JPS6155075B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention is capable of measuring the neutron flux inside or outside a unit subcritical system including a fuel assembly having a neutron source, in the case of only the unit subcritical system, and in the case of a composite system including the unit subcritical system. This paper compares the case of a subcritical system and relates to a method for determining the subcriticality, that is, the negative reactivity of a unit subcritical system.

A unit subcritical system includes a fuel assembly having at least one neutron source. Fuel assemblies with neutron sources include fuel assemblies containing transuranium elements that spontaneously emit neutrons (hereinafter these neutrons are referred to as spontaneous neutrons), such as irradiated fuel, and fuel assemblies that contain high-energy elements such as irradiated fuel. Fuel assemblies that are equipped with deuterium, beryllium, etc. that emit neutrons through (γ, n) reactions inside the fuel assemblies that emit gamma rays, and fuels that are equipped with external neutron sources such as californium-252 or antimony/beryllium. There are also aggregates. The external neutron source may be mounted either inside or outside the fuel assembly.

As a complex subcritical system, a nuclear reactor core that is shut down,
These include spent fuel transport containers and fuel racks.

Typical examples to which the present invention is applied are described below.

(1) Measurement of subcriticality of nuclear reactor core during shutdown (2) Measurement of subcriticality of spent fuel transport containers (3) Measurement of subcriticality of fuel racks (4) Measurement of subcriticality of new fuel storage such as plutonium (5) Subcriticality measurement of irradiated fuel Of these, (1) to (4) belong to the subcriticality measurement of a composite subcritical system, and (5) belongs to the subcriticality measurement of a unit subcritical system. The subcriticality, or negative reactivity, of a nuclear reactor during shutdown in (1) indicates the nuclear integrity of the control rods, safety during control rod replacement, safety in the event of a hypothetical control rod dropout accident, or evaluation of nuclear design methods. It is extremely effective. (2) Subcriticality of the spent fuel transportation container is an essential condition for safe transportation. The subcriticality of the fuel rack in (3) is effective for the effective use of spent fuel storage sites and for evaluating the validity of the nuclear design method for the rack. The subcriticality of the new fuel storage in (4) is effective in evaluating the safety of flooding accidents, the effective use of the storage, and design methods. The subcriticality of irradiated fuel (5) is effective for checking the combustion state, effectively utilizing the fuel, and evaluating design methods.

The following describes in detail the method (1) for measuring the subcriticality of a nuclear reactor core during shutdown, which is a typical example of a composite subcritical system. The above-mentioned (2) to (4) can also be implemented in the same manner.

In general, nuclear reactions such as nuclear fission and neutron capture take place very actively in power reactors. For example, when uranium is used as nuclear fuel, the amount of uranium-235 is depleted and plutonium is produced instead. Depletion of uranium reduces the positive reactivity of the reactor, while production of plutonium conversely increases the positive reactivity. In addition, some products produced by nuclear fission, such as xenon-135, have extremely large neutron absorption cross sections, but the production of xenon-135 in particular varies not only depending on the operating output of the nuclear reactor. , increases significantly once the reactor is shut down and then decreases, but if the reactor is shut down for 10 days, it almost disappears. Xenon during reactor shutdown
When 135 disappears, the subcriticality of the reactor decreases. In addition, burnable poisons such as gadolinium are sometimes used in fuel assemblies to suppress excess reactivity in the reactor, improve power distribution, or improve the control rod reactivity effect. . This burnable poison is gradually or rather rapidly destroyed as the nuclear fuel burns, creating an associated positive reactivity effect in the reactor.

As mentioned above, in a power reactor, the potential reactivity of the reactor changes in a complex manner as the nuclear fission reaction progresses. During reactor operation, this potential reactivity is suppressed by control rods, etc., resulting in a state of zero reactivity. When a nuclear reactor is shut down, control rods are used, and the reactivity of the control rods hardly changes as the nuclear fuel burns. When a nuclear reactor is shut down, it must be shut down safely and with plenty of time. Therefore, the subcriticality (referred to as shutdown margin) of a nuclear reactor during shutdown is extremely important for the safety of the reactor.

