JP6814049B2 - Subcriticality measurement method for nuclear fuel - Google Patents

Description

The present invention relates to a method for measuring and evaluating the subcriticality of nuclear fuel (damaged nuclear fuel, etc.).

In the criticality safety management of nuclear fuel materials, the subcriticality (margin to criticality) of the nuclear fuel to be managed, especially the nuclear fuel significantly damaged by severe events in the nuclear reactor (damaged nuclear fuel), is measured safely and accurately in real time. And monitoring is extremely important. As a method for measuring the subcriticality of nuclear fuel, for example, a negative period method, a control rod drop method, a compensation method, a neutron source multiplication method, a pulsed neutron source method, a reverse motion characteristic method, a neutron noise analysis method, etc. are proposed. Has been done. Among these, in the methods other than the neutron noise analysis method, the detailed state of the system including nuclear fuel is known, and the critical operation of the system (for example, the factors that influence the subcriticality are changed to approach the critical state. There are restrictions such as the need for control means such as control rods and other complicated equipment for that purpose. On the other hand, the neutron noise analysis method has no such limitation, and since the neutron noise analysis method can be applied to substances other than the nuclear fuel loaded in the reactor core, the subcriticality of the damaged nuclear fuel is particularly high. It is considered to be practically useful as a method for measuring.

As an application example of such a neutron noise analysis method, Patent Document 1 describes subcriticality determination by applying a frequency analysis method or a Fineman alpha method to a plurality of states having different subcriticalities in a neutron multiplication system. Devices and subcriticality determination programs have been proposed. In this device and program, the subcriticality of the system is evaluated by estimating the detector efficiency and prompt neutron lifetime so that the fitting error between the obtained measured data and the theoretical curve is minimized. .. In addition, Non-Patent Document 1 describes improvements to the Fineman Alpha method and the Miharuzo method, which apply a step difference filter to data processing, as subcriticality measurement technology that can be applied to fast reactor fuel reprocessing facilities with strict measurement conditions. An example of applying the time correlation analysis Miharuzo method, which is a method, is described. In this case, in the subcriticality measurement of the heavy water subcritical experimental facility, the feasibility of real-time measurement for a system in which the subcriticality changes and the applicability to a high neutron flux field are evaluated. Furthermore, in Patent Document 2, the applicant relates to the measured values of two different measurement methods and a plurality of measured values obtained by adding parameters to the measurement target in order to solve the problem of the conventional subcriticality measurement. We proposed a method to obtain the subcriticality by regarding the parameters as simultaneous equations.

Japanese Unexamined Patent Publication No. 2010-210613 Japanese Unexamined Patent Publication No. 2014-228362

Hane-samahei et al., "Development of subcriticality determination technology", Cycle Mechanism Technical Report No. 14, 2002.

However, according to a detailed study by the present inventor, the subcriticality measurement method using the conventional neutron noise analysis method described in Patent Document 1 and Non-Patent Document 1 has the above-mentioned restrictions. Although it is small, in the subcriticality evaluation calculation, it is necessary to give the prompt neutron lifetime or the spatial correction factor in the system to be evaluated as known state parameters in advance. On the other hand, since the exact composition (content ratio), shape, properties, etc. of damaged nuclear fuel are usually unknown, detailed state parameters such as prompt neutron lifetime and spatial correction factor in the system including such damaged nuclear fuel are detailed. It must be said that it is almost impossible to accurately grasp or estimate the information and to actually measure their state parameters. Therefore, even if the above-mentioned conventional neutron noise analysis method is applied to the subcriticality measurement of a system including an actual nuclear fuel, particularly a damaged nuclear fuel, it is extremely difficult to accurately measure and evaluate the subcriticality. Further, the present inventor has confirmed that the simultaneous equations by the method described in Patent Document 2 cannot be mathematically solved, and it is not effective as a means for solving the above-mentioned conventional problems. It turned out not.

Therefore, the present invention has been made in view of such circumstances, and even if detailed information on the state parameters of the measurement target including nuclear fuel is unknown, the subcriticality of the measurement target is accurately determined based on the measured value. It is an object of the present invention to provide a subcriticality measurement and monitoring method for nuclear fuel that can be measured and evaluated well.

In order to solve the above problems, in the method for measuring the subcriticality of nuclear fuel according to the present invention, a plurality of simulated calculation systems having a virtual measurement target including nuclear fuel and a virtual neutron detection unit are set, and a plurality of simulated calculations are performed. For the system, obtain multiple simulation values of the effective neutron multiplier or subcriticality of the virtual measurement target and the reactor noise method measurement values measured by the virtual neutron detector, and perform multiple simulations of them. From the values, the correlation equation between the effective neutron multiplier or subcriticality and the measured value by the reactor noise method is calculated, and the actual neutron detection unit is used for the measurement system having the actual measurement target including nuclear fuel and the actual neutron detection unit. By obtaining the measured value of the furnace noise method measurement value measured by and substituting the measured value of the furnace noise method measurement value into the correlation formula, the neutron effective multiplication factor or subcriticality of the actual measurement target is calculated. It should be noted that finding the subcriticality ρ is equivalent to finding the neutron effective multiplication factor k (see equation (1-3) below).

In addition, for the virtual measurement target and the virtual neutron detector, a plurality of virtual environmental conditions different from each other are set, and for each of the plurality of environmental conditions, a plurality of simulated calculation systems are set to calculate the correlation equation. For the actual measurement target and the actual neutron detector, the actual environmental conditions are measured, virtual environmental conditions that are close to the actual environmental conditions are selected, and the correlation calculated under the selected virtual environmental conditions. By substituting the measured value of the furnace noise method measurement value into the equation, the neutron effective multiplication factor or subcriticality of the actual measurement target may be calculated. In this case, the environmental condition is at least one of the distance between the nuclear fuel region surface and the neutron detection unit in the measurement target and the amount and distribution of the substance existing between the nuclear fuel region surface and the neutron detection unit in the measurement target. Is preferable.

Specifically, it is preferable to use the following formula (X) as the correlation formula.

Further, as the neutron detector, it is also preferable to use a neutron generator having a neutron source and a neutron detector without a neutron source integrally configured.

More specifically, the furnace noise method measurement value may be the partition coefficient ratio CR obtained by the time correlation analysis Miharuzo method.

Alternatively, the furnace noise method measurement may be the parameter Y∞ obtained by the function fitting of the deviation Y (Δt) of the “dispersion-to-average ratio” obtained by the Fineman-alpha method, where Δt is a neutron. The time gate width, which is the time interval between the pulses, is shown.

Further, by substituting the parameter Y∞, which is the measured value by the furnace noise method, into the following equation (D), the further neutron effective multiplication factor or subcriticality of the actual measurement target may be calculated, and the parameter Y may be calculated. ∞ is obtained by function fitting using the following equation (I).

Here, in equation (I), Y ₀ is an intercept parameter obtained by function fitting, and α indicates a prompt neutron attenuation coefficient obtained by function fitting.

Further, Y∞ is set by performing a function fitting using the above equation (I) on the measured value of the deviation Y (Δt) of the “dispersion to average ratio” determined by the following procedures (1) to (3). You may try to get it.

Procedure (1): The initial value of the number of selected data of the measured value of the deviation Y (Δt) of the “dispersion to average ratio” used for the function fitting of the above equation (I) is N ₀ , and the N ₀ “variance pairs”. Let α obtained by performing the function fitting of the above equation (I) on the measured value of the deviation Y (Δt) of the “ratio-moving ratio” as the initial value α ₀ of the prompt neutron decay coefficient.

