JP2016142623A - Method and apparatus for measuring effective delayed neutron fraction - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technology for precisely measuring an effective delayed neutron fraction without requiring a special instrument.SOLUTION: A method for measuring an effective delayed neutron fraction comprises the steps of: obtaining a critical water level of a core tank housing a core; slightly elevating the level and obtaining reactivity applied to a core system of the core by the slight elevation; obtaining extrapolation distance in a core axial direction; determining a calculation code for calculating an effective neutron multiplication factor of the core system; using the determined calculation code to obtain an infinite multiplication factor of a fuel rod cell representing the core system; using the determined calculation code to obtain a proportion of neutron leakage in a lateral direction to neutron leakage in an axial direction of the core system; and obtaining an effective delayed neutron fraction of the core system on the basis of the acquired information about the critical water level, etc. and the obtained information about the extrapolation distance in the core axial direction, etc.SELECTED DRAWING: Figure 6

Description

  Embodiments described herein relate generally to a method for measuring an effective delayed neutron ratio and a measurement apparatus thereof.

  Commercial reactors for power generation require high economic efficiency, but first of all it is essential to ensure safety. Therefore, when constructing a commercial nuclear reactor, the application for permission to install a nuclear reactor requires a study on the operational performance of the nuclear reactor, and it is necessary to study in detail the stability when a disturbance is applied during steady operation. Is done.

  Stability is also called transient characteristics of the reactor. When the reactor is in a steady operation state, the reactor operates stably even if physical conditions change due to changes in the performance of peripheral equipment that supports the operation state. A detailed study will be done on whether the state can be maintained or can be safely stopped. For example, in a commercial light water reactor power plant, light water in the core tank is circulated by a motor-driven pump, but even if the rotation speed of this motor changes and the circulation speed of the water in the core changes, the output of the nuclear reactor It is designed not to go up suddenly and into a dangerous state.

  The theory used when investigating the changes in power output of a nuclear reactor is called a dynamic equation, and an important concept in the dynamic equation is a physical quantity called reactivity. Reactivity is a physical quantity that controls temporal changes in nuclear fission reaction (power). Positive reactivity increases nuclear fission reaction, and negative reactivity decreases fission reaction. In the case of positive reactivity, the rate of time increase of the fission reaction increases as the value increases.

  The magnitude of the reactivity is discussed by the ratio to the effective delayed neutron fraction, ie the value divided by the effective delayed neutron fraction. The magnitude of the reactivity when the reactivity is equal to the effective delayed neutron ratio is called 1 dollar (dollar). When the reactivity is 1 $, the nuclear fission reaction increases explosively, leading to what is called a reactivity accident. Therefore, in commercial light water reactors, in any case, the reactor is designed so that a positive reactivity of $ 1 is not added.

The delayed neutron fraction is a physical quantity that distinguishes neutrons by paying attention to the time difference of neutrons released by fission reaction. In the fission reaction, tens of seconds to several hundreds of microseconds [μsec], that is, prompt neutrons released in about 10 ^-4 seconds and neutrons delayed by several tens of seconds due to decay events from fission products (fission fragments) There is. The proportion of neutrons that are generated late is called the delayed neutron proportion.

For example, when uranium 235 ( ²³⁵ U) undergoes fission, approximately 99.3% of the generated neutrons are prompt neutrons and the remaining approximately 0.7% are delayed neutrons. The role of delayed neutrons is great. If all neutrons are promptly neutral, the time for generating neutrons after fission is about ^10-4 seconds, but 0.7% is delayed neutrons. For example, the effective time for fission and generation of neutrons is about 0.07 seconds.

In the reactor, not only ²³⁵ U but also uranium 238 ( ²³⁸ U) has undergone fission, and the proportion of delayed neutrons differs between ²³⁵ U and ²³⁸ U, respectively. This is an average value obtained by examining in detail the behavior of the fission state of the entire reactor core. This value is called the effective delayed neutron ratio. Also, by convention, this value is often called “beta effective” βeff (beta effective).

  The effective delayed neutron ratio (beta effect) βeff of the core is the most important value in evaluating the effect of reactivity added to or subtracted from the reactor. It can be said that a reactor with a larger effective delayed neutron ratio has less influence on the disturbance that changes the nuclear fission reaction.

  To summarize the above, when evaluating changes (transient characteristics) due to disturbances in the nuclear fission reaction in a commercial reactor, a quantitative evaluation is made using a dynamic characteristic equation. The ratio of effective delayed neutrons, which calibrate the size of, is a very important physical quantity.

  In addition, before constructing and operating commercial power reactors, reactor physics tests to see if the fission reaction behaves as designed, and the ability of the control rod to stop the fission reaction, etc. In this case, the effect is evaluated using the effective delayed neutron ratio value.

  Thus, the effective delayed neutron ratio is an extremely important basic physical quantity directly related to operation and safety in commercial power reactors. The effective delayed neutron ratio is a very important numerical value for grasping the dynamic characteristics and reactivity change of the reactor, and if it can be actually measured by experiment, the calculation code (calculation program) can be calculated. It greatly contributes to the validity of the method, confirmation of the quality of the nuclear data used, and improvement of the quality. Therefore, there is a great need and desire to measure the effective delayed neutron ratio by critical experiments.

  On the other hand, this effective delayed neutron ratio is a physical quantity that is extremely difficult to obtain by measurement. Several methods have been proposed so far, but at present, it is temporally, economically, and technically feasible to actually measure the effective delayed neutron ratio in commercial reactors for power generation. Is extremely low. Therefore, in a commercial nuclear reactor, a computer is used to perform detailed calculations using a high-quality computer program (often called computer code) and a well-established nuclear data library to obtain an average value for the nuclear reactor. The effective delayed neutron ratio is calculated.

  In this case, check the accuracy and quality of the calculation method, the computer program (computer code) used for the calculation, and the delayed neutrons for each fissile nuclide recorded in the nuclear data library. There is a need. Because the value of delayed neutrons for each fissile nuclide is a physical quantity that is directly related to the safety of commercial reactors for power generation, it is extremely important to understand the calculation accuracy of this effective delayed neutron ratio. It is. And in order to confirm the reliability of the design and operation of commercial reactors, there is a great demand for confirming the calculation accuracy of the effective delayed neutron ratio.

  Several projects have been carried out to confirm the accuracy of calculating the effective delayed neutron ratio. In the past, there has been an international benchmark experiment of βeff measurement conducted by the Japan Atomic Energy Research Institute (JAERI) and the French Atomic Energy Agency (CEA) from 1996 (1998) to 1998 (1998). This was a joint experiment between France and Japan aimed at measuring the effective delayed neutron fraction with a critical experiment device for the purpose of comparing with the calculated values.

  The method of measuring the effective delayed neutron ratio is a technique that evaluates physical quantities by mathematically processing the signal based on reactor noise (such as neutron detector signal fluctuations). REACTOR NOISE) has been measured based on theory. Among these methods, the Bennett method (neutron correlation experiment method) was used in this international benchmark experiment. The feature of this measurement is the technique of obtaining the measured value from the covariance value by electrically processing the output signal of the neutron detector based on the reactor noise theory and obtaining the measured value from the covariance value. Yes.

JP 2008-217139 A

  In the neutron correlation measurement using the Bennett method described above, it is necessary to correlate the signals of the neutron detectors, so that at least two types of neutron detectors having very similar detection characteristics and the neutron detectors are obtained. It is necessary to have a processing device that performs signal processing on the electrical signal to be generated. Of these, the electrical signal processing itself is not so difficult with current computer technology, but at least two types of neutron detectors with very similar detection characteristics can always be prepared easily. It is not a thing. For this reason, preparation of the system of the whole experiment is not easy, and time and economical cost are required. That is, there is a problem that any critical experimental apparatus is not a method that can be easily applied using current equipment.

  Thus, in the conventional technology, it is necessary to calculate the effective delayed neutron ratio with high accuracy in terms of safety and design for commercial reactor design and operation, and the calculation code used for the calculation There is a need (need) to confirm the quality of nuclear data. On the other hand, when comparing the quality of the calculation code and nuclear data with the effective delayed neutron ratio βeff measured with a critical experiment device, the measurement is not easy, so a lot of time and cost are required. It was.

  In view of the circumstances described above, an embodiment of the present invention aims to provide a technique for accurately measuring the effective delayed neutron ratio without requiring a special device.

  In order to solve the above-described problem, a method for measuring an effective delayed neutron ratio according to an embodiment of the present invention supplies water into a core tank that houses a core in which a plurality of fuel rods are arranged at intervals in the horizontal direction. This is an effective delayed neutron ratio measurement method for calculating the effective delayed neutron ratio of a critical device that achieves criticality by adjusting the water level of the light water, and is the water level in the core tank when the criticality is achieved Obtaining a critical water level, and slightly increasing the water level in the core tank from the critical water level, and based on the output from the neutron detector for detecting neutrons resulting from the fission reaction in the critical device, the water level The step of obtaining the reactivity applied to the core system of the core by the rise of the core, obtaining the nuclear axial fission rate distribution of the critical device, and based on the obtained axial axial fission rate distribution A step of obtaining an extrapolation distance in the axial direction, and selecting one calculation code of the calculation program from a plurality of calculation programs prepared for calculating the effective neutron multiplication factor of the core system of the core Using one calculation code, the geometry and atomic density of the core system of the core and the critical water level, the neutron effective multiplication factor is calculated using the obtained values, and the calculation result is A step of determining whether or not the selected calculation code is correct based on whether or not it is within a set allowable error range, and if it is acceptable, confirming the selection of the selected one calculation code And representing the core system by a calculation code determined to pass the calculation accuracy among a plurality of calculation programs prepared for calculating the neutron effective multiplication factor of the core system of the core Calculating the neutron leakage in the lateral direction and the axial direction of the core system using the calculation code determined in the step of determining the infinite multiplication factor of the fuel rod cell and the step of determining the selection of the calculation code, respectively. Determining the ratio of the lateral neutron leakage to the axial neutron leakage of the core system from the results, the effective delayed neutron ratio of the core system of the core, the critical water level, the rise in the water level, the reactivity From the relationship between the axial extrapolation distance, the infinite multiplication factor of the fuel rod cell representing the core system, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, Infinite multiplication factor of representative fuel rod cell, critical water level, rise of water level, reactivity, extrapolation distance in the axial direction, and neutron leakage in the axial direction of the core system Obtaining a ratio of lateral neutron leakage to obtain an effective delayed neutron ratio of the core system of the core.

