JP5396140B2 - Addition amount calculation method using concentrated elvia credit - Google Patents

Description

  The present invention relates to an addition amount calculation method using concentrated erbia credits, and more particularly to an addition amount calculation method using concentrated erbia credits that are calculated using data relating to erbia credits already created based on natural erbia.

  In order to reduce the amount of spent fuel generated at nuclear power plants, use a fuel whose U235 enrichment (hereinafter also simply referred to as “enrichment”) exceeds 5 wt% (hereinafter also simply referred to as “%”). It is effective to increase the burnup. However, in order to handle such fuel with a concentration exceeding 5%, it is necessary to change the design and modification of existing processing facilities, transport containers, storage facilities, etc., and the cost required for these can be very large. There is sex.

Therefore, by adding erbia (erbium oxide: Er ₂ O ₃ ) as a flammable poison to a fuel powder with a concentration exceeding 5%, subcriticality (reactivity) equivalent to an existing fuel with a concentration of 5% is added. A concept (Elvia Credit) has been proposed (Patent Document 1, Non-Patent Documents 1 to 3) that guarantees that the existing infrastructure (processing facility, transport container, storage facility, etc.) need not be modified.

  In this Elvia Credit, the amount of Elvia added to make the reactivity of a fuel with an enrichment of over 5% equivalent to the reactivity of a fuel with an enrichment of 5% (hereinafter referred to as “addition by Elvia Credit”). It is necessary to determine the amount).

  For this reason, an ECOS (abbreviation of “Erbia Content for Subcriticality Judgment”) as shown in FIG. 1 is shown as a minimum required amount of elvia enveloped in consideration of all environmental conditions that the fuel receives. (Attached Figure 4.4 of Non-Patent Document 2). In FIG. 1, the horizontal axis indicates the enrichment (%) of U235, and the vertical axis indicates the amount of added elvia (wt%).

  Elvia is a very toxic substance from the standpoint of reducing reactivity such as suppression of temperature coefficient and output peaking. However, among the isotopes of erbium, which is the raw material of erbia, Er167 has a large contribution as a poison and decreases with combustion, but since Er166 absorbs neutrons and converts to Er167, Er167 does not disappear, There is a defect that elvia remains at the end of combustion and slightly impairs the neutron economy (Non-patent Document 3).

  Therefore, it has been studied to use an elvia obtained by concentrating Er167 from natural elvia or removing Er166 from natural elvia (which can suppress generation of Er167), that is, concentrated elvia.

JP-A-4-301593

"Innovative Practical Nuclear Technology Development Fund Subsidy Project Summary of FY2006 Results Report Technology Development for Next-Generation High Burnup Fuels with Elvia", Nuclear Fuel Industry Co., Ltd., Osaka University, Nagoya University, Kyoto University, Nuclear Engineering Co., Ltd. Co-authored, March 2007 "Innovative Practical Nuclear Technology Development Cost Subsidy Project 2007 Summary Report on Technology Development for Next-Generation High Burnup Fuels with Elvia", Nuclear Fuel Industries, Ltd., Osaka University, Nagoya University, Kyoto University, Nuclear Engineering Co., Ltd. Co-authored, March 2008 F. Franceschini, B.H. Petrovic, “Use of Isotopically Modified Erbium in Advanced LWR Fuel”, Workshop on Advanced Reactors With Innovative Fuels, Tsuruk, 8

  However, since the above-mentioned ECOS diagram is obtained for the required erbia concentration on the premise of erbia having a natural composition, it cannot be applied to concentrated erbia having a changed isotope composition. That is, erbium has six naturally stable isotopes (Er164, Er165, Er166, Er167, Er168, Er170), and as a result, the isotopic composition of enriched erbia is complicated. There are also four types of uranium in the reactor.

  For this reason, in order to obtain the amount of enriched erbia added by Elvia Credit (hereinafter referred to as “the amount added by Concentrated Elvia Credit”), the composition of the enriched erbia and the enrichment of uranium are calculated assuming various cases. There is a need.

The decrease in reactivity (erbia penalty) by adding erbia is
(1) Neutron absorption by Er167 generated from Er166, and neutron absorption by Er168 generated from Er167 (2) Caused by two factors: decrease in uranium (particularly U235) weight by adding and mixing erbia .

On the other hand, the increase in reactivity by adding Erbia enriched with Er167 is
(1) Since there is no Er167 produced by neutron absorption of Er166, there is no neutron absorption by the produced Er167 (however, neutron absorption by Er168 produced from Er167 remains as it is but is negligible)
(2) Since the isotope of erbia other than Er167 is reduced, the amount of mixed erbia can be reduced, and the weight of uranium (particularly U235) can be increased accordingly.
It is brought about by these two factors.

  As a result, especially when narrowing down appropriate conditions at the planning stage, it is assumed that there are many cases of highly enriched fuel and its usage, etc. Although it is necessary to calculate the amount of addition by Elvia Credit while considering the above, it is necessary to perform a very complicated calculation at this time, and there is a possibility that work efficiency may be reduced.

  For this reason, for the fuel with a concentration exceeding 5%, the amount of addition by Elvia Credit required to make the reactivity equivalent to the fuel with the enrichment of U235 of 5% using the concentrated Elvia can be easily and Development of technology that can be obtained with sufficient accuracy is desired.

In view of the above problems , the present inventors have found that the above problems can be solved by the following technologies as a result of intensive studies.

The first technique related to the present invention is:
A method of calculating an addition amount by an Elvia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
An addition amount calculation method using concentrated elvia credits, wherein the addition amount ε using elvia credits is obtained based on Equation 3.

但し、ε：濃縮エルビアの添加量
α_ｉ：エルビア同位体の反応度係数（ｉはＥｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８及びＥｒ１７０）
ν_ｉ：濃縮エルビアの同位体組成（ｉはＥｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８及びＥｒ１７０）
β_ｊ：ウラン同位体の反応度係数（ｊはＵ２３４、Ｕ２３５、Ｕ２３６及びＵ２３８）
μ_ｊ：ウランの同位体組成（ｊはＵ２３４、Ｕ２３５、Ｕ２３６及びＵ２３８）

Where ε is the amount of concentrated elvia added
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168 and Er170)
ν _i : isotopic composition of enriched erbia (i is Er164, Er165, Er166, Er167, Er168 and Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236 and U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236 and U238)

In the present technology , the reactivity (left side) of the enriched erbia-containing uranium fuel is made equivalent to the reactivity (right side) of the uranium-free uranium fuel having the 5 wt% enrichment (elvia credit). At this time, the above-mentioned ECOS diagram is obtained by determining ε using the concentrated elvia as a natural elvia.