Step (2): When the initial value α ₀ is substituted into α _n-1 of the following equation (J), the range of the time gate width Δt satisfying the following equation (J) is obtained, and within the range of the time gate width Δt. A measured value of the deviation Y (Δt) of the above-mentioned “dispersion to average ratio” is selected, the number of selected measured values is defined as the number of selected data N _1, and the deviation Y of the N ₁ “dispersion to average ratio”. Let α obtained by performing the function fitting of the above equation (I) again on the measured value of (Δt) be the next value α ₁ of the prompt neutron attenuation coefficient.

Step (3): Step (2) is repeated n times until the number of selected data N _n-1 and the number of selected data N _n become equal, and the deviation Y (Δt) of the final N _n “dispersion to average ratio”. ) Is determined, or if the number of selected data N _n-1 and the number of selected data N _n alternately increase or decrease by ± 1, whichever is greater, N _n-1 or N _n. Alternatively, the smaller one is consistently selected to determine the final measured value of the deviation Y (Δt) of N _n-1 or N _n “dispersion to mean ratio”.

In addition, in the function fitting for obtaining the parameter Y∞ using the above equation (I), the “variance-to-average ratio” weighted by the reciprocal of the statistical error of the measured deviation Y (Δt) of the “variance-to-average ratio”. Deviation Y (Δt) of may be used.

According to the present invention, for a plurality of simulated calculation systems having a measurement target and a neutron detection unit, the simulation values of the neutron effective multiplication factor or subcriticality of the measurement target and the measured values by the furnace noise method are obtained, and their correlation equations are calculated. Then, by substituting the measured value of the furnace noise method measurement value into the correlation formula, the neutron effective multiplication factor or subcriticality of the actual measurement target is calculated, so the composition, shape, properties, etc. of the measurement target including nuclear fuel, etc. Even if the detailed information about the state parameter such as is unknown, the subcriticality of the measurement target can be measured and evaluated accurately and accurately.

It is a schematic diagram which shows the structure of the measurement system schematicly. It is a graph which plotted (white circle) the simulation result of the calculated value (subcriticality ρ) and the measured value (dispersion coefficient ratio CR) in the measurement system of FIG. A graph in which the neutron effective multiplication factor k (estimated value from the correlation equation) obtained from the fitting curve of FIG. 2 and the neutron effective multiplication factor k (analyzed value) obtained for the same measurement system are plotted (white circles). Is. It is a graph which shows the change of the neutron effective multiplication factor k (ε + Δε) with respect to the relative error Δε / ε of the neutron detection efficiency ε. It is a graph which shows the change of the neutron effective multiplication factor k (Δl / l) with respect to the relative error Δl / l of the prompt neutron lifetime l. It is a graph (white circle) which plotted the simulation result of the calculated value (subcriticality ρ) and the measured value (Y∞) in the measurement system of FIG. It is a graph which shows the change of the deviation Y (Δt) of "variance to average ratio" with respect to time gate width Δt. A graph in which the neutron effective multiplication factor k (estimated value from the correlation equation) obtained from the fitting curve of FIG. 6 and the neutron effective multiplication factor k (analyzed value) obtained for the same measurement system are plotted (white circles). Is. It is a graph which shows the result of having performed fitting by applying the nonlinear least squares method using equation (O).

Hereinafter, embodiments of the present invention will be described in detail, including comparison with the prior art. Therefore, it should be noted that in the following, not only the description of the embodiment of the present invention but also the description of the prior art will be referred to. Unless otherwise specified, the positional relationship such as up, down, left, and right shall be based on the positional relationship shown in the drawings. Moreover, the dimensional ratio of the drawing is not limited to the ratio shown in the drawing. Furthermore, the following embodiments are examples for explaining the present invention, and the present invention is not intended to be limited only to the embodiments thereof. Furthermore, the present invention can be modified in various ways as long as it does not deviate from the gist thereof.

[Explanation of prior art]
In order to facilitate understanding of the embodiments of the present invention, first, the contents of the prior art and its problems will be described in detail again prior to the description thereof.

(Patent Document 1)
In the subcriticality determination device and the subcriticality determination program described in Patent Document 1, the neutron noise analysis method is used for a plurality of states having different subcriticality in the neutron multiplication system including the nuclear fuel material, as described above. A certain frequency analysis method or Fineman Alpha method is applied to estimate the detector efficiency and prompt neutron lifetime so that the fitting error between the measured data in the neutron measurement and the theoretical curve is minimized. As a result, it is intended to measure and evaluate the subcriticality without estimating the detector efficiency and prompt neutron lifetime in neutron measurement in advance by calculation. In other words, according to Patent Document 1, the prompt neutron lifetime, which has a dominant effect on the subcriticality measurement by the neutron noise analysis method other than the Miharuzo method, is obtained together with the subcriticality based on the measured results.

More specifically, although it is not exactly the same as the measurement and evaluation procedure described in Patent Document 1, the neutron multiplication system to be measured and evaluated is not yet developed by the following procedure (substantially equivalent). Along with the criticality, the detector efficiency and prompt neutron lifetime in neutron measurement are estimated. That is, taking the second embodiment of Patent Document 1 (see paragraphs 0058 to 0906 of Patent Document 1) as an example, first, the "dispersion to average ratio" equivalent to the formula (8) described in Patent Document 1 is obtained. The deviation Y (Δt) from 1 (a function of the time gate width Δt, which is the time interval between neutron pulses) ”is expressed by the following equation (1-1). In this equation (1-1), the actually measured values obtained by the function fitting of the deviation Y (Δt) of the “dispersion to average ratio” which is the measurement data are C _n and α.

On the other hand, the relationship expressed by the following equation (1-2) holds between the effective neutron multiplier k for calculating the subcriticality and the prompt neutron attenuation constant α, and the prompt neutron calculated from the measured value is established. If the decay constant α, the prompt neutron lifetime l and the delayed neutron ratio β on the right side of the equation (1-2) are known, the effective neutron multiplier k can be obtained.

The subcriticality is defined by the relationship represented by the following equation (1-3) using the effective neutron multiplication factor. In this way, finding the subcriticality ρ is equivalent to finding the neutron effective multiplication factor k.

By the way, from FIG. 7 of Patent Document 1, the left side Yn (Δt) of the above equation (1-1) is obtained as actual measurement data (measured value) for each time gate width Δt which is a time interval between neutron pulses. Be done. On the other hand, the value on the right side of the above equation (1-1) is generally a curve theoretically established as the relationship between the prompt neutron attenuation constant α and the time gate width Δt. Therefore, the neutron count C _n and the prompt neutron attenuation constant α _n , which are the parameters on the right side of the above equation (1-1), are used as fitting coefficients when fitting the measured value on the left side to the theoretical curve on the right side by the least squares method or the like. can get.

Here, two subcritical states n (n = 1 and 2) are applied to the neutron multiplication system to be measured and evaluated, following the verification test in the second embodiment of Patent Document 1 (paragraphs 809 to 0906 of Patent Document 1). ), It is expressed by the following equation (1-4) as an equation for the neutron count C _n (that is, C ₁ , C ₂ ), which is the measured value obtained by neutron measurement in the above equation (1-1). Two relational expressions are obtained.

In equation (1-4), C ₁ , C ₂ , α ₁ , and α ₂ can be obtained as fitting coefficients of the measurement data by giving an appropriate value as the Diven number in advance as the initial setting value. Therefore, there are only two unknowns in Eq. (1-4): neutron detection efficiency ε and prompt neutron lifetime l. Then, since the two relational expressions shown in the equation (1-4) are given to those two unknowns, the two relational expressions of the equation (1-4) are given the neutron detection efficiency ε and the prompt promptness. The neutron detection efficiency ε and the prompt neutron lifetime l of these neutron multiplication systems can be obtained by solving them as simultaneous equations for the neutron lifetime l.

