Criticality safety criteria

4.2.4.1. Bounding conditions in assembly depletion calculation

The reactivity of spent fuel is affected by the degree of spectrum hardening caused by the depletion conditions. Keeping all the depletion parameters constant (specific power, fuel temperature, moderator temperature and density, presence of soluble boron in the moderator, presence of burnable poison rods, control rod insertion - cf. working group report given in section 3.1), increasing of the fuel’s burnup results in an increasing hardening of the neutron spectrum during irradiation of the fuel. Additional spectrum hardening due to a change in any depletion parameter (e.g. decrease in moderator density) or any depletion condition (e.g.

change in the core environment due to usage of MOX fuels) results, compared to the case of unchanged depletion conditions, in an increase of the reactivity of the spent fuel. Possible changes in depletion parameters and conditions have therefore to be covered by choosing bounding depletion parameters and conditions.

•

Specific power:

It was agreed that a change in the specific power has a negligible effect on the reactivity of the spent fuel. However, participants pointed out that the value used for the specific power during depletion calculations has a complex, but slight effect on the reactivity depending on the burnup credit model (actinide-only or actinide + FP BUC) and the cooling time.

•

Fuel (pellet) temperature:

It is conservative to use a high value for the fuel temperature as it leads to more resonant captures on U238 and hence to more production of Pu239. After the first irradiation cycle, the pellet average temperature usually decreases below 600°C.

Therefore, usage of a pellet average temperature of Tf = 600°C were often recommended in the past, but meanwhile it was also proposed (in USA in particular) to use Tf = 1000K as conservative fuel temperature.

•

Moderator temperature and density (PWR):

Participants agreed on the use of the water outlet temperature, which corresponds to the lower moderator density and consequently to the higher conversion factor.

•

Moderator temperature and density (BWR):

Due to the physics of an operating BWR the moderator temperature changes very little axially once the height were boiling begins is reached, but the moderator density significantly changes axially since the void fraction increases with increasing height.

Due to the variations in the axial power peaking in an operating BWR the void fraction can change significantly both axially and as a function of time. It is obvious, therefore, that depletion effects have to be studied as a function of moderator density or void fraction instead of moderator temperature.

Variations in moderator temperature are in fact of no interest. In an operating BWR the outlet temperature usually is about 560 K. A variation of this temperature by 5 K results in a variation of the pressure by more than 5 bar (= 5⋅105 Pa = 72.52 psi). In reality variations of the mean core pressure are less than 2 bar (under stretch-out operating conditions less than 2.5 bar). So, actual variations in the core moderator temperature are irrelevant to burnup credit criticality safety analysis of BWR spent fuel.

•

Soluble boron concentration of the moderator (PWR):

An increase in the B10 concentration of the moderator results in spectral hardening due to stronger absorption of thermal neutrons. Consensus was reached that use of a cycle-averaged boron concentration represents a bounding condition. (In many cases a cycle-averaged boron concentration of CB = 600 ppm may be bounding, but the actual bounding cycle-averaged boron concentration should be derived from the boron let-down curves of all the cycles to be considered.)

•

Presence of integral burnable absorbers in the fuel design:

The effect of integral burnable absorbers initially present in a fuel design of interest should be studied in a sensitivity analysis on the spent fuel reactivity. The presence of so called “IFBA” rods (fuel rods with boron-coated pellets) in particular can result — compared to the same but unpoisoned fuel design — in an increase of the reactivity of the irradiated fuel after burnout of the absorber.

Since integral burnable absorbers are usually used in the center region of the fuel zone only the initial presence of the absorber can impact the axial end effect (i.e. the reactivity effect due to the axial distribution of the burnup) even after burnout of the absorber.

•

Usage of removable Burnable Poison Rods (BPRs):

BPRs, inserted in guide thimbles of fuel assemblies during irradiation, are usually removed at the end of the first irradiation cycle of the fuel assemblies. As noticed by US representatives, the increase Δk in reactivity of pool storage or transport cask due to the usage of BPRs in the first cycle is less 0.01. The usage of BPRs may impact the axial end effect.

In contrast to many other countries BPRs are not used in Germany (with the exception of the first cycle, where the initial enrichments were however low so that a burnup credit, if needed at all, is of very small amount).