  In order to solve the above-described problem, the effective delayed neutron ratio measuring apparatus according to the embodiment of the present invention supplies water into a core tank that houses a core in which a plurality of fuel rods are arranged at intervals in the horizontal direction. This is an effective delayed neutron ratio measuring device that calculates the effective delayed neutron ratio of the critical device that achieves criticality by adjusting the water level of the light water, and is the water level in the core tank when the critical is achieved Based on the output from the critical water level acquisition unit for obtaining the critical water level, and the output from the neutron detector that slightly raises the water level in the core tank from the critical water level and detects neutrons resulting from the fission reaction in the critical device , A reactivity acquisition unit for obtaining the reactivity added to the core system of the core due to the rise of the water level, and obtaining the core axial fission rate distribution of the critical device, and obtaining the obtained core axial fission rate fraction An axial extrapolation distance acquisition unit for obtaining an extrapolation distance in the axial direction based on the calculation code of the calculation program from a plurality of calculation programs prepared for calculating the neutron effective multiplication factor of the core system of the core And selecting one of the calculation codes, the geometry and atomic density of the core system of the core and the critical water level, and using the obtained values, the neutron effective increase is obtained. The magnification is calculated, and when the calculation result is within the set allowable error range, the selection of the selected one calculation code is confirmed, and the infinite number of fuel rod cells representing the core system is determined by the determined calculation code. The infinite multiplication factor acquisition unit for obtaining the multiplication factor and the neutron leakage in the lateral direction and the axial direction of the core system are calculated by the determined calculation code, respectively, and the axial direction of the core system is calculated from the calculation result. Neutron leakage ratio acquisition unit for determining the ratio of lateral neutron leakage to neutron leakage, the effective delayed neutron ratio of the core system of the core, the critical water level, the rise in water level, the reactivity, the axial direction The fuel rod cell representing the core system from the relationship between the extrapolation distance, the infinite multiplication factor of the fuel rod cell representing the core system, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system Obtaining an infinite multiplication factor, the critical water level, an increase in the water level, the reactivity, the extrapolated distance in the axial direction, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, And an effective delayed neutron ratio acquisition unit for obtaining an effective delayed neutron ratio of the core system of the core.

  According to this embodiment, in the tank-type critical experiment equipment for the purpose of research on light water reactors, the current experimental technology and calculation method can be used without adding new equipment only by using the existing equipment. The effective delayed neutron ratio can be accurately measured.

The elevation sectional view showing the composition of the critical experiment device which the measuring device of the effective delayed neutron ratio concerning an embodiment makes object. FIG. 2 is a plan view of a core constituted by a 19 × 19 system, which is an example of the core of the critical experiment apparatus shown in FIG. 1. FIG. 2 is a plan view of a core constituted by a 28 × 28 system, which is an example of a core of the critical experiment apparatus shown in FIG. 1. The block diagram which shows the structure of the measuring apparatus of the effective delayed neutron ratio which concerns on embodiment. The block diagram which shows the more detailed structure of the calculating part in the measuring apparatus of the effective delayed neutron ratio which concerns on embodiment. The processing flow figure (flowchart) of the effective delayed neutron ratio measurement procedure which the measuring apparatus of the effective delayed neutron ratio which concerns on embodiment performs. The flowchart which illustrates the processing flow of the experimental system parameter acquisition process (step S1: FIG. 6) in an effective delayed neutron ratio measurement procedure. The flowchart which illustrates the processing flow of the calculation system parameter acquisition process (step S2: FIG. 6) in an effective delayed neutron ratio measurement procedure. The flowchart which illustrates the processing flow of the infinite multiplication factor correction process (step S4: FIG. 6) in an effective delayed neutron ratio measurement procedure. The flowchart which shows the processing flow which concerns on the 1st example (step S5a: FIG. 6) of the effective delayed neutron ratio calculation process (step S5: FIG. 6) in an effective delayed neutron ratio measurement procedure. The flowchart which shows the first half part of the processing flow which concerns on the 2nd example (step S5b: FIG. 6) of the effective delayed neutron ratio calculation process in an effective delayed neutron ratio measurement procedure. The flowchart which shows the second half part of the processing flow which concerns on the 2nd example of the effective delayed neutron ratio calculation process in an effective delayed neutron ratio measurement procedure.

  Hereinafter, a method for measuring an effective delayed neutron ratio and a measurement apparatus thereof according to an embodiment of the present invention will be described with reference to the drawings. In the description, substantially the same components are denoted by the same reference numerals, and redundant description is omitted.

[Critical experiment equipment]
FIG. 1 is an elevational sectional view showing a configuration of a critical experiment apparatus 1 targeted by an apparatus for measuring an effective delayed neutron ratio according to an embodiment of the present invention.

  The critical experiment apparatus 1 is an example of a critical experiment apparatus for the purpose of research and development of commercial reactors for power generation, particularly light water reactors. The critical experiment apparatus 1 includes, for example, a fuel rod 3 disposed in a core tank 2, a control rod 5 for controlling the reactivity of the core 4, a neutron detector 6 for detecting neutrons generated as a result of the reaction, and a core tank 2 In addition, it is configured as a tank-type critical experiment apparatus including a supply / discharge section 7 having a liquid supply section 7a and a drainage section 7b for supplying and discharging light water (supply or discharge).

The core tank 2 is a container having an open top, and can store the core 4 and light water (H ₂ O) as a moderator. Further, the core tank 2 is provided with a supply / discharge section 7 (7a, 7b) for supplying / discharging light water, and the liquid level in the core tank 2 is adjusted by supplying / discharging light water from the supply / discharge section 7. be able to. Further, the core tank 2 is provided with a liquid level transmitter 8 for measuring the liquid level in the tank.

  The fuel rod 3 is supported by its own weight on the fuel support plate 9 at the lower end. The fuel rod 3 is supported by lattice plates 11a and 11b. More specifically, the upper and lower portions of the fuel rod 3 are supported by the upper lattice plate 11a and the lower lattice plate 11b, respectively. The outputs of the neutron detector 6 and the liquid level transmitter 8 are input to the measuring device 30 (FIG. 4). Here, the measuring apparatus 30 can be realized by, for example, a computer in which a measurement program 50 that causes the computer to function as the measuring apparatus 30 is installed.

  In the critical experiment apparatus 1 illustrated in FIG. 1, after gradually increasing the amount of light water in the core tank 2 to a certain height determined by the operation procedure, the core tank 2 is further supplied by the supply / discharge unit 7. The core 4 is made critical by adjusting the level of the light water.

  FIGS. 2 and 3 are plan views of an example of the core 4 of the critical experiment apparatus 1 targeted by the effective delayed neutron ratio measuring apparatus according to the embodiment of the present invention. FIG. 2 is a 19 × 19 system. FIG. 3 is a plan view of the core 4 constituted by a 28 × 28 system.

  The nuclear material used in the core 4 of the critical experiment apparatus 1 has a shape similar to that of the fuel of a fuel assembly of a normal commercial light water reactor, that is, a shape called a fuel rod 3. The fuel rods 3 are arranged in a square lattice pattern such as 19 × 19 at regular intervals. Here, the enrichment of the fuel rods 3 is all the same (one type).

  The core 4 has, for example, a rectangular parallelepiped shape in which the horizontal cross section has a square shape and the square horizontal cross section extends in the vertical direction. When the shape of the core 4 is a rectangular parallelepiped shape, the core shape is set such that the length and width are sufficient and the horizontal cross section is not too small. For example, the length of one side of the square in the horizontal section is set to 40 cm or more. The effective critical water level obtained from the effective length of the fuel rod 3 is set to exceed 90 cm. Here, the critical water level is the water level in the core tank 2 when the core 4 achieves criticality.

  Therefore, in the critical experiment apparatus 1, the fuel rod 3 can be easily loaded and removed from the core 4, and the gamma ray emitted from the fuel rod is measured by increasing the ratio of the fission reaction. The fission reaction rate can be measured from the gamma ray emission rate at the position.

  Note that, in the effective delayed neutron ratio measuring apparatus according to the embodiment of the present invention, it is necessary to accurately obtain the ratio of the ratio of leakage in the axial direction and the lateral direction of the core system. Is preferably a rectangular parallelepiped shape as illustrated in FIGS. However, even in the case of a cylindrical shape, it is possible to accurately obtain the ratio of the axial and lateral (radial) leakage ratio by appropriate measurement and calculation, so the axial and lateral leakage ratio. As long as the above ratio can be accurately obtained, the core system may have a shape other than a rectangular parallelepiped such as a cylindrical shape.

The fuel rod 3 to be used is generally a uranium dioxide (UO ₂ ) fuel rod, but may be another type of fuel rod such as a fuel rod containing plutonium (Pu).

[Measurement principle]
The measurement method of the effective delayed neutron ratio and the measurement principle in the measurement apparatus according to the embodiment of the present invention will be described.

  The basic theory is a simple one-point reactor dynamics equation representing the temporal change in nuclear fission reaction in seconds, the inverse time equation derived from the dynamic equation, and the critical condition of the reactor. The modified group 1 diffusion equation expressed in Hereinafter, the related theory and mathematical formula will be mainly described.

(A) Inverse time equation Starting from a critical experimental system, an operation that increases the fission reaction is performed, and the fission reaction (neutron flux or output has the same meaning) is doubled (multiplication time) : Doubleing time). The reactivity added to the experimental system is obtained from this multiplication time. The equation used to determine the reactivity is called an inverse time equation, and can be obtained by Laplace transforming the equation based on the one-point furnace dynamic characteristic equation. For example, when the delayed neutrons are divided into six groups (groups) of the first group to the sixth group, the reactivity ρ ($ unit) uses an inverse time equation represented by the following formula (1). Can be calculated.

What is important here is the effective delay required for the calculation of the inverse time equation represented by the equation (1) (here, the inverse time equation of the 6-group format adapted to the above example is assumed). The neutron ratio is the ratio (relative value) a _i of each group, and even if the value obtained by a simple technique is used, the degree of reactivity ρ ($ unit) can be calculated with sufficient accuracy. That is, a sufficiently accurate reactivity ρ can be obtained without using a numerical value that is accurately obtained by a complicated method for obtaining the reactivity.

The advantage that the value obtained by such a simple method can be used is that the decay constant λ _i, which is one of the numerical values for each group used in the inverse time equation represented by the equation (1), is an experimental system. Is a constant value, and the numerical value related to the delayed neutron ratio is a relative value for each group (that is, the total of 6 groups is set to 1.00). This is due to the fact that the proportion of the data to be transmitted is small (substantially does not depend on the experimental system).

Therefore, for example, the well-known value of Keepin (values of ²³⁵ U and ²³⁸ U nuclides alone) is directly substituted into the inverse time equation (formula (1)) for the ratio a _i of each group of effective delayed neutron ratios. Thus, even when the reactivity (¢ unit: reactivity of 1/100 of 1 $) is calculated, the value of the obtained reactivity (¢) itself hardly changes. In addition, if it can be estimated that the fission rate is 95% for ²³⁵ U and 5% for ²³⁸ U in the experimental system, the values of ²³⁵ U and ²³⁸ U for the measured values of Keepin are 0.95,. It is sufficient to take the sum of products at the rate of 05. The same applies to the case of obtaining the reactivity with a reactivity meter described later.

(B) Reactivity meter Some critical experiment apparatuses are equipped with a reactivity meter that can display the reactivity added to the experimental system as a numerical value every time. When the critical experimental device for measuring the effective delayed neutron ratio includes a reactivity meter, the reactivity added to the experimental system can be obtained directly from the reactivity meter.

  In the reactivity meter, a technique called an IK (Inverse Kinetics) method (reverse motion characteristic method) is mainly used. The equation on which the IK method is based is a one-point reactor dynamic characteristic equation, and the reactivity can be obtained by using the output signal of the neutron detector as an input.

  In the IK method, the ratio (ratio) of the effective delayed neutron ratio of each group to the effective delayed neutron ratio is required. However, as with the inverse time equation, it is sufficient to use a value obtained by a simple method. It is. Moreover, the reactivity which can be calculated | required with a reactivity meter is a $ unit.

