Progress
Pergamon www.elsevier.com/locate/pnucene
SUMMARY
in Nuclear Energy, Vol. Q 2002 Elsevier
41. No. Science
I-4, pp. 285-301. 2002 Ltd. All rights reserved Printed in Grat Britain
0149.1970/02/%
see front
matter
PII: SO149-1970(02)00015-X
ON INTERNATIONAL
EXPERIMENTS
FOR EFFECTIVE
NEUTRON
FRACTION
BENCHMARK DELAYED (&.n,
S. OKAJIMA”, T. SAKURAI”, J. F. LEBRAT”‘, V. Z. AVERLANT” and M. MARTIN12’ 1) Japan Atomic Energy Research Institute Tokai-mura, Naka-gun, Ibaraki-ken 3 19-1195, Japan 2) Commissariat a 1’Energie Atomique, CE de Cadarache 13 108 Saint-Paul-lez-Durance Cedex, France
ABSTRACT To improve the accuracy of prediction of &R, an international program of benchmark This program consisted of two parts; the experiments was planned. BERENICE-MASURCA and the FCA XIX series of experiments. The former was carried out in the fast critical facility MASURCA of CEA, FRANCE between 1993 and 1994. The latter one was carried out in the FCA, JAERI between 1995 and 1998. In these benchmark experiments, various experimental techniques were applied to measure the &,r. Through the synthesis of the different results, a recommended value for each core was provided and the accuracy of the measurements was evaluated to be better than 3%. The calculations showed good agreement of the recommended &values within 3% for JENDL-3.2 and ENDF/B-VI delayed neutron data sets. 0 2002 Elsevier Science Ltd. All rights reserved. KEYWORDS delayed neutrons, delayed neutron fraction, benchmark experiment, measuring method, fast critical facility, JENDL-3.2, ENDF/B-VI, JEF-2.2, computer calculations, criticality, central fission rate ratio
1. INTRODUCTION The effective delayed neutron fraction peg, which allows the conversion between calculated and measured reactivity values, plays an important role in the theoretical interpretation of reactivity measurements. In
285
7.86
S. Okajima et al.
the systematic analysis for the & experiments which were previously performed in ten different core configurations, the ratio between calculation and experiment, C/E values, ranged from 0.93 to 1.04 [‘I. From this result the current prediction accuracy of & was estimated to be about *5%(10). This prediction accuracy strongly affects the uncertainty for the reactivity measurement either in a power reactor or in a critical facility. To improve the accuracy of prediction of De/, a program of benchmark experiments, carried out as an international collaboration, was planned [2, 3r. It comprised experiments at the MASURCA facility of Accuracy was ensured by using several CEA-Cadamche and at the FCA facility of JAERI-Tokai. different techniques for the measurements and by different groups of experts carrying out the measurements. In these experiments five different core configurations were selected taking into consideration the systematic change of the nuclide contribution from 235U, 23RU and 239Pu to the &y. The &r measurement was carried out by each Several countries participated in the experiments. participant with their own measurement technique, and the measured results were compared with each These experiments were conducted under the NEA/NSC Working Party on International other. Evaluation Cooperation (WPEC), Subgroup 6 on Delayed Neutron Data Validation.
2. EXPERIMENT 2.1 Measurement techniaue To ensure accuracy, several different measurement techniques were used and different groups of experts carried out the measurements with their own e uipment and techniques. The details of the measurement % procedures are described in references [4,5,6,7,STI. Here the relationship used to derive the &rvalues from the measured and/or calculated parameters for each technique is shown as follows:
(1)
(2)
(3)
(4)
Covariance to Mean &
Bennett
=i/[l+(l-G)/Z]
?
(5)
Summary
on international
benchmark
287
experiments
The symbols appearing in these equations are described in references 14,5’6’” ” 9’. 2.2 International &benchmark experiment at MASURCA I” lo1 There were two different core configurations: R2(U-core) and Zona2(MOX-core). The main characteristics of these cores are shown in Table 1 t2’ lo’ “I. The atomic number densities and the 2-dimensional RZ models of these cores are summarized in Appendix A. The purpose of the R2 core was to calibrate and to optimize experimental techniques. The other was to obtain the different contribution to p,,,for 238U and 239Pu. The core was surrounded by a SO-50 U02-Na mixture blanket. The per/ measurements were carried out between April, 1993 and March, 1994 by the following groups: CEA/Cadarache (France), IPPE/Obninsk (Russia), JAERI (Japan) and LANL (USA). Prior to the &measurement, the CEA, IPPE and JAERI teams measured fission rates of 235U, 238U and 239Pu, and corresponding rate ratios in the core center using their own absolute fission chambers. The results were compared with each other to reduce the uncertainty of the fission integral E for &f evaluation, and were found to be in good agreement within the experimental error of 2% or less. Consequently, the uncertainty of the fission integral was estimated to be about 2%. The experimental results for pef obtained by each participant are summarized in Table 2. Each value was obtained within an experimental error of *3%. Some results in the table are different from those in references [2] and [IO], since they were carefully checked and were corrected.
