ISSN 10637788, Physics of Atomic Nuclei, 2011, Vol. 74, No. 14, pp. 1908–1911. © Pleiades Publishing, Ltd., 2011.
Original Russian Text © M.N. Zizin, S.N. Zizina, L.V. Kryakvin, V.A. Pitilimov, V.A. Tereshonok, 2010, published in Voprosy Atomnoi Nauki i Tekhniki. Seriya: Fizika Yadernykh
Reaktorov, 2010, No. 3, pp. 43–47.
1908
The choice of kinetic parameters and the method
for their estimation substantially influence the reactiv
ity in processing signals from ionization chambers
obtained during transient processes; this influence is
especially pronounced for the scram system effective
ness. Here, the kinetic parameters are the relative
yields
α
i
of delayed neutrons and the constants
λ
i
of
decay of delayed neutron precursors.
This study analyzes the influence of kinetic param
eters on the value of scram system effectiveness
obtained using the inverse solution of the kinetic equa
tion with the use of ionization chamber currents
recorded in the course of measurement of the scram
system effectiveness. The measurements were per
formed for the first fuel load of the third unit of the
Kalinin nuclear power plant in the case of operation at
a minimum controllable power level at the stage of
physical startup [1].
The reduction of the scram system effectiveness on
February 12, 2005, at 9 a.m. (
t
= 362.6 s) when the rod
13–36 (ninth group) was stuck and then sent in 20 s
later was considered. The corrections to the back
ground current were 0.190
×
10
–10
, 0.180
×
10
–10
, and
0.105
×
10
–10
for ionization chamber nos. 3, 14, and
25, respectively. The scram system effectiveness was
calculated using a program written in MathCad. This
program implements the integral form of the inverse
solution of the kinetic equation according to the algo
rithm described in [2]. The calculations were per
formed with and without the background current
taken into account.
The results of calculation were verified using a pro
gram written in Fortran; this program implements the
same integral algorithm. The results of calculations
performed by S.V. Tsyganov also completely agreed
with our results. The differential algorithm was also
implemented; the calculations using this algorithm for
smooth curves yield the same result under the condi
tion that a finer time step is used. The differential algo
rithm cannot be used for processing experimental
data. Thus, the correctness of implementation of
numerical methods in the programs was proved by the
complete agreement of the results obtained using sev
eral programs for the same initial data.
One of the aspects of the problem is taking into
account the isotopic composition in calculation of the
parameters of delayed neutrons. The sets of kinetic
parameters for fissionable isotopes differ for different
nuclides. This causes difficulties in formation of the
set of kinetic parameters for the real fuel, in which fis
sion takes place simultaneously in several nuclides.
For thermal reactors, a heterogeneous multigroup
cell calculation is usually performed; the homoge
neous fewgroup cross sections are prepared on the
basis of this calculation. At this stage, the kinetic
parameters should also be prepared; these parameters
are then used in space–time calculations. The same
parameters can be used in processing ionization
Calculation of Reactivities Using Ionization Chamber Currents
with Different Sets of Kinetic Parameters for Reduced Scram System
Efficiency in the VVER1000 of the Third Unit of the Kalinin Nuclear
Power Plant at the Stage of Physical StartUp
M. N. Zizin
a
, S. N. Zizina
b
, L. V. Kryakvin
b
, V. A. Pitilimov
b
, and V. A. Tereshonok
b
a
Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia
b
JSC VNIIAES, ul. Ferganskaya 25, Moscow, 109507 Russia
email: [email protected].kiae.ru
Received February 18, 2010
Abstract
—The effectiveness of the VVER1000 reactor scram system is analyzed using ionization chamber
currents with different sets of kinetic parameters with allowance for the isotopic composition in the calcula
tion of these parameters. The most “correct, aesthetically acceptable” results are obtained using the eight
group constants of the ROSFOND (BNABRF) library. The difference between the maximum and minimum
values of the scram system effectiveness calculated with different sets of kinetic parameters slightly exceeds
2
β
. The problems of introducing corrections due to spatial effects are not considered in this study.