In the above, two subcritical states are assumed, but three or more states may be assumed. In that case, the neutron detection efficiency ε and the prompt neutron lifetime l are used by using the least squares method or the like. Should be decided.

By the way, in such a method described in Patent Document 1, as shown in the equation (1-4), the analysis is performed under the condition that the prompt neutron lifetime l is the same in a plurality of subcritical states. However, when the subcriticality of the neutron multiplication system is different, it is considered extremely rare that the prompt neutron lifetime l is the same, and it is presumed that the difference in the prompt neutron lifetime l cannot be ignored in many cases. Then, as described in Patent Document 1, it becomes necessary to estimate and evaluate the prompt neutron lifetime l together with the effective neutron multiplication factor k by some method. However, Patent Document 1 does not disclose or suggest a specific method or procedure for that purpose.

However, in the method described in Patent Document 1, it is impossible in principle to simultaneously obtain the prompt neutron lifetime l, which differs depending on the difference in subcriticality ρ, together with the neutron effective multiplication factor k. It is extremely difficult to find an engineeringly significant solution. That is, assuming that the prompt neutron lifetimes l in the two states represented by the above equation (1-4) are different from each other and they are the prompt neutron lifetimes l ₁ and l ₂ , the above equation (1-4) is the following equation (1). It can be rewritten as shown in -5).

In this case, there are three unknowns, neutron detection efficiency ε and prompt neutron lifetime l ₁ and l ₂ , and the relational expressions given to these three unknowns are the two shown in the above equation (1-5). Therefore, it is impossible to uniquely obtain their neutron detection efficiency ε and prompt neutron lifetime l ₁ and l ₂ . Even if n (n ≧ 3) states are prepared as a plurality of subcritical states, for n relational expressions, the unknowns are the neutron detection efficiency ε and the prompt neutron lifetime l ₁ , l ₂ , ... , L _n, that is, the number of unknowns is n + 1, so it is impossible to uniquely find the solution even in this case. This is a problem in the example described in the second embodiment of Patent Document 1, but other embodiments of Patent Document 1 also set the subcriticality ρ via the prompt neutron attenuation constant α and the prompt neutron lifetime l. Since there is no difference in the calculation, it can be said that the same problem is inherent in each of these embodiments.

Therefore, in the subcriticality measurement method described in Patent Document 1, if the unknown number can be reduced by one by obtaining the neutron detection efficiency ε in advance by using some means, for example, it is an actually measured value obtained by neutron measurement. For the neutron counts C ₁ and C ₂ (the left side of equation (1-5)), the unknowns on the right side are the prompt neutron lifetimes l ₁ and l ₂ , and it is possible to uniquely obtain them. For that purpose, it is necessary to prepare a plurality of subcritical states that can be regarded as having the same value of the prompt neutron lifetime l, and then obtain the neutron detection efficiency ε in these plurality of states in advance.

However, since the prompt neutron lifetime l is easily affected by the neutron spectrum, it is necessary to change the subcritical state so that the neutron spectrum does not change. As one of the methods for that, for example, it is recalled to change the amount of fissile material contained in the system, but it is applied to a system in which the subcriticality ρ is unknown (for example, a system containing damaged nuclear fuel). That is considered unrealistic. That is, in order to change the amount of fissile material, it is sufficient to add fissile material to the system or remove fissile material from the system, but the former is an increase in fissile material in the system. On the other hand, the latter may reach the criticality due to the increased neutron deceleration when water flows into the cracks formed in or around the removed part of the damaged nuclear fuel. In this way, changing the amount of fissile material in the system without grasping and monitoring the subcriticality ρ is considered to be an operation that should be avoided.

On the other hand, as a method of changing the subcriticality ρ without changing the amount of fissile material, a method of adding a neutron absorbing material or excluding water around the nuclear fuel is assumed. However, if such an operation is performed, the neutron spectrum is inevitably changed, so that the prompt neutron lifetime l cannot be maintained in a state that can be regarded as the same value. Alternatively, it is possible to consider a method of adding a neutron absorbing substance or removing water around the damaged nuclear fuel within a range in which the prompt neutron lifetime l can be regarded as the same value, but in that case, it is not critical. There is a concern that the degree of change in the state is small and the desired significant result cannot be obtained.

(Non-Patent Document 1)
On the other hand, the subcriticality measuring method described in Non-Patent Document 1 is the Fineman Alpha method or the time correlation analysis Miharuzo method using a difference filter as described above, and according to Non-Patent Document 1, it is subcritical. We have succeeded in measuring the subcriticality ρ in real time and with high accuracy in the subcritical experimental facility where the degree ρ fluctuates. Here, the time correlation analysis Miharuzo method does not include a detector with a neutron source such as a Cf-252 neutron source, which is generally used as a neutron detector, and a neutron source which can also be used in the Fineman Alpha method. This method uses both detectors without a neutron source. That is, according to the time correlation analysis Miharuzo method, the measurement data used for that purpose and the measurement data used in the Feynman alpha method can be obtained at the same time.

Then, it is reported in Non-Patent Document 1 that the measurement result of the subcriticality ρ can be obtained in a response time of about 1 minute in a system in which the subcriticality ρ changes, especially in the time correlation analysis Miharuzo method. (However, since the response time is approximately proportional to the relative intensity of the detector built-in neutron source with respect to the subcritical neutron source under evaluation, the higher the intensity of the detector built-in neutron source, the shorter the response time). .. In addition, in Non-Patent Document 1, there is no problem in the influence of the dead time of the detector even on a high neutron flux field, such a method can be applied, and the intensity of the intrinsic neutron source included in the measurement target is high. It is stated that it is possible to prepare a neutron source (Cf-252 neutron source) with a realistic intensity level even when the value is high.

Taking into consideration the contents of Non-Patent Document 1, the subcriticality measuring method described in Non-Patent Document 1 can be used as a method for measuring and monitoring the subcriticality ρ of a system including damaged nuclear fuel in real time. It is presumed to be suitable. Therefore, the method described in Non-Patent Document 1 will be described below. That is, first, although slightly different from the conversion formula and the notation method related to the Feynman alpha method described in FIG. 1 of Non-Patent Document 1, a formula equivalent thereto is shown in the following formula (2-1).

Here, the delayed neutron ratio β varies depending on the fissile nuclide, but is less than about 0.01 in the case of U nuclide and Pu nuclide. Therefore, the delayed neutron ratio β due to these nuclides is within ± 0.04 in the region of the subcriticality measurement accuracy (0.95> neutron effective multiplication factor k ≧ 0.8) targeted in Non-Patent Document 1. , 0.8> Neutron effective multiplication factor k ≧ 0.4 (within ± 0.10), which is sufficiently small. Therefore, it is presumed that the approximate expression (the second expression on the right side) in the above equation (2-1) may be practically acceptable.

Further, although the conversion formula and the notation method for the time correlation analysis Miharuzo method described in FIG. 6 of Non-Patent Document 1 are slightly different, the equivalent formula is shown in the following formula (2-2).

The “CR (Δt)” on the left side in this equation (2-2) is obtained as an actually measured value for each time gate width Δt, which is the time interval between the measured neutron pulses. However, unlike the Feynman-alpha method described in the above description of Patent Document 1, theoretically, there is no dependence on the time gate width Δt. In this specification, the hyphen "-" is deleted from the "dispersion-counting ratio (CR)" described in the rectangular frame in FIG. 6 of Non-Patent Document 1 as the parameter name of "CR". It is referred to as the variance count ratio CR.