Table 1
Core characteristics of MASURCA cores
Item Geometry Core: R x H (cm) Criticality (R-Z-model) Keff Central Fission Rate U-238/U-235 Pu-239/u-235
Table 2 Organization _- .
JAERI LANL
R2
Zona2
48.40x60.96
49.83x60.96
0.99884*0.00012
0.99945+0.00006
0.0413*1.5% ___
0.0418*1.5% 1.04*1.5%
Measured Results of j&r in MASURCA Cores , I__
(Cfl (Nelson #)
697*20 ___
___
I
I
2.3 International &,rbenchmark experiment at FCA 13’4’5’6’” s’9’“I Three different core configurations were selected so that these cores could be complementary to those studied previously in the MASURCA facility: XIX-l (U-core), XIX-2 (Pu/NU core) and XIX-3 (Pu core). Figure 1 shows the nuclide contribution to j&f for each core. The systematic change of nuclide
S. Okajima et al.
288
contribution was found. The nuclide contribution to & in the XIX-2 core is similar to that in the MASURCA Zona2 core. The purpose of the XIX-I core is to compare the experimental techniques among participating parties through the j&r measurement for the standard material, 23sU, since the contribution of 235U in this core is about 95%. The purpose of the XIX-3 core is to evaluate the &r for 239Pu. Thus it is possible to separate the delayed neutron contributions of the three principal isotopes. The main characteristics shown
in Table
number
densities
RZ
models
of
of these cores are
3 t3, ‘*I.
The atomic
these
cores
are
also
summarized
in Appendix A.
The core is
surrounded
by two blanket
regions:
inner blanket containing
region a
I *
and the 2dimensional
PU core
*
an
of 30cm thickness
significant
depleted uranium-oxide
u core
amount
of
and sodium, and
an outer blanket region of 15cm thickness containing
only depleted uranium
The contribution
metal.
0
of these blanket regions
FCA XIX-I
FCA XIX-2
YiR_ Yz?lKEA
FCA XIX-3
Core name to &fwas less than 10%. to j&p The experiments were carried out between Fig. 1 Nuclide contribution January, 1996 and April, 1998. The following are the participating groups: CEA/Cadarache (France), IPPE/Obninsk (Russia), JAERI (Japan), KAERI (Korea), LANL (USA) and Nagoya Univ. (Japan). To estimate the uncertainty of the central fission rates, the CEA and JAERI teams measured fission rates of 235U, 238Uand 239Pu, and corresponding rate ratios using their own absolute fission chambers in the XIX-l and XIX-3 cores. The results were compared with each other to reduce the uncertainty of the fission integral for &~~evaluation, and were found to be in good agreement within the experimental error of 2% or less. The experimental results for Pen obtained by each participant are shown in Table 4. The &was measured by each participant within the experimental error of *3%.
Table 3 Item Geometry Core: R x H (cm) Criticality (R-Z model) Keff Central Fission Rate Ratio U-238/U-235 Pu-239/u-235
Core characteristics of FCA cores XIX-1
XIX-2
XIX-3
33.0x50.8
35.7x61.0
35.1x61.0
1.0075~0.0006
1.0032*0.0003
1.003 1*0.0004
0.0395+1.3% ___
0.0408+1.4% 1.056*1.3%
[email protected]% 1.083*1.2%
Summary on international benchmark experiments
Table 4
Measured Results of &in
289
FCA Cores cm
2.4 Recommendation of measured &values ‘13] The results measured by different teams with their own techniques were synthesized to provide a recommended value for each core. For this purpose, the correlation between the measurement techniques was taken into account since several parameters are commonly used as shown in the previous section. The covariance matix C,, is defined as the following: c, =SCp
.s’,
(7)
where S is the sensitivity
matrix, Sris the transposed matrix of S and C,, is the covariance matrix of
parameters used in the /?8~measurements.