Therefore, in the present technology , when the addition amount ε of the concentrated erbia is obtained from the above equation, the addition amount ε of the concentrated erbia can be easily obtained using the ECOS diagram.

  In the above equation, the first term on the left-hand side shows the contribution to the infinite multiplication factor due to the concentrated elvia, and the second term is also to the infinite multiplication factor of uranium (concentration over 5 wt%) to which the enriched elvia is added. The first term on the right-hand side shows the contribution to the infinite multiplication factor by uranium having a concentration of 5 wt%, and the second term also shows the contribution to the infinite multiplication factor by other uranium.

As described above, in the present technology , the two factors of the above-mentioned elvia penalty take into account not only the equivalence of the elvia reactivity but also the reactivity of uranium. ε can be obtained.

  Various nuclear properties such as the neutron absorption cross section when calculating the reactivity coefficient of each isotope of uranium necessary for the calculation based on the above formula are well-known matters described in many documents. is there.

In the present technology , “a nuclear fuel having a given U235 enrichment” refers to a nuclear fuel having a U235 enrichment exceeding 5%.

  Further, “enriched elvia credit” means that a nuclear fuel having an enrichment of U235 exceeding 5 wt% has a reactivity equivalent to a fuel having an enrichment of U235 of 5% using enriched elvia. Further, the “concentrated elvia” includes both an elvia in which Er167 is concentrated and an elvia in which Er167 is concentrated as a result of removing Er166.

The second technique related to the present invention is:
In obtaining the addition amount ε by the elvia credit,
Uranium isotopes are simplified to U235 and U238 only,
Even if both U235 and Elvia have different weight ratios in the total nuclear fuel, the uranium reactivity coefficient is the same,
The method for calculating the amount of addition by concentrated erbia credit according to claim 1, wherein the isotope composition of natural erbia is simplified to Er166, Er167, and other erbia.

  The inventor diligently studied the more practical operation of the formula 3, and even if the above three types of simplification are performed, there is almost no difference in the value of the addition amount ε by the obtained elvia credit, It has been found that it has sufficient accuracy for practical use.

As described above, according to the present technology , calculation is performed with appropriate simplification, so that the amount of addition by Elvia Credit can be obtained more easily.

In this technique , the reason why the uranium isotope compositions are only U235 and U238 is that the other uranium is small, has little influence on the infinite multiplication factor, and can be safely ignored.

  In addition, the composition of natural erbia isotopes of Er166, Er167 and other erbia. The other erbia isotopes other than Er166 and Er167 are treated together and have no effect on the infinite multiplication factor. This is because it is small.

  And the calculation of the infinite multiplication factor of nuclear fuel containing elbia is obtained by calculating its composition × reactivity coefficient for each elbia isotope, determining its composition × reactivity coefficient for each uranium isotope, and calculating the sum of both. However, at this time, even if Erbia is Er166, Er167 and other erbia, and uranium is only U235 and U238 (other uranium isotopes are combined in U238), the difference in the amount of erbia is slight, The influence on the nuclear properties of uranium can be ignored.

The third technique related to the present invention is:
A method of calculating an addition amount by Elvia Credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. This is a method of calculating the addition amount by credit.

但し、ε ：濃縮エルビアの濃度
α_ｉ：エルビア同位体の反応度係数（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
ν_ｉ：濃縮エルビア同位体組成（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
β_ｊ：ウラン同位体の反応度係数（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）
μ_ｊ：ウランの同位体組成（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

This technique prescribes | regulates a 1st technique from another angle, and this technique calculates | requires the addition amount by concentrated elvia credit using the existing data. Furthermore, at this time, formulas were created that took into account the decrease in reactivity due to the addition of erbia and the increase in reactivity due to the concentration of Er167 alone, and interpolation or extrapolation was performed from the calculation results of this formula. ing.

  As a result, even for concentrated erbia that concentrated Er167 and made Er167 more than natural erbia, the data related to erbia credits already created based on natural erbia, that is, the ECOS diagram shown in FIG. By using this, it is possible to easily and accurately determine the amount of addition by concentrated erbia credit for nuclear fuel having a enrichment of U235 exceeding 5 wt%.

In the present technology , “a nuclear fuel having a given U235 enrichment” refers to a nuclear fuel having a U235 enrichment exceeding 5%.

  Further, “enriched elvia credit” means that a nuclear fuel having an enrichment of U235 exceeding 5 wt% has a reactivity equivalent to a fuel having an enrichment of U235 of 5% using enriched elvia. Further, the “concentrated elvia” includes both an elvia in which Er167 is concentrated and an elvia in which Er167 is concentrated as a result of removing Er166.

  In addition, the target for obtaining the infinite multiplication factor when the enrichment degree of U235 in the basic infinite multiplication factor calculation step is 5 wt% is to use nuclear fuel having the given U235 enrichment, and also to use enriched elvia. The planned nuclear reactor. Therefore, the constants used for the calculation can be specifically determined if the nuclear reactor and its nuclear conditions are determined. This also applies to the calculations in the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step.

By using this technology , it is possible to obtain the relationship between the enrichment of fuel and the amount of addition by the corresponding concentrated elvia credit for each predetermined enriched elvia. By using this result, it is possible to create an ECOS diagram based on the concentrated elvia credit corresponding to the ECOS diagram targeting the natural elvia shown in FIG. 1, and thereafter, the ECOS diagram based on the concentrated elvia credit is used. Thus, the amount of concentrated erbia added corresponding to the degree of concentration can be determined very simply.

The fourth technique related to the present invention is:
Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Erbia isotope reactivity coefficient (i is Er166, Er167 and other erbia)
ν _i : concentrated erbia isotope composition (i is Er166, Er167 and other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0) This is a method for calculating the addition amount by the concentrated elvia credit of the third technique characterized by the above.

Since this technique simplifies the isotope composition of uranium and elbia, the calculation can be performed more easily than the third technique .

  It should be noted that the isotopic composition of natural erbia is Er166, Er167 and other erbia, and other trace isotopes other than Er166 and Er167 are handled together.

