Modelling of the Wwer-440 Reactor for Determination of the Spatial Weight Function of Ex-Core

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 MCNP- 4C2 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) (E)dE  R , 0

where R is reaction rate (weight value), N - atomic density of the 3He, (E) - neutron fluence in a 3He filled neutron sensitive volume of the ex-core detector, 3 R(E) - microscopic cross-section of the (n, p) reaction for He 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 2 23 3 (Reactimeter)

22 Source 4 (ECR) Regionx

21 Spatial 5 Weight Function 20 (ECR) 6

19 (RES) A A Investigated 18 8 Ex-Core Detector Plane of No 7 17 Symmetry 9 Energy range Scattering and 16 Absorption 10 Source range Region 15 11 (RES) Intermediate range 12 (ECR) 14 13

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 ex- core 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 Creation of model and input file for calculation of the file for calculation of the single weight values fission density distribution

Calculation of the weight Calculation of the fission values by MCNP-4C2 density distribution by MCNP-4C2 or BIPR-7

Fitting an analytical function onto the single weight function values

Spatial weight function of the Spatial function of the fission ex-core detector 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 - Central Processor Unit ECR - Emergency Control Room MCNP - Monte Carlo N-Particle Transport Code RES - Reserve WWER - Water-Water Energetic Reactor

REFERENCES

[1] Csom, Gy., Czifrus, Sz.: Calculation of Spatial Weight Function for VVER-440 Ex- Core Neutron Detectors. In: The 11th AER Symposium, Csopak, Hungary, p. 711 – 715 [2] Briesmeister, J.F.: MCNP - A General Monte Carlo N – Particle Transport Code, Version 4C, Los Alamos National Laboratory, Los Alamos, 2000 [3] 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