Need for a bounding irradiation history

By definition, a loading criterion specifies a unique average burnup value (or a corresponding value of a related parameter) for a given initial enrichment. A loading criterion accordingly applies to any fuel position of the spent fuel management system of interest and does not take credit for any real loading scheme of the system. A loading criterion must therefore cover not only the variety of axial burnup profiles, as well as horizontal burnup profiles to be considered, but also the variety of irradiation histories of the fuel to be loaded into the system. The task of determining a loading criterion thus implies the need to look for a bounding irradiation history given by those reactor operating conditions (depletion conditions) leading, at given initial enrichment and given burnup, to the highest reactivity of the spent nuclear fuel. As follows from section 4.3, the use of such a bounding irradiation history on the depletion calculations affects the outcomes (DkAX(e,B,t)) in relation to the reactivity effects of axial burnup profiles.

The reactor operating conditions (depletion conditions) for PWR, WWER or BWR UOX fuel are characterized by the following parameters:

(a) Specific power and operating history;

(b) Fuel temperature;

(c) Moderator temperature and density;

(d) Presence of soluble boron in the core (PWR);

(e) Core environment (e.g. presence of MOX fuel in the core);

(f) Use of fixed neutron absorbers (control rods or blades, burnable poison rods, axial power shaping rods, control absorber cells);

(g) Use of integral burnable absorbers.

It has already been shown (e.g. in Ref. [3]) how the depletion parameters have to be chosen to ensure application of a bounding history leading, at a given initial enrichment and a given burnup, to the highest reactivity of the spent nuclear fuel. The depletion parameters are related to neutron spectrum hardening. Spectrum hardening results in an increased buildup rate of plutonium due to increased neutron capture in U-238 (Fig. 3) and leads, therefore, to a higher Pu-239 fission rate and hence, at a given power, to a lower U-235 fission rate. Therefore, spectrum hardening has the effect of increasing the reactivity of the spent fuel. Figure 9 illustrates the increase in the concen-trations of Pu-239 and U-235 due to spectrum hardening arising from the use of control rods. Since spectrum hardening also increases with increasing burnup,

CURRENT ISSUES IN CRITICALITY SAFETY

FIG. 8. Correlation between equivalent uniform burnup (Fig. 7) and average burnup:

The points shown in this figure represent the results obtained for axial profiles analysed according to Fig. 7. From these results, a bounding correlation between equivalent uniform burnup and average burnup can be derived. This bounding correlation can be used for determining the loading curve at given initial enrichment of the fuel: The intersec-tion of k_eff as a function of the uniform burnup with the maximum allowable neutron multiplication factor gives the minimum required uniform burnup (as shown in Fig. 7).

This minimum required uniform burnup can be transformed into the minimum required average burnup with the aid of the bounding correlation between equivalent uniform burnup and average burnup (for details, see Ref. [20]).

Fig. 9 presents the change of the isotopic composition due to control rod (CR) insertion for different periods. The first period ranges from 0 MW·d/kg U to 5 MW·d/kg U, the second from 0 MW·d/kg U to 10 MW·d/kg U, etc., and the last one from 0 MW·d/kg U to 45 MW·d/kg U. As shown in Fig. 9 the relative change in the number densities of U-235 and Pu-239 increases exponentially with an increasing duration of CR insertion. The behaviour of the plutonium isotopes Pu-240, Pu-241 and Pu-242 is dictated by the differences in the energy dependence of the neutron capture cross-sections of Pu-239, Pu-240, Pu-241 and Pu-242, as well as by the energy dependence of the fission cross-sections of Pu-239 and Pu-241 (Fig. 3).

The fission products Sm-149, Sm-151 and Gd-155 are strong neutron absorbers, mainly in the thermal range (Table 1 and Ref. [12]) so that the concentrations of these isotopes in the spent fuel increase with increasing spectrum hardening during depletion. However, the increase in spent fuel’s reactivity worth arising from the increase of the concentrations of the fissile actinides dominates by far the decrease in the spent fuel’s reactivity worth due to the increase of the concentration of neutron absorbing nuclides. This is demonstrated in Figs 10 and 11 showing the neutron multiplication factor of a generic cask loaded with 21 fuel assemblies of type 17 × 17–(24 + 1) as a function of the CR insertion depth during depletion up to average burnups of 30 MW·d/kg U and 50 MW·d/kg U [22]. From these figures, the increase in k_eff with increasing CR insertion depth is significant. The k_eff values represented by FIG. 9. Relative change of isotopic number densities due to CR insertion in a 17 × 17–

(24 + 1) fuel assembly.