Then, as described in Non-Patent Document 1, the method of simultaneously applying the time correlation analysis Miharuzo method and the Feynman alpha method has, at first glance, the prompt neutron lifetime, which is a drawback of the Feynman alpha method. It can be said that it is a method that can complement each other in that it is easily affected by the neutron spectrum and that the subcriticality conversion coefficient χ, which is a drawback of the time correlation analysis Feynman method, is easily affected by the detector arrangement. .. However, Non-Patent Document 1 does not show any specific method or means for complementarily eliminating such mutual defects. Therefore, even in the method described in Non-Patent Document 1, the prompt neutron lifetime l in the formula (2-1) or the subcriticality conversion coefficient χ in the formula (2-2) is set prior to the subcriticality measurement. , For example, it is necessary to estimate or assume by prior analysis and then use them in combination with the measured values.

(Patent Document 2)
The invention described in Patent Document 2 is by the present inventor, and includes measurement values obtained by the Fineman-Alpha method and the time correlation analysis Miharuzo method, and a plurality of measurement values obtained by perturbing the measurement target. It is characterized in that the subcriticality ρ is obtained by regarding the related parameters as simultaneous equations. However, as shown below, it has been confirmed by the inventor that a mathematical solution cannot be obtained, and it is not effective as a means for solving the above-mentioned problems.

That is, the simultaneous equations of the methods described in Patent Document 2 are as shown in the following equations (11) to (16).
CR _1,1 = χ ₁・ (1-k ₁ )… (11)
CR _1,2 = χ ₂・ (1-k ₁ )… (12)
α ₁ = 1 / l ₁・ (1-k ₁ )… (13)
CR _2,1 = χ ₁・ (1-k ₂ )… (14)
CR _2,2 = χ ₂・ (1-k ₂ )… (15)
α ₂ = 1 / l ₂・ (1-k ₂ )… (16)

Here, the unknowns are the neutron effective multiplication factor k ₁ , k ₂ , the prompt neutron lifetime l ₁ , l ₂ , and the subcriticality conversion coefficients χ ₁ , χ ₂ .

By the way, the equations (11) and (14) are based on the equation (2-2) of Non-Patent Document 1, in which (1-k) is proportional to CR via the conversion coefficient χ _1. It just shows that you do. Further, since the equation (14) is simply a multiplication of the equation (11) by (1-k ₂ ) / (1-k ₁ ), the equations (11) and (14) are completely relational expressions. It is the same. Similarly, equation (15) is merely a product of equation (12) multiplied by (1-k ₂ ) / (1-k ₁ ), and equations (12) and (15) are exactly the same as relational expressions. Is. That is, among the equations (11) to (16), there are practically four relational expressions that are valid as equations, and it is impossible to obtain a solution from four relational expressions for six unknowns. .. Therefore, Patent Document 2 is not effective as a means for solving the above-mentioned conventional problems.

From the above, as described above as the "problem to be solved by the invention", in any of the conventional methods described in Patent Document 1, Non-Patent Document 1, and Patent Document 2, the system including nuclear fuel is subcritical. In order to measure and evaluate the degree ρ, it is necessary to give in advance spatial correction factors such as the prompt neutron lifetime or the subcriticality conversion coefficient in the system as known state parameters. However, as described above, it is almost impossible to accurately grasp, estimate, or actually measure detailed information on such state parameters, especially in a system including damaged nuclear fuel. It must be said that it is extremely difficult to measure and evaluate the subcriticality ρ with practical reliability by applying the conventional methods described in Patent Document 1 and Patent Document 2 to an actual nuclear fuel, particularly a damaged nuclear fuel. I don't get it. On the other hand, the subcriticality measurement monitoring system and method according to the present invention provide an effective method for compensating for such shortcomings of the prior art. Hereinafter, embodiments according to the present disclosure will be described.

(First Embodiment)
In the method for measuring the subcriticality of nuclear fuel according to the present embodiment, (A) a plurality of simulated calculation systems having a virtual measurement target including nuclear fuel and a virtual neutron detection unit are set, and (B) a plurality of simulated calculation systems. For each of the neutron effective multiplication factor or subcriticality of the virtual measurement target and the furnace noise method measurement value measured by the virtual neutron detection unit, (C) multiple simulations From the values, the correlation equation between the effective neutron multiplier or subcriticality and the measured value by the reactor noise method is calculated, and (D) the actual measurement system having the actual measurement target including the nuclear fuel and the actual neutron detector is obtained. By obtaining the measured value of the furnace noise method measurement value measured by the neutron detection unit and substituting the measured value of the furnace noise method measurement value into the (E) correlation equation, the neutron effective multiplication factor or subcriticality of the actual measurement target is obtained. Calculate the degree.

Specifically, it is preferable to use the following formula (X) as the correlation formula.

More specifically, as the furnace noise method measurement value X, the partition coefficient ratio CR obtained by the time correlation analysis Miharuzo method can be mentioned. This point will be described in detail including the background to the present invention.

First, if the inventor can use a coefficient for converting the measured value to the subcriticality in the time correlation analysis Miharuzo method and the Fineman Alpha method, which is hard to depend on the state of the measurement target, the inventor can perform pre-calibration or pre-calibration. Even if the conversion coefficient obtained by the simulation is applied to the measurement target whose state is unknown, we thought that the effective neutron multiplier and thus the subcriticality could be estimated accurately. Therefore, for example, the prompt neutron lifetime l in the above formula (2-1) of Non-Patent Document 1 which is the conversion formula in the Fineman Alpha method, or the formula of Non-Patent Document 1 which is the conversion formula of the time correlation analysis Miharuzo method ( The degree to which the subcriticality conversion coefficient χ in 2-2) depends on the state of the measurement target is considered.

First, as described above, the prompt neutron lifetime l is easily affected by the neutron spectrum, and specifically, it changes by an order of magnitude depending on the neutron spectrum. Therefore, the nuclide composition and amount in the measurement target are unknown. The uncertainty is high in the situation, and the uncertainty of the estimated effective neutron multiplier is considered to be unacceptably large. On the other hand, the subcriticality conversion coefficient χ, which is a conversion coefficient related to the detection efficiency, has little dependence on the neutron spectrum as described above, but is affected by the positional relationship between the measurement target and the detector (that is, the detector arrangement). In a situation where it is easily received and it is unknown, it is considered difficult to estimate the effective multiplication factor as in the Fineman Alpha method.

However, the inventor thinks that the subcriticality conversion coefficient χ is probably dominated by the influence of the distance between the Cf-252 built-in ionization chamber and the neutron detector among the geometric conditions, and Cf-252. We devised a measuring instrument that integrates the built-in ionization chamber and the neutron detector. With such a device configuration, it is possible to keep the distance between the Cf-252 built-in ionization chamber and the neutron detector always constant, and thereby alleviate the uncertainty included in the subcriticality conversion coefficient χ. Conceivable.

On the other hand, the conventional awareness of the problem that the subcriticality conversion coefficient χ is easily affected by the detector arrangement is raised by the following stereotypes that are not based on technical grounds, according to the present inventor. It is probable that it was.

That is, the measurement principle in this case is that the neutrons emitted by the Cf-252 spontaneous fission in the Cf-252 built-in ionization chamber induce the nuclear fuel fission in the nuclear fuel region, and the neutrons generated thereby reach the neutron detector. Where subcriticality measurement is possible, the arrangement of these Cf-252 built-in ionization chambers, nuclear fuel region, and neutron detectors in a one-dimensional manner is schematically considered, so the actual detector arrangement is also possible. It is presumed that, in a fixed concept, a configuration was adopted in which the nuclear fuel region was sandwiched between the Cf-252 built-in ionization chamber and the neutron detector. For example, FIGS. 4-1 to 4-4 of "Hane-samahei et al.," Development of subcriticality measurement technology in DCA ", JNC-TN9400-2001-044." (hereinafter referred to as "references"). Such a detector arrangement is described.

