Necessity of Formulating the Evaluation of Axial Burnup Profiles as a Decision Problem

PARAMETERS AFFECTING BURNUP CREDIT

EVALUATION OF AXIAL AND HORIZONTAL BURNUP PROFILES

2. EVALUATION OF AXIAL BURNUP PROFILES

2.1. Necessity of Formulating the Evaluation of Axial Burnup Profiles as a Decision Problem

Due to all the history effects affecting the axial shapes one gets for each axial height z of the fuel zone a burnup dependent statistic on the ratio =(z,Bav) of the normalized burnup (Bav

denotes the averaged burnup). The distributions shown in Figures 10, 15, 20, and 25 for example are samples on this statistic, but the true distribution of the ratio =(z,Bav) remains unknown until the plant of interest is finally shut down – and this goes for all the plants of interest. So therefore, having a statistic on the ratios =(z,Bav) which may be biased with respect to the true distribution of =(z,Bav) one has to decide whether or not the highest end

effect that may occur under normal core operating conditions is covered by the loading curve of the spent fuel management system of interest. One needs a decision theory, therefore, which is closely tied to the methods of statistics. This means that one has to analyze a sufficiently large number of observed axial shapes in order to construct a sufficiently high confidence level that the highest end effect that may occur under normal core operating conditions is covered by the loading curve of the spent fuel management system of interest.

In order to be able to analyze a large number of axial shapes curves representing the neutron multiplication factor of the spent fuel management system of interest as a function of the axially uniformly distributed burnup at given initial enrichments are used as ”calibration curves”, as exemplified in Figure 26. As illustrated in this figure, the difference ,k between the neutron multiplication factor obtained with an axial burnup shape and the neutron multiplication factor obtained by assuming the average burnup of the shape uniformly distributed is represented by the difference between the average burnup and the so-called

”equivalent uniform burnup” which is the uniformly distributed burnup that leads to the same neutron multiplication factor as obtained with the axial shape. As indicated in Figure 26, this equivalent uniform burnup is obtained by comparing the neutron multiplication factor obtained with the axial shape to the calibration curve taking account of course of all the statistical uncertainties that might be involved in such a comparison [3]. Due to these statistical uncertainties each axial shape analyzed in this way is represented by a bar in a diagram which shows the equivalent uniform burnup of a shape in correlation with the average burnup of this shape. Figure 27 shows such a diagram, and – as can be seen from this figure – a big lot of analyzed axial shapes is represented in that diagram. From this big lot of results a correlation between equivalent uniform and average burnup can be derived which represents the end effect (i.e., the reactivity effect due to the fact that the axial distribution of burnup is non-uniform) in an enveloping manner. This correlation is represented by the solid line in Figure 27 (the dashed line corresponds to zero end effect – in that case is the equivalent uniform burnup equal to the average burnup). As can be seen from Figure 27, this correlation is defined in fact in an enveloping manner: All the bars representing the axial shapes analyzed are above the solid line representing the correlation derived.

The correlation of equivalent uniform burnup to average burnup can be used as set forth below:

1. First, with this correlation one is able to derive a loading curve from the calibration curves. As indicated in Figure 28, once a minimum required uniform burnup is determined, the average burnup which covers the end effect can be calculated with the aid of the correlation - and the minimum required uniform burnup is obtained in fact by comparing the upper 95%/95% tolerance limit of the calibration curve with the maximum neutron multiplication factor allowed (cp. Figure 29).

2. Secondly, with the aid of the correlation one is able to made a decision whether or not axial burnup profiles obtained later meet the loading curve. An axial profile is acceptable only then if the related equivalent uniform burnup is not beneath the correlation curve.

Text cont. on page 206.

FIG. 1: Evaluation of a Sample of 708 Axial Burnup Shapes given in Reference [4].

FIG. 2: Illustration of the Siemens/KWU’s Aeroball System [5].

FIG. 3: Axial Power Distribution Typical of the Begin of the First Cycle [9].

FIG. 4: Axial Power Distribution Typical of the End of the First Cycle [9].

FIG. 5: Axial Power Distribution Typical of the Begin of the Second Cycle [9].

FIG. 6: Axial Power Distribution Typical of the End of the Second Cycle [9].

FIG. 7: NPP Neckarwestheim I: Axial Power Distributions at the Begin of the Nineteenth Cycle (at 7 EFPD).

FIG. 8: NPP Neckarwestheim I: Axial Power Distributions at 196 EFPD of the Nineteenth Cycle.

FIG. 9: Evaluation of a Sample of 708 Axial Burnup Shapes given in Reference [4]:

Distribution of the Average Burnups of the Shapes.

FIG. 10: Evaluation of a Sample of 708 Axial Burnup Shapes given in Reference [4]: