Investigation of the characteristics of the container for storage of radioactive waste of nuclear power plants with uranium-graphite reactors

. The article presents the results of the study of neutron-physical characteristics of the container for storage of radioactive waste of nuclear power plants with uranium-graphite reactors. The interaction of gamma quanta (in the energy range from 0.1 to 2 MeV) with the structural materials of the container is simulated. The numerical values of the parameters determining the radiation characteristic of the container with the estimation of the calculation error are obtained. The following main characteristics of the container are determined: the attenuation coefficient of the equivalent dose, the numerical factor of gamma radiation accumulation. These characteristics can be used to justify the radiation safety of the container, in particular when selecting protection materials, as well as when building additional heterogeneous protection barriers.


Introduction
The development of nuclear power in Russia and abroad envisages the construction of new power units and the decommissioning of reactors that have exhausted their life, which will lead to an increase in the rate of accumulation of radioactive waste (RW) [1][2][3][4][5][6][7][8][9].
Radioactive waste requires special handling. Waste is placed in special containers, which must provide the necessary biological protection during transportation and temporary storage.
Loading a container with radioactive material requires that the equivalent dose rate on the surface of the packaging will be matched to the standardized values.
At the moment, a conservative approach to this task is being applied. The tolerances for the loading of radioactive waste (mass, volume, radionuclide composition, activity) for each container are established, under which the standardized parameters will meet the requirements of regulatory documents. The disadvantage of this method is that it is impossible to justify the safe handling of waste characteristics of which exceed the permissible limits. This requires additional complicated and time-consuming calculations with large time costs. The delay in decision-making related to the justification of safety will lead to an increase in the dose burden on personnel and financial losses.
In this study, it is proposed to use the engineering calculation of biological protection against extended gamma sources for a particular container. The proposed method is based on the use of universal tables to calculate the protection from photon radiation. Such data were obtained [10] and have practical application in determining the required thickness of protection only for point isotropic sources. In this paper, similar tables are calculated for an extended isotropic source, taking into account the geometry and materials of the container. For this purpose, the interactions of monoenergetic gamma quanta (in the energy range from 0.1 to 2 MeV) with structural materials of the container were considered. Radiation characteristics of the container are determined: the number of attenuation, the numerical factor of gamma radiation accumulation.
Based on the calculated radiation characteristics of this container, it is possible to create a library of constants and further supplement it with new information (the type of container and the corresponding values of the attenuation factor, accumulation factors). Such constants will allow designing an information system that automatically detects the amount of radioactive waste to be loaded into a container. The use of such a system will provide support for decision-making in the handling of radioactive materials.

Formulation of the problem
We studied the reduction of gamma-quanta radiation by wall of reinforced concrete container intended for the storage of radioactive contaminated graphite from the uraniumgraphite reactor. The graphite masonry contamination takes place due to neutron activation of graphite ( 13 C(n, gamma) 14 C), impurities (Cl, Fe, Co, Zn, Cs, Eu, Th, U, etc.) [11], nuclides which settle on the masonry from damaged technological channel (H, O, Fe, Cr, particles of fuel, the fission products, etc.) [12][13][14], and also radioactive carbon from the reaction ( 14 N(n, p) 14 C) [15]. The radionuclide of carbon 14 C is a source of low-energy βradiation (Eβ=156 keV), due to the self-absorption of carbon and the reduction of the wall of the container its contribution to the dose rate at the point of detection will be small. Thus, the main contribution will be formed at the expense of radionuclide which is deposited in the graphite stack as a result of the channel damage and activation of impurities. These are mainly gamma-radiation sources with the energy of gamma-quanta of up to 2 MeV.
Due to the fact that there are no the reliable data on the radioactive pollutions for graphite blocks, it is necessary to obtain a universal data able to simulate it. To determine the flux density of gamma-quanta on the surface of the container from any radionuclide, polluting graphite blocks, we with the help of the program MCC 3D [16] had simulated weakening of the gamma-irradiation by the wall of the container.
In this way we considered the reduction of gamma-quanta radiation with energies 0. For this purpose a volumetric container model with graphite was created, and one should determine physical and chemical properties of the container, graphite source (polluted part of the graphite), and the detectors. The container is made of concrete with density 2.34 g/cm3 in the form of a parallelepiped: its external dimensions are 1200х1200х1430 mm, internal dimensions are 960х960х1150 mm, wall thickness is 120 mm. Within it the graphite with density 1.65 g/cm3 is placed, which fills the entire volume of the container.
Graphite is presented in two graphite blocks, placed in the container. Dimensions of the first block are 959.8х954.7х1149.8 mm, the dimensions of the second block (polluted part of graphite) are 959.8х5х1149.8 mm.
Detectors have the following characteristics: diameters are 40 mm, they are located in two rows at distances of 1 mm and 1 m from the container surface, with the height step of 160 mm.
Here is considered the limiting case, when the polluted layer of graphite is located along one of the inner wall. Flux of gamma-quanta is registered by means of 18 ideal gammadetectors, which are located at an altitude of the container along the outside of the walls and at a distance of 1 m from the container ( fig. 1). For each energy gamma-quanta 109 stories are modelled.