In general research reactors and critical experiment equipment,
Subcriticality has been measured using various methods such as the pulsed neutron source method, control rod drop method, and noise method, but in the case of power reactors, the core is extremely large and gamma rays are The various methods described above are not applicable due to reasons such as strong strength. For this reason, there have been no actual measurements of the shutdown margin of power reactors, and currently we rely solely on theoretical calculations. In order to safely and reliably keep the reactor subcritical even when there are complex changes in the shutdown margin as described above, this problem has conventionally been solved by adding more margin to the results of theoretical calculations.

By implementing the method according to the present invention, it is possible to experimentally evaluate the results of theoretical calculations, which can be useful for the economical design of nuclear reactors. It can be used to evaluate the safety during control rod and fuel replacement.

The principle of the present invention will be explained using mathematical formulas.

Fast neutrons, or spontaneous neutrons, emitted from transuranium elements produced in irradiated fuel and fast neutrons, or induced neutrons, emitted by chain-induced nuclear fission both have almost the same energy spectrum. The diffusion equation that describes the behavior of fast neutrons in the system of interest (in this case, a stopped reactor core) is as follows.

Since spontaneous neutrons and induced neutrons coexist in a steady state, the following equation (1) holds true.

<(Σ _r +DB ² ) _F φ _F > ^s = <νΣ _f φ>+S (1) On the other hand, in the absence of spontaneous neutrons, in order to express the equation in steady state form, the effective multiplication factor k
_eff is used and can be expressed by equation (2).

<(Σ _r + DB ² ) _F φ _F > = <νΣ _f φ>/k _eff (2) Here <>: A symbol indicating that the value inside <> is the average value of the given system.

F: Index indicating that the value corresponds to fast neutrons Σ _r : Removal cross section D: Diffusion coefficient B: Buckling νΣ _f φ: The induced neutron generation rate due to all neutrons from fast neutrons to thermal neutrons φ _F : Fast neutron flux S: Spontaneous neutron generation rate s in <> ^s in equation (1) is an index indicating that the system contains spontaneous neutrons.

The value of the neutron flux in equation (1) is greatly influenced by the spontaneous neutron generation rate S, but the value of the neutron flux in equation (2) is a completely relative value. Therefore, now the left side of equation (1) and (2)
If the neutron flux level in equation (2) is normalized so that it is equal to the left side of the equation, the following equation (3) can be obtained.

<νΣ _f φ> ^s + S = <νΣ _f φ>/k _eff (3) If this equation (3) is transformed by the definition of subcriticality, that is, negative reactivity ρ, the following equation (4) is obtained. .

ρ=(1/k _eff )−1 = (S/<νΣ _f φ>)+[(<νΣ _f φ> ^s /<νΣ _f φ>)−1] (4) Figure 1 shows a boiling water type atom FIG. 1 is a diagram showing a core part 1 of a reactor.

2 is a fuel assembly, and 3 is a cross-shaped control rod. 1
The control rods control four fuel assemblies surrounded by dashed lines 4.

FIG. 2 is a diagram showing the fuel assembly taken out from inside the integrated reactor core and placed in a water pool. The fuel assembly, generally designated by 2, has a large number of fuel rods 6 (a total of 49 fuel rods are shown in 7 rows and 7 columns in the figure) arranged regularly in a channel box 5. Light water 7 serving as a moderator is filled between the fuel rods. The outside of the channel box is also filled with pool water 8.

Now, for the system shown in Figure 2 and the system surrounded by the broken line 4 in Figure 1, the neutron flux distribution and k _ef are calculated using calculation codes based on neutron diffusion theory.
A strict analysis of _f shows that the neutron flux distribution when spontaneous neutrons and induced neutrons coexist based on equation (1) is quite similar to the neutron flux distribution when only induced neutrons exist based on equation (2). It can be seen that they match well. The reason for this is that the travel distance of spontaneous neutrons and the size of the fuel assembly (distance between opposite sides) are approximately the same. In addition, in the above analysis of the inside of the broken line 4 in FIG. 1, it is assumed that there is no inflow of neutrons from the broken line 4 inward or outflow to the outside.

The fact that there is not much difference between the neutron flux distribution based on equation (1) and the neutron flux distribution based on equation (2) means that <νΣ _f
This means that φ> ^s and <νΣ _f φ> are approximately equal, so the value of [ ] in equation (4) is approximately zero. Therefore, [ ] on the right side of equation (4) can be seen as a correction term. If the correction term [ ] in equation (4) cannot be ignored, the one determined by theoretical calculation can be used. In the following discussion, for simplicity, the correction term in equation (4) is ignored, and ρ=S/<νΣ _f φ> (4a) is obtained. <νΣ _f φ> may also be <νΣ _f φ>.

