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

of delayed neutrons and the constants

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. (

= 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

, 0.180

–10

, and

0.105

–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

, S. N. Zizina

, L. V. Kryakvin

, V. A. Pitilimov

, and V. A. Tereshonok

Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia

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

. 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:

and

= , where

is the number of the

group of delayed neutrons,

is the nuclide index, and

is the weight taking into account the contribution of

fission on nuclide

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

()

∑

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);

−

350 370

, $

, s

−

390 410 430 450 470 490

−

Ionization chamber no. 25

Ionization

chamber no. 3

chamber no. 14

Fig. 1.

Reactivity

, $ upon dropping rods of the scram sys

tem. Kinetic parameters BNAB78 (Kipin) only for U235

(with allowance for background current).

−

350 370

, $

, s

−

390 410 430 450 470 490

−

Ionization chamber no. 25

Ionization

chamber no. 3

chamber no. 14

Fig. 2.

Reactivity

, $ upon dropping rods of the scram sys

tem. Kinetic parameters BNAB78 (Kipin) with

U235

0.85 and

U238

= 0.15 (with allowance for background

current).

350 370

, $

, s

−

390 410 430 450 470 490

−

Ionization chamber no. 25

Ionization

chamber no. 3

chamber no. 14

Fig. 3.

Reactivity

, $ upon dropping rods of the scram sys

tem. Kinetic parameters BNAB90 with

U235

= 0.85 and

U238

= 0.15 (with allowance for background current).

−

350 370

, $

, s

−

390 410 430 450 470 490

−

Ionization chamber no. 25

Ionization

chamber no. 3

chamber no. 14

Fig. 4.

Reactivity

, $ upon dropping rods of the scram sys

tem. Kinetic parameters BNABRF with

U235

= 0.85

and

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

Relative yield of

group of delayed neutrons

Decay constant of precursors of

group of delayed neutrons

U235 U238

Averages

U235

= 0.85,

U238

= 0.15

U235 U238

Averages

U235

= 0.85,

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

U235

= 0.85 and

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

are obtained if the ROSFOND (BNABFR)

constants with

U235

= 0.85 and

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

A physical law should be mathematically elegant. P.A.M. Dirac.

nuclides. For eightgroup constants, the problem of

averaging is eliminated, since they are independent of

the nuclide.

(3) If the weights

U235

= 0.85 and

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

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.

, 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).

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 (

= 400 s)

Constants

, $

without

allowance for

background

current

, $

with allowance

for background current

Averages

U235

= 0.85,

U238

= 0.15

Only

U235

Averages

U235

= 0.85,

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

= –8.64 $.