FISSION PRODUCT REACTIVITY WORTH AND UNCERTAINTY IN THE NEUTRON MULTIPLICATIN FACTOR OF SPENT FUEL MANAGEMENT SYSTEMS

3.1 Without Cooling Time Credit

The concentration and hence the contribution of the isotopes to neutron absorption, resulting in either fission or simple neutron capture reactions are dependent on cooling time. In burnup credit methodologies applied to spent PWR fuel storage pools the fission product isotopes are frozen at the concentrations existing at the time of shut down, except for I-135 and Xe-135 which are not considered because of their small half-lives. Consequently, as exemplified in Figure 14 by the case of irradiated KONVOI UO2 fuel assemblies stored in region II type storage racks typical of KONVOI plants, among the fission products usually considered in burnup credit applications [10-11] only the isotopes Rh-103, Xe-131, Cs-133, Nd-143, Sm-149, and Sm-151 show a considerable reactivity worth for all the burnups specified in Figure 14, whereas the isotopes Tc-99, Nd-145, Pm-147, and Sm-152 have a significant reactivity worth only in the range of the higher values of these burnups. As indicated in Figure 14, these burnups correspond to the loading curve of the region II KONVOI fuel storage racks mentioned above. As can be seen from Figure 14, the reactivity worth of the isotopes Mo-95, Pm-148, and Sm-150 is of minor importance, and the reactivity worth of all the remaining fission products is more or less negligible. So therefore, as regards depletion code validation for burnup credit applications to spent fuel storage pools the attention can mainly be focused on the verification of the calculated inventory of actinides plus a few fission products.

As can be seen from a comparison of Figure 14 to Figures 11 and 13, the fission products with a considerable reactivity worth for all or, at least, some of the burnups specified in Figure 14 are those ones for which mostly fairly good agreement between measured and calculated mass ratios were found. This is not surprising. With the exception of the Sm isotopes Sm-149 and Sm-151 which have very high thermal cross sections for neutron capture [10] the considerable reactivity worth of all the other fission products specified in Figure 14 is mainly due to the isobaric yields for fission of U-235 and hence to the number densities of these fission products. Accordingly, a higher accuracy can be achieved in the chemical assay of these fission products.

It is not surprising, therefore, that the differences between the measured and calculated fission product mass ratios as obtained from the ARIANE programme (cp. Figure 11) result in a

relatively small bias of the neutron multiplication factor of the region II KONVOI fuel storage

where k(C) refers to the calculated isotope number densities and k(E) refers to the corrected isotope number densities obtained with the aid of the differences shown in Figure 11. I(,k) denotes the one standard deviation of ,k.

The result (3.1) refers to the fission products only and gives the underestimation of the neutron multiplication factor of the region II KONVOI fuel storage racks due to the observed differences between the measured and calculated fission product mass ratios. The isotope number densities of the actinides were not corrected. Due to the slight underestimation of the fertile isotopes U-236, Pu-240, and Pu-242 and due to the slight overestimation in the fissile isotopes U-235, Pu-239, and Pu-241 a correction of the actinide number densities would result in a decrease of the calculated neutron multiplication factor of a spent fuel storage pool.

As shown in [10], the result (3.1) is confirmed by evaluations of experimental results of the French programme on burnup credit [11-12].

3.2 With Cooling Time Credit

The reactivity worth of the fission products referring to a loading curve of a PWR transport or storage cask system designed for burnup credit should not be very different from Figure 14, because the loading curve of that system is based on the case of a fully flooded cask, i.e., on a thermal system. However, in burnup credit methodologies applied to spent fuel transport and storage casks often credit for cooling time is taken. One has to take into account, therefore, that the bias in the neutron multiplication factor of the cask may increase with the cooling time due to radioactive decay of some isotopes.

Figure 15. shows for example the relative changes

) 1

of the bias in the neutron multiplication factor of the region II KONVOI fuel storage racks used already for Figure 14. due to the radioactive decays of:

(a) Pu-241 to Am-241 (half life 14.4 a), (b) Pm-147 to Sm-147 (half-life 2.62 a), (c) Eu-155 to Gd-155 (half-life 4.96 a).

The outcomes obtained for the relative changes (3.3) at an initial enrichment of 4.0 wt.-% and a burnup of 36.7 MWd/kg U (cp. Figure 14) are derived from the GKN II results shown in Figures 12 and 13 indicating:

(a) an overestimation of Pu-241 by 9%,

(b) an underestimation of Pm-147 and Sm-147 by 64% and 1% respectively,

(c) an overestimation of Eu-155 and Gd-155 by 57% and 57.45% (the value for Gd-155 is corrected in order to prevent negative number densities for Gd-155 at time of shut down).

As shown in Figure 15.:

1. Due to the fact that the fissile isotope Pu-241 is overestimated in the depletion calculation and due to the fact that no result for Am-241 is available from the chemical assay (cp. Figure 12) expression (3.3) is negative for the Pu-241 decay and increases with increasing cooling time (converges towards zero due to the fact that no correction was made for Am-241),

2. Because the fission products Pm-147 and Sm-147 are underestimated in the depletion calculation and the underestimation of Pm-147 is significantly higher than the underestimation of Sm-147 expression (3.3) is negative for the Pm-147 decay and increases with increasing cooling time (converges towards zero nearly due to the fact that the underestimation of Sm-147 is nearly negligible),

3. Due to the overestimation of Eu-155 and Gd-155 in the depletion calculation the absolute amount of the uncertainty in the number density of Gd-155 increases with increasing cooling time and hence the bias in the neutron multiplication factor increases with the cooling time.

So therefore, as follows from Figure 15, if credit for cooling time is taken one has to be aware of the possibility that the bias in the neutron multiplication factor of the spent fuel management system of interest may increase. To which extent the bias is changing depends on the outcomes of the depletion calculation in comparison to chemical assay data. As follows from Figures 11 and 13 as well as from the results from the French programme on burnup credit [10-12] the isotopes Eu-155 and Gd-155 seem to be overestimated always in depletion calculations. There are grounds for the assumption that there are some difficulties either in the calculational or in the experimental methods, therefore. It is a good thing, therefore, that in the REBUS programme [13] it is planned not only to analyze the isotopic concentrations through chemical assay but also to measure the reactivity worth of the spent fuel. The reactivity worth measurement provides an additional tool to check the chemical assay data on consistency, and in addition to that, the reactivity worth measurement makes it possible to recalculate the experimental mock-up with criticality calculation codes, thus benchmarking these codes.

REFERENCES

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”Sixth International Conference on Nuclear Criticality Safety”, ICNC’99, September 20-24 (1999) Versailles.

THE IMPLEMENTATION OF BURNUP CREDIT IN