Keywords
: VVER1000, scram system effectiveness, BNAB78, BNAB90, ENDF/B6, ENDF/BVII.0,
TVSM, BNABRF.
DOI:
10.1134/S1063778811140110
PHYSICS OF ATOMIC NUCLEI
Vol. 74
No. 14
2011
CALCULATION OF REACTIVITIES USING IONIZATION CHAMBER CURRENTS 1909
chamber readings under the condition that these
parameters are averaged over the physical domains of
the reactor.
The practice of application of the parameters of
delayed neutrons for separate nuclides still exists in
processing experimental data on reactivity. In this
case, it is desirable to use the procedure of averaging
these parameters with preliminarily estimated weights.
In [3], it was recommended to use the following for
mulas for averaging over the nuclides:
α
i
=
and
λ
i
= , where
i
is the number of the
group of delayed neutrons,
A
is the nuclide index, and
ε
A
is the weight taking into account the contribution of
fission on nuclide
A
.
It should be noted that the problems of corrections
to spatial effects and the methods for estimation of
weights for the averaging of parameters are not consid
ered here.
εα
()
AA
i
A
αεαλ
()
AA A
iii
The following sets of kinetic parameters covering
nuclides (Table 1) were used in the inverse solution of
the kinetic equation: BNAB78 (Kipin [4]), BNAB90,
ENDF/B6, ENDF/BVII.0, the parameters of
TVSM (variant of 2008), and BNABRF.
The parameters for BNAB78, BNAB90, and
ENDF/B6 were taken from dissertation [5], and the
eightgroup parameters BNABRF came from the
library JEFF3.1 (estimation by V.M. Piksaikin) and
were included in the Russian library of files of evalu
ated neutron data ROSFOND (http://www.ippe.ru/
podr/abbn/libr/rosfond.php). These data were pro
vided by S.V. Zabrodskaya. The data from ENDF/B
VII.0 were prepared by V.V. Sinitsa. The parameters of
TVSM [6] (version of 2008) were provided by Tsyga
nov.
The kinetic parameters were used in the following
combinations:
(i) U235 only for BNAB78 (Kipin);
8
350 370
ρ
, $
t
, s
9
390 410 430 450 470 490
7
6
5
4
3
2
1
0
Ionization chamber no. 25
Ionization
Ionization
chamber no. 3
chamber no. 14
Fig. 1.
Reactivity
ρ
, $ upon dropping rods of the scram sys
tem. Kinetic parameters BNAB78 (Kipin) only for U235
(with allowance for background current).
8
350 370
ρ
, $
t
, s
9
390 410 430 450 470 490
7
6
5
4
3
2
1
0
Ionization chamber no. 25
Ionization
Ionization
chamber no. 3
chamber no. 14
Fig. 2.
Reactivity
ρ
, $ upon dropping rods of the scram sys
tem. Kinetic parameters BNAB78 (Kipin) with
ε
U235
=
0.85 and
ε
U238
= 0.15 (with allowance for background
current).
350 370
ρ
, $
t
, s
8
390 410 430 450 470 490
7
6
5
4
3
2
1
0
Ionization chamber no. 25
Ionization
Ionization
chamber no. 3
chamber no. 14
Fig. 3.
Reactivity
ρ
, $ upon dropping rods of the scram sys
tem. Kinetic parameters BNAB90 with
ε
U235
= 0.85 and
ε
U238
= 0.15 (with allowance for background current).
8
350 370
ρ
, $
t
, s
9
390 410 430 450 470 490
7
6
5
4
3
2
1
0
Ionization chamber no. 25
Ionization
Ionization
chamber no. 3
chamber no. 14
Fig. 4.
Reactivity
ρ
, $ upon dropping rods of the scram sys
tem. Kinetic parameters BNABRF with
ε
U235
= 0.85
and
ε
U238
= 0.15 (with allowance for background cur
rent).
1910
PHYSICS OF ATOMIC NUCLEI
Vol. 74
No. 14
2011
ZIZIN et al.
Ta bl e 1 .