(C) Dynamic characteristic parameters (numerical data of delayed neutron precursor nuclei in group 6)
Both the method for obtaining the reactivity by solving the inverse time equation (water level difference method) and the method for obtaining the output of the reactivity meter based on the inverse dynamics method as the reactivity (sample driving method) are one point. It is based on the reactor dynamic characteristic equation. Usually, the early nuclei of delayed neutrons treated in the one-point reactor dynamics equation are often handled in six groups based on the value of the time constant that decays and releases neutrons. Is explaining the case of being divided into six groups (groups) of the first group to the sixth group. The dynamic characteristic parameters are required for both the inverse time equation and the reactivity meter, but vary depending on the core configuration.

(D) Water level reactivity coefficient After making the core system configured in the critical experiment apparatus critical, if the water level is raised slightly from the critical water level z obtained, the fission reaction (output) starts to increase, and the neutron detector If the multiplication time is measured based on the above signal and the inverse time equation is used or the reactivity meter is used, the reactivity ρ ($ unit) applied to the core system can be obtained. At the same time, the value of the water level Δz increased with respect to the critical water level z is accurately measured using a water level meter. The water level reactivity coefficient can be calculated as ρ / Δz at a height of z + Δz / 2.

  The characteristic of the above formula (4) is based on the concept of treating neutron energy as one group without considering the difference due to energy with respect to the neutron flux of the reactor. Therefore, it is assumed that the buckling included in the right side of the above formula (4) does not depend on the energy of the neutron flux and has the same value. In an embodiment of the present invention, numerical values are processed assuming that the axial neutron flux follows a cosine distribution with respect to the modified first group diffusion equation.

Here, in a general critical experiment apparatus including a critical experiment apparatus 1 described later, in many cases, the axial cross section has the same core cross section at any position with respect to the effective length position of the fuel rod, and can be regarded as homogeneous. Therefore, the axial neutron flux distribution may be considered as a cosine distribution. In this case, buckling B _Z ² of the core in the axial direction (z-axis direction) is represented by the following formula (5).

  Further, in this reactivity measurement, the measurement is started from the critical state, and the degree of reactivity to be changed is not so large. That is, the neutron effective multiplication factor (keff) is always considered to be about 1.00 even if the reactivity change is brought about in the core. Applying all of these assumptions, and based on the modified group 1 diffusion equation, the water level reactivity coefficient can be expressed as the third power of the sum of the effective water level and the extrapolated distance (effective water level + extrapolated distance).

(F) Theoretical formula of the water level reactivity coefficient In deriving the theoretical formula of the water level reactivity coefficient used in the present invention, (F-1) that the modified group 1 diffusion equation can be applied in the experimental system, (F-2) the core It is assumed that the axial distribution can be approximated by a cosine distribution, and (F-3) that the water level difference between the case with and without the measurement sample is about several centimeters [cm] to 10 centimeters [cm].

  Here, in order for the above assumption (F-1) to be sufficiently established, it is necessary that the core system configured in the critical experiment apparatus is not excessively small.

  In order for the above assumption (F-2) to be fully established, the axial configuration of the core configured in the critical experiment apparatus has a homogeneous configuration, that is, the radial configuration of the core differs in the axial position. In short, it is important that the radial configuration is the same at any position in the axial direction. Of course, there are structures such as a lower grid plate for inserting and supporting fuel rods in the lower part in the core axis direction, and there is an upper grid plate and air in the upper part, so the upper and lower ends cannot be completely the same configuration. However, the homogenous configuration with respect to the axial configuration of the core mentioned here is not a strict meaning, but means that the configuration is homogeneous in the axial direction within the effective length range of the fuel rod. Therefore, it suffices to satisfy that the configuration is homogeneous in the axial direction within the effective length range of the fuel rod.

Here, a virtual neutron infinite multiplication factor (infinite neutron multiplication factor) in the radial section of the core system is denoted as k _∞ , and a lateral (radial) buckling in the core system (usually referred to as Br ² ). In many cases, A), M ^{2 is} the core area moving area (Migration area), z is the core effective axial height, δ is the axial extrapolation distance, and π is the circumference. For these physical quantities, it is assumed that the core effective axial height z changes, but other physical quantities remain constant (do not change) during this experiment (period).

Under the above assumption, assuming that the axial neutron flux distribution is a cosine distribution, buckling B _Z ² in the longitudinal direction of the core system (axial direction) is expressed by the above equation (5). Further, the effective neutron multiplication factor keff of the core is expressed by the following formula (6) in the modified first group diffusion theory.

(G) Method for calculating effective delayed neutron ratio (beta effective: βeff) The effective delayed neutron ratio βeff is obtained from the measured value of the water level reactivity coefficient. Since the water level reactivity coefficient of the value of water level z + Δz obtained from the measured value is $ units (value divided by βeff), it is expressed by the following formula (11) from the above formula (10). If equation (11) below is transformed and solved by βeff, equation (12) below is obtained.

[measuring device]
FIG. 4 is a block diagram showing a configuration of an effective delayed neutron ratio measuring apparatus (hereinafter simply referred to as “measuring apparatus”) 30 which is an example of an effective delayed neutron ratio measuring apparatus according to an embodiment of the present invention. is there.

  The measuring device 30 can be realized by, for example, a computer in which a measuring program 50 (FIG. 1) that causes a computer to function as the measuring device 30 is installed. That is, the measuring device 30 can be realized by, for example, the cooperation of a computer that is a hardware resource and a measurement program 50 that is a software resource.

  The measuring device 30 includes, for example, an input unit 31 that inputs information, an output unit 32 that outputs information, a transmission unit 33 that transmits information to and from an external device, a calculation unit 34 that performs calculation processing, A storage unit 35 that provides a storage area in which reading (reading) and writing (writing) are possible, and a control unit 36 that controls these processing units 31 to 35 are provided.

  The input unit 31 has a function as an input interface (input unit) for inputting information, and is configured by an input device such as a keyboard and a mouse, for example.

  The output unit 32 has a function as an output interface (output unit), and includes, for example, a general display unit that performs output by image display, a print unit that performs output by printing, and a voice output unit that outputs sound. Consists of output means.

  The transmission unit 33 has an information transmission function with an external device. In the measurement device 30, outputs from the neutron detector 6 (FIG. 1) and the water level transmitter 8 (FIG. 1) as external devices are input to the measurement device 30 via the transmission unit 33.

  The calculation unit 34 outputs the output of the neutron detector 6 that detects neutrons generated in the critical experiment apparatus 1 (FIG. 1) and the output of the water level transmitter 8 that measures the liquid level in the core tank 2 (FIG. 1). Based on this, an operation for measuring the effective delayed neutron ratio is executed. Details of the calculation unit 34 (FIG. 5) will be described later.

  The storage unit 35 includes a storage area in which data can be read (read) and written (write), and has a function of holding data in the storage area. The storage unit 35 holds information necessary for the execution of the calculation for the calculation unit 34 to measure the effective delayed neutron ratio, and is read as necessary when the calculation is executed.

  In the measurement apparatus 30, the calculation unit 34 is referred to, for example, as the measurement program 50 (FIG. 1) and the measurement program 50 as information necessary for the execution of the calculation for measuring the effective delayed neutron ratio. Information such as parameters and calculation formulas is held in the storage unit 35. In addition, when the measuring device 30 provides a program (calculation code) for obtaining an infinite multiplication factor of fuel rod cells representing the core system of the core 4, the program is also stored in the storage unit 35.

  As the calculation code, for example, a calculation code capable of calculating a representativeity factor (Representativeity factor) using a covariance matrix of a nuclear data library, and a calculation code capable of transporting a critical experiment apparatus in a three-dimensional system are provided. Use. As the former calculation code, for example, there is a SCALE system developed at a national laboratory in the United States. Examples of the latter calculation code include a DANTSYS system developed in the United States.

  The control unit 36 has a function of controlling the input unit 31, the output unit 32, the transmission unit 33, the calculation unit 34, and the storage unit 35. When information is input from the input unit 31, the control unit 36 receives the input information, and based on the received information, issues a command to the processing unit necessary for processing execution and controls it.

FIG. 5 is a block diagram showing a more detailed configuration of the calculation unit 34 in the measurement apparatus 30.
The calculation unit 34 includes, for example, a critical water level acquisition unit 34a, a reactivity acquisition unit 34b, an axial extrapolation distance acquisition unit 34c, a calculation code applicability determination unit 34d, an infinite multiplication factor acquisition unit 34e, and a neutron leakage A ratio acquisition unit 34f, an infinite multiplication factor correction unit 34g, a moving area acquisition unit 34h, and an effective delayed neutron ratio acquisition unit 34i are provided.

  The critical water level acquisition unit 34 a has a function of obtaining the water level in the core tank 2. The critical water level acquisition unit 34a receives a signal from the liquid level transmitter 8 for the critical water level z that is the water level in the core tank 2 when the core 4 of the criticality experiment apparatus 1 (FIG. 1) achieves criticality. Obtain the critical water level z when the criticality is achieved. Even when the water level in the core tank 2 is slightly increased (Δz) from the critical water level z, the water level z + Δz in the core tank 2 after the increase is received by receiving a signal from the liquid level transmitter 8. You can get about.

  The reactivity acquisition unit 34b slightly (Δz) raises the water level in the core tank 2 from the critical water level z acquired by the critical water level acquisition unit 34a to z + Δz, and neutrons generated as a result of the fission reaction in the critical experiment apparatus 1 On the basis of the output from the neutron detector 6 for detecting the reactivity, the reactivity ρ added to the core system of the core 4 due to the rise of the water level is obtained.

  More specifically, the reactivity acquisition unit 34b increases the neutron flux to be doubled based on the output from the neutron detector 6 as a function for obtaining the reactivity ρ added to the core system of the core 4. Using the function of measuring the double time and the value of a known fissile material (constant), the number of delayed neutrons grouped in advance into a predetermined number (for example, six groups) that matches the core system of the core 4 Using the function to calculate the ratio of the effective delayed neutron ratio for each group to the effective delayed neutron ratio for each group, and the obtained multiplication time and the ratio of the effective delayed neutron ratio for each group to the effective delayed neutron ratio Thus, for example, it has a function of calculating the reactivity ρ using a method such as a method for solving an inverse time equation or an IK method (reverse dynamic characteristic method).

  When the reactivity acquisition unit 34b employs a method of solving the inverse time equation as a method of calculating the reactivity ρ, the ratio of the effective delayed neutron ratio for each group to the obtained multiplication time and the effective delayed neutron ratio And the reactivity ρ is calculated using the above-described equation (1).

  Further, when the reactivity acquisition unit 34b employs the IK method (reverse motion characteristic method) as a method for calculating the reactivity ρ, the effective delay for each group with respect to the obtained multiplication time and the effective delayed neutron ratio. The reactivity ρ is obtained by using the ratio of the neutron ratio and the one-point reactor dynamic characteristic equation that is the basis of the IK method.

  In addition, when the critical experiment apparatus 1 (FIG. 1) includes a reactivity meter, the reactivity acquisition unit 34b may acquire the output value of the reactivity meter as the reactivity ρ.

