Sensitivity Analysis Using the Initial Composition Based on Measured Data

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.

Table 20.10 Concentration of activation products in SUS304 stainless steel

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.

Table 20.11 Sensitivity coefficient of cross section in SUS304 stainless steel

Target nuclide

Sensitivity coefficient of cross section

First largest

Second largest

Ni-59

Ni-58

(n, γ)

1.00

Ni-63

Ni-62

(n, γ)

1.00

Fe-55

Fe-54

(n, γ)

0.99

Ni-58

(n, α)

0.01

Co-60

Co-59

(n, γ)

0.46

Co-59

(n, γ)m

0.46

Mn-54

Fe-54

(n, p)

1.00

C-14

N-14

(n, p)

1.00

Cl-36

Cl-35

(n, γ)

1.00

Fig. 20.3 Dominant generation pathways of activation products in SUS304 stainless steel

Conclusion

This study shows the sensitivity analyses of initial compositions and cross sections for activation products of in-core structure materials. The results clarified the source elements and nuclear reactions dominating the generation pathways of the activation products even for the nuclides generated through complicated pathways. The sensitivity coefficients of initial compositions are beneficial for the evaluation of the error propagated from the uncertainty of the initial composition of target materials. The sensitivity coefficients of cross sections are effective in selecting the objectives of nuclear reactions for the improvement of nuclear data. These results will contribute to improvement of the accuracy of numerical evaluations for the concentration of activation products.

The methodology of sensitivity analyses stated in this study is efficient for acquiring information about important impurity elements and nuclear reactions to evaluate the activation product concentrations. This methodology can be applied to the activations of ex-core structure materials if the appropriate one-group cross sections are prepared with a corresponding neutron spectrum.

 
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