CHANGE OF QUALITY OF A RADIOACTIVE WASTE UNDER LONG STORE TERMS

By calculation methods, the dose rate of the radioactive waste, behind concrete protection, was evaluated in current work. Parameters, which were taken in account in the calculations, are geometry of the protection shell, size of the source and its isotopic composition. As model geometrical parameters the spent fuel assembly’s size and thickness of the concrete wall of the ventilated storage container (VSC)-VVER were taken. The computer program that does numerical calculation was composed in the Wolfram Alpha environment. The program takes into account change of the isotopic composition and spectra of gamma-radiation with time. Calculation results were compared to the known data on the spent nuclear fuel heat dissipation. Approach described in this work can be used for fast estimation of change in the quality of radioactive waste (RAW) in the long-term storage without recycling, for different initial isotopic composition. Obtained results were analyzed on the matter of change in gamma-radiation of RAW.

Leaving aside the cosmic origin and associated with uranium mining radionuclides, in this paper we will consider 2 forms of RAW: 1) contained in SNF; 2) the so-called operational waste of nuclear plant. According to the established terminology, in countries, where radiochemical or other recycling is not intended (for example -Ukraine), it belongs to the high-level RAW (HLW).  The calculation uses the percentage value of the contribution to the total activity of the isotope source at a time (2) Renormalizing condition according to (1) (3) Data on the total activity of SNF and its behavior were investigated and presented in [12]. The dose rate can be calculated based on the isotopic composition.

CALCULATION OF GAMMA-CONSTANT
Rationale for a common approach When working with the real sources of ionizing radiation such as SNF four factors should be accounted for: 1) the geometry of the problem, 2) self-absorption in the source, 3) the effect of shielding, 4) the isotopic composition of the emitter. Since the isotopic composition of the radionuclide mix changes over time, factors 2 and 3 does not remain constant. In this context, it is convenient to use, as a characteristic of the source, a generalized gamma constant (GGC) [13,14], which takes into account the self-absorption in the volume source and the possible presence of protection and is numerically equal to the ratio of gamma-radiation at the observation point to the activity of the source. Generalization means that in calculations several factors are accounted for such as different radioisotopes in the sources, each with its differential gamma constant and account self-absorption in the body of the source and possible protective screen, absorption of which different for each energy of radiation.
As a model for the calculation of the source fragment of the standard VVER-1000 has been selected, presented in the form of a cylinder with diameter of 250 mm and height of 2.5 meters with the closest to the real filling, consisting of 322 kg of uranium dioxide, 109 kg of zirconium and 14 kg of steel, located in the air. The disposition of fuel and concrete protection is shown on the Fig. 3.
Radionuclide composition of the SNF was taken according to 2000 y. [15] data and is given in Table 1 below. There are also differential values of gamma constant of the radionuclides components.
The composition of fission products from Table 1 after 3 years of aging was selected for calculation. For smaller aging time the SNF data was not considered because the problems, discussed in this article, related to the quality of the radiation protection of the concrete, where the fuel is stored after 3 years of aging. Another reason is the intense radiation of short-lived isotopes in fresh spent fuel, making it difficult to measure its composition.  3. Geometry for computation [12] The attenuation coefficient for concrete protection can be taken from known tables. And the attenuation coefficient due to self-absorption for the spent fuel assembly (SFA), consisting of several components with total amount of (uranium -450 kg, 55 kg oxygen and zirconium 200 kg). For calculations instead of zirconium the data for attenuation coefficient were taken for the nearest element with known tables of absorption coefficients, in this case molybdenum. It was assumed that these elements are distributed uniformly over the volume. Accordingly, knowing the density of each element and the mass attenuation coefficient [13] it is possible to calculate the total linear attenuation coefficient.

Method of calculation of the GGC
The dose rate of gamma radiation was calculated by the standard method [13] at the point opposite the midcylinder power at a distance of 1 m from its axis, also with placing concrete wall with thickness of 30 or 60 cm between the source and the observation point. Gamma constant of the j-th isotope containing several gamma lines can be calculated as follows: (4) where -gamma constant for a certain line of energy -quantum yield of photons of a given energy. Here, j -the index of the isotope in the mixture, i -the index of the gamma line.
Total dose rate of a mixture of isotopes can be expressed as: where j is the index of isotope, r is the distance from the source to the observation point.
Generalized gamma constant -the ratio of gamma radiation and the activity of A at a distance r, which can be written as follows: (6) Substituting in (6) the expression (5) yields: This expression was used by us to calculate the GGC for ideal point source. For the volume cylindrical source dose rate calculated according to [13]: (8) here h is the height of the cylinder, b is the distance from its axis to the observation point, R is the radius of cylindrical source, and d is the thickness of the protection screen.
Reduction factors for self-absorbing cylinder ( ) and protection (μ) depends on the energy of photons, therefore, the dose must be calculated separately for each gamma line. The total dose rate -the sum of the partial dose powers.
For radiation of one isotope, we have: And GGC of the self-absorbing cylinder with one emitting isotope with a protective screen we get: As you can see, this value does not vary with time as it does not contain time dependent arguments. For GGC isotope mixture, the total activity A can be obtained: In this expression activity and gamma constant of individual elements are multiplied, making it impossible to separate them into two separate sum (sum of the activities and the amount of gamma constant). In this case, the value of the GGC is time dependent because for different isotopes half-life is different, thus the percentage contribution of the j-th mixture isotope will vary.
Expression (12) was used to calculate the generalized gamma constant (GGC) cylindrical self-absorbing source with protection.

The results of calculations of external radiation SNF
Authors have developed a unique computer program, which calculated gamma constant according to the eq. (12). The decay of the SNF isotopes was also taken inti account as a change to the energy distribution of the gamma spectrum. Fig. 4,5 show the calculated dependence of the GGC versus time for an ideal point source and a source with selfabsorption accordingly. Accounting for self-absorption in the source characterizes the heat release caused by gamma radiation of the SFA. Obtained GGC is consistent with the data from [11], if the activity is calculated for the data of the Table 1. Also, from this graph, you can conclude that the dose rate of the ideal source decreases slower than activity with time the first five years, and then decline is at the same speed. This is due to the rapid depletion of the isotopic composition of gamma emitters in the first 3-5 years of age and accompanied by an increase of GGC. Values of the GGC curve on Fig. 5 about an order of magnitude smaller than on Fig. 4 due to self-absorption power. Also, this graph proves the rule, which says that the total activity of the SNF mixture the first 30 years is decreasing faster than the decay heat.