  The axial extrapolation distance acquisition unit 34c obtains the core axial fission rate distribution of the critical experiment apparatus 1 (FIG. 1), and sets the axial extrapolation distance δ based on the obtained core axial fission rate distribution. It has the required function. As for the nuclear fission rate distribution of the critical experiment apparatus 1 (FIG. 1), for example, the fuel rod 3 at an appropriate position in the center of the core 4 is extracted, and integral γ-ray measurement is performed with respect to the axial direction of the fuel rod 3. Can be obtained. Further, the extrapolation distance δ in the axial direction can be obtained by fitting (calculating) the obtained core axis direction fission rate distribution to a cosine curve.

  It should be noted that the fuel rod 3 at an appropriate position in the center of the core 4 is preferably the case where the core system of the core 4 is composed of an odd number of sides as in a 19 × 19 type (FIG. 2). In the case where the fuel rod 3 located in the center of the core 4 and the core system of the core 4 are composed of an even number of sides such as a 28 × 28 type (FIG. 3), the four in the position close to the center Any one of the fuel rods 3.

  The calculation code applicability determination unit 34d calculates the neutron effective multiplication factor using the calculation code used for the calculation execution selected by the user, and determines whether the calculation result is within the set allowable error range.

  Since the neutron effective multiplication factor keff calculated by the calculation code is calculating the critical state, it should be physically neutron effective multiplication factor keff = 1, but the calculation method of the nuclear data library and calculation code The effective neutron multiplication factor keff is not necessarily 1 due to the influence of the error based on the above. Therefore, an allowable error is set in advance for the theoretical value of 1.

  The calculation code applicability determination unit 34d determines that the result of calculating the effective neutron multiplication factor keff is within a preset allowable error range, and selects the selected calculation code in the axial direction of the core system of the critical experiment apparatus 1 (FIG. 1). On the other hand, if the result of calculating the effective neutron multiplication factor keff is not within the set allowable error range, it is determined that the method is not applicable.

The infinite multiplication factor acquisition unit 34e obtains the infinite multiplication factor k _∞ of the fuel rod cell representing the core system of the critical experiment apparatus 1 (FIG. 1) based on the calculation code determined to be applicable.

  The neutron leakage ratio acquisition unit 34f calculates the neutron leakage in the lateral direction and the axial direction of the core system of the critical experiment apparatus 1 (FIG. 1) based on the calculation code determined to be applicable, and the core system is calculated from the calculation result. The ratio of lateral neutron leakage to axial neutron leakage is determined.

The infinite multiplication factor correction unit 34g is obtained by the infinite multiplication factor acquisition unit 34e in consideration of an error recognized from the difference between the effective neutron multiplication factor obtained by the calculation code used by the infinite multiplication factor acquisition unit 34e and 1. It has a function to correct the infinite multiplication factor. Thus, the measuring device 30 is provided with a infinite multiplication factor correcting unit 34g is because there is a possibility that an error occurs in the calculated value of the infinite multiplication factor k _∞ of the infinite multiplication factor acquisition unit 34e can calculate .

Error occurring in the calculation value of the infinite multiplication factor k _∞ is due to errors and uncertainty contained in the core data library used in the calculation. Therefore, the infinite multiplication factor correction unit 34g performs infinite multiplication factor correction processing in consideration of errors and uncertainties included in the nuclear data library (the principle of error correction for the infinite multiplication factor k _∞ and specific processing contents). Will be described later).

  Whether or not the effective delayed neutron ratio is calculated using the corrected infinite multiplication factor corrected by the infinite multiplication factor correction unit 34g (the infinite multiplication factor acquisition unit 34e without the correction determines the infinite multiplication factor). Whether to calculate the effective delayed neutron ratio using the multiplication factor) is alternatively determined by the setting of the measurement apparatus 30. For example, by setting whether the infinite multiplication factor correction is set to “ON” or “OFF”, the measuring apparatus 30 uses the corrected infinite multiplication factor to determine whether to calculate the effective delayed neutron ratio. Can be switched.

The moving area acquisition unit 34h calculates and acquires at least the moving area of the core system for obtaining the average moving area of the core 4 (FIG. 1) by the first method (hereinafter referred to as “first moving area calculation”). Called "function"). Further, the moving area acquisition unit 34h has a function of calculating and acquiring the moving area of the core system for obtaining the average moving area of the core 4 by the second method (hereinafter, referred to as an additional (optional) function). referred to as "second moving area calculation function".) and a first determined using the first and transfer area M ₁ ² obtained by using the first moving area calculation function and the second transfer area calculation function 2 and a transfer area M ₂ ² of the functions of the weighting calculation.

The first method, by substituting the parameters of the critical water level and the like obtained from measurement equations derived from the modified first group diffusion theory, a method of calculating a first transfer area M ₁ ^2. In the first method, the critical water level obtained by the critical water level acquisition unit 34a, the extrapolation distance in the axial direction obtained by the axial extrapolation distance acquisition unit 34c, and the infinite increase of fuel rod cells obtained by the infinite multiplication factor acquisition unit 34e. Based on the magnification (or the corrected infinite multiplication factor corrected by the infinite multiplication factor correction unit 34g) and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system obtained by the neutron leakage ratio acquisition unit 34f, the first The moving area M ₁ ² is calculated.

The second method is based on reliable calculation, that is, using a calculation code determined to be applicable in advance, the effective delayed neutron ratio (estimated value) calculated by this calculation code, the obtained critical water level, etc. by substituting in the formula is derived parameters and the corrected one group diffusion theory, a method for calculating a second transfer area M ₂ ^2. In the second method, the effective delayed neutron ratio (estimated value) calculated by the calculation code determined to be applicable in advance, the critical water level obtained by the critical water level acquisition unit 34a, the rise in the water level, and the reactivity The reactivity obtained by the acquisition unit 34b, the axial extrapolation distance obtained by the axial extrapolation distance acquisition unit 34c, and the infinite multiplication factor of the fuel rod cell representing the core system obtained by the infinite multiplication factor acquisition unit 34e based on the bets, calculates a second transfer area M ₂ ^2.

If to be obtained in the form of use as far as possible the measurement of only the critical experiment effective delayed neutron fraction, in formula (17) may be ignored second transfer area M ₂ ^2. That is, it handled as v given as error or appropriate weights are estimated to occur at the time of obtaining the second transfer area M ₂ ² is zero (v = 0).

For a more detailed theory such as the derivation of the equations (15) and (16) used to determine the average moving area M ² of the core 4 (FIG. 1), the average moving area M ^{The second} effective delayed neutron ratio calculating step (FIGS. 11 and 12) for determining the effective delayed neutron ratio using ² will be described (described later).

  The effective delayed neutron ratio acquisition unit 34i is configured to determine the effective delayed neutron ratio of the core system of the core, the critical water level, the rise in the water level, the reactivity, the extrapolation distance in the axial direction, and the infinite number of fuel rod cells representing the core system. From the relationship between the multiplication factor and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, at least the infinite multiplication factor of the fuel rod cell that represents the core system, the rise in water level, the reactivity, the axial direction Is obtained, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system is obtained to obtain the effective delayed neutron ratio of the core system of the core.

  The effective delayed neutron ratio βeff acquired in this way is sent to the output unit 32 as an output interface as a measurement result of the measurement device 30. The effective delayed neutron ratio βeff sent to the output unit 32 is provided to the user as visual information, for example, displayed on a display.

  5 includes a critical water level acquisition unit 34a, a reactivity acquisition unit 34b, an axial extrapolation distance acquisition unit 34c, a calculation code applicability determination unit 34d, and an infinite multiplication factor acquisition. Although it is an example provided with the part 34e, the neutron leakage ratio acquisition part 34f, the infinite multiplication factor correction | amendment part 34g, the movement area acquisition part 34h, and the effective delayed neutron ratio acquisition part 34i, it is not necessarily limited to this example.

  The calculation unit 34 includes at least a critical water level acquisition unit 34a, a reactivity acquisition unit 34b, an axial extrapolation distance acquisition unit 34c, an infinite multiplication factor acquisition unit 34e, a neutron leakage ratio acquisition unit 34f, and an effective delay. What is necessary is just to provide the neutron ratio acquisition part 34i. That is, the calculation code applicability determination unit 34d, the infinite multiplication factor correction unit 34g, and the moving area acquisition unit 34h are optional components for the measurement apparatus 30, and are not necessarily provided in the calculation unit 34.

  For example, the calculation unit 34 includes a critical water level acquisition unit 34a, a reactivity acquisition unit 34b, an axial extrapolation distance acquisition unit 34c, an infinite multiplication factor acquisition unit 34e, a neutron leakage ratio acquisition unit 34f, and an effective delayed neutron ratio acquisition unit 34i. In the example including, the pass / fail determination of the calculation accuracy of the selected calculation code performed by the calculation code applicability determination unit 34d is executed by another computer different from the measurement device 30.

  The measuring device 30 receives a selection of a calculation code that is determined to have passed the calculation accuracy from a calculation code of the calculation program, and obtains an infinite multiplication factor when receiving a selection of the calculation code to be executed. The unit 34e starts calculation for obtaining the infinite multiplication factor of the fuel rod cell representing the core system by one calculation code selected, and obtains the infinite multiplication factor.

  The measurement of the effective delayed neutron ratio βeff by the measurement device 30 described above requires evaluation by calculation, but it is not so difficult to calculate based on today's calculation technique, and can be obtained by a calculated value with little error. It is also useful that no special equipment is required for the measurement itself.

[Measurement method of effective delayed neutron ratio]
Subsequently, a method for measuring the effective delayed neutron ratio according to the embodiment will be described. In the method for measuring the effective delayed neutron ratio according to the embodiment, the effective delayed neutron ratio in the critical experiment apparatus 1 (FIG. 1) is measured by the measuring apparatus 30.

Here, the core 4 disposed in the critical experiment apparatus 1 is
(I) The enrichment of the fuel rods 3 to be used is one type (ii) The pitch of the fuel rods 3 is constant (iii) The rectangular parallelepiped system has a rectangular cross section, and the above (i) to (i) It is assumed that the condition (iii) is satisfied.

  In measuring the effective delayed neutron ratio, attention should be paid so that the core configuration of the core 4 is sufficiently small in length and width and the cross section is not too small. For example, care should be taken that the length of one side of a square appearing as a cross section is 40 cm or more.

  The number of fuel rods 3 arranged on one side is preferably an odd number of fuel rods 3 arranged on one side because of the necessity to set the fuel rod 3 positioned at the center of the core 4 in the radial cross section. However, even if the number of fuel rods 3 arranged on one side is an even number, measurement is possible if the fuel rod 3 corresponding to the center of the core 4 is appropriately set.

  Further, in the critical experiment apparatus 1, the effective critical water level obtained from the effective length of the fuel rod 3 is set to exceed 90 cm.

  FIG. 6 is an explanatory diagram (flow chart) for explaining the processing flow of the effective delayed neutron ratio measurement procedure for measuring the effective delayed neutron ratio performed by the measuring apparatus 30. The subroutine (steps S1, S2, S4, S5 (specifically S5a, S5b)) in the flowchart shown in FIG. 6 will be described in detail with reference to the other drawings (FIGS. 7 to 11). .