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the brown lines in these figures refer to the use of a bounding profile generated for 30 MW·d/kg U average burnup and 50 MW·d/kg U average burnup respec-tively, by means of the procedure described in Ref. [21]. The blue line represents the k_eff values obtained by assuming the respective average burnups uniformly distributed over the active fuel zone and dividing this zone into two axial zones according to the CR insertion depth during depletion, in order to account for the change in the isotopic concentrations due to the CR insertion.

The red line represents the resulting axial effects Δk_AX as a function of the CR insertion depth.

As can be seen, with increasing CR insertion depth, first the relative reactivity importance of the top end region of the fuel zone increases due to the increased fissile content (Fig. 9) and hence the end effect increases. But with further increasing CR insertion depth the relative reactivity importance of the centre region of the fuel zone increases more and more, and finally dominates the increase in the reactivity of the top end zone because of the exponential increase of the U-235 and Pu-239 concentrations with increasing burnup (Fig. 9); the consequence is that the axial end effect Δk_AX decreases. For the 30 MW·d/kg U average burnup case (Fig. 10), Δk_AX becomes negative at full CR insertion depth, which means that the ‘bounding’ burnup profile being used no longer represents the bounding case.

FIG. 10. Neutron multiplication factor, k_eff (brown and blue) and axial effects, Δk_AX (red) as functions of the CR insertion depth.

However, for most of the countries the assumption that CRs are inserted in a fuel assembly during all the irradiation periods of this assembly is also not realistic, nor is the assumption that CR insertion depths greater than 80 cm are used for a total cycle. These assumptions lead to an overly conservative estimate of the neutron spectrum hardening effects due to CR insertion and, hence, to an overly conservative estimate of the k_eff value of the system of interest.

Unfortunately, tendencies to choose each of the depletion parameters in such a way that spectrum hardening is maximized have already been observed in practice. In fact, it has been observed for PWR UOX BUC cases that use of the highest fuel temperature and highest moderator temperature (lowest moderator density) has been combined with the use of a very conservatively estimated averaged soluble boron concentration, plus the assumption that the CRs are inserted at least 80 cm during all the irradiation periods, plus the assumption that the UOX fuel assemblies are completely surrounded by MOX of the highest possible plutonium content. Maximizing spectrum hardening in such a way produces an extremely unrealistic evaluation of the situation. It should be kept in mind that the chosen depletion parameter combination has a significant impact on:

FIG. 11. Neutron multiplication factor, k_eff (brown and blue) and axial effects, Δk_AX (red) as functions of CR insertion depth.

CURRENT ISSUES IN CRITICALITY SAFETY

(1) The outcome of the validation of the predicted isotopic inventory;

(2) The outcome of the criticality validation performed with the aid of a set of experiments selected by means of sensitivity/uncertainty tools;

(3) The reactivity effects due to variations and tolerances in the parameters describing the spent fuel system of interest;

(4) The outcomes for reactivity effects due to axial and horizontal burnup profiles.

Unnecessary maximizing of spectrum hardening can lead to overesti-mation of the correction of the predicted isotopic inventory. Chemical assay data usually originate from commercial fuel. Isotopic correction factors are therefore based on comparisons of these assay data to calculated data predicted by using the real irradiation histories of the fuel rods from which the assays were taken. Application of correction factors greater than 1 to a fissile content that is already overestimated results in an overly conservative estimated k_eff value. Unnecessary maximizing of spectrum hardening restricts the experimental data and configurations which are accepted as representative for a spent UOX fuel system of interest to MOX fuel data and configurations only [6]. Criticality validation is thus unnecessarily constricted.

Unnecessary maximizing of spectrum hardening can be misleading when the loading criterion of the spent fuel system of interest is directly determined by using an axial burnup profile, which is assumed to be bounding due to its shape but which is no longer bounding due to the overestimation of the relative reactivity importance of the centre region of the active fuel zone. Credit should not be taken for negative axial end effects since this leads, for small average burnups in particular, to wrong conclusions when an axial profile is used which is assumed to be ‘bounding in shape’.

Unnecessary maximizing of spectrum hardening results in a significant reduction of the economic benefit and, hence, of the safety benefit of BUC, since more neutron absorbing material and/or greater distances between the fuel positions inside the spent fuel system of interest are required. A reasonable choice of the set of depletion parameters suitable for the plant(s) of interest should be based on statistics of realistic reactor operation strategies and irradiation histories. As reported in Ref. [6], activities are ongoing to sample such statistics.