  In addition, the composition ratio of erbia other than Er167 in the concentrated erbia is preferably based on measured data, but it is the same as the composition ratio of natural erbia, or other trace isotopes are handled together as described above. However, since the error is slight, appropriate processing may be appropriately performed depending on the case or required calculation accuracy.

  The reason why the uranium isotope composition is only U235 and U238 is that the other uranium is small, has little influence on the infinite multiplication factor, and can be ignored. In addition, the composition of natural erbia isotopes of Er166, Er167 and other erbias. Even if erbia isotopes other than Er166 and Er167 are handled together, the effects on the infinite multiplication factor are affected. This is because it is small.

  Of the three simplifications, the first two points to the following. In other words, the calculation of the infinite multiplication factor of nuclear fuel containing elvia is to determine the composition x reactivity coefficient for each elbia isotope, to obtain the product of the composition x reactivity coefficient for each uranium isotope, and to obtain the sum of both In this case, Erbia is Erbia with Er 166, Er 167, and other isotopes that have a nuclear property that combines other isotopes, and Uranium is only U235 and U238 (other uranium isotopes are combined into U238). Since the difference in the amount of erbia added is slight, its influence on the nuclear properties of uranium can be ignored.

The fifth technique related to the present invention is:
Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
In the third technique or the fourth technique, the abundance ratio of Er167 is 90 wt% or more.

This technique is a case where the concentration of the elvia 167 in the third technique or the fourth technique is 90% or more.

The sixth technique related to the present invention is:
Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
In the third technique or the fourth technique, the abundance ratio of Er167 is 100 wt%.

This technique is a case where the concentration of the elvia 167 in the third technique or the fourth technique is 100%.

The seventh technique related to the present invention is:
Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
In the third technique or the fourth technique, the abundance ratio of Er167 is 90 wt%.

This technique is a case where the concentration of the elvia 167 in the third technique or the fourth technique is 90%.

The eighth technique related to the present invention is:
A method for calculating the amount of addition by elvia credit when using an enriched erbia in which the abundance ratio of Er166 is less than that of natural elvia for a nuclear fuel having a given U235 enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on the natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Erbia excluding Er166 is A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data for natural elvia,
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. This is a method of calculating the addition amount by credit.

但し、ε ：濃縮エルビアの濃度
α_ｉ：エルビア同位体の反応度係数（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
ν_ｉ：濃縮エルビア同位体組成（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
β_ｊ：ウラン同位体の反応度係数（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）
μ_ｊ：ウランの同位体組成（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

This technology is a case of calculating the amount of addition by erbia credits when using concentrated erbia in which the abundance ratio of Er166 is less than that of natural erbia, and has already been created based on natural erbia as in the third technology . Using the data related to Elvia Credit, that is, the ECOS diagram shown in FIG. 1, the addition amount of enriched Elvia Credit can be easily set for nuclear fuel with U235 enrichment exceeding 5 wt%, as in the above technique. In addition, it can be obtained with sufficient accuracy.

  It should be noted that “Er166 has a smaller abundance ratio of Er166 than natural elvia” is described as “enriched elvia”, regardless of whether Er166 is removed due to Er166 removal or Er167 concentration. This is because the abundance ratio is increased and concentrated.

The ninth technique related to the present invention is:
Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Elvia isotope reactivity coefficient (i is Er166, Er167, other erbia)
ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0) It is the addition amount calculation method by the concentrated elvia credit of the 8th technique characterized by the above.

Since this technique simplifies the isotope composition of uranium and elbia, the calculation can be performed more easily than the eighth technique .

  Note that “weight ratio of Erbia excluding Er166” refers to the total weight ratio of Er167 and other Elvia as a result of simplification.

The tenth technique related to the present invention is:
Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The abundance ratio of Er166 is 10 wt% or less, which is an addition amount calculation method using concentrated elvia credits according to the eighth technique or the ninth technique .

This technique is a case where the abundance ratio of the elvia 166 in the eighth technique or the ninth technique is 10% or less.

The eleventh technology related to the present invention is:
Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The abundance ratio of Er166 is approximately 0 wt%, which is an addition amount calculation method using concentrated elvia credits according to the eighth technique or the ninth technique .

This technique is a case where the abundance ratio of the elvia 166 in the eighth technique or the ninth technique is approximately 0 wt%.

The twelfth technique related to the present invention is:
Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The abundance ratio of Er166 is 10 wt%, which is an addition amount calculation method using concentrated elvia credits according to the eighth technique or the ninth technique .

This technique is a case where the abundance ratio of the elvia 166 in the eighth technique or the ninth technique is 10 wt%.

The thirteenth technique related to the present invention is:
For the nuclear fuel having the given U235 enrichment, the amount of erbia credit added when using the concentrated erbia between the two cases is calculated using the already determined erbia credit amount of the concentrated erbia between the two cases. A method of calculating,
The amount of addition by Erbia credit when using Erbia with Er167 concentrated to Awt% is Pawt%, and the amount of addition with Elvia Credit when using Erbia with Er167 concentrated to Cwt% (A <C) is Pcwt%. And when
The added amount Pbwt% of erbia in which Er167 is concentrated to Bwt% (A <B <C),
Pb = Pc + (Pa−Pc) × (CB) / (CA)
It is an addition amount calculation method using concentrated elvia credits, characterized by having an interpolation step to be obtained by interpolation.

This technology is simpler because it is possible to interpolate the amount of addition by Elvia credit in the case of the concentration of Er167 between the two based on the calculation result of the concentration of Er167 that has already been created. In addition, the amount of addition by concentrated elvia credit can be obtained.

In this technique , the difference between A and C is preferably 10% or smaller for interpolation, but it may be larger depending on the purpose for which a rough study is performed. Also good.

The fourteenth technology related to the present invention is:
The amount of addition by Erbia credit when using Erbia enriched with Er167 to ₁₀₀ wt% is P ₁₀₀ wt%, and the amount of addition with Erbia credit when using Erbia with Er 167 enriched to ₉₀ wt% is P ₉₀ wt%. When
The addition amount Pwt% of elvia in which the Er167 is concentrated to (90 + x) wt%,
_{P = {P 100 × x +} P 90 × (1-x)} / 10
An addition amount calculation method using concentrated elvia credits according to claim 13, further comprising an interpolation step to obtain by interpolation.

This technique is a case where A is 90 wt% and C is 100 wt% in the thirteenth technique .