  Upon receiving an execution request for the effective delayed neutron ratio measurement procedure (steps S1 to S5), the measurement device 30 executes the effective delayed neutron ratio measurement procedure (START). The effective delayed neutron ratio measurement procedure is executed as a parameter acquisition step (steps S1 and S2) for acquiring parameters necessary for measuring the effective delayed neutron ratio, and when necessary (in the case of YES in step S3). And an infinite multiplication factor correction step (step S4) for correcting the infinite multiplication factor acquired in the parameter acquisition step, and an effective delayed neutron ratio calculation step (step S5).

  The parameter acquisition step (steps S1 and S2) includes experimental system parameters (critical water level, water level rise from the critical water level, reactivity added to the core system due to the water level rise) obtained by the experiment using the critical experiment apparatus 1 (FIG. 1). And an extrapolation distance in the axial direction) (step S1) and calculation system parameters (fuel rods representing the core system) obtained by executing a calculation program for calculating the neutron effective multiplication factor of the core system A step (step S2) of obtaining an infinite multiplication factor of the cell and a ratio of the lateral neutron leakage to the axial neutron leakage of the core system.

  In the parameter acquisition step (steps S1 and S2), the calculation unit 34 in the measurement apparatus 30 acquires experimental parameters and calculation parameters. When the calculation unit 34 acquires the experimental system parameter and the calculation system parameter, it checks whether or not there is an execution request as to whether or not to execute the infinite multiplication factor correction step (step S4) (step S3).

  If there is a request to execute the infinite multiplication factor correction process (YES in step S3), the arithmetic unit 34 executes the infinite multiplication factor correction process and stores the corrected infinite multiplication factor (step S4). Thereafter, the calculation unit 34 executes an effective delayed neutron ratio calculating step (steps S5 (S5a, S5b)) using the corrected infinite multiplication factor to calculate an effective delayed neutron ratio. When the effective delayed neutron ratio is calculated, the calculation result is given to the output unit 32, and the output unit 32 outputs the calculation result as a measurement result of the effective delayed neutron ratio.

  When the calculation process of the effective delayed neutron ratio (step S5) is completed and the calculation result of the effective delayed neutron ratio, that is, the measurement result of the effective delayed neutron ratio is obtained, the calculation unit 34 measures the effective delayed neutron ratio. The procedure (step S1 to step S5) is terminated (END).

  On the other hand, in step S3, when there is no execution request for the infinite multiplication factor correction process (NO in step S3), the infinite multiplication factor obtained in step S2 is used when calculating the effective delayed neutron ratio. The Thereafter, the effective delayed neutron ratio measurement procedure proceeds to step S5 (S5a, S5b), and the effective delayed neutron ratio calculation step is executed.

  In the effective delayed neutron ratio measurement procedure illustrated in FIG. 6, in the parameter acquisition step (steps S1 and S2), the calculation system parameter acquisition step (step S2) is executed after the experimental system parameter acquisition step (step S1). However, the calculation system parameter acquisition process may be started without waiting for completion of all the processing steps of the experimental system parameter acquisition process. The calculation system parameter acquisition step is performed after the critical water level is acquired in the experimental system parameter acquisition step (step S11: FIG. 7), even if other experimental system parameters are not acquired. Can start.

  FIG. 7 is a flowchart showing a processing flow of an experimental system parameter acquisition step (step S1: FIG. 6) for acquiring experimental system parameters.

  In the experimental system parameter acquisition step (steps S11 to S14: FIG. 7), the measurement device 30 uses the critical water level z, the water level rise Δz from the critical water level, and the reactivity ρ applied to the core system as the water level rises as the experimental system parameters. And a parameter of the extrapolation distance δ in the axial direction.

  The experimental system parameter acquisition step includes a critical water level acquisition step (step S11) for acquiring a critical water level z, a water level increase acquisition step (step S12) for acquiring a water level increase Δz from the critical water level, and a reactivity ρ. A reactivity acquisition step (step S13), and an extrapolation distance acquisition step (step S14) for acquiring the extrapolation distance δ.

  Experimental system parameters including critical water level z, water level rise Δz from critical water level, reactivity ρ applied to the core system due to the water level rise, and axial extrapolation distance δ are liquid level transmitter 8 (FIG. 1), etc. The measurement device 30 (FIGS. 1 and 4) is automatically supplied from the device of FIG. 4 manually by the user operating the input unit 31 (FIG. 4) or both of them.

  Next, a critical experiment by the critical experiment apparatus 1 (FIG. 1) performed to acquire experimental system parameters will be described. Prior to the critical experiment, it is assumed that the critical experimental apparatus 1 including the core 4 for measurement is prepared.

(1) Measurement of critical water level z The critical experiment apparatus 1 is brought into a critical state. Let the water level of the core tank 2 in the critical state be the critical water level z. The critical water level z means a measured water level obtained by converting the critical water level with the lower end position of the fuel pellet of the fuel rod 3 as the origin (zero), and is a value called an effective critical water level. The critical experiment apparatus 1 is provided with a liquid level transmitter 8, and the critical water level z can be obtained from a signal transmitted from the liquid level transmitter 8.

(2) Acquisition of Reactivity ρ When the critical experiment apparatus 1 is brought into a critical state, the water level of the core tank 2 is raised by about 10 to 20 [mm] from the critical water level z. If the water level of the core tank 2 is raised, the fission reaction increases and the indicated value of the neutron detector 6 increases. This increase rate is checked, and the time (multiplication time) for which the indicated value is doubled is recorded (acquired). Further, the raised water level width Δz (or the raised water level z + Δz) is recorded. The water level of the core tank 2 can be obtained from a signal transmitted from the liquid level transmitter 8. The water level width Δz to be raised is adjusted in advance so that the multiplication time is about 60 seconds to 100 seconds based on simple calculation or experimental experience and confirmation.

  Subsequently, after recording the multiplication time, the reactivity ρ applied to the critical experiment apparatus is acquired from the multiplication time. Examples of the method for obtaining the reactivity ρ include the above-described methods (for example, the output of the reactivity meter, the calculation by the inverse dynamic characteristic method, or the inverse time equation (formula (1)) is solved).

(3) Acquisition of extrapolation distance δ The extrapolation distance δ is determined by measuring the axial fission distribution (power distribution) of the fuel rod 3 located in the center of the core system.

  In the critical experiment apparatus 1, after bringing the core 4 into a critical state, the fission reaction (output) is increased, and then the target fuel rod 3 (located in the core center) is taken out and integrated γ-ray measurement is performed. Thus, the axial fission rate distribution (power distribution) of the fuel rod 3 is obtained.

  Instead of the integral γ-ray measurement, a method of calculating (determining) the axial fission rate distribution (output distribution) of the fuel rod 3 that is theoretically the target by calculation may be employed. This is because of the calculation theory used in the current reactor calculation code and the quality of the calculated values, in a critical experiment of such a rectangular parallelepiped system with high homogeneity, after standardizing each with very high accuracy. This is because the calculated value matches the measured value.

  The calculation codes that can be used for the above calculation include, for example, a calculation code based on diffusion theory, a continuous energy general purpose Monte Carlo code that solves an integral Boltzmann transport equation using random numbers, a transport calculation code, and the like. In order to obtain a high quality calculation value, it is desirable to use a transport calculation code rather than a calculation code based on diffusion theory. An example of the three-dimensional transport calculation code is a DANTSYS system.

  In addition, when using the continuous energy general-purpose Monte Carlo code, the calculation system can be handled geometrically very accurately and the approximation accuracy is extremely high, but the final calculation accuracy depends on the time required for the calculation. It is necessary to note that it is determined.

  Subsequently, as an example of calculating the extrapolation distance δ using a calculation code, an example in which use of a multi-group energy three-dimensional transport calculation code based on determinism is assumed will be described.

  Normalize the axial fission rate (output) distribution obtained in the criticality experiment (or calculation), and measure the number of points including the position with the largest value, excluding the measurement value near the top or bottom of the fuel rod. Is fitted (calculated) into a cosine curve represented by the following formula (19) by an appropriate computer program (may be a commercially available application).

  The extrapolation distance δ is a value inherent to the critical experiment apparatus 1 (FIG. 1), and it is empirically understood that the dependence on the individual core system of the core 4 configured in the critical experiment apparatus 1 is small. Therefore, when a highly reliable extrapolation distance δ value is obtained in another experiment, the value may be used.

  In this way, the measuring device 30 obtains experimental system parameters including the critical water level z, the water level rise Δz from the critical water level, the reactivity ρ applied to the core system due to the water level rise, and the axial extrapolation distance δ. Then, the experimental system parameter acquisition process (steps S11 to S14) is completed. When the experimental system parameter acquisition process is completed, the process returns to the effective delayed neutron ratio measurement procedure (FIG. 6) as the main routine, and the calculation system parameter acquisition process (step S2: FIG. 6) following the experimental system parameter acquisition process (step S1: FIG. 6). 6) is executed (RETURN).

  FIG. 8 is a flowchart showing a processing flow of a calculation system parameter acquisition step (step S2: FIG. 6) for acquiring a calculation system parameter.

In the calculation system parameter acquisition step (steps S21 to S28), the measurement device 30 uses the infinite multiplication factor k _∞ of the fuel rod cell representing the core system as a calculation system parameter, and the transverse to the neutron leakage in the axial direction of the core system. This is a step of obtaining a parameter of the directional neutron leakage ratio a.

In the calculation system parameter acquisition step, the calculation code applicability determination unit 34d determines whether the calculation method and the calculation code used for calculating the calculation parameter can guarantee a desired calculation accuracy (the error is within an allowable range). and step (step S21~ step S26), and using the calculation method and calculation code can assure calculation accuracy, steps for infinite multiplication factor acquisition unit 34e acquires the infinite multiplication factor k _∞ (step S27), the neutron The leakage ratio acquisition unit 34f includes steps (steps S27 to S28) for acquiring the neutron leakage ratio a.

  In the step of determining whether or not the calculation accuracy can be guaranteed (steps S21 to S26), first, the calculation code applicability determination unit 34d determines the geometrical shape, the atomic structure of the core system of the core 4 in the critical experiment apparatus 1 (FIG. 1). The number density and the critical water level z are acquired (step S21). On the other hand, an allowable error is set for an allowable error (determination threshold) for the calculation result of the effective neutron multiplication factor keff calculated by the calculation code applicability determination unit 34d (step S22).

Subsequently, the calculation code applicability determining unit 34d accepts the selection of the calculation methods and calculation code used to obtain the infinite multiplication factor k _∞, the calculation method and calculation used to obtain the infinite multiplication factor k _∞ A code is temporarily selected (step S23).

  Subsequently, the calculation code applicability determination unit 34d calculates the neutron effective multiplication factor keff using the temporarily selected calculation method and calculation code, and obtains the neutron effective multiplication factor keff as a calculation result (step S24). Subsequently, the calculation code applicability determination unit 34d compares | keff−1 | which is an absolute value of a value obtained by subtracting 1 from the obtained neutron effective multiplication factor keff and a predetermined threshold for determination. It is determined whether the result is equal to or less than the threshold value (step S25).