Kinetic parameters
i
Relative yield of
i
th
group of delayed neutrons
α
i
Decay constant of precursors of
i
th
group of delayed neutrons
λ
i
U235 U238
Averages
ε
U235
= 0.85,
ε
U238
= 0.15
U235 U238
Averages
ε
U235
= 0.85,
ε
U238
= 0.15
BNAB78 (Kipin)
1 0.033 0.013 0.03000 0.0124 0.0132 0.01251376
2 0.219 0.137 0.20670 0.0305 0.0321 0.03072975
3 0.196 0.162 0.19090 0.111 0.139 0.11445846
4 0.395 0.388 0.39395 0.301 0.358 0.30836454
5 0.115 0.225 0.13150 1.14 1.41 1.17371297
6 0.042 0.075 0.04695 3.01 4.02 3.12787867
BNAB90
1 0.0350 0.0139 0.031835 0.0133 0.0136 0.01334415
2 0.1807 0.1128 0.170515 0.0327 0.0313 0.03248207
3 0.1725 0.1310 0.166275 0.1208 0.1233 0.12116851
4 0.3868 0.3851 0.386545 0.3028 0.3237 0.30576125
5 0.1586 0.2539 0.172895 0.8495 0.9059 0.85750812
6 0.0664 0.1031 0.071905 2.853 3.0487 2.88073754
ENDF/B6
1 0.0350 0.0139 0.031835 0.0133 0.0136 0.01334415
2 0.1871 0.1128 0.175955 0.0327 0.0313 0.03248207
3 0.1725 0.1310 0.166275 0.1208 0.1233 0.12116852
4 0.3868 0.3851 0.386545 0.3028 0.3237 0.30576125
5 0.1586 0.2540 0.172910 0.8495 0.9062 0.85754836
6 0.0643 0.1031 0.070120 2.853 3.0492 2.88080478
ENDF/BVII.0
1 0.0319727 0.0103413 0.02872799 0.0124906 0.0124942 0.01249114
2 0.166371 0.114820 0.15863836 0.0318241 0.0302552 0.03157847
3 0.161310 0.127807 0.15628457 0.109375 0.115938 0.11031167
4 0.459647 0.451836 0.45847535 0.316990 0.341476 0.32043657
5 0.133499 0.233507 0.14850020 1.35398 1.31863 1.34855700
6 0.0471998 0.0616887 0.04937313 8.63638 9.97903 8.81427097
TVSM
1 0.038 0.013 0.03425 0.0127 0.0132 0.01277257
2 0.213 0.137 0.20160 0.0317 0.0321 0.03175936
3 0.188 0.162 0.18410 0.115 0.139 0.11805761
4 0.407 0.388 0.40415 0.311 0.358 0.31724745
5 0.128 0.225 0.14255 1.4 1.41 1.40149081
6 0.026 0.075 0.03335 3.87 4.02 3.89178228
BNABRF
1 0.0328 0.0084 0.029140 0.0125 0.0125 0.0125
2 0.1539 0.1040 0.146415 0.0283 0.0283 0.0283
3 0.0913 0.0375 0.083230 0.0425 0.0425 0.0425
4 0.1969 0.1370 0.187915 0.1330 0.1330 0.1330
5 0.3308 0.2940 0.325280 0.2925 0.2925 0.2925
6 0.0902 0.1980 0.106370 0.6665 0.6665 0.6665
7 0.0812 0.1281 0.088220 1.6348 1.6348 1.63488
8 0.0229 0.0931 0.033430 3.5546 3.5546 3.5546
PHYSICS OF ATOMIC NUCLEI
Vol. 74
No. 14
2011
CALCULATION OF REACTIVITIES USING IONIZATION CHAMBER CURRENTS 1911
(ii) for the mixture of U235 and U238 with the
weights
ε
U235
= 0.85 and
ε
U238
= 0.15. This approxi
mate weight ratio was recommended by Tsyganov for
fresh fuel of a VVER1000.
The results of calculations are given in Table 2 and
in the plots (Figs. 1–4). The data obtained on the basis
of readings of ionization chamber no. 3 were used in a
comparative analysis.
