20. Sensitivity Analyses of Initial Compositions and Cross Sections for Activation Products of In-Core Structure Materials

As stated in Sect. 20.1, activations of in-core structure materials, such as cladding tubes, end plugs, and spacers of fuel assemblies and channel boxes, were investigated in this study. The materials of the in-core structures of PWR and BWR are shown in Table 20.1. The compositions of Zircaloy-2, Zircaloy-4, SUS304 stainless steel, and INCONEL alloy 718 are shown in Table 20.2. In Table 20.2, the average value of the upper and lower limits of the standard specification was applied to the calculation condition for additive elements and the upper limit was applied for impurity elements. The effect of impurity elements that are not specified in the standard are investigated in Sect. 20.3.4.

Typical conditions of BWR were assumed for the cross-section libraries and the irradiation condition, because the difference between the conditions of PWR and BWR is not so significant for the purpose of this study, which is clarifying the dominant generation pathways of activation products.

The cross-section libraries used in these analyses (Table 20.3) were chosen to correspond to the condition of the void ratio in the axial direction. A library made with an average void ratio (40 %) was applied to cladding tubes, spacers, and channel boxes for which the void ratio varies from 0 % to 70 %.

A BWR typical irradiation history consists of four cycles of irradiation of about 377 days with constant flux and 90 days of cooling time in the intervals of irradiation (Fig. 20.1). Considering the period for processing of radioactive wastes, 10 years of cooling time after irradiation was assumed in these analyses. The flux intensities at the center, top, and bottom in the axial direction are shown in Table 20.4. The flux intensity at the center corresponds to the average power in typical BWR fuel assemblies. The flux intensities at the top and bottom were determined to be 5 % of that at the center, based on flux distribution evaluated by the one-dimensional neutron diffusion calculation.

The representative radioactive nuclides in this study (Table 20.5) include not only the important nuclides for various evaluations of radioactive wastes but also the nuclides whose concentrations have been measured in the past, which will be useful for the validation of numerical evaluations.

Target nuclides of sensitivity analyses were selected on the basis of two criteria. The first was that the concentrations of activation products be larger than or comparable to the concentration of fission products generated from impurity uranium in the materials. The contents of impurity uranium in Zircaloy-2 and SUS304 stainless steel were 0.00035 wt% and 0.0001 wt% [5], respectively. This value in INCONEL alloy is unknown. The second criterion was that the concentrations of activation products be comparatively large. In these analyses, activation products with concentrations more than 1 × 10⁻⁹ g/t were chosen.

The concentrations of activation products larger than 1 × 10⁻⁹ g/t and fission products generated from impurity uranium are shown in Table 20.6. The fission products were calculated under the condition that the initial composition contains only the uranium impurity. Table 20.6 also shows the selected target nuclides that satisfy the foregoing criterion: 17 nuclides in Zircaloy-2 and Zircaloy-4, 8 nuclides in SUS304 stainless steel, and 16 nuclides in INCONEL alloy were selected as the target nuclides of sensitivity analyses.

Sensitivity analyses were conducted for several selected nuclides in Zircaloy-2, SUS304 stainless steel, and INCONEL alloy. Analyses in Zircaloy-4 were skipped because the sensitivity coefficients were thought to be almost the same as that in Zircaloy-2 because calculation conditions were similar. For SUS304 stainless steel, activations using the cross-section library of void ratio 0 % were evaluated because the concentrations in the case of void ratio 0 % were larger than that of void ratio 70 %.

The sensitivity coefficients of initial compositions are shown in Table 20.7. As defined in Eq. (20.1), the value shows the relative amount of variation in concentration of the target nuclide when the initial composition of element varies by a unit amount. Therefore, the source elements leading to the generation of target nuclides was clarified from the results. For example, Table 20.7a shows that Fe-55 is generated from both iron and nickel and that the contribution from iron is dominant. The results can also be useful in the evaluation of the error propagated from the measurement uncertainty of initial composition.

