1. MODELLING OF THE VVER-440 REACTOR FOR DETERMINATION OF THE SPATIAL WEIGHT FUNCTION OF EX-CORE DETECTORS USING MCNP-4C2 CODE Gabriel Farkas, Vladimír Slugeň SUT Bratislava

2. Objective Determination of the spatial weight function of ex-core detectors for the VVER-440 reactor type, taking into account different operational parameters such as power, burn-up, boric acid concentration and position of the control assembly group No 6.

3. Concept of the spatial weight function The spatial weight function of the ex-core detector provides relationship between the spatial neutron flux density (or fission density) distribution in the reactor core and the ex-core detector response.

4. Definition of the weight function of ex-core detector The weight function can be defined in various ways. In this case, the weight function is a multivariable function which gives the average number of reactions in the ex-core detector for one neutron born with Watt fission spectra in the twentieth of a fuel pin in different core positions.

5. Application The weight function of the ex-core detector will be useful for: ▪interpretation of reloads startup rod drop measurements ▪evaluation of the ex-core detector response at deep subcritical reactor conditions ▪safety analysis of the reactor ▪ other applications.

7. Determination of the Reaction Rate – Weight Value The weight function is detector dependent function. The reaction rate – average number of reactions occurred in the ex-core detector for one source neutron will be calculated by MCNP tally multiplier card according to the expression: R - reaction rate (weight value) N - atomic density of the 3 He Φ(E) - neutron fluency in a 3 He filled neutron sensitive volume of the detector σ R (E) - microscopic cross section of the (n, p) reaction for 3 He isotope

8. The calculation model n Considering the fact that the ex-core detectors are located symmetrically, it is sufficient to model only one of the detectors and the core region in its vicinity. n The model of the core is divided into two region – source region created by fuel assemblies from which neutrons are started and scattering region from which neutrons are not started, but it is present due to its neutron scattering effects. The geometric model extends to the core region from which the contribution to the ex-core detector response is not negligible. In respect to the symmetry conditions it is not necessary to calculate contributions from both sides of the symmetry plane. Ex-core detector source region scattering and absorption region plane of symmetry spatial weight function A A

9. HORIZONTAL SECTION OF THE MODEL Considering the objective to determine the weight function with high accuracy, the reactor core, space between the core and the ex-core detector and the detector itself are modelled in the finest possible detail.

10. Reactor pressure vessel Barrel Core basket Fuel assembly Coolant Sheet metal Ionization chamber Biological shielding Channel of ionization chamber Twentieth of a fuel pin Calculation of the single weight values WEIGHT FUNCTION Plane of symmetry 12.2 cm VERTICAL SECTION OF THE MODEL The weight function gives the average number of reactions occurred in the ex-core detector for one source neutron born in the twentieth of a fuel pin in different core positions. The signal of the detector is given by the weight function and fission density function product and its integration over the whole core region in interest.

11. MCNP model of the fuel assembly Fuel pin with enrichment 3.3% Fuel pin with enrichment 3.6% Fuel pin with enrichment 4.0% Spacer capture rod Spacer grid Casing Investigations will be started to determine the influence of two burn-up levels and two boric acid concentration levels – zero and the maximal on the weight values. If there will be shown weight function independence on the operational parameters such as burn-up, boric acid concentration and others during the whole reactor operation cycle, it is possible consider the weight function as invariable, i. e. generalize the function, and determine the detector response to the neutron flux density distribution during the whole cycle of operation.

12. MCNP model of the FA – horizontal cross sections protective grid carrier grid fuel pins/spacer grid

13. MCNP model of the FA – vertical cross sections upper part of the FA bottom part of the FA Head Compensation volume/ fixation string Foot Carrier grid Carrier grid of the core basket Protective grid twentieths of fuel pins

14. MCNP model of the CA fuel part upper partbottom part Joining rod Head Foot

15. MCNP model of the reactor components barrel core basket surveillance specimen channel distance strip RPV horizontal cross sectionvertical cross section

16. Ex-core detector Transfer function between the channel and the detector- detection efficiency Channel of the ex-core detector Reactor core Spatial weight function of the ex-core detector Spatial weight function of the ex-core detector channel Spatial weight function of the ex-core detector as a composite function Considering prospective replacement of the existing ex- core detectors for another detector types in the future, it is possible to reach the spatial weight function for the channel of the ex-core detector and after that to determine an additional transfer function between the ex- core detector channel and new known detector type. Consequently, the final spatial weight function of the ex-core detector is given as a composite function of these two function.

17. Fitting an analytical function An analytical function will be fitted onto the single weight values in two steps. The first step will be to find an optimal analytical function which follows reliably vertical distribution of the calculated single weight values – vertical (one-dimensional) fitting. The second step will be a horizontal (two-dimensional) fitting which means that an analytical function will be fitted onto calculated and by vertical fitting “smoothed” weight values.

18. Summary The exact knowledge of the spatial weight function of the ex-core detector can 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 and for evaluation of the detector signal at deep subcritical reactor conditions. Calculation of weight values and fitting of the weight function will be completed soon.