PARAMETERS AFFECTING THE END EFFECT

The optimum balance between increased reactivity due to lower burnup and increased leakage due to closer proximity to the fuel ends is affected by all the parameters, which have an impact on:

• the isotopic concentrations and hence the reactivity of the fuel (depletion parameters, cooling time);

• the neutron spectrum of the spent fuel management system of interest and hence the reactivity worth of the nuclides (design parameters, depletion parameters, cooling time);

• the axial bounding conditions (highly reflective, high leakage) (design parameters).

One of these parameters is the initial enrichment of the fuel, which determines, together with the depletion parameters, the burnup and the cooling time, the isotopic content of the spent fuel. In the paper on hand the impact of the initial enrichment on the end effect is analyzed.

2.1. Initial Enrichment, Fission Product Buildup and End Effect A higher initial enrichment results in

• a lower U-238 capture rate and;

• a higher U-235 depletion rate and hence in a higher fission product buildup rate (cp.

Figure 1, e.g.).

This is true for the center zone of the fuel as well as for the end zones. However, the net buildup rates of plutonium and the fission products are usually lower in the center zone (due to the higher burnup in this zone) than in the end zones. It is to be expected, therefore, that the end effect decreases with increasing initial enrichment.

FIG. 1. Depletion of the Westinghouse 16x16-21 Standard Fuel Assembly in the Krzko Core (NEK, Slovenia): Sm-149 Number Density as a Function of Burnup and Initial Enrichment for Bounding Depletion Conditions. (As indicated, up to a Burnup of 15 MWd/kg U Burnable Poison Rods were assumed to be present).

Figure 1 shows for example the number density of Sm-149 as a function of burnup at initial enrichments between 2 wt.-% and 5 wt.-% U-235. It is instructive to observe how the ratio between the number density at a higher burnup and the number density at a lower burnup is changing with increasing initial enrichment:

• At 2 wt.-% initial enrichment this ratio remains always greater than one. With increasing initial enrichment this ratio may become less than one and may decrease with increasing initial enrichment. Accordingly, given any axial burnup distribution, at 2 wt.-% initial enrichment the Sm-149 content of the spent fuel is greater in the center zone of the fuel than at the end zones. With increasing initial enrichment however, the Sm-149 content of the center zone may fall below the Sm-149 contents of the end zones, in particular in case of higher average burnups. Thus, due to the fact that Sm-149 is a very important absorber,

it is to be expected that, for higher average burnup values, the end effect tends to decrease with increasing initial enrichment;

• On the other hand, as can be seen from Figure 1, the ratio of the number density at 30 MWd/kg to the number density at any given burnup less than 15 MWd/kg is decreasing with increasing initial enrichment. Therefore, it is to be expected that also for lower average burnup values the end effect decreases with increasing initial enrichment.

However, the end effect is affected by all the parameters mentioned in section 2. Thus, it is not self-evident whether or not the impact of the initial enrichment on the end effect can be really observed.

FIG. 2. Example for the Axial Burnup Distributions Obtained from Ref. [3] and Modeling of these Distributions.

2.2. Brief Account of the Parameters Affecting the End Effect

Due to the higher moderator density in the lower half of the core axial burnup shapes are usually asymmetrical, [1]. It is known that the end of the fuel zone, which is burned least, determines the end effect. This end is usually the top end of the fuel zone, cp. [1] and Figure 2. The asymmetry of an axial shape and hence the end effect are strongly dependent on the average burnup and significantly affected by

• reload patterns (determining the interactions between fresh fuel assemblies and fuel assemblies with different burnup shapes at begin of cycle, cp. Ref. [1], Figures 3 and 5),

• control rod movements;

• the use of axial power shaping rods;

• the presence of integral burnable poisons;

• the presence of axial blankets;

• extended low power operations;

• all the depletion conditions affecting the U-238 capture rate and the U-235 depletion rate (specific power, spectrum hardening due to higher boron concentration or presence of burnable poison rods);

• the cooling time.

In addition, the end effect is also dependent on the active length of a fuel assembly. This is often missed. Usually the end effect decreases, at given average burnup, with decreasing active length. This is due to the process of the flattening-out of the axial power distribution with increasing burnup.

2.3. Asymmetry of the Axial Shapes, Initial Enrichment and End Effect

Due to the flattening-out of the axial power distribution with increasing burnup the impact of the initial enrichment on the end effect should become more apparent for lower average burnups. The flattening-out of the axial power distribution with increasing burnup is reflected by the fact that, as shown in Ref. [1], the ratio of the burnup of the top end of the fuel zone to the average burnup increases with increasing burnup. Thus, the higher the average burnup is, the lower should be the impact of a change in the initial enrichment and hence a change in the U-238 capture rate, the U-235 depletion rate and the fission product buildup rate on the end effect. In other words, it is to be expected that the impact of the initial enrichment on the end effect is increasing with decreasing average burnup. On the other hand however, the end effect is decreasing with decreasing average burnup, cp. Ref. [1].

In the following the analysis performed to reveal the impact of the initial enrichment on the end effect is presented.

3. STUDY OF THE IMPACT OF THE INITIAL ENRICHMENT ON THE END EFFECT