Delayed neutron group parameter influence on reactivity estimation
Benoît. Geslot and Christian Jammes
DEN/CAD/DER - CEA – Centre de Cadarache, 13108 Saint Paul-Lez-Durance, France, christian.jammes@cea.fr
INTRODUCTION
Reactivity is undoubtedly a key-parameter for reactor
safety. Most of the measurement methods to assess it are
based on the analysis of a neutron flux transient. All those
methods depend on a reliable evaluation of the delayed
neutron group parameters. Recently, 8-group parameters
have been proposed instead of the standard 6-group ones
[1-3]. We first compare various sets of delayed neutron
parameters obtained from precursor data fits. We then
appraise the influence of those sets on the reactivity
uncertainty and biases by means of flux transient
simulations.
GENERATION OF DELAYED NEUTRON DATA
SETS
Using the JEFF-3.1 nuclear data library, we
simulated U235 neutron source decay curves for three
incident neutron energies: thermal, fast and fusion. The
delayed neutrons parameters, namely the relative
abundances and the decay constants, were derived from
fitting simulated decays. Pseudo-experimental
uncertainties were obtained by adding a Poisson noise.
Fitting models with different numbers of groups and
independent parameters were applied (TABLE I). Models
with the lowest number of degrees of freedom provided
the best root mean squared errors (RMSE) and the largest
uncertainties. Conversely, models with fixed decay
constants gave smaller uncertainties and worse quality of
fit.
INFLUENCE OF THE FITTING MODEL
A neutron flux transient corresponding to a reactivity
change of -1 dollar was simulated using the precursor data
set. Reactivity estimates shown in TABLE I were
obtained by a transient analysis method [4] using the
delayed-neutron parameter obtained as aforementioned.
It is important to note that the proposed uncertainties are
only the ones without correlations given that they are
always larger than those with correlations and the
correlation matrix is usually unknown. It is noteworthy
significant biases happen with low RMSE. As a
consequence, the RMSE value is likely not the most
appropriate indicator to validate the fitting model. It is
clearly more relevant to in-depth investigate the impact in
terms of uncertainty. This way, an 8-group model with
fixed decay constants exhibits very satisfactory results.
TABLE I. Reactivity estimation using thermal nuclear
parameter sets.
Num. of Num. of Bias (%) Uncert.
RMSE
groups
param.
(%)
6
12
0.40
9.2
2.05E-2
6
10
0.34
3.6
4.54E-2
6
6
0.80
0.8
2.30E-1
7
12
5E-4
10.7
1.13E-2
7
7
0.50
1.4
1.70E-1
8
14
-0.04
31
2.70E-3
8
8
-0.16
1.3
8.70E-2
INFLUENCE OF THE NEUTRON SPECTRUM
In order to investigate the effect of a biased nuclear
data set on reactivity estimation, we studied the influence
of the incident neutrons spectrum. An inconsistency
between the incident neutron spectrum of the delayed
neutron parameter set and the spectrum of the neutron
flux transient must lead to a biased reactivity estimation.
That way, a bias of about 10% is obtained when analyzing
a thermal transient with a fast data set and reciprocally.
We also showed the uncertainties depend on the data sets
only and not on the transient. The highest uncertainty of
about 9% is obtained with the fusion data set. For a
thermal data set, it is even greater than 5%.
We then used the previously generated delayed
neutron group parameter sets to analyze an experimental
transient measured during the RACE-T program [5, 6]. A
non-linear fitting method [4] was employed to estimate
the reactivity in order to be capable of evaluating the
quality of fit using residuals and RMSE. Several
parameter sets for 3 spectra were used. The fit RMSE
values did not help discriminate between biased reactivity
estimates obtained with the fast and fusion sets from the
unbiased one obtained with the thermal sets. Biases were
larger than 10% and 8% in case of a fusion and fast
spectrum, respectively. In addition, very few statistical
tests applied on residuals could reject wrong reactivity
estimates: only two tests could do it in case of the fusion
parameter sets.
CONCLUSION
The result of this work is twofold. First, we showed
delayed neutron models with few parameters yield
smaller uncertainty but greater bias when using a transient
analysis method for assessing reactivity. The 8-group
model with 8 fitted parameters appeared as the most
satisfactory and is highly recommended. Second, we
investigated the influence of a biased delayed neutron
data set on reactivity estimation. As an example, we
showed a reactivity bias due to the use of a delayed
neutron parameter set not adapted to the neutron flux
spectrum is difficult to identify a posteriori. When using a
fitting-based method, only two statistical tests (T-test and
the randomness test) for detecting correlations in residuals
allowed us to identify biases higher than 8%. Lower
biases were unrevealed. The question of how to better
detect biases of that sort is thus still open.
REFERENCES
1.
2.
3.
4.
5.
6.
D. SPRIGGS, J. M. CAMPBELL, Prog. Nucl.
Energy, 41, 145 (2002).
J. LOAIZA, Nucl. Sci. Eng, 134, 22 (2000).
D. SPRIGGS et al., Prog. Nucl. En 41, 223 (2002)
B. GESLOT, PhD Thesis, Université Louis Pasteur,
Strasbourg, France (2006)
G. IMEL et al., “ADS Reactivity Measurements from
MUSE to TRADE (and Where Do We Go From
Here?) ,” in Int. Conf. PHYSOR 2006, Vancouver,
Canada , Sep. 11-14 (2006).
C. JAMMES et al., “Absolute Reactivity Calibration
of Accelerator-Driven Systems after RACE-T
Experiments,” in Int. Conf. PHYSOR 2006,
Vancouver, Canada, Sep. 11-14 (2006).