The development of nuclide inventory benchmarks for BWR spent fuel presents different challenges from those of similar efforts for pressurized water reactor (PWR) spent fuel, given the increased radial and axial heterogeneity of the fuel configuration and complexity of the operating history for BWRs compared to PWRs. Axial information (e.g., water coolant density, presence of full- or part-length rods, rod power, and assembly power) for BWRs is essential for adequately capturing the underlying physics. Often, this type of axial information is not available, and well-founded assumptions are necessary. The most significant challenge is how to treat the uncertainty for time-dependent operating parameters such as the operating power history, which is not commonly reported. Although most nuclides present in spent fuel generally have low sensitivity to power history for a given burnup, there are several short-lived fission products with high sensitivity, especially to power history near the end of irradiation [
2].
Because of incomplete or missing data and the associated uncertainty for assembly design, fuel characteristics, and operating history parameters, the benchmark being developed for the Fukushima-Daini-1 spent fuel samples included several assumptions. The basis of these assumptions and their impact on the C/E nuclide concentration ratio are presented here. The impacts of these assumptions are assessed based on the direct perturbation of specific modeling parameters. The type of uncertainties and assumptions include the following:
4.1. Power History
Ideally, the time-dependent variation of power or equivalently burnup at the radial and axial locations within the fuel assembly that corresponds to the measured fuel sample is needed to accurately simulate the nuclear transmutation and decay processes in the sample during irradiation. This type of data is not generally available. What is usually available from the reactor core simulator used to manage the reactor operation is the so-called nodal power, which is the radially averaged power across the assembly within an axial layer or node (node height ~10 cm) of the assembly. The power within the measured sample (sample height ~1 cm) can significantly differ from the nodal power because of heterogeneities within the assembly and the intranodal variation of the neutron flux. Additionally, there are uncertainties in the reported nodal power due to inherent uncertainties associated with the reactor core simulation method.
The benchmark specifications assumed that the time-dependent power at the sample axial location is proportional to the time-dependent nodal power available from the core simulator. The sample-specific power for the benchmark was calculated by scaling the nodal power history to the reported sample burnup. Because it is easy to implement, this type of approach is generally used by analysts. The effect of this assumption is evaluated herein using an alternate approach for deriving the sample power.
This second approach includes two steps. In the first step, a depletion simulation for the fuel assembly is performed with Polaris using the provided nodal average power as input assembly power, which is consistent with the available input data for that node; in this case, the neutron flux solution within the assembly is normalized by Polaris to this input assembly power. Note that the neutron flux solution in Polaris for an assembly depletion simulation can be normalized, based on the user’s selection, to the assembly power, power of a specific rod, or power of a set of specific rods.
The resulting output of the Polaris simulation in the first step includes the time-dependent power distribution within the assembly for each of the fuel rods, including the rod from which the measured fuel sample was selected. This time-dependent variation of the power in the fuel rod of interest serves as input for the second step. In the second step, the time-dependent variation of the power within the fuel rod is scaled to the reported sample burnup and then used as input for a second Polaris depletion simulation of the assembly. In this second depletion simulation, the flux solution is normalized to the power for the fuel rod of interest.
The two approaches presented above for power history modeling can be summarized as follows: (1) time-dependent sample power is obtained by scaling the available nodal average power history with the provided sample burnup, and (2) time-dependent sample power is obtained by scaling the derived fuel rod power history with the reported sample burnup. Although the second approach is code-dependent, it provides an estimate of the uncertainty in predicted nuclide concentration due to the modeling assumption (1) used for the benchmark. Both approaches have consistent sample burnups, but the trajectories of the power to reach that burnup may differ.
A comparison of the sample power history determined via the two approaches is illustrated in
Figure 2 for a regular fuel rod (sample 2F1ZN3-C3-UM) and for a gadolinia rod (sample 2F1ZN3-C2-GdM) in assembly 2F1ZN3. Whereas the two approaches mentioned above lead to similar power trajectories for the regular fuel rod, the power trajectories for the gadolinia fuel rod show significant differences, which is expected because gadolinia rods have different neutronic characteristics from the average assembly behavior that is dominated by the regular fuel rods. This indicates that for regular fuel rods, the use of a sample power history based on node power history is adequate, whereas for the gadolinia fuel rods, it is not warranted.
The effect of the assumption for sample power history on the C/E nuclide concentration ratios for U and Pu isotopes is illustrated in
Figure 3 for three samples from assembly 2F1ZN3. These samples were selected to cover different types of fuel rods: corner rod, regular fuel rod, and gadolinia rod. Detailed C/E values are provided in
Section 4, along with all other estimated uncertainties for these samples. The change in C/E is the primary focus here. For convenience, only the rod and the axial location of the sample ID are shown in the legend of
Figure 3. For the regular fuel samples C3-UM and A9-UM, the power history approach leads to changes in C/E for U and Pu isotopes of less than ~1.5%. Conversely, the magnitude of the effect is greater for the gadolinia fuel sample C2-GdM for
234U and
235U (~2%) and for
238Pu (~5%).
4.2. Coolant Density
The density of the water coolant at the sample axial location is not generally provided. Available data usually include coolant void fractions for each axial node in the assembly. The usual approach, which was also applied for the benchmark specifications, is to assume that the void fraction at the sample axial location is the same as the corresponding axial node void fraction. This assumes that the void fraction is radially uniform within the node. However, the intranodal void fraction distribution is not uniform and may vary with the fuel rod power and fuel radial location in the assembly, particularly for rods in proximity to the water box and the channel box, as previously noted in the literature [
13]. The coolant density around the sample could therefore be significantly different from the node’s average coolant density. Previous studies indicated that nodal average void fractions can have relative uncertainties of ~5% and that the void fraction for fuel rods that are close to the assembly periphery or in proximity to water rods can be significantly smaller—by up to 25%—than the node’s average void fraction [
13].
The effect of the void fraction assumption on the C/E nuclide ratios is estimated herein by assuming a 5% change in the void fraction. The results are illustrated in
Figure 4 for U and Pu isotopes in samples from assembly 2F1ZN3. This figure shows the change in C/E due to a 5% relative increase (
Figure 4a) and a 5% relative reduction (
Figure 4b) in the sample void fraction. An increase in void fraction (decrease in coolant density) leads to the hardening of the neutron flux spectrum due to less moderation and consequently to an increase in predicted actinide concentrations, which are sensitive to the spectrum. Depending on the isotope, the C/E for Pu isotopes increases by up to 2%, and it increases by more than ~4% for
235U with increasing void fraction. The opposite behavior is observed if the void fraction is reduced. The largest change in C/E values is observed for sample 2F1ZN3-A9-UM from the corner rod A9. The large overprediction of
235U in this sample indicates that the actual void fraction history for this corner rod is likely lower than the node’s average void fraction.
It is important to note that the magnitude of the change in C/E with void fraction variation, for a constant variation of this fraction, is expected to increase with increasing axial elevation. This would result from a larger absolute value change in the void fraction (and therefore in the coolant density) with axial elevation, given that the void fraction increases with increasing elevation.