However, technically, it is not necessary to arrange the nuclear fuel region between the ionization chamber with built-in Cf-252 and the neutron detector, and rather, the ionization with built-in Cf-252 in a system with a deep subcriticality ρ. It is considered that it is advantageous to integrally configure (integrately bundle) the box and the neutron detector because it is easy to obtain a high correlation between the neutron detectors.

This is because in a system with a deep subcriticality ρ, the fission chain reaction induced in the nuclear fuel region does not propagate widely to the surroundings and tends to terminate locally, so that it is built in Cf-252. The probability that neutrons emitted from the ionization chamber will induce fission of nuclear fuel in the nuclear fuel region and the neutrons generated by this will reach the neutron detector is that both detectors, even if the nuclear fuel region is sandwiched between both detectors. This is because if the distance between them is long, it will be significantly reduced and measurement will be substantially impossible. In fact, in FIG. 4-2 of the above reference, the measurement can be performed only by the neutron detector A arranged near the ionization chamber built in Cf-252, and the neutron detector B arranged at a relatively distant position can be used for measurement. , The result that could not be detected is described. In addition, the results of simulation analysis in the measurement system shown in FIGS. 4-1 to 4-4 of the above reference are shown in FIGS. 4-6, 4-8, 4-10, and 4-12 of the same document. It can be seen that the farther the distance between the two detectors is, the lower the sensitivity of the measurement result is, and therefore the more disadvantageous the measurement is.

If the Cf-252 built-in ionization chamber and the neutron detector are integrally configured with respect to such a conventional arrangement, the neutrons emitted by the Cf-252 spontaneous fission in the Cf-252 built-in ionization chamber will be the Cf-252 built-in ionization chamber. By inducing nuclear fission in the nearby nuclear fuel region and the neutrons generated by this inducing a process leading to the neutron detector near the Cf-252 built-in ionization chamber, it is easy to obtain a correlation between the two detectors, and measurement is possible. It can be said that it is more suitable from the viewpoint of improving the accuracy.

In addition, as an effect on the measurement result when the Cf-252 built-in ionization chamber and the neutron detector are integrally configured, in some cases, when Cf-252 in the Cf-252 built-in ionization chamber causes spontaneous fission, it is simultaneous. By simultaneously measuring the generated neutrons with adjacent neutron detectors, a correlation of generation probability (deviation from the Poisson process, which is a random neutron generation process) occurs between the generated neutrons other than the induced nuclear fission process. In the measurement results, it is observed that apparently induced nuclear fission occurs, and there is a concern that accurate measurement cannot be performed.

Therefore, regarding such concerns, measurement is performed in a system (blank) in which nuclear fuel does not exist, the detector is calibrated by understanding the effect of the effect on the measurement result, and the effect is measured when measuring nuclear fuel. It is considered that it can be solved by excluding it from. Further, since the intensity of the neutrons emitted from the Cf-252 built-in ionization chamber is high, there may be a concern that the dead time of the neutron detector may increase. However, regarding such concern, the side facing the Cf-252 built-in ionization chamber may be concerned. It is considered that this can be solved by providing a neutron shielding material on the side surface of the neutron detector.

In order to confirm the effectiveness of the above Cf-252 built-in ionization chamber and neutron detector integrally configured, in various systems with different subcriticality ρ, neutron flux distribution shape, neutron spectrum, and detector placement position. A simulation was performed. FIG. 1 is a schematic diagram schematically showing the configuration of the measurement system. In the simulation in this measurement system, a disk-shaped fuel debris 10 containing damaged nuclear fuel was assumed as a measurement target, the system height h1 was fixed at 40 cm, and the system diameter d1 was changed in the range of 40 to 120 cm. In addition, the influence of the presence or absence of the central hole 20 formed when the core boring for sampling was applied was confirmed. Further, a neutron detector 50 in which a Cf-252 built-in ionization box 30 (a neutron generator having a neutron source) and a neutron detector 40 without a Cf-252 (a neutron detector having no neutron source) are integrated is used as fuel. It was placed on the upper surface of the debris 10, and the arrangement position of the neutron detection unit 50 was appropriately changed in the direction of the horizontal arrow 60 (12 cases in total). The Cf-252 built-in ionization box 30 detects spontaneous fission by detecting the ion pair of the atmosphere inside the ionization box generated by the fission product (Fission Product: FP) generated by the spontaneous fission of Cf-252. It is essentially different from the neutron detector 40 without Cf-252 in that it has the function of (detecting the generation time of neutrons that are generated together during spontaneous fission).

FIG. 2 is a graph in which the simulation results of the calculated values (subcriticality ρ) and the measured values (dispersion coefficient ratio CR) in the measurement system of FIG. 1 are plotted (marked with white circles). Further, in FIG. 2, the fitting curve obtained by fitting the above equation (X) (measured value by the furnace noise method X = dispersion coefficient ratio CR) to the plurality of plotted data is shown by a solid line. As shown in FIG. 2, it was found that the simulation results of the calculated value of the subcriticality ρ and the measured value of the dispersion coefficient ratio CR are accurately regressed to the nonlinear function represented by the equation (X).

From this, first, the subcriticality conversion coefficient χ itself does not become a constant value with respect to the measured value (dispersion coefficient ratio CR), but is a non-linear function having dependence on the measured value (dispersion coefficient ratio CR) itself. It was confirmed that (when the subcriticality ρ becomes deeper, the neutron detection efficiency ε itself is recognized to have a strong dependence on the subcriticality ρ). Then, for various system conditions in which the subcriticality ρ, the neutron flux distribution shape, the neutron spectrum, and the detector arrangement position are different, the neutron effective multiplication factor k (and thus the subcriticality ρ) and the measured value are as shown in FIG. A correlation equation (formula (X)) showing the relationship with (dispersion coefficient ratio CR) was created in advance by simulation prior to actual measurement, and the measured value (dispersion coefficient ratio CR) obtained in the actual measurement system was used. By substituting into the correlation equation, it is suggested that the neutron effective multiplication factor k (and thus the subcriticality ρ) can be estimated accurately.

Next, in order to evaluate the fitting error of the correlation equation shown in FIG. 2, the neutron effective multiplication factor k (estimated value from the correlation equation) obtained from the fitting curve of FIG. 2 and the same measurement system were obtained. The effective neutron multiplication factor k (analyzed value) was plotted in FIG. 3 (white circles). The alternate long and short dash line shown in the figure is a 45 ° gradient line, and since the plotted data is located on or near the line, the correlation equation obtained by fitting the above equation (X) should be used. Therefore, it is understood that the effective neutron multiplier k (and thus the subcriticality ρ) can be estimated within a range sufficiently acceptable for practical use.

From the above results, it is possible to grasp the degree of uncertainty of the correlation equation by creating the correlation equation not only for the 12 cases shown in FIG. 2 but also for a wide variety of more cases. , It is understood that a more reliable evaluation of the neutron effective multiplication factor k (and thus the subcriticality ρ) becomes possible.

Subsequently, the inventor evaluated the effect on the measured value (dispersion coefficient ratio CR) when the distance between the region surface of the nuclear fuel and the neutron detection unit 50 in the fuel debris 10 to be measured was changed. It was confirmed that it has a large dependence. This is because the viewing angle (solid angle) when the nuclear fuel region is viewed from the neutron detection unit 50 changes depending on the distance from the nuclear fuel region surface, and the neutron detection efficiency ε changes. It is presumed that this is due to. Further, when water exists in the region between the nuclear fuel region and the neutron detection unit 50, the presence of the water shields the neutrons and reduces the probability of reaching the neutron detection unit 50, that is, the neutron detection efficiency also in this case. Since ε changes, the influence on the measured value (dispersion coefficient ratio CR) tends to increase as well.

