THE DEVELOPMENT OF AN EMPIRICAL PCI CRITERION FOR SIEMENS FUEL TO BE LOADED INTO SIZEWELL B

J.H. SHEA

Nuclear Technology Branch, British Energy, Gloucester, United Kingdom

Abstract

Siemens fuel will be loaded into the core of Sizewell B Power Station. Many Siemens fuel ramp tests have been conducted in test reactors and power reactors. The database has been applied to develop a rod power PCI criterion to describe the failure behaviour of the fuel. Account has been taken of previous experience in this area with the previous vendor’s fuel. Qualitative differences are noted between the two PCI databases which indicate different failure probability models are required. The new criterion is discussed in detail. The experience gained has provided guidance for possible relaxation of the criteria while also maintaining safety at the required statistical level.

1. INTRODUCTION

In September 2000 it is intended to load Siemens PCA-2a clad fuel into the Sizewell B cycle 5 core. Amongst the issues requiring to be addressed to aid the planning of this task has been the establishment of a description of the Pellet Clad Interaction (PCI) characteristics of Siemens fuel in normal operation and frequent faults.

A database of almost 200 ramp tests from Studsvik and Petten, and several tests in the operating power reactors at Biblis and Obrigheim were made available by Siemens to aid British Energy in its task. This database has been described in an open literature overview [1].

This paper describes the development of the PCI performance constraint to which Siemens fuel is subject. This has the form of an empirical expression which has been used to assess the suitability of core designs for Sizewell B cycle 5. The expression bears a strong resemblance to that used previously in Sizewell B but has nevertheless some distinctive features.

The determination of the best estimate PCI failure criterion for Siemens fuel was the primary objective of the analysis, where ‘best estimate’ implies that relation which describes the 50%

failure likelihood locus of the entire database. Safety constraints in Sizewell B are however based on the so-called 95/95% criterion line which is that locus below which the likelihood of failure is less than 5% at the 95% confidence level. The safety threshold is based on this latter locus.

2 PREVIOUS PRACTICE WITH PCI

The fuel loaded into Sizewell B prior to cycle 5 has been from a single vendor. The vendor made available a database of ramp results which were used to examine the propensity to PCI failure in this particular fuel [2]. The following features of the database were noted:

(1) The best estimate criterion is a threshold power to failure which decreases weakly with burnup.

(2) The most satisfactory failure probability model for the fuel was a normal distribution based on the end of ramp power with a standard deviation, σf, expressed as a fraction of the best estimate transient uprate to failure, ∆P.

FIG. 1. Comparison of best estimate criterion with 95/95% criterion (equation 2) currently used at Sizewell B.

This conclusion is a consequence of a statistical analysis which uses the failure probability model to maximise the likelihood that the failure rods failed and the survivor rods survived by variation of the model parameters. The model parameters were respectively the best estimate or mean power to failure, the fractional standard deviation σf and the linear coefficient of burnup dependence.

The 95/95% criterion is derived from the best estimate threshold power to failure by reducing it by the number of standard deviations to achieve the required bound.

P95/95 = Pbe – KN σ (1)

The 95/95% factor for N data items, KN, is derived from standard Owens Factor tables [3].This expression thus accounts for the intrinsic failure probability distribution and the finite size of the database. Additionally:

Pbe = [ Pc + ∆P ]be

….where Pc is the conditioned power prior to transient.

Since, for the particular fuel under discussion, the standard deviation is proportional to the transient uprate, ∆P, it follows that:-

P95/95 = Pbe – KN σf ∆Pbe

…or alternatively:-

Conditioned Power (arbitrary units)

0

Transient Uprate (arbitrary units)

0

Best Estimate PCI Criterion

95/95% PCI Criterion

P95/95 = Pbe – KN σf (Pbe – Pc) (2)

…from which it follows that a further observation may be made in addition to the two noted above:

(3) The resultant 95/95% criterion is a function of the prior-to-transient conditioned power.

This latter statement has had an important effect on the analysis of the database and on the derivation of the PCI criterion. It has required the prior-to-transient powers Pc to be determined with particular care by using the fuel performance code ENIGMA [4]. For each of the items in the frequent fault database a detailed clad temperature and rating history has had to be constructed to enable the ENIGMA calculations to be performed. The conditioned power prior to the ramp has been defined as either 1) the specified start of transient power if the power has prevailed sufficiently long for the clad hoop stress to be unchanging with time, or 2) the power into the transient at which the clad hoop stress is 50 MPa, whichever is appropriate to the circumstances. The ENIGMA calculations have enabled the database to be transformed from one consisting of values of start of ramp power, transient uprate and burnup to one consisting of conditioned power, Pc, uprate ( that is, Pfinal-Pc) and burnup. This transformed dataset is the one from which the currently used PCI criterion for Sizewell B is derived.

FIG. 2. Siemens final power database versus local burnup.

The final outcome of the analysis described in this section is a best estimate PCI failure criterion having a slope of –1 on a plot of uprate against conditioned power, but with a

Local Burnup (GWd/tU)

0 10 20 30 40 50 60 70

Final Power (kW/m)

20 30 40 50 60 70

KWU ramp survivors Biblis A

Obrigheim

KWU ramp failures

95/95% PCI Criterion 50% Failure Criterion

95/95% criterion on the same plot having a slope of -KN which is in practice of order –0.7.

Figure 1 depicts these two criteria in arbitrary power units.

3. FUTURE PRACTICE WITH PCI

The previous methodology for the development of a PCI criterion for Sizewell B has been described in some detail to allow the qualitative distinctions between the two types of fuel to be outlined.