By distinguishing the values of equation (4a) by adding "o" to the value in the pool and "c" to the value at the time of insertion into the core, and finding the ratio of subcriticality ρ, we get ρc/ρo. = (Sc/So) (<νΣ _f φ>o /<νΣ _f φ>c) (5). The value of S does not change inside the core or outside the core, but within the core it is likely to change somewhat due to the influence of the surroundings of the fuel assembly.
Sc and So are shown separately. When S of the fuel concerned and S of the surrounding fuel assembly are approximately equal, Sc
≒So, and the following equation (5a) is obtained.

ρc/ρo≒<νΣ _f φ>o/<νΣ _f φ>c
(5a) Here, <νΣ _f φ>=<νΣ _f ><φ>, where <νΣ _f > and <φ> are the average νΣ _f (number of induced neutrons generated per unit neutron flux) of the fuel assembly, respectively. and neutron flux.

In the example of a boiling water reactor, combustion management of fuel assemblies such as fuel exchange is performed so that the four fuel assemblies surrounding the control rod surrounded by the broken line 4 in Figure 1 form a unit cell. Therefore, the dependence of the unit cell on its position within the core is small. In other words, since <νΣ _f > hardly changes within the reactor core, equation (5a) can be transformed into the following (5b)
It can be written as expression.

ρc/ρo≒<φ>o/<φ>c (5b) By the way, when actually measuring neutron flux,
The neutron flux distribution within the fuel assembly is measured when the fuel assembly is inserted into the reactor core and when it is placed outside the reactor core, and the ratio of the respective average values <φ>c and <φ>o is calculated. The search is relatively troublesome in terms of effort. Therefore, for example, assume that the neutron flux is measured only at an appropriate location (near the center) of the fuel assembly, and φc and φo are obtained, respectively. <
If the proportionality constants connecting φ>c and φc and <φ>o and φo are Gc and Go, respectively, <φ>c=
Gcφc, <φ>o=Goφo.

If the position at which the neutron flux is measured is chosen appropriately as described above, Gc≒Go can be obtained, but Gc and Go are
Since it is a value relatively close to 1.0, it can be determined accurately even by theoretical calculations. Therefore, equation (5b) is written as ρc≒(Go/Gc) (φo/φc) ρo = (Go/Gc) (φo/φc) [(1/(k _eff ) o) −1] (6) be able to. ( _keff )o is an effective multiplication factor when one fuel assembly is placed in pool water, and is approximately 0.4 to 0.5 in the case of a fuel assembly for a current boiling water reactor. The relative error in [ ] in equation (6) becomes very large if (k _eff )o changes slightly near 1.0, but there is no risk of the relative error becoming large even if it changes slightly near 0.4 to 0.5. In reality, (K _eff ) o = 0.4 to 0.5, so when measuring ρc, it is not necessary to find the value of (k _eff ) o particularly precisely, and the value can be easily found by calculation etc. I can do it.

Approximation from equation (4) to equation (4a), equation (5) to (5a),
The approximation to equation (5b) can of course be equated by making a relatively small correction with the help of theoretical calculations.

FIG. 3 is a diagram in which a plate-shaped neutron detector support 10 equipped with a neutron detector 9 is inserted into the light water 7 portion of the fuel assembly shown in FIG. Of course, it is not necessary to limit the setting position of the neutron detector within the fuel assembly. Alternatively, one fuel rod in the fuel assembly may be pulled out and a rod-shaped neutron detector support equipped with a neutron detector may be inserted therein.

The gist of the present invention is to determine the subcriticality of a unit subcritical system of unknown subcriticality, such as an irradiated fuel assembly, from the subcriticality of a composite subcritical system of known subcriticality. It can be determined accurately from the subcriticality of the composite subcritical system as follows.