The time at which the value of reactivity given in
Table 2 was determined was chosen in such a way that
the reactivity coincided with that given in [1] in the
processing of readings of ionization chamber no. 3;
this time was equal to 400 s (the time of beginning of
motion of the rods of the scram system was 364.7 s,
and the time step was 0.1 s). In [1], the reactivity was
calculated using the Kipin kinetic parameters only for
uranium235.
CONCLUSIONS
(1) Eightgroup constants of delayed neutrons pre
pared for the system of constants ROSFOND
(BNABRF) yield practically the same result as the
Kipin constants (BNAB78) with acceptable reactiv
ity time evolution with allowance for the contribution
of U238 fission.
(2) The most “correct,” aesthetically acceptable
pictures
1
are obtained if the ROSFOND (BNABFR)
constants with
ε
U235
= 0.85 and
ε
U238
= 0.15 are used.
This gives grounds for a thorough examination of our
proposal on introducing into practice calculations and
processing of experimental results. Unlike the Kipin
constants, BNABRF contains a much larger list of
1
A physical law should be mathematically elegant. P.A.M. Dirac.
nuclides. For eightgroup constants, the problem of
λ
i
averaging is eliminated, since they are independent of
the nuclide.
(3) If the weights
ε
U235
= 0.85 and
ε
U238
= 0.15 are
used, the scram system effectiveness is reduced by
approximately 8% as compared to the kinetic parame
ters for U235 only.
(4) The application of kinetic parameters from
ENDF/B6 and the constants BNAB90 based on
them yields incorrect and similar pictures of the time
evolution of reactivity. The situation is repeated if
ENDF/BVII.0 is used. Here, the reactivity curve for
only BNAB90 was given for illustration.
(5) Accounting for the background current
increases the scram system effectiveness by 7.7% and
influences the reactivity and the slope of the curve,
which is noticeable for the TVSM constants. This cir
cumstance requires more thorough examination. On
the whole, the TVSM constants yield an acceptable
result.
(6) It is reasonable to include the possibility of
obtaining the microscopic fission cross sections neces
sary for estimating the fission fractions of separate
nuclides in cells and the reactor in the programs of
generation of fewgroup constants. The fractions of
fission on each nuclide in a cell can also be directly
estimated.
(7) The difference between the maximum and min
imum scram system effectiveness with different sets of
kinetic parameters slightly exceeds 2
β
.
ACKNOWLEDGMENTS
We thank S.V. Zabrodskaya, V.G. Zimin,
L.D. Ivanov, A.A. Pinegin, V.V. Sinitsa, S.V. Tsyganov,
and L.K. Shishkov for materials and discussion of the
problems formulated in this study. We especially thank
M.N. Nikolaev for reading the preliminary version of
the paper and providing critical remarks, most of
which were taken into account.
REFERENCES
1. V. L. Tereshonok et al., Report VNIIAES No. OE
3395/2005 (2005).
2. Guidance Document No. RD EO 01512004.
3. R. J. Tuttle, Nucl. Sci. Eng.
56
, 37 (1975).
4. G. R. Keepin,
Physics of Nuclear Reactor Kinetics
(AddisonWesley, London, 1965; Atomizdat, Moscow,
1967).
5. S. V. Zabrodskaya, Candidate’s Dissertation in Physics
and Mathematics (GNTsRFFEI, Obninsk, 2001).
6.
Attestation Passport of Program Mean TVSM
, vers. 1.3,
Registration No. 135 (2002).
Translated by E. Baldina
Ta bl e 2 .
Reactivity upon dropping rods of the scram system
calculated with different constants (
t
= 400 s)
Constants
ρ
, $
without
allowance for
background
current
ρ
, $
with allowance
for background current
Averages
ε
U235
= 0.85,
ε
U238
= 0.15
Only
U235
Averages
ε
U235
= 0.85,
ε
U238
= 0.15
BNAB78 (Kipin) –8.02 –8.71* –8.08
BNAB90 –6.63 –6.68
ENDF/B6 –6.80 –6.85
ENDF/BVII.0 –6.46
TVSM –7.83 –7.89
BNABRF –8.06 –8.12
* Without allowance for background current
ρ
= –8.64 $.