The fi, j)-th element si j in the sensitivity matrix S is obtained
as follows:
(8) where pfl’ means the &
values obtained by the measurement
technique
In this sensitivity
measured/calculated parameter used to derive the /?=f value. equations for the &Rwere approximated as follows: Rossi-a
(9)
Nelson # p,
)
-p,l[(&$-I%s]
(10)
Covariance to Mean P,
_tl[U-
P$~/~]
?
i, and p’
(11)
means the j -th
calculation
some of
290
S. Okajima et al.
Bennett P,
=/[(I-
Table 5 shows the correlation between parameters relevant (l), and the neutron
(12)
,
&)/%I
correlation matrix for each core. In this table a negative value was found in the the Cf and Nelson # techniques in the XIX-1 core. This value, originated from the to the Cf source: the pseudo reactivity worth which appeared in the numerator of Eq. intensity which appeared in the denominator of Eq. (10).
Table 5
Correlation matrix of &measurement
MASURCA R2 Core
~
MASURCA Zona2 Core Noise Cf (CEA) Cf (JAERJ)
1.00 0.33 0.00
0.33 1.00 0.23
XIX-l Core
FCA XIX-2 Core Meas. technique Cf Bennett
Cf 1.00 0.35
Bennett 0.35 1.oo
0.00 0.23 1.00
Summary
The mean value (s,>
on international
benchmark
experiments
291
was finally obtained by the following relation:
(13) where the i-th element in the column vector b denotes thePfl’ equal to unity.
x* = r
The statistical parameter c,-’
and u is the row vector with all elements
x2 was calculated by
rrr
(14)
where the i-th element of the row vector r denotes the residual between pqc/j and (p&). and external uncertainties
q,,
of (p,>
The internal
were calculated following the error propagation law:
=JW,
(15) (16)
where f means the number of degrees of freedom.
The results for (P,),
S,,, and g,
are shown in
Table 6. When we compare the internal and external uncertainties, the former uncertainties are almost same as the latter ones except for the XIX-l cores. In this core the internal uncertainty is smaller than external one. In this case we decided to adopt the external uncertainty instead of the internal one since number of degrees of freedom f is larger than the X*value. Consequently the recommended results be summarized as follows; h4ASURCA R2 MASURCA Zona2 FCA XIX- 1 FCA XIX-2 FCA XIX-3
721 +/-I 1 pcm, 349 +I- 6 pcm, 742 H-24 pcm, 364 +I- 9 pcm, 25 1 +/- 4 pcm.
From these results it was found that the achieved accuracy of the measurements accuracy of 3%.
Table 6
the the the can
Recommended
was better than the target
Results of a, in MASURCA and FCA Cores
292
S. Okajima
et al.
3. ANALYSIS l”, I3314’ The core calculation was made by using a 70 group cross section set, JFS-3-J3.2, processed from the JENDL-3.2 library. The effective cross sections of the core and the blanket regions were calculated by the conventional collision probability code. The criticality and the forward and adjoint fluxes were calculated by a two-dimensional R-Z diffusion code using the homogenized atomic number densities and the following effects were considered; the heterogeneous cell effect and the transport effect. The comparison between calculation and measurement is shown in Table 7. Criticality For the MASURCA cores the calculation overestimates the criticality by 0.9%. For the FCA cores the calculation gives good agreement with the experiment in the XIX-l core, 0.4% underestimation for the XIX-2 core and 0.9% overestimation for the XIX-3 core. Central Fission Rate Ratio The calculation of the central fission rate ratios showed good agreement with the measurement within 1.5% except for the ratios of 238Uto 235Uin the MASURCA cores. Calculation overestimates these ratios by 3%. This overestimation could result in the larger C/E values for the &. Effective The /&Rvalue was calculated by the following equation;
In this calculation, the delayed neutron data from the following libraries were used: JENDL-3.2 and ENDF/B-VI. The comparison of the calculated fl,f values between delayed neutron data sets is also shown in Table 7. Calculations have also been made at CEA Cadarache using the ERALIBl data set to obtain the fluxes and The ERALIBl reaction rates combined with the delayed neutron yield data in JEF-2.2 and ENDF/B-VI. data set has been derived from the JEF-2.2 library but has been adjusted on the basis of a wide range of integral measurements. The effect of the use of a different data set to calculate the reaction rates can be seen by comparing the two sets of results which use the ENDF/B-VI yield values, the differences in & values being up to about 1%. It can be seen that the agreement of the &f values is generally within 3% for the three delayed neutron yield data sets. The ENDF/B-VI data set gives larger &fvalues than the JENDL-3.2 data set except for the Zona2 and XIX-2 cores. The larger values of the delayed neutron emission per fission event vd, for 235U and 239P,uin the ENDF/B-VI data set are primarily responsible for this tendency. On the other hand, since in the Zona2 and XIX-2 cores, the larger vd, values of 238U in JENDL-3.2 give the larger &values the contribution of 238U to the &fis 40% in these cores. The JEF-2.2 data set gives larger values than JENDL-3.2 in all cores. The 238U vd data in JEF-2.2 are the same as in JENDL-3.2 but the vd data for 23sU and ‘39Pu are larger.