•

Control Rod (CR) insertion (PWR):

In France the depletion calculations for UOX fuel assemblies is carried out with CRs fully inserted throughout all the irradiation. This procedure results in a significant increase of the reactivity of the fuel at end of life and thereafter: As noticed by French representatives, reactivity increases in the range of Δk = 0.03 to Δk = 0.04 have been observed for pool storage racks or transport casks loaded with 40 GWd/t 17x17 assemblies. In the ongoing Phase II-E Burnup Credit Benchmark conducted by the Expert Group on Burnup Credit Criticality Safety under auspices of the NEA/OECD it has been found that the assumption of full CR insertion during the entire irradiation time increases the reactivity of a conceptual transport/storage cask by about

Δk = 0.035 for loadings with 30 GWd/t 17x17 fuel assemblies and by about Δk = 0.06

for loadings with 50 GWd/t 17x17 fuel assemblies. In addition it is observed that it may happen that a “bounding” axial burnup profile does not remain bounding (i.e.

results in a negative end effect, so that the uniform distribution of the average burnup then represents the bounding profile) when the CR insertion depth becomes greater than about the half of the active fuel length (see J.C. Neuber, this meeting, Figures 8 and 9 in the paper entitled “Calculation Routes to Determine Burnup Credit Loading Curves”).

In USA PWRs typically do not operate with CRs inserted. The tips of the rods may

however rest at the fuel ends, which results in an insignificant reactivity effect

(Δk < 0.002) on a burnup credit cask. Studies performed by Oak Ridge National

Laboratory (ORNL) under auspices of the U.S. NRC show that full CR insertion for

burnups around 5 GWd/t leads to an increase in cask keff values of the same order as

observed for BPRs. Therefore, since BPRs and CRs cannot be inserted in an assembly

at the same time, it follows that inclusion of BPRs in the assembly irradiation model (up to burnup values that encompass realistic operating conditions) adequately account for potential reactivity increase that may occur for spent fuel exposed to CRs during irradiation (for more details see C.V. Parks et al., this meeting, paper entitled

“U.S. regulatory recommendations for actinide-only burnup credit in transport and storage casks”).

As in USA, to avoid burnup delays, PWRs in Germany typically do not operate with CRs inserted, although the tips of the CRs may rest at the fuel ends. Since BPRs are not used in Germany it may be demonstrated by means of sensitivity studies on plant-specific bounding CR insertion histories derived from CR insertion statistics of the plant of interest that the reactivity effect due to some CR usage is typically insignificant and covered by far by assuming for instance a soluble boron concentration somewhat higher than the cycle-averaged boron concentration. Since the determination of the axial end effect has to be performed in Germany on the basis of a sufficient number of plant-specific axial burnup profiles, any distortion of a burnup profile due to CR insertion is covered by deriving an average-burnup-dependent bounding axial burnup profile from all the EOC burnup profiles available from the plant of interest.

•

Control blade insertion (BWR):

Siemens Power Generation Group (KWU) demonstrated within the framework of a reracking project for the storage pool of the Spanish BWR plant Santa Maria de Garoña in 1996 that full insertion of control blades does not lead to a change in the bounding reactivity level at the maximum reactivity point of the BWR fuel. However, the burnup value where the maximum reactivity point is situated was slightly changed, so that the curve showing keff as a function of the burnup was slightly changed. This change however is probably mainly due to the fact that it were taken into account that insertion of control blades results in a reduction of power and hence a decrease in the void fraction, which counteracts spectral hardening.

It should be noted that the insertion depth of the control blades has a significant effect on the axial power shape and hence on the resulting axial burnup profile.

•

MOX environment effects:

Participants agreed on the need to account for MOX environment effects in UOX assembly depletion calculation in PWRs.

French representatives told that in France for 900MWe reactors recycling the plutonium from La Hague reprocessing plant conservative depletion calculation of UOX assemblies is performed with MOX completely surrounding an UOX assembly.

A bounding, but more realistic approach is usually taken in Germany, since in reality an UOX assembly is not completely encircled by MOX assemblies.

4.2.4.2. Isotopic biases and correction factors

Isotopic correction factors are derived from comparisons of Calculated (C) (predicted) isotopic masses/concentrations to Experimental (E) isotopic masses/concentrations measured in Post-Irradiation Experiments (PIE). It was agreed that isotopic correction factors, given for instance in form of C/E values for each BUC nuclide, make up the basis for estimating the isotopic bias of the neutron multiplication factor of a spent fuel configuration of interest.