Therefore, in the present embodiment, a plurality of virtual environmental conditions different from each other are set for the virtual measurement target (fuel debris 10) and the virtual neutron detection unit 50, and simulated calculation is performed for each of the plurality of environmental conditions. A plurality of systems are set, a correlation formula is calculated, actual environmental conditions are measured for the actual measurement target (fuel debris 10) and the actual neutron detection unit 50, and virtual environmental conditions approximate to the actual environmental conditions. By substituting the measured value of the reactor noise method measurement value (dispersion coefficient ratio CR) into the correlation formula calculated under the selected virtual environmental conditions, the neutron effective multiplication factor k of the actual measurement target or It is preferable to calculate the subcriticality ρ. In this case, the environmental conditions are the distance between the nuclear fuel region surface and the neutron detection unit 50 in the fuel debris 10 to be measured, and the nuclear fuel region surface and the neutron detection unit 50 in the fuel debris 10 to be measured. It is preferably at least one of the amount and distribution of the substances present between the two.

At that time, by applying remote sensing technology such as electromagnetic exploration and sonar, the identification of the nuclear fuel region surface in the fuel debris 10 to be measured, the position where the detector is planned to be arranged in the neutron detector 50, and the nuclear fuel region surface are reached. It is possible to estimate or grasp the actual environmental conditions such as the distance and the amount of existing water, and select and use the correlation equation corresponding to the actual environmental conditions from the correlation equation group obtained in advance. is there. Understanding the environmental conditions of the measurement target in advance is much more feasible than the conventional estimation of the nuclide composition and amount required to evaluate the prompt neutron lifetime l. It is considered to be expensive.

(Second Embodiment)
By the way, according to the time correlation analysis Miharuzo method shown in the first embodiment, as described above, there is a feature that the measurement results of the Feynman-alpha method can be obtained at the same time. Therefore, the present inventor pays attention to this point and, together with the measured value of the time correlation analysis Miharuzo method (dispersion coefficient ratio CR), the deviation of the measured value of the Fineman Alpha method (★ measurement data “dispersion to average ratio”). It was found that by utilizing the information of Y∞ ) obtained by the function fitting of Y (Δt), the reliability of the neutron effective multiplication factor k estimated in the first embodiment and the subcriticality ρ can be further improved. It was. This point will be described in more detail below.

As described above, the prompt neutron lifetime l in the above formula (2-1) of Non-Patent Document 1, which is a conversion formula in the Fineman alpha method, changes by an order of magnitude depending on the neutron spectrum, and therefore, it is included in the measurement target. Uncertainty is large in situations where the nuclide composition and amount are unknown, and the uncertainty of the estimated effective neutron multiplier is considered to be unacceptably large. Therefore, it is considered difficult to apply the prompt neutron lifetime l as it is to the estimation of the effective neutron multiplication factor k and thus the subcriticality ρ.

Therefore, in the Fineman-Alpha method, a method of converting the measured value (deviation Y (Δt) of the “dispersion to average ratio”) into the subcriticality ρ was examined without using the prompt neutron lifetime l. First, the theoretical formula of the Feynman-alpha method is described according to the following formula (A), following Patent Document 1 (see formula (1-1)).

Here, the parameters obtained by the function fitting of the measurement data (deviation Y (Δt) of “variance to average ratio”) are Y∞ and α in the equation (A), and Y∞ is the following equation (B). It is represented (see C _n in equation (1-1)).

By the way, from the above formula (2-1) equivalent to the conversion formula related to the Feynman alpha method described in Non-Patent Document 1, the following formula (C) is between l · α and the neutron effective multiplication factor k. The approximate relationship represented by is established.

As already described in the explanation of the above equation (2-1), this is presumed to be an approximation within a range that does not hinder practical use. By substituting this equation (C) into the above equation (B), which is the definition equation of Y∞, the following equation (D) is obtained.

Here, among the right sides of the above formula (D), the Diven number has a relatively small dependence on the fission nuclide, and therefore a predetermined representative value can be applied. Therefore, the conversion coefficient of the equation (D) to the subcriticality ρ is substantially only the neutron detection efficiency ε. The neutron detection efficiency ε has a relatively large effect depending on the distance from the surface region of the nuclear fuel to the neutron detection unit 50 in the fuel debris 10 to be measured, the abundance of water etc. in the region, and the subcriticality ρ itself. Although it can be affected, it tends to be less affected by the composition of the nuclear fuel itself.

Therefore, as described in the first embodiment, remote sensing techniques such as electromagnetic exploration and sonar are applied to identify the surface of the nuclear fuel region in the fuel debris 10 to be measured, and the detector in the neutron detector 50. It can be said that it is possible to contribute to the estimation of the effective neutron multiplier k and the subcriticality ρ by estimating or grasping the actual environmental conditions such as the planned placement position, the distance to the surface of the nuclear fuel region, and the amount of existing water. ..

Further, even if the method of the present embodiment considers the influence of the relative error of the neutron detection efficiency ε on the estimated value of the neutron effective multiplication factor k and thus the subcriticality ρ, the neutron effect based on the conventional equation (C) is considered. It is as follows that it is more preferable than the estimation of the multiplication factor k. That is, when the neutron detection efficiency ε includes an error of Δε, the estimated value of the neutron effective multiplication factor k has a relationship represented by the following formula (E) from the above formula (D).

Here, k (ε + Δε) indicates that the neutron effective multiplication factor is estimated with the neutron detection efficiency ε including the error Δε (the neutron effective multiplication including the error due to the error Δε of the neutron detection efficiency ε). magnification). By dividing this equation (E) by the above equation (D) and rearranging for k (ε + Δε), the following equation (F) is derived.

As described above, the equation (F) expresses the influence of the relative error Δε / ε included in the neutron detection efficiency ε on the estimated value of the neutron effective multiplication factor k. Since the neutron detection efficiency ε is physically defined as a positive value, the relative error Δε / ε can take a value of -1 or more, but from equation (F), the neutron effective multiplication factor k in the subcritical system. (Ε + Δε) is in the range of 0 to 1 as shown in FIG. Here, FIG. 4 is a graph showing the change of the neutron effective multiplication factor k (ε + Δε) with respect to the relative error Δε / ε of the neutron detection efficiency ε, and the true value of the neutron effective multiplication factor k = 0.3, 0. This is the result of evaluating the change in the neutron effective multiplication factor k (ε + Δε) when the values are 5, 0.7, and 0.9.

Similarly, the estimated value of the effective neutron multiplication factor k when the prompt neutron lifetime l includes an error of Δl has a relationship represented by the following formula (H) from the above formula (C).

As described above, the equation (H) expresses the influence of the relative error Δl / l included in the prompt neutron lifetime l on the estimated value of the neutron effective multiplication factor k. Since the prompt neutron lifetime l is physically defined as a positive value, Δl / l can take a value of -1 or more, but from the equation (H), the neutron effective multiplication factor k (l + Δl) in the subcritical system ) Is in the range of −∞ to 1 as shown in FIG. Here, FIG. 5 is a graph showing the change in the effective neutron multiplier k (Δl / l) with respect to the relative error Δl / l of the prompt neutron lifetime l, and the true value of the effective neutron multiplier k = 0.3. This is the result of evaluating the change in the effective neutron multiplier k (Δl / l) when the values are 0.5, 0.7, and 0.9.

Comparing FIGS. 4 and 5, the neutron effective multiplication factor k (ε + Δε) is within the entire defined range of the relative error of the neutron detection efficiency ε or the prompt neutron lifetime l, which is a conversion coefficient to the substantial neutron effective multiplication factor k. It was confirmed that the error (rate of change) was smaller than the error (rate of change) of the neutron effective multiplication factor k (l + Δl). Therefore, the effective multiplication factor conversion method according to the above equation (D) does not need to use the prompt neutron lifetime l, which may change by orders of magnitude depending on the neutron spectrum, so the conversion factor to the neutron effective multiplication factor k is in the first place. It can be said that it has a desirable feature in that the sensitivity given to the neutron effective multiplication factor k is small with respect to the relative error of.

