily applied.

Next, another embodiment of the present invention will be described. This embodiment is an example of a case where the nuclear constant database is arranged by the average combustion moderator density in the same manner as the conventional method in the nuclear constant calculation of the first embodiment. In this case, correspondence data between the spectral ratio S and the moderator density, and correspondence data between the parameter << S >> and the average combustion moderator density are prepared for each assembly type and representative burnup. The equivalent moderator density and the average combustion moderator density are calculated from S, << S >> and the burnup E, and then the corresponding nuclear constant is calculated from the nuclear constant database. Such S,
By associating << S >> with the moderator density and the combustion average moderator density, the present invention can be easily applied to the conventional characteristic calculation method.

Next, still another embodiment of the present invention will be described. This embodiment is also an example of a case where the nuclear constant database is organized by the moderator density and the combustion average moderator density as in the previous case. In this embodiment, the moderator density and the combustion average deceleration are determined by the difference between S and the spectrum ratio S (∞) in the infinite system, and the difference between << S >> and the combustion average spectrum ratio << S (∞) >> in the infinite system. Correct the nuclear constants arranged by material density. The infinite multiplication factor is corrected as in the following Expression 10.

[0046]

(Equation 10)

Incidentally, the correction may be made by the following equation 11 instead of the equation 10.

[0048]

[Equation 11]

FIG. 5 is a block diagram of an apparatus for predicting the core characteristics in accordance with the above-described calculation procedure, drafting an operation plan, and monitoring the core performance. The present apparatus comprises a nuclear constant calculating means 20
Neutron diffusion calculation means 21, history spectrum (update) calculation means 22, and nuclear constant table storage means 23. The history spectrum calculation unit 22 updates the history spectrum value based on the spectrum index value calculated by the neutron diffusion calculation unit 21 and the output distribution. When used as a core performance monitoring device, the history spectrum value is updated by the power distribution measurement value evaluated by processing the signal from the in-core instrumentation system 24 and the spectrum index from the neutron diffusion calculation means 21. I do.

[0050]

According to the present invention, high-precision nuclear constant data can be given to each part in the core, so that core characteristics such as power distribution and reactivity in the reactor can be accurately predicted. In addition, the operation of the plant becomes easy.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a flow of core calculation according to an embodiment of the present invention.

FIG. 2 is a configuration diagram of an infinite system core composed of two types of assemblies.

FIG. 3 is an analysis diagram showing a difference in a combustion change of a neutron infinite multiplication factor between a homogeneous system and a heterogeneous system.

FIG. 4 is a graph showing an evaluation error between the embodiment of the present invention and the prior art.

FIG. 5 is a configuration diagram of an operation planning device according to an embodiment of the present invention.

[Explanation of symbols]

20: Numerical constant calculation means, 21: Neutron diffusion calculation means, 2
2 ... history spectrum (update) calculation means, 23 ... nucleus constant table storage means.

──────────────────────────────────────────────────続 き Continuing from the front page (72) Inventor Yoshihiko Ishii 1168 Moriyama-cho, Hitachi City, Ibaraki Prefecture Within the Energy Research Laboratory, Hitachi, Ltd. Engineering Co., Ltd. (72) Inventor Mitsuya Nakamura 3-2-1 Sachimachi, Hitachi City, Ibaraki Prefecture Hitachi Engineering Co., Ltd. (72) Inventor Seiichi Yuki 3-2-1 Sachimachi, Hitachi City, Ibaraki Hitachi (56) References JP-A-1-199195 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) G21C 17/00

Claims (10)