US representatives however emphasized the lack of unrestricted radiochemical assays that

jeopardizes the definition of reliable isotopic correction factors on BUC nuclide

concentrations.

With respect to the application of isotopic correction factors French representatives proposed to apply these factors as fixed “penalty factors” such that a conservative estimate of the spent fuel’s reactivity is a priori guaranteed.

The standpoint of German representatives was as follows: First of all, C/E values are not fixed numbers but statistics (random numbers) since experimental results are statistics. Second, the C/E values of groups of the BUC isotopes are correlated, first due to the production processes of these isotopes during irradiation and thereafter and second due to the chemical separation processes required and measurement methods applied. Therefore, a correct statistical analysis of the C/E values is required in order to be able to derive the isotopic bias with sufficient

confidence. In addition it has to be considered that significant systematic deviations in

experimental results have been observed (this was for instance the case in the ARIANE experiments, where experimental results delivered from different laboratories for one and the same sample differed by a factor of 2). So, it is necessary to try to asses the quality of the experimental data by checking the consistency of the data with respect to the physics of production, depletion and decay of the BUC isotopes. This may be very difficult in many cases or even impossible, so that the only solution is to analyze for each BUC isotope as many C/E values as available. With respect to this requirement there is still a need for more experimental results for some of the BUC isotopes.

4.2.4.3. Bias in prediction of BUC nuclide reactivity worth and correction factors

In France, the reactivity worth of each BUC fission product was measured, and the current OSMOSE oscillation experiment in MINERVE will supply the reactivity worth of each actinide. For each BUC nuclide a conservative penalty factor is or will be derived from the measurement results. This factor is combined with the penalty factor linked to fuel inventory bias. This conservative method is only used in France at present, even though reactivity worth correction factors (named as “confidence factors”) are listed in Appendix D of the June 2005 draft version of ANSI 8.27.

4.2.4.4. Sensitivity-based criticality validation techniques, representativeness of experiments, and a posteriori uncertainty

With the SCALE-5 package the Sensitivity/Uncertainty (S/U) module TSUNAMI became available. This module computes sensitivity coefficients Sk = δkeff/δα of the calculated keff to parameters α (e.g. cross-sections) within an energy structure. Sk is an M × N matrix where M is the number of systems being considered and N is the number of nuclear data parameters being involved. (Typically, N is given by the number of nuclide-specific reaction channels times the number of energy groups used.). Due to the linearity of the changes δ

keff

to the perturbations

δα the covariance matrix (also named as “uncertainty matrix”) of the changes δkeff

is given by

C_kk =S_kC_ααS^T_k

. The covariance matrix C

αα

(which obviously is an N × N matrix) contains all the information about the uncertainties in the α parameters. The resulting C

kk

matrix is an M × M matrix. Its diagonal elements give the variances

σ²_i

for each of the systems considered, and its off-diagonal elements represent the covariance

cov_ij

between the systems.

cov_ij ≠0

means that the systems i and j are correlated. The degree of correlation is expressed by the correlation coefficient

( )

_{ij i}^{2 2}_j

k

,i j cov

c

= σ ⋅σ

.

So, if one of the systems represents an application case and all the other (M – 1) systems are experiments, the correlation coefficients c

k

express the representativeness of each of the experiments with respect to the application case.

At the present the ORNL team recommends to use the criterion c

k

> 0.8 for accepting an experiment as representative of an application of interest. No theory-based rationale has been found for this criterion up to the present. However, as in mathematical statistics, a correlation coefficient of 0.8 represents a significant degree of correlation and hence a significant degree of similarity of two systems.

TSUNAMI has already been used extensively in USA (see D.E. Mueller et al, this meeting, paper entitled “Application of Sensitivity/Uncertainty Methods to Burnup Credit Validation”;

in addition the ORNL team reported that c

k

coefficients have also been used to assess the representativeness of Pu experiments for MOX powder validation). TSUNAMI is also used in Germany and will be probably used in other Central European countries.

S/U tools also exist in Russia but they are not used for BUC studies. In the UK, the code MONK also has some S/U capabilities.

In the French CRISTAL package, adjoint flux and sensitivity profiles can be calculated. A

“Characterization System” allows the location of the calculated application amongst the available experimental benchmarks (through neutron balance comparison). A new approach based on representativeness factors will soon enable the automated calculation of the a priori k

eff

uncertainty (due to nuclear data covariances) and the a posteriori uncertainty associated with the corrected k

eff

value accounting for experimental information; this method has already been implemented for MOX powders and MOX fuel pin storage at MELOX plant.