Summary on infernafional benchmark experiments
Table 7
t
Ratios between Calculated+ and Experimental
The calculation was performed by a the homogenized atomic number heterogeneous cell effect, the XYZ/RZ tt The Fl/JEF-2.2 and El/B-VI values set and combined with the JEF-2.2 values.
293
Results
two-dimensional R-Z diffusion code using densities with corrections for the effect and the transport effect. were calculated using the ERALIBl data and ENDF/B-VI delayed neutron yield
4. SUMMARY To improve the accuracy of prediction of pen; international benchmark experiments have been carried out. The primary intent of these benchmark experiments was to obtain the &-values with an accuracy better than 3% using a wide variety of experimental techniques. The different results have been synthesized to provide a recommended value for each core. It is possible to separate the delayed neutron contributions of the three principle isotopes. Finally the achieved accuracy of the measurements was better than the target accuracy of 3%. On the basis of these results, the reliability of delayed neutron data can be verified using current calculation methods. The calculated &g values were compared between JENDL-3.2 and ENDF/B-VI delayed neutron data sets. The agreement of the &values is generally within 3% for both data sets. The calculated results reflect the tendency of vd, values in both data sets.
ACKNOWLEDGEMENT The authors wish to thank Dr. J. L. Rowlands and Dr. A. D’Angelo for their valuable comments on this paper.
REFERENCES
113 D’Angelo A. and Filip A. (1993), The Effective Beta Sensitivity to the Incident neutron energy Dependence of the Absolute Delayed Neutron Yeilds, Nucl. Sci. and Eng., 114,332-341. PI Bertrand P., Pierre J., Martini M., Belov S., Doulin V., Kotchetkov A., Matveenko I., Mikhailov G., Nemoto T., Sakurai T. and Spriggs G. (1996), BERENICE - Inter Laboratory Comparison of &r Proc. of Int. Conf on the Physics of Reactors PHYSOR Measurement Techniques at MASURCA, 96, E-190 - E-199, Mito. [31 Sakurai T., Okajima S., Sodeyama H., Osugi T., Martini M., Chaussonnet P., Philibert H., Matveenko I. P., Belov S. P., Doulin V. A., Kochetkov A., Mikhailov G. M., Song H., Kim Y., Spriggs G. D., Yamane Y., Takemoto Y. and hnai T. (1998), Benchmark Experiments of Effective Delayed Neutron
294
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Okajima et al.
Fraction &in JAERI-FCA, Proc. of Int. Conf: the Physics of Nuclear Science and Technology, ~01.1, 182-189, Long Island. [4] Chaussonet P., Martini M., Philibert H., Zammit V. (1999), International &Benchmark experiments in FCA - CEA Results, Prog. Nucl. Energy, 35, 157-162. [5] Doulin V. A., Mikhailov G. M., Kotchetkov A. L., Matveenko I. P., Belov S. P. (1999), The &r Measurement Results on FCA cores, ibid., 35, 163-168. [6] Spriggs G. D., Sakurai T., Okajima S. (1999), Rossi-a and &r Measurements in a Fast Critical Assembly, ibid., 35, 169-181. [7] Yamane Y., Takemoto Y., Imai T., Okajima S., Sakurai T. (1999), Effective Delayed Neutron Fraction Measurements in FCA XIX cores by Using Modified Bennett Method, ibid., 35, 183- 194. [8] Sakurai T., Okajima S., Song H., Kim Y. (1999), Measurement of Effective Delayed Neutron Fraction /lenby 252CfSource Method for Benchmark Experiments of p&at FCA, ibid., 35, 195-202. [9] Sakurai T., Sodeyama H., Okajima S. (1999), Measurement of Effective Delayed Neutron Fraction /&-by Covariance-to Mean Method for Benchmark Experiments of /&rat FCA, ibid., 35,203-208 [lo] Averlant, V. Z. (1998), Validation Integrale des Estimations du Parametre Beta Effectif pour les Reacteurs MOX et Incenerateurs, PhD Thesis, Universit& de Marseille I - U.F.R. de Sciences Physiques, 19 Nov. [ 1l] Smith P., Rimpault G., Soule R., Toupin M.F. (1995), Analysis of the Fundamental Parameters of the BERENICE R2 and ZONA2 Clean Cores, CEA/Cadarache/DER/SPRCnEPh Technical Note, SPRULEPh 95-204. [12] Sakurai T., Okajima S., Andoh M., Osugi T. (1999), Experimental Cores for Benchmark Experiments of Effective Delayed Neutron Fraction &flat FCA, Prog. Nucl. Energy, 35, 13 1- 156. [ 131 Sakurai T. and Okajima S. (1999), Analysis of Benchmark Experiments of Effective Delayed Neutron Fraction /&rat FCA, ibid., 35,209-225. [ 141 Okajima S., Zuhair, Sakurai T., Song H. (1998), Evaluation of Delayed Neutron Data using FCA & Benchmark Experiment, J. Nucl. Sci. and Technol., 35,963-965. [ 151 E. Fort, (1999), Private Communication, 3 May.