(57) [Claims] 1. A nuclear reactor cross-sectional area required for each neutron transport calculation and neutron diffusion calculation is calculated to evaluate the power distribution and reactivity in the reactor core, and a control rod is inserted into the reactor. In the operation planning method for a reactor for preparing a plan, the energy of neutrons in each region is divided into a plurality of groups, and a region average neutron flux φi of one group i and a region average neutron flux φj of another group j are defined as The reactor operation is characterized in that the calculated value of the aggregate nuclear constant is arranged by using the average value of the ratio φi / φj of the burnups, and the nuclear reaction cross section is obtained by the arranged aggregated nuclear constant calculated value. Planning method. 2. A nuclear constant calculation is performed on the assumption of an infinite lattice system for each type of fuel assembly, and a one-group diffusion calculation on neutron energy is performed using the obtained nuclear constant value, and the power distribution in the reactor is calculated. In a nuclear reactor operation planning method for calculating core characteristics such as reactivity and drafting a plan for inserting a control rod into a reactor, the fuel assembly type in a region of interest in the reactor and a region adjacent thereto is provided. , The neutron energy is divided into a plurality of groups and one group i and another group j
Furnace average neutron flux .phi.i, obtaining the ratio .phi.i / .phi.j of .phi.j, a furnace core constants of the space required for the first group diffusion calculation using a value obtained by averaging relates burnup the ratio .phi.i / .phi.j A method for planning an operation of a nuclear reactor. 3. A value obtained by averaging a ratio of a region average neutron flux φi of one group i to a region average neutron flux φj of another group j with respect to a region average burnup E according to claim 1 or 2. When represented by << S (E) >>, An operation planning method for a nuclear reactor, characterized in that: 4. The method according to claim 1, wherein
Either group or group j is about 0.01-0.1 eV
A method for planning an operation of a nuclear reactor, comprising a group of thermal neutrons including a range of energy. 5. The core according to claim 1, wherein when calculating core characteristics such as the amount of fissile material of a core in which a plurality of types of columnar fuel assemblies having different compositions are regularly arranged. A method for calculating the operation of a nuclear reactor, wherein the boundary is calculated by making the boundary of the column coincide with the boundary of the arrangement of the columnar fuel assemblies. 6. The core according to claim 1, wherein when calculating core characteristics such as the amount of fissile material of a core in which a plurality of types of columnar fuel assemblies having different compositions are regularly arranged. The operation planning method for a nuclear reactor, wherein the calculation is performed by making the boundaries of the fuel rods coincide with the arrangement boundaries of the fuel rods. 7. The neutron flux ratio φi / φj in each region in a reactor when calculating a neutron flux distribution by a group model relating to neutron energy according to claim 2 .
And calculating the average value based on the calculated values to determine the nuclear constants of the first group model such as the neutron infinite multiplication factor in the region. 8. The method according to claim 1, wherein
Several tables are organized by average combustion moderator density
When using the constant table to determine the nuclear constant, one
Group-averaged neutron flux in one group and region-averaged neutron flux in other groups
The average of the ratio of
In both cases, the value of the average combustion moderator density equivalent to the averaged value is calculated.
The equivalent combustion average moderator density value and the nuclear constant table
Nuclear constants from nuclear reactors
Drawing method . 9. A nuclear reactor cross-sectional area in each region required for neutron transport calculation and neutron diffusion calculation is determined, power distribution and reactivity in the reactor core are evaluated, and a control rod is inserted into the reactor. In the operation planning method of a reactor for making a plan, detection means for detecting neutron energy in each of the regions,
Means for dividing the detected neutron energy into a plurality of groups according to the magnitude of the detected value to obtain a ratio between the area average neutron flux of one group and the area average neutron flux of another group; Means for organizing the calculated value of the aggregate nuclear constant using the obtained average value, and means for obtaining the nuclear reaction cross-sectional area with the calculated aggregate nuclear constant calculated value. Furnace operation planning device. 10. A reactor core characteristic monitoring method for calculating a nuclear reaction cross-sectional area of each region in a reactor necessary for neutron transport calculation and neutron diffusion calculation to evaluate power distribution and reactivity in a reactor core. The neutron energy in each region is divided into a plurality of groups, and the calculated value of the aggregate nuclear constant is obtained by averaging the ratio of the region average neutron flux of one group to the region average neutron flux of the other group with respect to the burnup. And a means for estimating a nuclear reaction cross-sectional area based on the calculated calculated nuclear constant of the assembly, and a means for evaluating core characteristics from the obtained nuclear reaction cross-sectional area. Monitoring device.