The fifteenth technology related to the present invention is:
For a nuclear fuel with a given U235 enrichment, the enrichment between the two cases using the erbia credit amount of enriched erbia in which the abundance ratio of Er166 in the two cases already required is lower than that of natural elbia. A method of calculating the amount of addition by Elvia Credit when using Elvia,
The amount of addition by Elvia credit when using Erbia credit with Er166 as Awt% is Qawt%, and the amount of addition with Elvia credit when using Erbia credit with Er166 as Cwt% (A <C) is Qcwt%. And when
The addition amount Qbwt% of the concentrated erbia in which the Er166 is Bwt% (A <B <C),
Qb = Qc + (Qa−Qc) × (C−B) / (C−A)
It is an addition amount calculation method using concentrated elvia credits, characterized by having an interpolation step to be obtained by interpolation.

This technology is also simpler because it is possible to interpolate the amount of addition by Elvia credit in the case of the existing ratio of Er166 based on the calculation result of the existing ratio of two Er166 created. In addition, the amount of addition by concentrated elvia credit can be obtained.

The sixteenth technology related to the present invention is:
The amount by El via credit if Er166 is used concentrated erbia which is to 0wt% _Q 0 wt%, and _Q 10 wt% of the amount by El via credit in the case of using concentrated erbia which Er166 is a 10 wt% When
The addition amount Qwt% of the concentrated erbia in which the Er166 is ywt%,
Q = {Q ₀ × (1−y) + Q ₁₀ × y} / 10
The fifteenth technology addition amount calculation method using the concentrated elvia credit is characterized by having an interpolation step to be obtained by interpolation.

This technique is a case where A in the fifteenth technique is 0 wt% and C is 10 wt%.

The seventeenth technology related to the present invention is:
For the nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia, It is a method of calculating based on the data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on the concentration of
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. This is a method of calculating the addition amount by credit.

但し、ε ：濃縮エルビアの濃度
α_ｉ：エルビア同位体の反応度係数（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
ν_ｉ：濃縮エルビア同位体組成（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
β_ｊ：ウラン同位体の反応度係数（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）
μ_ｊ：ウランの同位体組成（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

With this technology , in the case of core conditions different from the ECOS diagram described above, U235 enrichment, for example, even if the specific enrichment is 6.0%, it has already been created for natural elvia. If there is data, the same effect as the third technique can be obtained.

The eighteenth technique related to the present invention is:
For nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credits when using enriched erbia in which the abundance ratio of Er166 is less than that of natural erbia, A calculation method based on data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on a specific enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when U235 is the specific enrichment;
With reference to the data on the erbia credits already created based on the natural erbia, the weight percentage of erbia excluding Er166 is calculated as follows. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data on natural elvia at a concentration of
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. This is a method of calculating the addition amount by credit.

但し、ε ：濃縮エルビアの濃度
α_ｉ：エルビア同位体の反応度係数（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
ν_ｉ：濃縮エルビア同位体組成（ｉは、Ｅｒ１６４、Ｅｒ１６５、Ｅｒ１６６、Ｅｒ１６７、Ｅｒ１６８、Ｅｒ１７０）
β_ｊ：ウラン同位体の反応度係数（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）
μ_ｊ：ウランの同位体組成（ｊは、Ｕ２３４、Ｕ２３５、Ｕ２３６、Ｕ２３８）

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

In this technique, enrichment of the different U235 was created ECOS view of the, even if the core conditions, and if there is data already created by the natural erbia subject, the eighth technical The same effect will be obtained.

The nineteenth technology related to the present invention is:
Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Elvia isotope reactivity coefficient (i is Er166, Er167, other erbia)
ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0)
It is the addition amount calculation method by the concentrated elvia credit of the seventeenth technology or the eighteenth technology characterized by

This technique specifically shows a simple calculation method of the infinite multiplication factor of nuclear fuel in the seventeenth technique and the eighteenth technique, and the fourth technique and the third technique with respect to the third technique and the seventh technique . It corresponds to 8 technologies .

  The present invention has been made based on the above technique, and the invention according to claim 1
  A method of calculating an addition amount by an Elvia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
  An addition amount calculation method using concentrated elvia credits, wherein the addition amount ε using elvia credits is obtained based on Equation 3.

    Where ε is the amount of concentrated elvia added
          α _i : Reactivity coefficient of erbia isotope (i is Er164, Er165, Er166, Er167, Er168 and Er170)
          ν _i : Isotopic composition of concentrated erbia (i is Er164, Er165, Er166, Er167, Er168 and Er170)
          β _j : Reactivity coefficient of uranium isotope (j is U234, U235, U236 and U238)
          μ _j : Isotopic composition of uranium (j is U234, U235, U236 and U238)

  The invention according to claim 2
  In obtaining the addition amount ε by the elvia credit,
  Uranium isotopes are simplified to U235 and U238 only,
  Even if both U235 and Elvia have different weight ratios in the total nuclear fuel, the uranium reactivity coefficient is the same,
  The method for calculating the amount of addition by concentrated erbia credit according to claim 1, wherein the isotope composition of natural erbia is simplified to Er166, Er167, and other erbia.

  The invention according to claim 3
  A method of calculating an addition amount by Elvia Credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
  A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
  With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
  A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
  From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. Step of calculating the amount of concentrated elvia added
The amount of addition by Elvia Credit is calculated by the calculation step including each step of
  The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
  The calculation of the infinite multiplication factor of the nuclear fuel to which the enriched erbia is added in the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step is calculated using Equation 2.
It is the addition amount calculation method by the concentrated elvia credit characterized by this.

    Where ε is the concentration of concentrated elvia
          α _i : Reactivity coefficient of erbia isotope (i is Er164, Er165, Er166, Er167, Er168, Er170)
          ν _i : Concentrated erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
          β _j : Reactivity coefficient of uranium isotope (j is U234, U235, U236, U238)
          μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

  The invention according to claim 4
  Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
  The only isotopes of uranium are U235 and U238.
  Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
  The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
  As a result, α in Equation 1 and Equation 2 _i , Ν _i , Β _j , Μ _j Respectively
          α _i : Reactivity coefficient of erbia isotope (i is Er166, Er167 and other erbia)
          ν _i : Concentrated erbia isotope composition (i is Er166, Er167 and other erbia)
          β _j : Reactivity coefficient of uranium isotopes (j is only U238 in Equation 1, U235 and U238 in Equation 2)
          μ _j : Isotopic composition of uranium (j is only U238 in Formula 1, Σμ _i = 0.95. In Equation 2, U235 and U238, and Σμ _i = 1.0)
It is the addition amount calculation method by the concentrated elvia credit of Claim 3 characterized by the above-mentioned.

