MODELLING OF THE WWER-440 REACTOR FOR
DETERMINATION OF THE SPATIAL WEIGHT FUNCTION OF
EX-CORE DETECTORS USING MCNP-4C2 CODE
Gabriel Farkas, Vladimír Slugeň
Slovak University of Technology, Faculty of Electrical Engineering and Information Technology,
Department of Nuclear Physics and Technology, Ilkovičová 3, 81219 Bratislava, Slovakia,
[email protected]
ABSTRACT
The contribution of fuel assemblies to the response of ex-core detectors does not only
depend on the power, but also on the position of the given assemblies in the reactor core. The
weight of the inner fuel assemblies is several orders of magnitude lower than the outer ones.
Therefore, the signal of the ex-core detectors for a given reactor power is strongly influenced
by the spatial power distribution and indirectly by the parameters which determine the
distribution, such as load pattern, time elapsed, etc.
The aim of the work is to describe the modelling and the methodology for calculation
of the spatial weight function of ex-core detectors for the WWER-440 reactor type using
Monte Carlo transport code system MCNP-4C2, taking into account different operational
parameters such as power, burn-up, boric acid concentration, position of the control assembly
group No 6, etc. The spatial weight function provides relationship between the spatial neutron
flux density distribution or the fission density distribution in the reactor core and the ex-core
detectors. The weight function is possible to define in various ways in dependence on solved
problem. In this case the function gives the average number of reactions occurred in the
detector for one neutron born with Watt fission spectra created in the twentieth of a fuel pin in
different reactor core position.
From the definition of the weight function follows that the response of the ex-core
detector is given by the weight function and the fission density distribution function product
and its integration over the reactor core or its part.
The spatial weight function will be used for interpretation of reloads startup rod drop
measurements, assessment of the ex-core detectors response at deep subcritical reactor stage
and for other applications.
1
INTRODUCTION
The contribution of the fuel assemblies to the response of the ex-core detectors does not
only depend on the power, but also on the position of the given assembly in the reactor core.
The weight of the inner fuel assemblies is several orders of magnitude lower than the outer
ones. Therefore, the signal of the ex-core detectors for a given reactor power is strongly
influenced by the spatial power distribution and, indirectly, by the parameters which
determine the distribution, such as load pattern, time elapsed in the cycle, etc.
2
PROBLEM SPECIFICATION
Spatial weighting function of ex-core detectors gives relationship between spatial
neutron flux density distribution or fission density distribution in the reactor core and
ionization chambers (ex-core detectors) placed outside of the core. The weighting function is
possible to define in various ways in dependence on solved problem. In this case the spatial
(three-dimensional) weight function gives the average number of reactions occur in the
ionization chamber for one neutron born with Watt fission spectra created in the twentieth of
a fuel pin in a different reactor core position [1]. The function will be calculated at a
twentieth-of-pins level of fuel assemblies within acceptable statistical uncertainty and
computing (CPU) time. From definition of the weighting function follows that response of the
ex-core detector (number of reactions occurred) is given by the weight function and the
fission density distribution function (as two spatial functions) product and its integration over
the reactor core or its part. Practically, it is sufficient to integrate over the core region where
the product of these two functions is negligible different from zero.
3
CALCULATION METHODOLOGY
Considering the complicated geometry of WWER-440 reactor core, space between the
core and the ex-core detectors, transport Monte Carlo method as a technique allowing
uncompromising treatment of three-dimensional geometry was chosen. The calculation will
be performed by transport Monte Carlo code MCNP-4C2 [2] run in forward mode which
gives more accurate results contrary of adjoint mode of running. The application of the
forward mode will make possible to eliminate the approximations which could result from the
homogenization of the cross sections libraries of the fuel assembly material and from using of
group-wise nuclear data in case of the adjoint mode of calculation. The calculation by MCNP4C2 transport code will be performed to determine the reaction rate in the ex-core detector
caused by fission neutron produced in the twentieth of a fuel pin. The reaction rate – average
number of 3He(n, p)3H reactions occurred in the ex-core detector (ionization chamber) for one
source neutron born with Watt fission spectra will be calculated by MCNP tally multiplier
card according to the following expression:

R  N  ( E ) R ( E )dE ,
0
where
R
N
(E)
is
-
R(E)
-
reaction rate (weight value),
atomic density of the 3He,
neutron fluence in a 3He filled neutron sensitive volume
of the ex-core detector,
microscopic cross-section of the (n, p) reaction for 3He
isotope
Considering prospective replacement of the existing ex-core detectors for another
detector types in the future, the spatial weight function will be reached for the channel of the
ex-core detector and than an additional transfer function between the ex-core detector channel
and new known detector will be determined as it is shown in Figure 1. Consequently, the final
spatial weight function of the ex-core detector is given as a composite function of these two
functions.
Figure 1: Determination of the spatial weight function of ex-core detector as a
composite function of weight function of the ex-core detector channel and transfer function
between the channel and the detector.
All geometrical details and material compositions are modelled with high accuracy. It
is assumed to obtain sufficiently low standard deviation within reasonable computation time
by using some appropriate variance reduction method such as weight window. Investigation
of influence of other operational parameters such as power, burn-up, boric acid concentration,
position of control assembly group No 6 on the weight function will be taken into account.
The fission density distribution will be determined in an independent calculation by BIPR-7
or MCNP-4C2 code.
4
GEOMETRICAL AND MATERIAL MODEL
Considering the fact that investigated ex-core detectors are used for the startup
reactivity measurements, furthermore that these three ex-core detectors are located
symmetrically (120% symmetry), it is sufficient to model only one of the ex-core detectors
and the core region in its vicinity. The geometrical model extends to the region from which
the contribution to the ex-core detector response is not negligible. Considering the symmetry
conditions it is not necessary to calculate contributions from both part of the symmetry plane.