As defined in Eq. (20.2), a sensitivity coefficient of a cross section shows the relative amount of variation in the concentration of the target nuclide when the cross section varies by a unit amount. Therefore, a positive value of this coefficient indicates that the target activation product is generated through the nuclear reaction. Thus, if a sensitivity coefficient is positive and large, the cross section of the nuclear reaction is significant for the generation of the target activation products. In the analyses, the objectives of reaction were six reactions treated in ORLIBJ40 library; the reaction of (n, γ), (n, 2n), (n, α), and (n, p) yielding to nuclides of ground state and the reaction of (n, γ) and (n, 2n) yielding to nuclides of meta-stable state. The summary of the results of sensitivity analyses of cross sections are shown in Table 20.8, where the sensitivity coefficients that are positive and more than 0.01 are extracted from all the results and listed in descending order. The results clarified the nuclear reaction dominating the generation of target nuclides. For example, it is thought that Fe-55 in Zircaloy-2 can be generated from the (n, γ) reaction of Fe-54, the (n, α) reaction of Ni-58, and the (n, 2n) reaction of Fe-56. Table 20.8a clearly shows the (n, γ) reaction of Fe-54 is dominant in the generation of Fe-55.

It was remarkable that the dominant generation pathways were clarified even for the target nuclides generated through complicated pathways. Some of the examples are shown in Fig. 20.2.

Figure 20.2a shows an example of nuclides generated with some contributing pathways. Be-10 is generated in Zircaloy-2 mainly through two pathways, the (n, p) reaction of Be-10 and the (n, α) reaction of C-13. It is not predictable which pathway is dominant from the initial composition of the material. The sensitivity coefficients clearly showed that the (n, α) reaction of C-13 is the dominant pathway for Be-10 generation in Zircaloy-2.

Figure 20.2b shows an example of nuclides generated through long and complicated generation chains. The source nuclide of Cl-36 generated in SUS304 stainless steel is ambiguous because the initial composition in this analysis does not contain chlorine, which could be the dominant source element of Cl-36. The sensitivity coefficients quantitatively clarified that S-34 is the source nuclide of Cl-36 even for the long and complicated chain.

The sensitivity coefficients shown in Sect. 20.3.3 are valid within the assumed analysis conditions in Sect. 20.3.1. However, the impurity elements that are not specified in the standard specification can be possibly present in the material. To know the effect of the difference in the initial composition on sensitivity coefficients, additional analyses were conducted using the initial composition based on measured data. The evaluation of activation products in SUS304 stainless steel is described here.

Except for the initial composition, the analysis conditions described in Sect. 20.3.1 were assumed. The composition data reported by the Atomic Energy Society of Japan [6] were applied in this analysis. In this reference, the concentration distributions of some elements with their mean values and standard deviations have been determined based on several measured data. The initial composition based on measured data is shown in Table 20.9 together with that based on the standard specification.

The concentration of activation products using the initial composition based on measured data is shown in Table 20.10. As a matter of course, the concentrations were changed from those in Table 20.6b because the different initial compositions were assumed. It was found that Nb-94, Tc-99, Mo-93, K-40, and Zr-93 appeared in Table 20.10 because of the presence of niobium, molybdenum, and potassium in the initial composition. For the comparison with the sensitivity coefficients shown in Sect. 20.3.3, sensitivity analyses of cross sections were conducted for the several nuclides Ni-59, Ni-63, Fe-55, Co-60, Mn-54, C-14, and Cl-36, which were listed in both Tables 20.6b and 20.10.

The sensitivity coefficients of cross sections using the initial composition based on measured data are shown in Table 20.11. It was found that the results of Co-60, C-14, and Cl-36 are much different from those in Table 20.8b, which indicates that the dominant generation pathways of these nuclides were changed. Figure 20.3 shows the comparison of dominant generation pathways of Co-60, C-14, and Cl-36 between different analysis conditions. The source nuclides of Co-60, C-14, and Cl-36 were Co-59, N-14, and Cl-35, respectively, under the conditions based on measurement data, whereas those were Ni-60, C-13, and S-34, respectively, under the conditions based on the standard specification.

As shown in the foregoing example, the dominant generation pathway can be changed corresponding to the initial composition. The reliable measured data of initial impurity elements should be used if they are available. For any condition, sensitivity analyses on the basis of the methodology stated in this study can systematically identify the dominant generation pathways of activation products.