  The invention according to claim 5
  Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
  The method of calculating the amount of addition using concentrated erbia credits according to claim 3 or 4, wherein the abundance ratio of Er167 is 90 wt% or more.

  The invention according to claim 6
  Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
  The method of calculating an addition amount using concentrated erbia credits according to claim 3 or 4, wherein the abundance ratio of Er167 is 100 wt%.

  The invention according to claim 7
  Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
  The method of calculating an addition amount by using concentrated erbia credit according to claim 3 or 4, wherein the abundance ratio of Er167 is 90 wt%.

  Further, the invention according to claim 8 is
  A method for calculating the amount of addition by elvia credit when using an enriched erbia in which the abundance ratio of Er166 is less than that of natural elvia for a nuclear fuel having a given U235 enrichment,
  A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
  With reference to the data on the Elvia Credit, which is created based on the natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Erbia excluding Er166 is A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data for natural elvia,
  A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
  From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. Step of calculating the amount of concentrated elvia added
The amount of addition by Elvia Credit is calculated by the calculation step including each step of
  The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
  The calculation of the infinite multiplication factor of the nuclear fuel to which the enriched erbia is added in the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step is calculated using Equation 2.
It is the addition amount calculation method by the concentrated elvia credit characterized by this.

    Where ε is the concentration of concentrated elvia
          α _i : Reactivity coefficient of erbia isotope (i is Er164, Er165, Er166, Er167, Er168, Er170)
          ν _i : Concentrated erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
          β _j : Reactivity coefficient of uranium isotope (j is U234, U235, U236, U238)
          μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

  The invention according to claim 9 is
  Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
  The only isotopes of uranium are U235 and U238.
  Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
  The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
  As a result, α in Equation 1 and Equation 2 _i , Ν _i , Β _j , Μ _j Respectively
          α _i : Reactivity coefficient of erbia isotopes (i is Er166, Er167, other erbia)
          ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
          β _j : Reactivity coefficient of uranium isotopes (j is only U238 in Equation 1, U235 and U238 in Equation 2)
          μ _j : Isotopic composition of uranium (j is only U238 in Formula 1, Σμ _i = 0.95. In Equation 2, U235 and U238, and Σμ _i = 1.0)). The method of calculating the amount of addition using concentrated erbia credits according to claim 8.

  The invention according to claim 10 is
  Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
  The abundance ratio of Er166 is 10 wt% or less, and the addition amount calculation method using concentrated erbia credits according to claim 8 or claim 9.

  The invention according to claim 11 is
  Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
  10. The method of calculating the amount of addition using concentrated erbia credits according to claim 8 or 9, wherein the abundance ratio of Er166 is approximately 0 wt%.

  Further, the invention according to claim 12 is
  Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
  10. The method of calculating the amount of addition using concentrated erbia credits according to claim 8 or 9, wherein the abundance ratio of Er166 is 10 wt%.

  The invention according to claim 13 is
  For the nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia, It is a method of calculating based on the data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on the concentration of
  A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
  With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
  A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
  From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. Step of calculating the amount of concentrated elvia added
The amount of addition by Elvia Credit is calculated by the calculation step including each step of
  The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
  The calculation of the infinite multiplication factor of the nuclear fuel to which the enriched erbia is added in the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step is calculated using Equation 2.
It is the addition amount calculation method by the concentrated elvia credit characterized by this.

    Where ε is the concentration of concentrated elvia
          α _i : Reactivity coefficient of erbia isotope (i is Er164, Er165, Er166, Er167, Er168, Er170)
          ν _i : Concentrated erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
          β _j : Reactivity coefficient of uranium isotope (j is U234, U235, U236, U238)
          μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

  The invention as set forth in claim 14
  For nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credits when using enriched erbia in which the abundance ratio of Er166 is less than that of natural erbia, A calculation method based on data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on a specific enrichment,
  A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when U235 is the specific enrichment;
  With reference to the data on the erbia credits already created based on the natural erbia, the weight percentage of erbia excluding Er166 is calculated as follows. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data on natural elvia at a concentration of
  A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
  From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. Step of calculating the amount of concentrated elvia added
The amount of addition by Elvia Credit is calculated by the calculation step including each step of
  The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
  The calculation of the infinite multiplication factor of the nuclear fuel to which the enriched erbia is added in the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step is calculated using Equation 2.
It is the addition amount calculation method by the concentrated elvia credit characterized by this.

    Where ε is the concentration of concentrated elvia
          α _i : Reactivity coefficient of erbia isotope (i is Er164, Er165, Er166, Er167, Er168, Er170)
          ν _i : Concentrated erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
          β _j : Reactivity coefficient of uranium isotope (j is U234, U235, U236, U238)
          μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238)

  The invention according to claim 15 is
  Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
  The only isotopes of uranium are U235 and U238.
  Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
  The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
  As a result, α in Equation 1 and Equation 2 _i , Ν _i , Β _j , Μ _j Respectively
          α _i : Reactivity coefficient of erbia isotopes (i is Er166, Er167, other erbia)
          ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
          β _j : Reactivity coefficient of uranium isotopes (j is only U238 in Equation 1, U235 and U238 in Equation 2)
          μ _j : Isotopic composition of uranium (j is only U238 in Formula 1, Σμ _i = 0.95. In Equation 2, U235 and U238, and Σμ _i = 1.0)
15. The method of calculating the amount of addition using concentrated erbia credits according to claim 13 or claim 14, characterized in that:

  According to the present invention, with respect to a fuel having a U235 enrichment exceeding 5%, it is possible to easily add an amount necessary to achieve a reactivity equivalent to a fuel having a U235 enrichment of 5% using a concentrated elvia. In addition, it can be obtained with sufficient accuracy.

It is a figure which shows the addition amount of the natural elbia required in order to make it equivalent to 5% fuel with respect to the enrichment of a certain uranium.

  Hereinafter, the present invention will be described based on embodiments. Note that the present invention is not limited to the following embodiments. Various modifications can be made to the following embodiments within the same and equivalent scope as the present invention.