  The reason for determining whether or not | keff-1 | ≦ threshold is satisfied is to determine whether or not an error occurring in the obtained calculation result exceeds an allowable error. More specifically, since the critical state is calculated, the effective neutron multiplication factor keff should be physically equal to 1, but due to errors based on the calculation method of the nuclear data library and calculation code. Actually, there is a deviation from the theoretical value (neutron effective multiplication factor keff = 1). If this error is too large, it can be said that the calculation accuracy cannot be guaranteed. Therefore, in the calculation system parameter acquisition step, the deviation from the theoretical value (neutron effective multiplication factor keff = 1), that is, | keff-1 | By calculating, an error based on the calculation method of the nuclear data library and calculation code is determined, and whether the error is within an allowable range is determined by comparing with a threshold value.

  In step S25, if | keff-1 | ≦ threshold is satisfied, that is, if the absolute value of the value obtained by subtracting 1 from the neutron effective multiplication factor keff is equal to or less than a predetermined threshold for determination (YES in step S25) ), It is determined that the desired calculation accuracy can be guaranteed if the calculation method and calculation code provisionally selected in step S23 are used, and it is determined to adopt the calculation method and calculation code temporarily selected in step S23 (step S26). ).

In the subsequent step S27, the infinite multiplication factor obtaining unit 34e calculates and obtains the infinite multiplication factor k _∞ using a calculation method, a calculation code, and a nuclear data library determined to be able to guarantee a desired calculation accuracy. The neutron leakage ratio acquisition unit 34f calculates and acquires the lateral leakage (lateral leakage value) and the axial leakage (axial leakage value) of the neutron core system.

  In subsequent step S28, the neutron leakage ratio acquisition unit 34f calculates the neutron leakage ratio a using the lateral leakage value and the axial leakage value acquired in step S27.

In this way, the measuring device 30 calculates the calculation system parameters including the infinite multiplication factor k _∞ of the fuel rod cell representing the core system and the ratio a of the lateral neutron leakage to the axial neutron leakage of the core system. When acquired, the calculation system parameter acquisition step (steps S21 to S28) is completed. When the calculation system parameter acquisition step is completed, the process returns to the effective delayed neutron ratio measurement procedure (FIG. 6) as the main routine, and step S3 (FIG. 6) following the calculation system parameter acquisition step (step S2: FIG. 6) is executed. (RETURN).

  On the other hand, if | keff-1 | ≦ threshold is not satisfied in step S25, that is, if the absolute value of the value obtained by subtracting 1 from the effective neutron multiplication factor keff exceeds a predetermined threshold for determination (NO in step S25). In this case, the calculation code applicability determination unit 34d determines that the calculation method and calculation code provisionally selected in step S23 cannot guarantee the desired calculation accuracy, and accepts the selection of the calculation method and calculation code again. If it demonstrates with the processing flow of a calculation system parameter acquisition process, it will return to step S23 from step S25, and the processing step after step S23 will be performed.

  Note that, in the calculation system parameter acquisition step, steps (steps S21 to S26) for determining whether the calculation accuracy can be guaranteed are executed, but a determination result is obtained as to whether the calculation accuracy can be guaranteed in advance. In cases where the user can be assured that the calculation accuracy desired by the user can be guaranteed, steps S21 to S26 may be omitted.

  In step S27, the calculation method and calculation code used by the infinite multiplication factor acquisition unit 34e and the neutron leakage ratio acquisition unit 34f are not necessarily the same calculation method and calculation code, and a desired calculation accuracy can be guaranteed. As long as the determined calculation method and calculation code are used, different calculation methods and calculation codes may be used.

  FIG. 9 is a flowchart showing a processing flow of the infinite multiplication factor correction step (step S4: FIG. 6) for correcting the infinite multiplication factor.

Infinite multiplication factor correcting step (step S41~ step S48) is a step of correcting errors measuring device 30 can occur infinite multiplication factor k _∞ obtained by calculation, the user desires to error correction of the infinite multiplication factor k _∞ If it is to be performed (step S3: FIG. 6), it is executed.

Before describing the processing steps of the infinite multiplication factor correction process, a description will be given of the principle of error correction of the infinite multiplication factor k _∞ executed in this step.

  A sensitivity coefficient can be defined for a calculation input parameter that is focused on the design value (= numerical value indicating performance) of the target product, etc., and there are multiple calculation input parameters, so a sensitivity coefficient can be obtained for each parameter. A sensitivity coefficient vector having the sensitivity coefficients of the plurality of calculation input parameters as components can be defined.

  Also, a representative factor (or simulation evaluation factor) RF can be defined as an index indicating how similar the design value of the product or facility intended for the simulation experiment is on the calculation simulation.

Here, with respect to calculation input parameters (such as nuclear cross section) of a physical quantity of interest (such as reactivity), a sensitivity coefficient vector S _R for a target product or facility, a sensitivity coefficient vector S _E for a simulation experiment system, and a calculation input If the covariance (error) matrix W representing the uncertainty of the parameter is used, the representative factor RF is expressed by the following equation (20). Note that R and E, which are subscripts of the sensitivity coefficient vector S, indicate a target fuel rod cell and a simulation experiment system, respectively. The letter T at the upper right of the matrix represents transposition (transpose matrix).

  One case is selected for a simulation experiment (critical experiment) in which the absolute value of the representative factor (or simulation evaluation factor) RF is sufficiently large (close to 1.0). In this embodiment, both the simulation experiment and the objective system are clear. The simulation experiment is the core system of the core 4 configured in the critical experiment apparatus 1 (FIG. 1), and the target system is the fuel rod cell of the core system of the core 4. (A two-dimensional system in which the used fuel rods 3 are positioned at the center of a square lattice having the fuel rod pitch as one side).

Next, a correction factor CF (Correction Factor: CF) will be described. The length obtained by projecting the sensitivity coefficient vector S _E in the direction of the sensitivity coefficient vector S _R, since the kcos, the ratio of the length of the vector S _R when aligned in the direction of the sensitivity coefficient vector S _R in simulation system Assuming that the error appears as a correction factor CF of how the error appears in a product or facility, the correction factor CF is expressed by the following equation (25).

  The nuclear characteristic R of the selected critical experiment is the critical eigenvalue (neutron effective multiplication factor). The calculated value keff of the neutron effective multiplication factor is obtained by the same method (the same nuclear data library and the same calculation code) for calculating the reactivity ρ of the product (fuel assembly etc.) intended for the criticality experiment. In the critical experiment, since the critical eigenvalue is physically 1.000, the relative error included in the calculated value keff is (keff-1).

Based on the relative error (keff-1) between the measured value and the calculated value of the critical experiment, excluding the relative error caused by the calculation method, the relative error of the measured value of the critical experiment, or according to the concept shown below, The relative error E _P caused by the error is evaluated.

Here, the concept of evaluating the relative error E _P will be described. In the assessment of the relative error E _P, "when it is computed model used for calculating the physical quantity of interest, has a sufficient accuracy, it does not cause a calculation error that is characterized in the calculation model used" (hereinafter, It is necessary to satisfy the following two conditions: “Condition 1”) and “Measurement error related to experiment is sufficiently small”.

  Regarding condition 1, for example, in the nuclear field, nuclear materials are sometimes loaded into a very small system. If such a system is calculated by diffusion calculation or a simple nuclear data library that handles energy groups in a small number group, A calculation error occurs because the quality of the calculation model is not sufficient. A sufficiently detailed calculation method should be used to avoid such errors. For example, general purpose Monte Carlo calculation using a continuous energy library is appropriate.

  Even when using general-purpose Monte Carlo calculations using a continuous energy library, the geometric descriptions of systems and products should be sufficiently detailed to avoid errors related to the description of geometric shapes, and statistical errors are sufficient. Care should be taken to make it smaller. It should be noted that the error in the numerical calculation itself is of a negligible level.

Note that statistical errors and experimental measurement errors that occur when Monte Carlo calculations are applied to numerical calculations are not systematic errors with systematicity in any case, but are classified as random errors that vary in positive and negative values depending on the case. I think. Therefore, these measurement errors are treated as “uncertainty” and are not directly related to the evaluation of the relative error E _P caused by the error of the calculation input parameter.

In this way, if the simulation is performed and the relative error E _P caused by the error of the calculated input parameter obtained from the measured value and the calculated value with respect to the physical quantity of interest is taken as the design calculated value of the target product or facility for the relative error ER _P due to errors in the calculation input parameters the aforementioned equations (14), i.e.,
^{_{ER P = E P × (S}} R T WS R) / (S E T WS R) ... (14)
It is represented by

The point to be noted here is that the value of the relative error E _P caused by the error of the calculation input parameter is given with positive and negative values, and the correction factor CF is also given with positive and negative values. for design calculation value of the facility, the relative error ER _P due to the error of the relative error calculation input parameter due to errors in the calculation input parameter is a point to be calculated automatically definite positive and negative. The above calculation can be performed by applying, for example, a SCALE system developed at a national laboratory in the United States.

  The covariance (error) matrix W is defined in principle for all the inputs used in the simulation, but when the evaluation is very difficult, the covariance (error) matrix W is changed to a unit matrix. May be handled as

Infinite multiplication factor correction step performed by applying the principle of error correction of such infinite multiplication factor k _∞: (Step S41~ step S48 9), firstly, the infinite multiplication factor correcting unit 34g, appropriate calculations effective neutron multiplication factor keff core system code, and deriving a sensitivity coefficient vector S _E nuclear data library, the infinite multiplication factor correcting unit 34g such as the storage unit 35 stores in a readable memory area (step S41).

Subsequently, the infinite multiplication factor correcting unit 34g is a calculation code using derives the infinite multiplication factor k _∞ of the fuel rod cells representing a core system in step S41, the storage unit 35 or the like (step S42).

Subsequently, the infinite multiplication factor correcting unit 34g derives the sensitivity coefficient vector _{S R} of the infinite multiplication factor k _∞ derived in step S42, the storage unit 35 or the like (step S43).

Subsequently, the infinite multiplication factor correction unit 34g selects the covariance error matrix W of the nuclear data library (step S44), and the correction factor CF (= S _R ^T WS _R / S _E expressed by the above equation (26). ^T WS _R) is calculated and stored in the memory unit 35 or the like (step S45).

Subsequently, the infinite multiplication factor correction unit 34g calculates a relative error E _P from “keff−1” corresponding to the relative error included in the calculated value keff of the neutron effective multiplication factor in consideration of other errors (step S46). ), the product obtained by multiplying the correction factor CF in _{E P} as relative error ER _P, the storage unit 35 or the like (step S47).

  FIGS. 10-12 are the process flow which concerns on the effective delayed neutron ratio calculation process (step S5: FIG. 6) in the effective delayed neutron ratio measurement procedure (FIG. 6) which measures the effective delayed neutron ratio which the measuring apparatus 30 performs. It is explanatory drawing (flowchart) which shows.

  More specifically, FIG. 10 is a flowchart showing the processing flow of the first example of the effective delayed neutron ratio calculating step (first effective delayed neutron ratio calculating step: step S5a (FIG. 6)), FIG. 12 is a flowchart showing a processing flow of a second example of the effective delayed neutron ratio calculating step (second effective delayed neutron ratio calculating step: step S5b (FIG. 6)). 11 and 12 is a connector for connecting the first half (FIG. 11) and the second half (FIG. 12) of the processing flow.