The entire Siemens fuel database is depicted in figure 2: the plot shows the final power for each ramped rod or rodlet as a function of the burnup. The black symbols indicate failure and it is notable that there are still many survivors even at the highest final powers. In total about 20% of the test reactor ramps resulted in rod failure. None of the power reactor ramps showed failure. This was intended since these ramps were performed with the intention of demonstrating the existence of a threshold inferred from the test reactor data [1]. It appears from the plot that the incidence of failure decreases at high burnups approaching 40 GWd/tU and beyond.

3.1. Preliminary analysis of the Siemens fuel database

The previous methodology was pursued with the Siemens database. Of the ramp tests performed in test reactors, 48 were determined to have history data suitable for use with the ENIGMA code. The version of the code used was one specially produced for the purpose of assessing the performance of Siemens fuel, ENIGMA 5.10 [4]. The preliminary analysis proceeded with the 48 item subset transformed in the manner described in the previous section so that the dataset ultimately consisted of 48 triplets of respectively conditioned power, uprate to the final power and burnup.

Analysis of this limited dataset initially proceeded with the failure probability model described above. However, the results of the maximum likelihood analysis were quite clear:

the fractional standard deviation normal distribution model did not give a reasonable description of the data.

Another, simpler hypothesis was studied. The normal error distribution was retained but the standard deviation was held constant, without any fractional dependence on the magnitude of the uprate. This model was very satisfactory and gave a convincing description of the ramp test results.

This observation has a significant effect on the interpretation of the database, since the confirmation of the effectiveness of a constant standard deviation implies that the 95/95%

criterion is a threshold power to failure at the lower 95/95% bound independent of the value of the conditioned power. This means that equation (1) above is sufficient to describe the PCI failure behaviour of the fuel at any statistical confidence level, without the additional complexity of equation (2), so that the 95/95% bound is parallel to the best estimate criterion unlike the situation of Figure 1.

Furthermore, the lack of conditioned power dependence of the power to failure in the criterion implies that the detailed histories for the ENIGMA code are not necessary. This is because for Siemens fuel the conditioned power prior to the ramp need not be determined. Hence the entire database of 182 test reactor ramp results can be included in the statistical optimisation

without additional calculations to determine the conditioned powers. This is the major conclusion from the present stage of analysis.

3.2. The analysis of the complete Siemens fuel test reactor database

The next stage of analysis was to use the final powers and the burnups of each of the 182 test ramps to perform a statistical optimisation with a normal distribution failure probability model, taking advantage of the increased database (from 48 items to 182) to allow definition of a less onerous 95/95% PCI criterion because of the improved precision in the statistics.

However, the database contains much more information than 182 test reactor ramps since, for example, the Biblis A power reactor tests were performed by ramping entire assemblies in relative isolation from the rest of the reactor. It follows that the database supports the adoption of a different failure probability model having a much reduced probability of failure at low powers. Indeed, one showing a threshold effect in PCI vulnerability is indicated. The currently assumed normal distribution does not have this property.

Another acceptable form for the failure probability model is the so-called uniform distribution. This naturally contains a threshold as demonstrated below:

Pfail = 0 if Pfinal < Pbe – W/2 Pfail = 1 if Pfinal > Pbe + W/2

Pfail = ( Pfinal - Pbe )/W+ 0.5 otherwise

…where W is the total width of the distribution, and [ Pbe – W/2 ] is the assessed threshold power.

The benefit of this failure model in comparison with a more complex one also demonstrating a threshold is that it is entirely sufficient for the purpose and its properties are well understood. It is effectively indistinguishable from the formerly used normal distribution for a broad range ( ~ ±1σ ) about the mean or best estimate. The distribution full width W can be related to the standard deviation of an equivalent normal distribution by W = 0.289σ.

The 95/95% factor, K182 , applied to the distribution width is readily determined by a Monte Carlo procedure [5] and the final 95/95% PCI criterion for Siemens fuel can be stated as:

P95/95 = 42.89 – 0.145 B (3)

…where the local power units are kW/m and the local burnup units are GWd/t U.

Figure 2 shows the 95/95% power to failure criterion, equation (3) for Siemens fuel, expressed as a function of burnup to allow comparison with the Siemens fuel database. The best estimate criterion is also illustrated to demonstrate the way it partitions of the database into failures and survivors, and it is clear the database does not actually encompass the 50%

failure likelihood level where numbers of failures and survivors are comparable. This is because the dynamic range of the tests has not reached the best estimate threshold power to failure, although the tests are fully representative of faults to be expected in Sizewell B.

In practice the PCI criterion has usually been defined in terms of the allowable uprate, ∆P95/95, from the current local power level, Pc. Also, the allowable uprate at high conditioned powers is constrained to be small but constant.

∆P95/95= MAX(42.89 - Pc - 0.145 B, 4.96 ) (4)

The uprate criterion of equation (4) is plotted in a total power form against conditioned power in figure 3, superposed on to the database. The test values of ∆P, the uprate, have been corrected by the burnup term, 0.145B, so that only one criterion locus need be plotted, namely 42.89 - Pc . The conservative nature of the criterion is evident since failures are predominantly above the criterion line.

FIG. 3. Siemens Fuel Database with PCI Criteria.

3.3. Further developments

Several additional developments are possible with the analysis already presented and this section will briefly allude to them and indicate the potential benefits.

The possibility of combining the databases for the fuel currently in Sizewell B and the Siemens fuel intended for loading in the imminent cycle 5 is not realistic since the failure probability models required for the respective database analyses have proved to be quite