The equivalent dose
To find the dose of gamma-radiation of continuous spectrum, one needs to divide the spectrum into the groups according to the particles' energies. The energies Eγi of the gamma-quanta are fixed and considered to be constant inside of each i-th group. The amount of gamma-quanta inside of each group are determined ( fig. 2) as the area of the trapezoid (of the spectrum part). The desired equivalent dose is calculated in the form of the sum of the partial dose for each group. The equivalent dose is: where m is the number of energy groups; Ni is the number of gamma-quanta caught up in the i-th group; h(Eγi) is equivalent dose of gamma-radiation with energy [17]; ΔEγi is the width of the energy interval of the i-th group. The width of the energy interval is chosen constant:∆E_γi=2 keV. The number of energy groups depends on the maximum energy of gamma-quanta of the ionizing radiation: Fig. 2. The gamma-ray spectrum division into the energy groups

The attenuation coefficient of gamma radiation
The attenuation coefficient Katt is the ratio of equivalent dose of the initial gamma radiation to the attenuated gamma radiation: The relation between the attenuation coefficient and initial energy of gamma radiation is shown in fig. 3. Gamma radiation is considered on a surface of the container and at the 1 m distance from it, the detectors are located at the height of H=715 mm.  Figure 3. Relation between the attenuation coefficient and initial energy of gamma radiation (---at the container surface --at a distance of 1 m from it) The relative error of attenuation coefficient depends on number of the registered gamma quanta, the less is the number of registered accounts, the more the statistical error is.
The attenuation coefficient decreases with increase of initial energy of radiation ( fig. 3). According to standards of radiation safety, maximum permissible levels on a surface of packing and at distance of 1 m are regulated. Knowing the attenuation coefficients, it is possible to calculate maximum permissible capacities of an equivalent dose of initial radiation on the surface of the container (Hperm1) and at distance of 1 m (Hperm2) which will satisfy the demanded level after attenuation by the container wall (Hd). Maximum permissible capacity of an equivalent dose of the monoenergetic gamma radiation which does not interact with the protection is provided in the table: = × Radioactive waste is usually a mixture of radioactive nuclides. Thus, the maximum permissible capacity of an equivalent dose of unreduced gamma radiation will be defined by a total contribution of each nuclide:

Numerical buildup factor of accumulation of ionization radiation
After passing the protection the gamma radiation consists of scattered and primary gamma radiation. In some cases, contribution of the scattered radiation increases the dose of the reduced primary radiation by 1-2 orders of magnitude. This effect is accounted for by introducing a buildup factor B in a law of reduction of the primary gamma rays: where µ is the linear attenuation coefficient for photons of the energy E0, d is the linear thickness of the protection, В is the buildup factor, E0 is the gamma quantum energy, Z is the atomic number of the material protection, r is the distance from the radiation source to detector of gamma radiation. Figure 4 shows the energy dependence of the buildup factor for protective container. Dose points are considered at the container surface and at the distance of 1 m.  ) with decreasing of the initial photon energies, and this reduces quantity of gamma-quanta. The competition between these processes leads to appearance of peaks in gamma-quanta spectrum and in the buildup factors.

Conclusions
The reinforced concrete container designed to transportation and temporary storage of radioactive contaminated graphite blocks of channel-type reactor was investigated. The reduction of gamma radiation by the protective container was simulated. The radiation characteristics of the container with their relative errors were calculated.
The relative errors of equivalent dose, attenuation coefficient and buildup factor are almost equal and reach 10 % for the scattered radiation and 5 % for initial gamma radiation.