FIG. 6 is a graph in which the simulation results of the calculated values (subcriticality ρ) and the measured values (Y∞) in the measurement system of FIG. 1 are plotted (marked with white circles) in the same manner as in FIG. Further, in FIG. 6, the fitting curve obtained by fitting the above equation (X) (measured value X = Y∞ by the furnace noise method) to the plurality of plotted data is shown by a solid line. As shown in FIG. 6, it was found that the simulation results of the calculated value of the subcriticality ρ and the measured value of Y∞ are accurately regressed to the nonlinear function represented by the equation (X).

From this, it was first confirmed that the neutron detection efficiency ε itself does not become a constant value with respect to the measured value (Y∞), but becomes a non-linear function having dependence on the measured value (Y∞) itself. It was. Then, for various system conditions in which the subcriticality ρ, the neutron flux distribution shape, the neutron spectrum, and the detector arrangement position are different, the neutron effective multiplier k (and thus the subcriticality ρ) and the measured value are as shown in FIG. A correlation equation (X) showing the relationship with (Y∞) is created in advance by simulation prior to actual measurement, and the measured value (Y∞) obtained in the actual measurement system is substituted into the correlation equation. This suggests that the effective neutron multiplier k (and thus the subcriticality ρ) can be estimated accurately.

By the way, when fitting the simulation result of the deviation Y (Δt) of the “dispersion to average ratio” which is the measurement data to the equation (A), if Y (Δt) does not pass through the origin (Y (Δt) = 0). However, the behavior of having a positive intercept was observed (see FIG. 7). FIG. 7 is a graph showing the change in the deviation Y (Δt) of the “dispersion to average ratio” with respect to the time gate width Δt.

In the first place, it is indistinguishable whether or not Y (Δt) of the formula (A) passes through the origin among the individual neutrons generated in the time gate width Δt, which is sufficiently smaller than the prompt neutron lifetime l, that is, whether it is induced fission or not. This is because it is regarded as a Poisson process, which is a completely random generation process that is not correlated with each other, and the deviation Y (Δt) of the “dispersion to average ratio” is 1 (that is, Y = zero). Therefore, it is considered that the behavior in which Y (Δt) has an intercept as shown in FIG. 7 is due to some correlation between individual neutrons even in the minimum time gate width of FIG.

Therefore, when the individual neutron detection times were confirmed, there were many pairs of neutrons detected almost at the same time, and the cause was Cf-252, which is required for the time correlation analysis Miharuzo method in the simulation measurement system shown in FIG. It was presumed that this was due to the simultaneous measurement of multiple neutrons generated when Cf-252 in the built-in ionization chamber undergoes spontaneous fission. It is presumed that such a phenomenon is a characteristic phenomenon in the first embodiment and occurs when an intrinsic neutron source that causes spontaneous fission is significantly present in the nuclear fuel even when the Cf-252 built-in ionization chamber is not used. Will be done. In reality, since the neutron detector has a dead time, it is limited to neutrons measured with a time difference longer than the dead time and shorter than the time gate width Δt (that is, almost simultaneously), and thus is shown in FIG. It is assumed that no such prominent section appears.

Therefore, in the present embodiment, in consideration of the phenomenon that Y (Δt) has an intercept as shown in FIG. 7, the following formula (I) is a generalization of the above formula (A) in order to obtain Y∞ more precisely. Is used.

Here, Y ₀ is a value obtained by fitting. Note that Y∞ (value on the horizontal axis) in FIG. 6 shown above is obtained by fitting based on the formula (I).

Further, in order to evaluate the fitting error of the correlation equation shown in FIG. 6, the neutron effective multiplication factor k (estimated value from the correlation equation) obtained from the fitting curve of FIG. 6 and the same measurement system were obtained. The neutron effective multiplication factor k (analyzed value) is plotted in FIG. 8 (white circles). The alternate long and short dash line shown in the figure is a 45 ° gradient line, and since the plotted data is located on or near the line, the correlation equation obtained by fitting the above equation (X) should be used. Therefore, it is understood that the effective neutron multiplier k (and thus the subcriticality ρ) can be estimated within a range sufficiently acceptable for practical use.

(Third Embodiment)
In this embodiment, a more specific and suitable fitting method of Y∞ of the Feynman alpha method described in the second embodiment will be described.

For the convenience of obtaining the prompt neutron attenuation coefficient α from the transient behavior in the region where the time gate width Δt is small, Y∞ needs to be obtained by fitting the time gate width Δt limited to a region where the time gate width Δt is small to some extent. Otherwise, the region where the deviation Y (Δt) of the “dispersion to average ratio” is saturated (the number of data to be handled is the largest at the minimum time gate width, so the statistical error is small at the minimum time gate width, and the time. The statistical error increases as the gate width increases), and the prompt neutron attenuation coefficient α may not be accurately determined.

Therefore, Y∞ is set by performing function fitting using the above equation (I) on the measured value of the deviation Y (Δt) of the “dispersion to average ratio” determined by the following procedures (1) to (3). It is preferable to obtain it.

Procedure (1): The initial value of the number of selected data of the measured value of the deviation Y (Δt) of the “dispersion to average ratio” used for the function fitting of the above equation (I) is set to N _0, and N ₀ “variance pairs” are set. Let α obtained by performing the function fitting of the above equation (I) on the measured value of the deviation Y (Δt) of the “ratio-moving ratio” as the initial value α ₀ of the prompt neutron decay coefficient.
Step (2): When the initial value α ₀ is substituted into α _n-1 of the following equation (J), the range of the time gate width Δt satisfying the following equation (J) is obtained, and within the range of the time gate width Δt. A measured value of a deviation Y (Δt) of a certain “dispersion-to-moving ratio” is selected, the number of the selected measured values is defined as the number of selected data N _1, and the deviation Y (variance-to-moving ratio” of N ₁ piece. Let α obtained by performing the function fitting of the above equation (I) again on the measured value of Δt) be the next value α ₁ of the prompt neutron attenuation coefficient.

Step (3): Step (2) is repeated n times until the number of selected data N _n-1 and the number of selected data N _n become equal, and the deviation Y (Δt) of the final N _n “dispersion to average ratio”. ) Is determined, or if the number of selected data N _n-1 and the number of selected data N _n alternately increase or decrease by ± 1, whichever is greater, N _n-1 or N _n. Alternatively, the smaller one is consistently selected to determine the final measured value of the deviation Y (Δt) of N _n-1 or N _n “dispersion to mean ratio”.

By systematically selecting the fitting target data by such a procedure, the prompt neutron attenuation coefficient α can be appropriately fitted in the Δt region focusing on the transient behavior of Y∞, and the fitting target data can be fitted. It is possible to suppress variations in fitting values as compared with the case where selection is performed personally. The result of FIG. 8 shown above was obtained by fitting using the data of the deviation Y (Δt) of the “dispersion to average ratio” selected by applying the above procedure.

In the region where the time gate width Δt is relatively large, the influence of delayed neutrons begins to be seen (see “Kyoto University Critical Assembly Experiment Equipment KUCA Experiment Text-4. Neutron Correlation Experiment Feynman-α Method”). In the formula (I) in which the influence of neutrons is not considered, it is preferable that the time gate width Δt of the fitting target is set to the upper limit in the range where the influence of delayed neutrons is not observed.

(Fourth Embodiment)
In this embodiment, a more specific and precise fitting method of Y∞ of the Feynman alpha method described in the third embodiment will be described.