Summary
on international
benchmark
experiments
295
For the benchmark calculation, the homogenized atomic number densities of MASURCA and FCA cores are given in Table A-l and A-2 and the 2-dimensional RZ models are given in Fig. A-l, A-2 and A-3. Table A-l
Homogenized Atomic Number Densities of MASURCA cores (unit: IO” atoms/cm
Si C
___ 2.3278E-5
t read as 2.5147~10-~
I )
___ 2.9131E-5
I 1
l.l634E-4 3.7109E-5
296
S. Okajima et al.
Table A-l (continue):
Homogenized Atomic Number Densities of MASURCA cores
t read as 3.9297x10”
Summary on international benchmark experiments
Table A-2
Homogenized Atomic Number Densities of FCA XIX Cores
t read as 2.2606~10”
Table A-2 (continue)
Homogenized Atomic Number Densities of FCA XIX Cores
t read as 1.8606~10-~
291
298
S. Okajima
(4
et al.
MA.WIRCA
z
R2
219.9
Ax. Shielding 164.16
Ax. Blanket 143.04’
Core R2
Rad.
Rad.
Blanket
Shielding
82.08’
Ax. Blanket 60.96
Ax. Shielding
0.00
-R 48.40
86.03
(cm)
134.93
* This geometry includes the diffuser with a thickness of 8 mm at the top and bottom of the axial blanket
Fig. A-l
RZ model for MASURCA R2 cow
Summary
(cm)
on international
benchmark
experiments
299
MASURCA ZONAZ
z A
219.9
Ax. Shielding 164.16
Ax. Blanket 143.04’
zo-NA2 Core ZONA2 PIT POA
Rad.
Rad.
Blanket
Shielding
I
82.08’
Ax. Blanket
j
60.96
Ax. Shielding
i
+
0.00 47.80
49.83
86.03
(cm)
134.93
* This geometry includes the diffuser with a thickness of 8 mm at the top and bottom of the axial blanket
Fig. A-2
RZ model for MASURCA ZONAZ core
S. Okajima
300
et al
FCA XLX Cores
7
(cm) 66.04 60.96
Sofl Blanket (SB) Soft Blanket Hc
I
t
t SCR
(SB) DUB
I
Core
Core
0.00
-R Ri
Ro
Rc
68.30
XIX-l core : Ri=14.99cm, Ro=16.23cm, Rc=32.96cm, Hc=25.40cm XlX-2 core : Ri=22.59cm, Ro=24.25cm, Rc=35.65cm, Hc=30.48cm XIX-3 core : Ri=22.59cm, Ro=24.25cm, Rc=35.10cm, Hc=30.48cm
Fig. A-3
RZ model for FCA cores
86.36
(cm)
Summary
on international
benchmark
experiments
301
APPENDIX B For the benchmark calculation, the following effects for the FCA cores were evaluated: the cell heterogeneity effect, the transport effect and the geometrical effect between two-dimensional R-Z and three-dimensional X-Y-Z models. These effects are summarized in Table B ‘13,14’. It was found that the cell heterogeneity effect for the FCA XIX-2 core is larger than the others since the core cell is composed of Pu and NU fuel plates. The other effects are not so significant.
Table B
Correction factors for benchmark calculations of FCA cores
Hetero/Homo
Hetero/Homo Transport/Diffusion