Hereinafter, a basic calculation formula for precisely determining the amount of added elvia, a simplified calculation of the present invention, and a verification result of the simplified calculation method will be described in order.
1. Basic Calculation Formula for Obtaining Elvia Addition First, a calculation formula for obtaining the elvia addition amount will be described.
As described above, various cases are envisaged for the composition of enriched erbia and the enrichment of uranium. Therefore, a formula that accurately incorporates the decrease in reactivity due to the first addition of erbia (erbia penalty) and the increase in reactivity due to the concentration of Er167 alone (elimination of the factor of erbia penalty). Create (calculation).

(1) Decrease in reactivity due to addition of elvia As described above, a decrease in reactivity due to addition of elvia is due to the following two factors.
A. Neutron absorption reaction of Er167 generated from Er166 and Er168 generated from Er167.
B. Decrease in reactivity due to decrease in weight of uranium (U235) by adding elvia.

(2) Increase in reactivity by adding Er167 in a concentrated manner Similarly, the increase in reactivity by adding Erbia in which Er167 is concentrated is due to the following factors.
A. Since there is no Er167 generated by neutron absorption of Er166, neutron absorption at the end of combustion is reduced.
B. Since the isotopes of Erbia other than Er167 are reduced, uranium (especially U235) in the nuclear fuel is increased accordingly.

  Therefore, the addition amount ε by the Elvia credit in the concentrated elvia is obtained based on Formula 3 created by accurately incorporating the above matters.

In the above formula 3, the meaning of each symbol is as follows.
ε: The theoretically required concentration ratio of concentrated elvia.
α _i : Reactivity coefficient of elbia isotope, where i = 164, 165, 166, 167, 168, 170.
ν _i : enriched erbia isotopic composition, where i = 164, 165, 166, 167, 168, 170.
β _j : Uranium isotope reactivity coefficient, where j = 234, 235, 236, 238.
μ _j : Isotopic composition of uranium, where j = 234, 235, 236, 238.

  Also, the first term on the left side of Equation 3 shows the contribution to the infinite multiplication factor due to enriched erbia, and the second term is also due to uranium enriched with more than 5% enriched erbia and U235 enriched. The contribution to the infinite multiplication factor is shown, the first term on the right side shows the contribution to the infinite multiplication factor by U235 concentrated to 5%, and the second term also shows the contribution to the infinite multiplication factor by other uranium. .

  Various nuclear properties such as the neutron absorption cross section when calculating the reactivity coefficient of each isotope of uranium necessary for performing the calculation are well-known matters described in many documents.

2. Simplification of calculation However, although Equation 3 is precise, both uranium and elvia consider many isotopes, and the calculation becomes complicated. Therefore, in the present invention, calculation is simplified in consideration of practicality. Next, calculation simplification will be described.

(1) Assumptions for simplification Specifically, the following assumptions are made to simplify the calculation.
Assumptions a. The only isotopes of uranium are U235 and U238.
B. Erbia isotopes are Er166, Er167 and other erbia.
C. The reactivity coefficient of uranium is the same on the left side and the right side of Equation 3 (Since both U235 and Elvia have different weight ratios in the whole nuclear fuel, the neutron spectrum is strictly different, and the reactivity coefficient of uranium is different. Is also different.
D. Regarding the removal of Er166 and the concentration of Er167, only the two cases shown in Tables 1 and 2 below are used. The numbers in Tables 1 and 2 are all wt%.

By this simplification, α _i and ν _i in Equation 3 are values for three types of Er166, Er167, and other elvias, and similarly, β _j and μ _j are values for U235 and U238.

  In addition to the above, various conditions such as the water density condition and the geometric shape are the same as the most severe conditions when the ECOS diagram is created for natural elvia.

Although it is a simplification of Elvia, the composition is as shown in Table 1 below.

(2) Simplified calculation method By the simplified calculation method based on the above assumption, the amount of concentrated erbia added when the concentration of U235 is 6, 7, 8, 9, 10% (concentrated erbia credit) An example of calculating the addition amount by the following two cases is shown below.

A. Case 1
Case 1 is a case where the concentrated elvia shown in Table 1, that is, the case where Er167 is 100 wt% and 90 wt% and the case where Er167 is 90-100 wt% are obtained by interpolation.

A. Calculation procedure when the concentration of Er167 is 100% a. When the U235 enrichment was 6%, the corresponding infinite multiplication factor was calculated for the aggregate rack system. In this case, the ratio of natural elvia is 0.251%.

  b. An infinite multiplication factor was calculated when Er167 having a concentration of 100% was added to U235 having a concentration of 6% so as to have the same concentration as Er167 when natural elvia was used as a flammable poison.

  c. An infinite multiplication factor was calculated when Er167 with a concentration of 100% was added to U235 with a concentration of 6% at a concentration that seems to be slightly higher than the required amount, for example 0.2%, in uranium.

  d. From the results of b and c, the concentration of Er167 having a concentration of 100% equivalent to the result of a was determined by interpolation. As a result, it was 0.062%.

  e. For confirmation, an infinite multiplication factor was calculated when Er167 with a concentration of 100% was added to U235 with a concentration of 6% so as to have a concentration of 0.062%. Confirmed that it is the same.

  The above calculations from a to e are performed for U235 enrichments of 7%, 8%, 9%, and 10%, and it is confirmed that these enrichments are the same as the calculation results of a. did.

B. Calculation Procedure when Er167 Concentration is 90% The following calculation was performed in the same manner as A described above.
a. Is the same as A's a, so the percentage of natural elvia is 0.251%.

  b. An infinite multiplication factor is calculated when Er167 having a concentration of 90% is added to U235 having a concentration of 6% so as to have the same concentration as Er167 when natural elvia is used as a flammable poison. At this time, the composition of the remaining 10% of the elvia excluding Er167 was the same composition as shown in Table 1 with the ratio of Er166 of natural erbia being 35.35% and the ratio of other elvia being 41.70%.

  c. An infinite multiplication factor was calculated when Er167 with a concentration of 90% was added to U235 with a concentration of 6% in uranium at a concentration that seems to be slightly higher than the required amount.

  d. From the results of b and c, the concentration of Er167 having a concentration of 90% equivalent to the result of a was determined by interpolation. As a result, it was 0.069%.

  e. For confirmation, the infinite multiplication factor is calculated when Er167 with a concentration of 90% is added to U235 with a concentration of 6% so that the concentration becomes 0.069%, and the calculation result of the above a Confirmed that it is the same.

  The above calculations from b to e are performed for U235 enrichments of 7%, 8%, 9%, and 10%, and it is confirmed that these enrichments are the same as the calculation results of a. did.