The model of the reactor core is divided into two regions – source region created by fuel
assemblies from which neutrons are started and scattering region created by fuel assemblies
from which neutrons are not started, but they are present in the core model due to their
neutron scattering effect. The model of the reactor core for calculation of the weight function
is shown in Figure 2.
1
24
23
2
3 (Reactimeter)
22
Source
x
Region
4 (ECR)
Spatial
Weight
Function
21
5
20 (ECR)
6
19 (RES)
A
A
Investigated
Ex-Core
8
Detector
No 7
18
Plane of
Symmetry
17
Energy range
Source range
Scattering and
Absorption
Region
16
15
Intermediate range
9
10
11 (RES)
14
13
12 (ECR)
ECR – Emergency Control Room, RES - Reserve
Figure 2: The model of the reactor core for calculation of the spatial weight function of ex-core
detector No 7 running in source range.
Geometric model consists of detail model of the WWER-440/V213 reactor core – fuel
assemblies including fuel rods, spacer grids, Zr-Nb tubes, spacer capture rod, casing,
assembly head and bottom, control assemblies; space between the core and ex-core detectors
– core basket, barrel, reactor pressure vessel and its cladding; biological shielding, ionization
chamber channels and ex-core detectors [3]. The vertical and horizontal sections of the
MCNP model are shown in Figure 3 and Figure 4.
Figure 3: The horizontal cross section of the MCNP model. The picture shows the reactor
core, space between the core and the ex-core detector and the detector itself which are
modelled in the finest possible detail considering the objective of the work to determine the
weight function with high accuracy.
Figure 4: The vertical cross section of the MCNP model. The picture shows the calculation of
single weight values which gives the reaction rate in the neutron sensitive volume of the excore detector for one neutron born with Watt fission spectra in the twentieth of a fuel pin in
given axial core position.
Regarding material model the fuel assemblies have radially-zoned enrichment
distribution; at present, individual fresh enrichments are 3.3%, 3.6% and 4.0%, average
enrichment of the fuel assembly is 3.82%. The fuel pellets are charged in Zr-Nb1% tubes.
Compositions of all used materials will be modelled to the highest accuracy. There will be
investigated influence of two burn-up levels and two boric acid concentration levels – zero
and the highest on the weight values. The isotopic composition of the fuel for given burn-up
level will be calculated by ORIGEN code. Considering that neutrons which became thermal
in the concrete of the biological shielding have a significant contribution to the ex-core
detector signal, the element composition of the concrete will have significant influence on the
calculated weight value accuracy. Because an exact element analysis of the concrete and its
mass density is not available normative values will be used in the material model. This will
have significant impact on the weight function accuracy; therefore investigation will be
performed to determine the influence of the concrete mass density and element composition
on the function. If there will be shown weight function independence on the operational
parameters such as burn-up and boric acid concentration, coolant temperature and other
parameters during the whole reactor operation cycle, we could consider the weight function as
invariable, i.e. generalize the function, and determine the ex-core detector response to neutron
flux density distribution in the whole cycle of operation. A simply flow diagram for
determination of the ex-core detector signal is shown in Figure 5.
Problem specification
Problem analysis and calculation methodology
Creation of model and input
file for calculation of the
single weight values
Creation of model and input
file for calculation of the
fission density distribution
Calculation of the weight
values by MCNP-4C2
Calculation of the fission
density distribution by
MCNP-4C2 or BIPR-7
Fitting an analytical function
onto the single weight
function values
Spatial weight function of
the ex-core detector
Spatial function of the fission
density distribution
Ex-core detector response
Validation by experiment
Figure 5: Simplify flow diagram for problem solving
5
FITTING AN ANALYTICAL FUNCTION
An analytical function will be fitted onto the single weight values obtained by MCNP
calculation in two steps. The fitting will be performed using an own program which will be
based on the method of flexible polyhedra. The first step of the fitting task will be to find an
optimal analytical function which follows well vertical distribution of the calculated weight
values. Second step will be horizontal fitting which means that a horizontal analytical
function will be fitted onto calculated and by vertical fitting “smoothed” weight values.
6
CONCLUSION
The exact knowledge of the spatial weighting function of the ex-core detector
response will be very useful for solution and interpretation of various reactor physical,
operational and safety problems, in particular for interpretation of reloads startup rod drop
measurements, assessment of the ex-core detectors response at deep subcritical reactor stage.
The goal of the work was to design and describe the calculation method for determination of
the weighting function at a twentieth-of-pins level within acceptable statistical uncertainty
and computing time using MCNP-4C2 transport code. The input file for calculation of the
weight values is now almost completed and prepared for testing and running. Fitting the
analytical weight function will be performed by own program which will be developed for
multi-dimensional regression.
LIST OF NOMENCLATURE
CPU
ECR
MCNP
RES
WWER
-
Central Processor Unit
Emergency Control Room
Monte Carlo N-Particle Transport Code
Reserve
Water-Water Energetic Reactor
REFERENCES
[1]
[2]
[3]
Csom, Gy., Czifrus, Sz.: Calculation of Spatial Weight Function for VVER-440 ExCore Neutron Detectors. In: The 11th AER Symposium, Csopak, Hungary, p. 711 – 715
Briesmeister, J.F.: MCNP - A General Monte Carlo N – Particle Transport Code,
Version 4C, Los Alamos National Laboratory, Los Alamos, 2000
Farkas, G., Slugeň, V., Ballo, P.: Monte Carlo Calculation of the Spatial Weighting
Function of Ex-Core Detectors for the WWER-440 Reactor Using MCNP-4C2 Code.
In: International Conference Nuclear Energy for New Europe 2005: Bled, Slovenia,
5.-8.9.2005