Figures 4 and 5 illustrate this method. The unit subcritical system consists of only one spent fuel assembly A as shown in Fig. 4a, and Fig. 4b~
The composite subcritical system shown in i is a unit subcritical system consisting of spent fuel assembly A, general spent fuel assemblies B ₁ , B ₂ , B ₃ and standard fuel assemblies C ₁ , C ₂ , C ₃ ,
Consists of C ₄ . Figure 4i consists only of standard fuel assemblies C ₁ , C ₂ , C ₃ and C ₄ whose nuclear properties are known. The above-mentioned complex subcritical system is the fourth
Assuming that the subcriticality ρo(a) in diagram a is known, b
The subcriticality of a system like ~i ρo(b) ~ρo
(i) was sought.

The solid line in FIG. 5 is a plot of ρo(b) to ρo(i) with the number of standard fuel assemblies on the horizontal axis. On the other hand, in the case of system i consisting of only standard fuel assemblies, the nuclear properties are known, so the degree of subcriticality can be determined correctly from ρo(i). The degree of subcriticality can be determined fairly accurately by theoretical calculations, but it can also be determined experimentally using the pulsed neutron method,
Conventional methods such as exponential experiment method, neutron source multiplication method, and noise method can be applied. When new fuel assemblies of the same type are used as standard fuel assemblies, they are easy to handle because the standard fuel has an extremely low level of radiation such as gamma rays. For example, in a new fuel assembly for a boiling water reactor, the infinite multiplication factor k∞ is
Since the neutron transfer area M ² is about 40 cm ² , the subcriticality of system i is about 0.25.

It has recently been discovered that conventional techniques can accurately measure subcriticality down to about 0.25, but there is no prospect of accurate measurement down to about 0.75. Although FIG. 4 shows a subcritical system consisting of four fuel assemblies as a composite subcritical system, the conventional technology can be applied to a subcritical system consisting of four new fuel assemblies.

The solid line 11 in FIG. 5 indicates that if the subcriticality of system a is ρoa as the first approximation, then the subcriticality of system i is ρo
(i), but since the subcriticality of system i is exactly ρ ₁ (i), the point ρ ₁ (i)
By drawing a broken line 12 that passes through and is proportional to the solid line 11, the degree of subcriticality of system b is expressed as ρo
(b) can be modified to ρ ₁ (b).
The subcriticality ρo(a) of the system a to be found is ρ ₁
It can be corrected by the relationship (a)=ρo(a)×ρ ₁ (i)/ρo(i). That is ρo
This is because the difference between (i) and ρ ₁ (i) is due to the inaccuracy of the first-order approximation value ρo(a) of the subcriticality of system a.

In this way, the method of calculating the degree of subcriticality of a unit subcritical system from the degree of subcriticality of a composite subcritical system is to correct the degree of subcriticality obtained in a composite subcritical system in which the degree of subcriticality can be determined correctly. This method correctly determines the degree of subcriticality of a unit subcritical system.
Although the subcriticality of a single spent fuel assembly may exceed 1.0, the present invention makes it possible to determine the subcriticality of such a highly subcritical system.

In the present invention, a method for measuring the subcriticality of a shut down boiling water reactor or a spent fuel assembly is explained as an example, but the present invention can be applied to any subcritical system as long as it is capable of measuring neutrons. method can be applied.

[Brief explanation of the drawing]

Figure 1 is a cross-sectional view of the reactor core of a stopped boiling water reactor, Figure 2 is a cross-sectional view of one fuel assembly taken out from the core and placed in a water pool, and Figure 3 is Figure 2 is a cross-sectional view of a neutron detector inserted inside a fuel assembly, and Figures 4 and 5 show the subcriticality of a unit subcritical system (in the case of only one spent fuel assembly). FIG. 2 is an explanatory diagram showing a determination method. DESCRIPTION OF SYMBOLS 1... Core, 2, 2a... Fuel assembly, 3... Control rod, 5... Channel box, 6... Fuel rod, 7...
Coolant (light water), 8...Pool water, 9...Neutron detector, 10...Support.

Claims (1)

[Claims] 1 Assuming the subcriticality of a single subcritical system including a fuel assembly having a neutron source, measure the neutron flux for the unit subcritical system and a composite subcritical system with known subcriticality, and Calculate the subcriticality of the composite subcritical system by the product of the subcriticality assumed in the subcritical system and the ratio of the neutron flux for both systems, and calculate the ratio of the known subcriticality and the calculated subcriticality. A method for measuring the degree of subcriticality, characterized in that the degree of subcriticality of the assumed unit subcriticality system is corrected from .