As mentioned in the third embodiment, the statistical error of the deviation Y (Δt) of the “dispersion to average ratio” at each time gate width Δt is statistical because the number of data handled in the minimum time gate width is the largest. The error is small at the minimum time gate width, and the statistical error tends to increase as the time gate width increases. Therefore, in fitting Y∞, the reliability is further improved by systematically selecting the target data as in the third embodiment and giving light weight to the handling at the time of fitting according to the statistical error of each target data. It is possible to perform enhanced fitting. That is, in the function fitting for obtaining the parameter Y∞ using the above equation (I), the “variance to average ratio” weighted by the reciprocal of the statistical error of the measured value of the deviation Y (Δt) of the “variance to average ratio”. It is preferable to use the deviation Y (Δt).

Specifically, it is as follows. First, the deviation Y (Δt) of the “dispersion to average ratio” is obtained by the following formula (K) as a measured value based on the measured neutron count. Although this formula (K) has a different form from the formula (5) in Patent Document 1, both are substantially the same.

Found statistical error √V _Y deviation "dispersion-average ratio" Y (Δt) (Δt) by applying the error propagation law against variance V _V of the variance V _M and the variance V of the average M , Given by the following formula (L).

Here, variance V _M, the general formula of the statistical error of V _V is as the following formulas (M) and formula (N) (Note that the formula (N) is an approximate equation).

When fitting, the residual square of the least squares method weighted by the reciprocal of the measured value of the deviation Y (Δt) of the “dispersion to average ratio” obtained by the equation (L) √V _Y (Δt) The following formula (O) is used as the difference.

FIG. 9 shows the result of fitting by applying the nonlinear least squares method using the equation (O). From this fitting result, it was confirmed that the fitting was performed so as to roughly pass the range of the statistical error of Y∞ of each time gate width Δt. The result of FIG. 8 shown above was obtained by fitting by applying the present embodiment.

As described above, the present invention is not limited to each of the above embodiments, and various modifications can be made without changing the gist thereof.

As described above, according to the subcriticality measurement method according to the present invention, for a plurality of simulated calculation systems having a measurement target and a neutron detection unit, the neutron effective multiplication factor or subcriticality of the measurement target and the measured values by the furnace noise method are measured. By obtaining simulation values, calculating their correlation formulas, and substituting the measured values of the furnace noise method measurement values into the correlation formulas, the neutron effective multiplication factor or subcriticality of the actual measurement target is calculated. Even if detailed information on state parameters such as composition, shape, and properties of the measurement target including the above is unknown, the subcriticality of the measurement target can be measured and evaluated accurately and accurately. Therefore, the subcriticality measurement method according to the present invention includes objects that require criticality control including nuclear fuel, especially criticality control of systems including damaged nuclear fuel, facilities and power plants where such systems are expected to occur. And, it can be widely and effectively used in technical fields such as electric and electric power industries related to them.

10 ... Fuel debris, 20 ... Central hole, 30 ... Cf-252 built-in ionization box (neutron generator with neutron source), 40 ... Neutron detector without Cf-252 (neutron detector without neutron source), 50 ... Neutron detector, 60 ... Horizontal arrow, d1 ... System diameter, h1 ... System height

Claims (8)

Set up multiple simulated calculation systems with virtual measurement targets including nuclear fuel and virtual neutron detectors.
For the plurality of simulated calculation systems, a plurality of simulation values of the neutron effective multiplication factor or subcriticality of the virtual measurement target and the furnace noise method measurement value measured by the virtual neutron detection unit are obtained. Ask,
From the plurality of simulation values, a correlation equation between the effective neutron multiplication factor or subcriticality and the measured value by the furnace noise method is calculated.
For a measurement system having an actual measurement target including nuclear fuel and an actual neutron detection unit, the measured values of the reactor noise method measured by the actual neutron detection unit are obtained.
By substituting the measured value of the furnace noise method measurement value into the correlation equation, the neutron effective multiplication factor or subcriticality of the actual measurement target is calculated.
A plurality of virtual environmental conditions different from each other are set for the virtual measurement target and the virtual neutron detection unit.
For each of the plurality of environmental conditions, a plurality of the simulated calculation systems are set and the correlation equation is calculated.
Measure the actual environmental conditions of the actual measurement target and the actual neutron detector,
Select the virtual environmental condition that is close to the actual environmental condition, and select
By substituting the measured value of the furnace noise method measurement value into the correlation equation calculated under the selected virtual environmental conditions, the neutron effective multiplication factor or subcriticality of the actual measurement target is calculated.
The environmental conditions are the distance between the nuclear fuel region surface and the neutron detection unit in the measurement target, and the amount and distribution of substances existing between the nuclear fuel region surface and the neutron detection unit in the measurement target. At least one of
Subcriticality measurement method for nuclear fuel. The subcriticality measuring method for nuclear fuel according to claim 1, wherein the following formula (X) is used as the correlation formula.
As the neutron detector, a neutron generator having a neutron source and a neutron detector without a neutron source are integrally configured.
The subcriticality measuring method for nuclear fuel according to claim 1. The furnace noise method measurement value is the dispersion coefficient ratio CR obtained by the time correlation analysis Miharuzo method.
The subcriticality measuring method for nuclear fuel according to any one of claims 1 to 3 . The furnace noise method measurement value is a parameter Y∞ obtained by the function fitting of the deviation Y (Δt) of the “dispersion to average ratio” obtained by the Fineman Alpha method.
Here, Δt indicates the time gate width, which is the time interval between the neutron pulses.
The subcriticality measuring method for nuclear fuel according to any one of claims 1 to 3 . By substituting the parameter Y∞, which is the measured value by the furnace noise method, into the following formula (D), the further neutron effective multiplication factor or subcriticality of the actual measurement target is calculated.
The parameter Y∞ is obtained by function fitting using the following equation (I).
The subcriticality measuring method for nuclear fuel according to claim 5 .
Procedures (1) to (3) shown below;
Procedure (1): The initial value of the number of selected data of the measured value of the deviation Y (Δt) of the “dispersion to average ratio” used for the function fitting of the above formula (I) is N ₀ , and the N ₀ pieces of the above “ Let α obtained by performing the function fitting of the above equation (I) on the measured value of the deviation Y (Δt) of the “dispersion to average ratio” as the initial value α ₀ of the prompt neutron decay coefficient.
Step (2): When the initial value α ₀ is substituted into α _n-1 of the following equation (J), the range of the time gate width Δt satisfying the following equation (J) is obtained, and within the range of the time gate width Δt. The measured value of the deviation Y (Δt) of the “dispersion to average ratio” is selected, the number of the selected measured values is defined as the number of selected data N ₁ , and the N ₁ “dispersion to average ratio”. The α obtained by performing the function fitting of the above equation (I) again on the actually measured value of the deviation Y (Δt) of is set to the next value α ₁ of the prompt neutron decay coefficient.
Step (3): The procedure (2) is repeated n times until the number of selected data N _n-1 and the number of selected data N _n become equal, and the final N _n deviations of the “dispersion to average ratio” Y If the measured value of (Δt) is determined, or if the number of selected data N _n-1 and the number of selected data N _n alternately increase or decrease by ± 1, either N _n-1 or N _n The larger or smaller one is consistently selected to determine the final measured value of the deviation Y (Δt) of N _n-1 or N _n of the above “dispersion to mean ratio”.
The Y∞ is obtained by performing a function fitting using the above equation (I) on the measured value of the deviation Y (Δt) of the “dispersion to average ratio” determined by.
The subcriticality measuring method for nuclear fuel according to claim 6 . In the function fitting for obtaining the parameter Y∞ using the above formula (I), the “dispersion to average ratio” weighted by the reciprocal of the statistical error of the measured value of the deviation Y (Δt) of the “variance to average ratio”. Using the deviation Y (Δt) of
The subcriticality measuring method for nuclear fuel according to claim 6 or 7 .