Effects of various types of reflectors on the 99Mo production in the VVER-Ts reactor targets*

The effects from introducing various types of reflectors in the VVR-Ts reactor core on the 99Мо production were analyzed. Earlier the effects of only the beryllium reflector on the VVR-Ts reactor core characteristics, such as reactivity margin, neutron flux in experimental channels, and activity of the accumulated 99Мо, were calculated. The calculations are based on a generated precision model of the core which comprises one experimental channel where targets are irradiated for the 99Мо production. The model was built using the SCALE code. The code allows a fairly broad range of calculations to be performed, from criticality estimation to radiological assessment tasks. As the result of the computational analysis of the model, such characteristics were obtained as the effective multiplication factor, the power density in the 99Мо production targets, the neutron flux in the target raw material, and the quantity of the produced 99Мо after 120 hours of irradiation. The data was compared with the results of similar calculations of the VVR-Ts reactor core parameters. Further, the list of the materials used extensively as the reactor core reflector or moderator was formed based on reference literature. A number of models were obtained and analyzed on its basis, in which the water space on the core periphery was substituted for the investigated materials.


Introduction
At the present time, 99 Мо is produced in the VVR-Ts reactor in the forcedly cooled vertical experimental channels which accommodate two targets of the tube-in-tube type placed one on the other. The outer diameter is 36 mm and the fuel portion height is 150 mm. Each of the targets is designed as two tubes between which there is a mixture of U 3 O 8 and ZnO . Such configuration has proved to be more efficient for the 99 Мо production than the previous version ("sleeve-in-sleeve").
As shown by the calculation results, the power density in the channel, with the targets of the new type loaded into it, was 32.9 kW which is 1.7 as high as with the loaded targets of the old design .
The effects of the beryllium reflector on the 99 Мо production have been calculated, and the calculation results are presented in (Kochnov et al. 2013). Depending on the beryllium layout in the core, the calculations showed that the 99 Мо production increased by at least 2% and by 9% at the greatest. The effects of the beryllium reflector on the VVR-Ts reactor core parameters were analyzed in Kolesov 2012, Kolesov et al. 2015). The calculation results showed a major increase in the reactor reactivity margin and up to a 10% flux growth in the experimental channels.
The optimization of the 99 Мо production was analyzed proceeding from the possibility of increasing the number of the experimental channels in the core. It was shown in the process of the studies that the "…placement of beryllium blocks in six cavities on the core periphery makes it possible to install one more experimental channel for the radionuclide production without reconfiguring the rest of the core and without affecting greatly the reactivity characteristics of the CPS rods" (Kochnov et al. 2018).
The 99 Мо production in the VVR-Ts reactor can be increased by redesigning the target. A new target design, which contains much starting material, was proposed as the result of a computational analysis. It has been proved that the new design satisfies the allowable thermal-hydraulic parameters in the experimental channel. The investigation results are provided in (Kochnov et al. 2019, Kolmykov et al. 2018a, b, c, d, Kolmykov and Zevyakin 2019. The purpose of the work is to compare the effects of various reflector materials on the 99 Мо production increase in the VVR-Ts reactor. Such type of calculations for the VVR-Ts reactor core was performed earlier only for the beryllium reflector, but no comparative analysis against other types has been conducted. Resolving this issue will make it possible to select the most effective reflector material from the list of the materials analyzed for producing the maximum possible quantity of 99 Мо after irradiation in the reactor core. The selection of the reflector material was based on the extent of its application as the reflector in nuclear power. The properties of extensively used reflectors and moderators are described in detail in (Bobkov et al. 2012) based on which the reflector materials were selected.

Initial data
The power density in the experimental channels was calculated using the SCALE code (Rearden and Jessee 2016), in which the model was analyzed with the use of two modules, KENO-VI and ORIGEN. The former calculates the core parameters using Monte Carlo method. The latter calculates the burn-up based on the numerical solution of a system of differential equations which describe the formation, depletion, and decay of nuclides (Rearden and Jessee 2016): where N i is the quantity of the nuclide i; λ i is the decay constant of the nuclide i; l ij is the yield of the nuclide i in the decay of the nuclide j; σ i is the spectrum-averaged removal cross-section for the nuclide i; f ij is the yield of the nuclide i in the burn-up of the nuclide j; Φ is the angle and energy integrated neutron flux; and S i is the time-dependent source.
Based on data in , Kolesov et al. 2011, 2014), a precision model of the VVR-Ts reactor core was formed with an experimental channel where 99 Мо is produced (Figs 1, 2).
To check the adequacy of the model built and the computation parameters, the following key characteristics were calculated: the effective multiplication factor, the neutron flux in the target material, and the power density in the targets. The automatic control (AC) and manual control (MC) rods in the computational model are half-submerged in the core. For KENO-VI, 750 neutron generations of 10000 neutrons each were selected as the parameters. The power of the model was rated for 10 MW in the fuel portions of all FAs. The obtained data was compared with the results of the calculations for a similar model in the MCNP code. Table 1 presents the results from the calculation of the power density in the upper target and in the lower target  The effective multiplication factor, as calculated using the SCALE code, is k eff = 1.01041±0.00026. In , k eff = 1.01097±0.00034. The calculation results for the effective multiplication factor, the neutron flux, and the power density in the target material converge with the data in  within the uncertainty limits.

Calculations
The most widely used moderators in nuclear power (graphite, beryllium, beryllium oxide, zirconium hydride) were selected as the reflector material. The reflector is situated along the side surface of the core. In the existing reactor core design, the region, where the reflectors were introduced, is filled with water.
The density and isotope composition data for the graphite reflector calculation were taken for the VPG and SGT graphite grades. VPG is the most widely used graphite grade in reactor industry and the SGT graphite has the highest density thanks to the silicon saturation. Table 2 presents data on the isotope composition and density of the considered reflector types. The material data was taken from (Bobkov et al. 2012).
The reflector blocks are situated on the core periphery filling all of the cavities between the reactor side wall and the peripheral FAs (Fig. 3). Table 3 presents calculated values of the neutron fluxes and power densities in the target material at the initial time.
The activity of the produced 99 Мо from the two targets after 120 hours of irradiation with various reflector materials in the core is presented in Table 4.
According to the calculation results for the power density and activity of 99 Мо in the targets, the introduction of only the beryllium reflector will increase the production as compared with the existing design in which the reflector region is filled with water. The activity of the produced 99 Мо in this case is 4% higher which is confirmed by the similar value in (Kochnov et al. 2013).

Conclusion
A precision model of the VVR-Ts reactor core has been formed which can be used for computational studies in future. The results of calculating the key characteristics of the VVR-Ts reactor core have a good fit with earlier results. The calculation of the power density and the 99 Мо production with various reflectors used on the core periphery has shown that it is only the beryllium reflector that contributes greatly to the production increase as compared with the water reflector. The activity of the produced 99 Мо after 120 hours of irradiation, when the beryllium reflector is used, is 4% as high as the value when the water reflector is used. Estimates show that other reflector types have worse or similar parameters.