In the first effective delayed neutron ratio calculation step (step S51 to step S52: FIG. 10), the measurement device 30 uses parameters such as the infinite multiplication factor k _∞ obtained so far and the above-described equation (18). This is a step of calculating the effective delayed neutron ratio βeff.

In the first effective delayed neutron ratio calculation process, when the processing step is started (ENTER: FIG. 10), first, the effective delayed neutron ratio acquisition unit 34i performs an infinite multiplication factor of the fuel rod cell representing the core system. _k∞ , critical water level z, water level rise Δz, reactivity ρ, extrapolation distance δ in the axial direction, and ratio a of lateral neutron leakage to axial neutron leakage in the core system are read (step S51).

  Subsequently, the effective delayed neutron ratio acquisition unit 34i calculates the effective delayed neutron ratio βeff by substituting the read parameters into the above-described equation (18), and the calculation result is used to measure the effective delayed neutron ratio βeff. Obtained as a value (step S52).

  When the effective delayed neutron ratio βeff is obtained, the first effective delayed neutron ratio calculation step (steps S51 to S52) is completed, and the process returns to the effective delayed neutron ratio measurement procedure (FIG. 6) as the main routine ( RETURN: FIG. 10).

  When the first effective delayed neutron ratio calculation step (step S5a: FIG. 6), which is an example of the effective delayed neutron ratio calculation process, is completed, the effective delayed neutron ratio measurement procedure completes all processing steps (step S1 to step S5). The process ends with the completion of (S5a)) (END).

On the other hand, in the second effective delayed neutron ratio calculation step (steps S51 and S53 to S57: FIGS. 11 and 12), the measurement device 30 obtains parameters such as the infinite multiplication factor k _∞ and the core 4 obtained so far. This is a step of calculating the effective delayed neutron ratio βeff using the average moving area M ² (FIG. 1) (formulas (15) to (17) and formula (12) described above).

Here, prior to explaining the processing flow of the second effective delayed neutron ratio calculation step, the first method (first step) for determining the average moving area M ² of the core 4 used in this step is described. A method for calculating _one moving area M ₁ ² ) and a second method (a method for calculating the ^second moving area M ₂ ² ) will be described.

The first method, by substituting the parameters of the critical water level and the like obtained from measurement equations derived from the modified first group diffusion theory, a method of calculating a first transfer area M ₁ ^2. In the modified group 1 diffusion theory, the effective neutron multiplication factor keff of the core 4 (FIG. 1) is expressed by the above-described equation (6). It is quite difficult to accurately obtain the value of the radial buckling A included in the right side of Expression (6) from the measurement.

  When determining from the measurement, perform integral γ measurement in the radial direction of the core system, determine the radial power distribution of the core system, normalize the radial axial fission rate (power) distribution, and have the largest value The measured values of a plurality of points including the position are fitted with a function form (cosine curve) represented by the following formula (27) by an appropriate computer program (or a commercially available application). In this case, L in the following equation (27) is an effective length in the lateral direction of the core system (usually fuel rod pitch × number of fuel rod cells), and Δ is a value called lateral extrapolation distance. In this way, the lateral extrapolation distance Δ is obtained.

  The evaluation of a which is the ratio of the buckling between the radial direction and the axial direction uses the calculated value of the three-dimensional transport calculation code in the deterministic code because of the simplicity of calculation and the good consistency. . Of course, although it is possible to evaluate by a continuous energy general-purpose Monte Carlo code, it is first recommended to use a three-dimensional transport calculation code for the above reasons.

  In a three-dimensional transport calculation code in which neutron energy is handled in multiple groups (10 or more groups), a rectangular parallelepiped core is calculated with a detailed spatial mesh, and the neutron leakage rate for every six planes is obtained as a calculation output. From the calculated values, the sum of the ratios of neutron leakage on the upper and lower surfaces in the axial direction (axial leakage) and the sum of the ratios of leakage on the four lateral surfaces (lateral leakage) are calculated to obtain the ratio.

  Therefore, if the effective neutron multiplication factor keff derived by the above-described equation (6) is expressed using a which is the ratio of the buckling between the radial direction and the axial direction, the following equation (30) is obtained.

In the second method, the effective delayed neutron ratio (estimated value) calculated by a calculation code determined to be applicable in advance and parameters such as the critical water level obtained are derived from a modified group 1 diffusion theory. it is substituted into a method of calculating the second moving area M ₂ ^2.

  The effective delayed neutron ratio can be calculated once using a computer program (calculation code) generally accepted in the nuclear field and a nuclear data library. For example, the DANTSYS system can be used as the calculation code, and JENDL-4.0 can be used as the nuclear data library. In general, this calculation value may have an error of about ± several% to 10% due to the calculation method and the uncertainty of the numerical value of the yield of delayed neutrons stored in the nuclear data library and the error. It is said that.

  Therefore, if this calculated value is the effective delayed neutron ratio βeff, the water level reactivity coefficient ($ units) already measured in this critical experiment is multiplied to replace the water level reactivity coefficient with a dimensionless numerical value. However, as described above, there is a possibility that an error of about ± several% to 10% may be included in the calculated value, so that it may occur that the accuracy is not sufficient.

  On the other hand, the reactivity ρ ($ unit: the effective delayed neutron ratio is evaluated as 1 $) by obtaining the multiplication time based on the increase in the indicated value of the neutron detector 6 (FIG. 1) and based on the inverse time equation. Therefore, if the reactivity ρ is multiplied by the calculated value (estimated value) of the effective delayed neutron ratio, the following equation (33) can be derived from the above equation (11).

In a second effective delayed neutron fraction calculation step of obtaining the effective delayed neutron fraction using a transfer area M ² that is derived by the method described above, the processing step is started (ENTER: 11), first, the mobile The area acquisition unit 34h and the effective delayed neutron ratio acquisition unit 34i have an infinite multiplication factor k _∞ , a critical water level z, a water level increase Δz, a reactivity ρ, and an extrapolated distance δ in the axial direction. And the ratio a of the lateral neutron leakage to the axial neutron leakage of the core system is read (step S51).

Subsequently, the moving area acquisition unit 34h acquires the calculated effective delayed neutron ratio estimated value using the calculation code determined to be applicable in advance (step S53), and the above-described formula (15) and formula Using (16), the first moving area M ₁ ² and the second moving area M ₂ ² are calculated (steps S54 and S55).

Subsequently, when the first moving area M ₁ ² and the second moving area M ₂ ² are calculated, the moving area acquisition unit 34h calculates the above-described equation (17), that is, the first moving area M ₁ ^2. and second transfer area M ₂ ² to be weighted to calculate the average movement area M ² of the core (step S56), together with other parameters read the calculation result in the infinite multiplication factor k _∞ step S51 in such Substituting into the above equation (12), the effective delayed neutron ratio βeff is calculated, and the effective delayed neutron ratio βeff is obtained (step S57).

  When the effective delayed neutron ratio βeff is obtained, the second effective delayed neutron ratio calculation step (steps S51, S53 to S57) is completed, and the process returns to the effective delayed neutron ratio measurement procedure (FIG. 6) as the main routine. (RETURN).

  When the second effective delayed neutron ratio calculating step (step S5b: FIG. 6), which is an example of the effective delayed neutron ratio calculating process, is completed, the effective delayed neutron ratio measuring procedure is completed for all processing steps (step S1 to step S5). The process ends with the completion of (S5b)) (END).

In the second effective delayed neutron ratio calculation step, when it is desired to obtain the effective delayed neutron ratio by using the measured value of the critical experiment as much as possible, the second moving area in the equation (17) it is sufficient to ignore the M ₂ ^2, in step S56, may be performing operations handled as v = 0.

Further, when the effective delayed neutron ratio is desired to be obtained using the measurement value of the critical experiment as much as possible, steps S53, S55, and S56 in the second effective delayed neutron ratio calculation step are omitted, and the calculation is performed in step S54. a first transfer area M ₁ ² is, it may perform handle calculated as the average transfer area M ² of the core which is calculated in step S56. In this case, the second effective delayed neutron ratio calculating step is executed in the order of step S51, step S54, and step S57.

  Furthermore, in the second effective delayed neutron ratio calculating step, step S53 only needs to be executed in a processing step prior to step S55. In the second effective delayed neutron ratio calculation step, for example, step S54 may be executed subsequent to step S51, and then step S53 may be executed.

  As described above, according to the effective delayed neutron ratio measuring method and the measuring apparatus 30, in order to confirm the quality of the nuclear data library used simultaneously with the computer program (calculation code) calculated by the computer, Normal experiment equipment (eg tank-type critical experiment equipment for the purpose of research on light water reactors) and experimental methods, as well as conventional nuclear calculation methods that are well known and confirmed in quality. In other words, the effective delayed neutron ratio βeff can be accurately measured easily and economically by using the current equipment, the current experimental technique and calculation method without adding new equipment. Can do.

  Therefore, according to the effective delayed neutron ratio measuring method and measuring apparatus 30, the neutron infinite multiplication factor, the moving area, and the effective delayed delay of the fuel rod cell representing the core system can be obtained without adding any special equipment. The neutron ratio can be evaluated easily and economically.

Further, according to the effective delayed neutron fraction measuring method and apparatus 30, an error that may occur neutron infinite multiplication factor k _∞ running infinite multiplication factor correction step of correcting errors that may occur neutron infinite multiplication factor k _∞ Since the influence can be further reduced, the effective delayed neutron ratio βeff can be measured with higher accuracy.

  Although the present embodiment has been described, the described content is presented as an example and is not intended to limit the scope of the invention. In the implementation stage, the present invention can be implemented in various forms other than the above-described embodiments. In the embodiment, the case where the present invention is applied to a critical experiment apparatus has been described. However, if the critical apparatus is a critical apparatus, for example, the same procedure can be performed in another critical apparatus such as a research reactor. It can be carried out in the same manner as the critical experiment apparatus.

  The present embodiment can be implemented in various other forms, and various omissions, additions, replacements, and changes can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

  DESCRIPTION OF SYMBOLS 1 ... Critical experiment apparatus, 2 ... Core tank, 3 ... Fuel rod, 4 ... Core, 5 ... Control rod, 6 ... Neutron detector, 7 (7a, 7b) ... Supply / discharge part, 7a ... Liquid supply part, 7b ... Drainage unit, 8 ... Liquid level transmitter, 9 ... Fuel support plate, 11a ... Upper grid plate, 11b ... Lower grid plate, 30 ... Measuring device, 31 ... Input unit, 32 ... Output unit, 33 ... Transmission unit, 34 (34a to 34i) ... calculation unit, 34a ... critical water level acquisition unit, 34b ... reactivity acquisition unit, 34c ... axial extrapolation distance acquisition unit, 34d ... calculation code applicability determination unit, 34e ... infinite multiplication factor acquisition unit, 34f ... Neutron leakage ratio acquisition unit, 34g ... Infinite multiplication factor correction unit, 34h ... Moving area acquisition unit, 34i ... Effective delayed neutron ratio acquisition unit, 35 ... Storage unit, 36 ... Control unit, 50 ... Measurement program.