C. Calculation Method when Er167 Concentration is 90 to 100% Next, a calculation method of the amount of concentrated erbia added in which the concentration of Er167 is 90 to 100% will be described.
a. Direct calculation method The concentration of Er167 was set to (90 + a)% (0 ≦ a ≦ 10), and it was confirmed that it could be directly calculated by the calculation procedure described in Case 1 B above.
b. Interpolation method Moreover, it confirmed that the addition amount could be calculated | required by the interpolation method using the calculation result by the calculation procedure of A and B of the said case 1. FIG. Specifically, the amount of addition by Ervia credit in the case of Erbia in which Er167 obtained in the calculation procedure of A is concentrated to ₁₀₀ wt% is P ₁₀₀ wt%, and the amount of Erbia in which Er 167 is concentrated to 90 wt% in the calculation procedure of B When the amount of addition by Elvia credit is P ₉₀ wt%,
_{P = {P 100 × a +} P 90 × (1-a)} / 10
P was obtained by interpolation using the following formula, and this was compared with the addition amount obtained by the direct calculation method of a above, but agreed with good accuracy.

B. Case 2
Case 2 is a case where the concentration Elvia II and Er166 shown in Table 1 are 0% and 10% and the cases where Er is 0 to 10% are obtained by interpolation.

A. Calculation procedure when the concentration of Er166 is 0% a. When the U235 enrichment was 5%, the corresponding infinite multiplication factor was calculated for the aggregate rack system. As in case 1, the ratio of natural elvia is 0.251%.

  b. The composition ratio is 6% for U235, Er166 is 0%, and the composition ratio of other erbia isotopes to fuel is the same as that of natural erbia. That is, the natural erbia Er167 shown in Table 1 is 22.95%. The infinite multiplication factor was calculated by determining the erbia concentration with the other erbia being 41.70%. In this case, since Er166 decreases, the proportion of uranium increases accordingly, and the infinite multiplication factor, that is, the reactivity, increases compared to a.

  c. Concentration is 6% for U235, Er166 is 0%, and other concentrations are considered to be slightly higher than erbia with the same composition as (2) above, for example 0.4% when added to uranium An infinite multiplication factor was calculated.

  d. From the results of b and c, the concentration of Er166 equivalent to the result of a is 0%, and in the other cases, the concentration in the fuel of erbia having the same composition as b is determined by interpolation. As a result, it was 0.175%.

  e. For confirmation, the infinite multiplication factor is calculated when the Er166 concentration is 0% with respect to U235, which has a concentration of 6%, and the others are added so that erbia with the same composition as b is 0.175%. And it confirmed that it was the same as the calculation result of said a.

  The above calculations from a to e are performed for U235 enrichments of 7%, 8%, 9%, and 10%, and it is confirmed that these enrichments are the same as the calculation results of a. did.

B. Calculation Procedure when Er166 Concentration is 10% The following calculation was performed in the same manner as A described above.
a. Is the same as A's a, so the percentage of natural elvia is 0.251%.

  b. The composition ratio of Er166 is 10% and the composition ratio of other erbia isotopes to fuel is the same as that of natural erbia compared to U235 with 6% enrichment, that is, Er167 is 22.95% from Table 1 and other erbia is The infinite multiplication factor was calculated by determining the elvia concentration as 41.70%. In this case as well, Er 166 decreases, so the proportion of uranium increases accordingly, and the infinite multiplication factor, that is, the reactivity increases compared to a.

  c. Concentration is 6% for U235, Er166 is 10%, others are the concentration which seems to be a little more erbia with the same composition as the above (2), infinite multiplication factor when added in uranium did.

  d. From the results of b and c, the concentration of Er166 equivalent to the result of a is 10%, and in other cases, the concentration in the fuel of erbia having the same composition as b is obtained by interpolation. As a result, it was 0.192%.

  e. For confirmation, the infinite multiplication factor is calculated when the Er166 concentration is 10% with respect to U235, which has a concentration of 6%, and in other cases, Erbia having the same composition as b is added to 0.192%. And it confirmed that it was the same as the calculation result of said a.

  The above calculations from b to e are performed for U235 enrichments of 7%, 8%, 9%, and 10%, and it is confirmed that these enrichments are the same as the calculation results of a. did.

C. Calculation Method for Concentrated Erbia when Er 166 is 0 to 10% because Er 167 is Concentrated Next, a calculation method for the addition amount of concentrated erbia with Er 166 being 0 to 10% will be described.
a. Direct Calculation Method It was confirmed that the Er166 concentration (abundance ratio) was b% (0 ≦ b ≦ 10), and the calculation procedure described in Case 2 B above could be directly calculated.
b. Interpolation method Moreover, it confirmed that the addition amount could be calculated | required by the interpolation method using the calculation result by the calculation procedure of A and B of the said case 2. FIG. Specifically, the amount of addition by Elvia credit when Er166 obtained by the calculation procedure of A is ₀ wt% is ₁ wt%, and the amount of Er166 obtained by the calculation procedure of B is 10 wt%. When the addition amount by Elvia Credit is Q ₁₀ wt%,
Q = {Q ₀ × (1−b) + Q ₁₀ × b} / 10
Q was obtained by interpolation using the following formula, and this was compared with the addition amount obtained by the direct calculation method of a above, but agreed with good accuracy.

(3) Reactivity coefficient The reactivity coefficient can be obtained based on various well-known nuclear properties, but it can be obtained by directly calculating several correlations between the erbia composition and the required concentration and fitting them. The degree coefficients α and β can also be obtained.

(4) ECOS diagram corresponding to concentrated elvia Based on the calculation result of case 1 described above, an ECOS diagram for concentrated elvia with Er167 of 90 to 100% can be provided, and based on the calculation result of case 2, As a result of concentrating Er167, an ECOS diagram for concentrated erbia with Er166 between 0 and 10% can be provided.

(5) Summary From the above, the concentration of Er166 required to make the fuel equivalent to 5% fuel is 0-10% or the concentration of Er167 is 90-100% for a nuclear fuel with an enrichment exceeding 5 wt%. When the amount of addition of a certain concentrated erbia is obtained using the above-mentioned equation 3, the following assumptions are made: The only isotopes of uranium are U235 and U238.
B. Erbia isotopes are Er166, Er167 and other erbia,
C. The reactivity coefficient of uranium is the same on the left and right sides of Equation 3.
It has been found that even if the calculation is performed using a simplified method under the assumption, a sufficient accuracy can be obtained in practice.