As noted by participants, the utilization of MCNP for sensitivity calculations is not obvious.

Finally, the working group emphasized the need for multigroup covariances of (n,γ) cross section of BUC nuclides, as well as covariances for fission and multiplicity of fissile isotopes.

It was therefore asked to the Working Party of Nuclear Criticality Safety (WPNCS) of the OECD/NEA to establish in the JEF 15-macrogroup structure the standard deviations/correlations for these BUC nuclide nuclear data (associated with the best evaluations involved in the recent international files).

4.2.4.5. Axial burnup databases and generation of bounding profiles

As a preamble, the issue of axial burnup profiles has to integrate the uncertainties within which a burnup is known. In general, it seems that the FA average burnup is conservatively known at ± 5 %, with ± 2 % around the mid-plan and ± 5 % around the axial ends. The burnup data are obtained either through in core measurements or using spectrometric methods after unloading.

US representatives stated that the available Yankee Atomic Corporation (YAC) axial burnup database, analyzed by Paris and Chen, has not been enlarged. Concerning bounding profiles, ORNL has revised the analysis from YAC database. New bounding profiles more realistic and meaningful are proposed (only 3 profiles are defined to span the whole burnup range).

The French database actually is a burnup profile information base. Different from US or

German databases which are usually derived with the aid of core calculations from in core

axial flux measurements, the French database consists of axial burnup profiles which were

measured by means of gamma-spectroscopy on unloaded PWR assemblies at La Hague facility. The database contains for instance 600 profiles corresponding to PWR assemblies from 1300MWe reactors, mainly in the 30-40 MWd/t average burnup range and often located under CR clusters. Evaluation of the database has shown that the measured axial profiles are very similar irrespective of their burnup and have no asymmetry.

EDF and the French BUC Group should derive bounding profiles from the La Hague burnup database before end of 2005. The French Safety Institute IRSN proposes the generation of more conservative profiles, which does not preserve the assembly average burnup: for each axial location the bounding burnup corresponds to the minimum measured value.

³⁾

In Germany, the axial end effect has to be determined from a sufficient number of

plant-specific axial burnup profiles. Up to the present more than 20000 EOC profiles from eight

different plants were analyzed; and bounding profiles were derived, for each plant separately.

The analyzed profiles are very similar irrespective of their average burnup, but they show some plant-specific components; and, in contrast to the French profiles, quite a lot of them have some asymmetry which decreases with increasing average burnup. The resulting plant-specific bounding profiles are therefore given as continuous functions of the average burnup.

The calculation procedure usually used in Germany for deriving axial burnup profiles from in-core flux measurements has been validated several times against samples of profiles measured by means of gamma spectroscopy. These samples include profiles from fuel assemblies exposed to partial CR insertion as well as profiles from fuel designs with integral burnable absorbers (Gd in particular).

The spent fuel rods provided by the German NPP Neckarwestheim 2 for one of the REBUS experiments were chosen since the calculated axial burnup profile of the fuel assembly from which the rods were taken showed no asymmetry. This was confirmed by rod gamma scans performed by SCK•CEN: Calculated and measured profiles were in excellent agreement.

Finally, German participants mentioned that about 2000 axial profiles from the NPPs Neckarwestheim 1 and 2 are available at OECD NEA. In addition to these profiles 850 profiles were provided by NPP Neckarwestheim 2 for the Phase II-C Burnup Credit Benchmark conducted by the Expert Group on Burnup Credit Criticality Safety under auspices of the OECD NEA.

In other Central European countries axial burnup profiles are derived from calculations.

Studies performed in Hungary and Czech Republic showed very small positive or even negative end effects for VVER fuel.

Finally, the working group recommended the use of bounding burnup profiles in criticality-safety calculations, if at all possible.

3) Comment (J.C. Neuber): The end effect, usually first negative for low average burnup values, increases - after having reached its minimum at a certain average burnup - with increasing average burnup. So, if the

3) Comment (J.C. Neuber): The end effect, usually first negative for low average burnup values, increases - after having reached its minimum at a certain average burnup - with increasing average burnup. So, if the

Dans le document Advances in Applications of Burnup Credit to Enhance Spent Fuel Transportation, Storage, Reprocessing and Disposition | IAEA (Page 50-56)