Claims (15)

Calculates the effective delayed neutron ratio of the critical device that achieves criticality by adjusting the level of light water supplied to the core tank that houses the core in which a plurality of fuel rods are horizontally spaced from each other. Effective delayed neutron ratio measurement method,
Obtaining a critical water level that is the water level in the core tank when the criticality is achieved;
Based on the output from the neutron detector that detects the neutrons generated as a result of the fission reaction in the critical apparatus by slightly raising the water level in the core tank from the critical water level, the core of the core is A step to get the degree of responsiveness added to the system,
Obtaining a core axial fission rate distribution of the critical device and determining an axial extrapolation distance based on the obtained core axial fission rate distribution;
One calculation code included in the calculation program is selected from a plurality of calculation programs prepared for calculating the effective neutron multiplication factor of the core system of the core, the selected calculation code, and the core of the core The system geometry and atomic density and the critical water level are obtained, and the neutron effective multiplication factor is calculated using the obtained value, and whether or not the calculation result is within a set allowable error range. Determining the pass / fail of the calculation accuracy of the selected one calculation code based on whether or not, if it is acceptable, confirming the selection of the selected one calculation code;
Among a plurality of calculation programs prepared for calculating the effective neutron multiplication factor of the core system of the core, an infinite increase of fuel rod cells representing the core system by a calculation code determined that the calculation accuracy is acceptable Determining a magnification;
Using the calculation code determined in the step of determining the selection of the calculation code, the neutron leakage in the lateral direction and the axial direction of the core system are respectively calculated, and from the calculation result, the lateral neutron leakage with respect to the axial neutron leakage of the core system is calculated. Determining the ratio of neutron leakage in the direction;
The effective delayed neutron ratio of the core system of the core, the critical water level, the rise in the water level, the reactivity, the extrapolated distance in the axial direction, the infinite multiplication factor of the fuel rod cell representing the core system, and From the relationship with the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, the infinite multiplication factor of the fuel rod cell representing the core system, the critical water level, the rise in the water level, the reactivity, Obtaining an extrapolated distance in the axial direction and a ratio of lateral neutron leakage to axial neutron leakage of the core system to determine an effective delayed neutron ratio of the core system of the core, A method for measuring the effective delayed neutron ratio. The effective delayed neutron ratio of the core system of the core is βeff, the infinite multiplication factor of the fuel rod cell representing the core system is k _∞ , the critical water level is z, the rise of the water level is Δz, and the reactivity is ρ When the axial extrapolation distance is δ and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system is a, the effective delayed neutron ratio βeff of the core system of the core is formula

The method for measuring the effective delayed neutron ratio according to claim 1, characterized in that: The infinite multiplication factor obtained in the step of obtaining the infinite multiplication factor is determined in consideration of an error recognized from the difference between the effective neutron multiplication factor obtained by the calculation code used in the step of obtaining the infinite multiplication factor and 1. A step of correcting the infinite multiplication factor;
3. The method for measuring the effective delayed neutron ratio according to claim 1, wherein the infinite multiplication factor is the corrected infinite multiplication factor corrected in the step of correcting the infinite multiplication factor. The step of correcting the infinite multiplication factor includes:
The effective coefficient of neutron obtained by the calculation code used in the step of obtaining the infinite multiplication factor is keff, keff−1 is E _P , and the sensitivity coefficient vector for the nuclear data library used for the infinite multiplication factor k _∞ is S _R. , For the effective neutron multiplication factor keff, the sensitivity coefficient vector for the nuclear data library is S _E , the covariance error matrix of the nuclear data library is W, the symbol representing transposition is T, and the neutron infinite due to the nuclear data library a relative error ER _P multiplication factor k _∞, further,

The method for measuring the effective delayed neutron ratio according to claim 3, wherein the effective delayed neutron ratio is obtained by using the method. The step of obtaining the reactivity includes slightly raising the water level in the core tank from the critical water level and detecting the output from the neutron detector for detecting neutrons generated as a result of fission reaction in the critical device. 5. The method for measuring the effective delayed neutron ratio according to claim 1, wherein an output value obtained by inputting to the step is obtained as the reactivity. 6. The step of obtaining the reactivity includes slightly raising the water level in the core tank from the critical water level, and detecting the neutrons generated as a result of fission reaction in the critical device based on the output from the neutron detector. While getting the multiplication time of the fission reaction,
For each group of delayed effective neutrons for each group of delayed delayed neutrons that are pre-grouped into a predetermined number that matches the core system of the core using known fissile material values (constants) Obtaining the ratio of the effective delayed neutron ratio of, obtaining the value of the obtained ratio,
Substituting the ratio of the obtained multiplication time of the fission reaction and the effective delayed neutron ratio for each group with respect to the effective delayed neutron ratio into the inverse time equation of the reactivity, and solving The method for measuring an effective delayed neutron ratio according to any one of claims 1 to 4. The step of obtaining the reactivity includes slightly raising the water level in the core tank from the critical water level, and detecting the neutrons generated as a result of fission reaction in the critical device based on the output from the neutron detector. While getting the multiplication time of the fission reaction,
For each group of delayed effective neutrons for each group of delayed delayed neutrons that are pre-grouped into a predetermined number that matches the core system of the core using known fissile material values (constants) Obtaining the ratio of the effective delayed neutron ratio of, obtaining the value of the obtained ratio,
The reactivity is calculated by calculation using the inverse dynamics method using the obtained multiplication time of the fission reaction and the ratio of the effective delayed neutron ratio for each group to the effective delayed neutron ratio. It is a step, The measuring method of the effective delayed neutron ratio of any one of Claim 1 to 4 characterized by the above-mentioned. Based on the critical water level, the extrapolated distance in the axial direction, the infinite multiplication factor of the fuel rod cell representing the core system, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, the core Further comprising determining an average moving area of

The method of measuring the effective delayed neutron ratio according to any one of claims 1 to 7, wherein the effective delayed neutron ratio is calculated using Obtaining necessary information from the nuclear data library, and calculating the effective delayed neutron ratio estimated value obtained by calculating the effective delayed neutron ratio of the core system of the core with one selected calculation code, the critical water level, The method further includes the step of obtaining an average moving area of the core based on the rise in the water level, the reactivity, the infinite multiplication factor of the fuel rod cell representing the core system, and the extrapolation distance in the axial direction. And

The method for measuring the effective delayed neutron ratio according to any one of claims 1 to 7, wherein the effective delayed neutron ratio is obtained by using the method. The critical water level, the extrapolated distance in the axial direction, the infinite multiplication factor of the fuel rod cell representing the core system, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system. The average moving area of the core is the first moving area, the necessary information is obtained from the nuclear data library, and the effective delayed neutron ratio of the core system of the core is calculated by one selected calculation code. Based on the obtained effective delayed neutron ratio estimate, the critical water level, the rise in the water level, the reactivity, the infinite multiplication factor of the fuel rod cell representing the core system, and the extrapolation distance in the axial direction The calculated average moving area of the core is set as the second moving area, and the calculation result obtained by performing the weighting calculation using the first moving area and the second moving area is the result of the core. Further comprising the step of determining a moving-area Hitoshiteki,

The method of measuring the effective delayed neutron ratio according to any one of claims 1 to 7, wherein the effective delayed neutron ratio is calculated using When the average moving area M ² of the core is obtained, the effective delayed neutron ratio βeff of the core system of the core is expressed by the following equation:

The method of measuring the effective delayed neutron ratio according to claim 10, wherein Calculates the effective delayed neutron ratio of the critical device that achieves criticality by adjusting the level of light water supplied to the core tank that houses the core in which a plurality of fuel rods are horizontally spaced from each other. Effective delayed neutron fraction measuring device,
A critical water level acquisition unit for obtaining a critical water level that is a water level in the core tank when the criticality is achieved;
Based on the output from the neutron detector that detects the neutrons generated as a result of the fission reaction in the critical apparatus by slightly raising the water level in the core tank from the critical water level, the core of the core is A reactivity acquisition unit for obtaining the reactivity added to the system;
An axial extrapolation distance acquisition unit for obtaining a core axial fission rate distribution of the critical device and obtaining an extrapolation distance in the axial direction based on the obtained core axial fission rate distribution;
One calculation code included in the calculation program is selected from a plurality of calculation programs prepared for calculating the effective neutron multiplication factor of the core system of the core, the selected calculation code, and the core of the core When the geometrical shape and atomic density of the system and the critical water level are obtained, the neutron effective multiplication factor is calculated using the obtained value, and the calculation result is within a set allowable error range. An infinite multiplication factor obtaining unit for confirming selection of the selected one calculation code and obtaining an infinite multiplication factor of a fuel rod cell representing the core system by the decided calculation code;
Calculate the neutron leakage in the lateral direction and the axial direction of the core system with the determined calculation code, and obtain the neutron leakage ratio for determining the ratio of the lateral neutron leakage to the axial neutron leakage in the core system from the calculation result And
The effective delayed neutron ratio of the core system of the core, the critical water level, the rise in the water level, the reactivity, the extrapolated distance in the axial direction, the infinite multiplication factor of the fuel rod cell representing the core system, and From the relationship with the ratio of the lateral neutron leakage to the axial neutron leakage of the core system, the infinite multiplication factor of the fuel rod cell representing the core system, the critical water level, the rise in the water level, the reactivity, An effective delayed neutron ratio acquisition unit that obtains the ratio of the lateral neutron leakage with respect to the axial extrapolation distance and the axial neutron leakage of the core system to obtain the effective delayed neutron ratio of the core system of the core An apparatus for measuring the effective delayed neutron ratio. In consideration of the error recognized from the difference between the effective neutron multiplication factor obtained by the calculation code and 1 and, further comprising an infinite multiplication factor correction unit for correcting the infinite multiplication factor obtained by the infinite multiplication factor acquisition unit The apparatus for measuring the effective delayed neutron ratio according to claim 12. The critical water level, the extrapolated distance in the axial direction, the infinite multiplication factor of the fuel rod cell representing the core system, and the ratio of the lateral neutron leakage to the axial neutron leakage of the core system. The average moving area of the core is the first moving area, the necessary information is obtained from the nuclear data library, and the effective delayed neutron ratio of the core system of the core is calculated by one selected calculation code. Based on the obtained effective delayed neutron ratio estimate, the critical water level, the rise in the water level, the reactivity, the infinite multiplication factor of the fuel rod cell representing the core system, and the extrapolation distance in the axial direction The calculated average moving area of the core is set as the second moving area, and the calculation result obtained by performing the weighting calculation using the first moving area and the second moving area is the result of the core. Further comprising a transfer area acquisition unit to Hitoshiteki movement area,
The moving area acquisition unit

In by the weighting operation defined, effective delayed neutron fraction measuring device according to claim 12 or 13, characterized in that it is configured to determine an average transfer area M ² of the core. The effective delayed neutron ratio acquisition unit has an effective delayed neutron ratio of the core system of the core βeff, an infinite multiplication factor of a fuel rod cell representing the core system, k _∞ , the critical water level z, and the water level In the case where Δz is an increase, ρ is the reactivity, δ is the extrapolation distance in the axial direction, and a is a ratio of lateral neutron leakage to axial neutron leakage of the core system,

The measurement of the effective delayed neutron ratio according to claim 12 or 13, wherein the effective delayed neutron ratio βeff of the core system of the core is obtained by obtaining a calculated value obtained by calculating apparatus.

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