  Further, it was confirmed that there was no large error even if the addition amount at the intermediate concentration was calculated by interpolation from the two addition amounts already calculated.

  The present invention can be used very effectively for various studies when the next generation high burn-up fuel containing erbia is used.

Claims (15)

A method of calculating an addition amount by an Elvia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
An addition amount calculation method using concentrated elvia credits, wherein the addition amount ε using elvia credits is obtained based on Equation 3.

Where ε is the amount of concentrated elvia added
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168 and Er170)
ν _i : isotopic composition of enriched erbia (i is Er164, Er165, Er166, Er167, Er168 and Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236 and U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236 and U238) In obtaining the addition amount ε by the elvia credit,
Uranium isotopes are simplified to U235 and U238 only,
Even if both U235 and Elvia have different weight ratios in the total nuclear fuel, the uranium reactivity coefficient is the same,
The method for calculating the amount of addition using concentrated erbia credits according to claim 1, wherein the isotope composition of natural erbia is simplified to Er166, Er167 and other erbia. A method of calculating an addition amount by Elvia Credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia for a nuclear fuel having a given U235 enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. Addition calculation method by credit.

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238) Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Erbia isotope reactivity coefficient (i is Er166, Er167 and other erbia)
ν _i : concentrated erbia isotope composition (i is Er166, Er167 and other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0) The addition amount calculation method by the concentrated elvia credit according to claim 3. Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
The method for calculating the amount of addition using concentrated erbia credits according to claim 3 or 4, wherein the abundance ratio of Er167 is 90 wt% or more. Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
The method for calculating the amount of addition using concentrated erbia credits according to claim 3 or 4, wherein the abundance ratio of Er167 is 100 wt%. Concentrated erbia whose Er167 abundance ratio is higher than natural erbia,
The method for calculating the amount of addition using concentrated erbia credits according to claim 3 or 4, wherein the abundance ratio of Er167 is 90 wt%. A method for calculating the amount of addition by elvia credit when using an enriched erbia in which the abundance ratio of Er166 is less than that of natural elvia for a nuclear fuel having a given U235 enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on the natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Erbia excluding Er166 is A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data for natural elvia,
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. Addition calculation method by credit.

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238) Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Elvia isotope reactivity coefficient (i is Er166, Er167, other erbia)
ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0) The addition amount calculation method by the concentrated elvia credit according to claim 8. Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The method for calculating the amount of addition using concentrated erbia credits according to claim 8 or 9, wherein the abundance ratio of Er166 is 10 wt% or less. Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The method for calculating the amount of addition using concentrated erbia credits according to claim 8 or 9, wherein the abundance ratio of Er166 is approximately 0 wt%. Concentrated erbia whose Er166 abundance ratio is less than natural erbia,
The addition amount calculation method according to claim 8 or 9, wherein the abundance ratio of Er166 is 10 wt%. For the nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credit when using an enriched erbia whose Er167 abundance ratio is greater than or equal to natural erbia, It is a method of calculating based on the data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on the concentration of
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when the concentration of U235 is 5 wt%;
With reference to the data on the Elvia Credit, which is created based on natural Elvia, in the nuclear fuel of the given U235 enrichment, the weight percentage of Er167 is the natural Elvia at the U235 concentration. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from the target data;
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. Addition calculation method by credit.

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238) For nuclear fuel having a given U235 enrichment under given conditions, the amount of addition by Erbia credits when using enriched erbia in which the abundance ratio of Er166 is less than that of natural erbia, A calculation method based on data on the amount of addition by elvia credit already created for natural elvia that has already been calculated based on a specific enrichment,
A basic infinite multiplication factor calculating step for obtaining an infinite multiplication factor when U235 is the specific enrichment;
With reference to the data on the erbia credits already created based on the natural erbia, the weight percentage of erbia excluding Er166 is calculated as follows. A first infinite multiplication factor calculating step for obtaining an infinite multiplication factor when added so as to be the same as the weight ratio determined from data on natural elvia at a concentration of
A second infinite multiplication factor calculating step for obtaining an infinite multiplication factor when an appropriate weight percentage of the enriched elvia is added to a nuclear fuel having a given U235 enrichment;
From the calculation results of the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the weight ratio of the concentrated elvia that becomes the infinite multiplication factor obtained in the basic infinite multiplication factor calculation step by interpolation or extrapolation is calculated. The amount of addition by Elvia Credit is calculated by the calculation step including each step of the calculation step of the concentrated elvia addition amount to be calculated,
The calculation of the infinite multiplication factor in the basic infinite multiplication factor calculation step is calculated using Equation 1.
In the first infinite multiplication factor calculation step and the second infinite multiplication factor calculation step, the calculation of the infinite multiplication factor of the nuclear fuel to which the enriched elvia is added is calculated using Equation 2. Addition calculation method by credit.

Where ε is the concentration of concentrated elvia
α _i : Erbia isotope reactivity coefficient (i is Er164, Er165, Er166, Er167, Er168, Er170)
ν _i : Concentrated Erbia isotope composition (i is Er164, Er165, Er166, Er167, Er168, Er170)
β _j : Uranium isotope reactivity coefficient (j is U234, U235, U236, U238)
μ _j : Isotopic composition of uranium (j is U234, U235, U236, U238) Prior to the calculations in the basic infinite multiplication factor calculation step, the first infinite multiplication factor calculation step, and the second infinite multiplication factor calculation step,
The only isotopes of uranium are U235 and U238.
Even if the weight ratio of both U235 and Elvia differs in the total nuclear fuel, the reactivity coefficient of uranium is the same.
The isotopic composition of natural erbia is Er166, Er167 and other erbia.
Three types of simplifications
As a result, α _i , ν _i , β _j , and μ _j in Equation 1 and Equation 2 are respectively
α _i : Elvia isotope reactivity coefficient (i is Er166, Er167, other erbia)
ν _i : Concentrated erbia isotope composition (i is Er166, Er167, other erbia)
β _j : Uranium isotope reactivity coefficient (j is only U238 in Equation 1, U235 and U238 in Equation 2)
μ _j : Isotopic composition of uranium (j is only U238 in Equation 1 and Σμ _i = 0.95. In Equation 2, U235 and U238 and Σμ _i = 1.0)
The addition amount calculation method using the concentrated elvia credit according to claim 13 or 14 , characterized in that:

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