An important dement of the engineered-barriers system used for burying radioactive wastes is the container in which the wastes are placed in solid or solidified form. The construction of the containers and the materials from which they are made can differ substantially. When choosing and developing a new construction, container types must be compared with one another according to their capability to retain radionuclides. For underground storage or burial of wastes radionuclides escape primarily by diffusion into the interstitial moisture through the container wall. Many factors influence the escape of radionuclides. The main ones are the character and rate of leaching from the solid matrix or solid wastes, the diffusion and sorption properties of the container wails and the medium surrounding the container, and the construction of the container, specifically, the shape of the container.It is most convenient to compare different container types or container constructions, taking account of the large number of variable factors, on the basis of a mathematical model describing the escape of radionuclides. As a measure or criterion characterizing the retaining properties of a container, it is convenient to choose the quantity of radionuclides escaping from the container surface per unit time into the surrounding medium (the flux from the entire surfaceor the escape rate). This quantity, as indicated in [1], can serve as a direct characteristic of an engineered barrier, such as a container. The amount of radionuclides entering the external medium and the amount remaining inside the container can be determined by summing the amount of radionuclides escaping from the container in a definite time interval.In the present paper a numerical-analytical method of calculating approximately the rate of escape of radionuclides from containers with different shapes -sphere, cylinder, parallelepiped -is proposed and investigated. It is assumed that a container with solid or solidified waste is placed in a medium whose properties are different from those of the container walls. The proposed computational method makes it possible to find the rate of escape of radionuclides when the diffusion properties of the container walls and of the surrounding medium differ substantially. The difference in the effective diffusion coefficients can reach a factor of 105. Ordinarily, the finite-difference methods employed in such cases are unstable near the location where different media abut one another. This instability results in the appearance of oscillating solutions and makes it impossible to calculate with acceptable accuracy the rate of escape of radionuclides.To confirm that the accuracy of the calculation of the rate of escape of radionuclides is adequate, the proposed method is compared with the grid method for cubic and cylindrical containers.The proposed method is used to investigate the influence of the container shape on the escape rate of radionuclides. The retaining properties of concrete containers with the most common shapes and s...
There are a large number of works (specifically, [1][2][3][4][5]) concerning methods for calculating the concentration of contaminating substances, propagating with ground waters, outside the pollution sources: holding ponds, disposal sites for tailings, contaminated water-bearing strata. However, there are no works, either here or abroad, on processes occurring simultaneously in the source of pollution and in its environment as a whole.The present paper fills this lacuna from both the methodological and computational standpoints. We present here a mathematical model and a numerical algorithm for solving the problem of the escape of radionuclides from containers with solidified radioactive wastes in a surface disposal site and their propagation along the site and the lower-lying layer of rock down to the surface of the water-bearing stratum located beneath the disposal site. Interstitial water, which enters the disposal site through the top insulating screen and the cover with the precipitation and snow melt, is the main agent which transports the radionuclides.Physical Model and Sehematization of the Conditions. The object of investigation is a surface disposal site for radioactive wastes in activity groups I and II. Concrete containers in the form of cylinders or rectangular parallelepipeds with solidified or solid wastes are placed here. The wastes themselves can be packed in steel barrels. The storage site consists of a square iron-concrete cavity in the surface layer of soil. The disposal site is covered with concrete slabs. An isolating screen consisting of compacted clay covered with a layer of earth is constructed above the top cover 9 A sorption layer consisting of a mixture of sand and clay cart be present beneath the disposal site. A water-bearing zone is located underneath the disposal site and separates it from a water-bearing stratum. According to the standard requirements, the thickness of this zone must be greater than 4 m.The containers in the disposal site are piled one on top of another. In some designs the space between the containers is filled with a filling material -sand or bentonite. The filling material can also be packed between the rows of containers.As a possible scenario of escape of radionuclides from the disposal site we consider a situation when the protective screen, the top cover, and the base at the bottom have fractured with time so that precipitation from the surface freely passes through them. It is assumed that the container walls have not changed and the radionuclides can escape through them to the outside only by diffusion in the moisture located between the interstitials. It can be assumed that the precipitation at the location of the disposal site is distributed uniformly throughout the year.In the model at hand, it is assumed that the concentration of radionuclides reaching the inner wall of the container and the change in this concentration in time are known.The aim of the calculations is to determine the concentration of the migrating radionuclides on the surface of t...
The design of surface storage pits for low-level radioactive solid waste has changed substantially as the nuclear industry has developed. The simplest design was a trench with no engineering structures, which was f'dled with wastes, spread with dirt, and then covered by a layer of earth. Today's design is a reinforced-concrete container, which can have an absorptive bottom if required, a cover consisting of absorptive and drainage layers, and water-resistant clay side walls.In spite of the significant changes, pit designs have retained their main features: an upper drainage layer, a more or less homogeneous mass of solid wastes inside (e.g., contaminated soil, debris, etc.), and a location near the surface of earth that is not completely saturated with moisture.In order to analyze the state of today's storage pits and to plan a generation of new ones, it is necessary to evaluate how they affect the environment over the time that the wastes are potentially hazardous.The essence of the safety analysis of surface storage pits is the calculation of the concentration of radionuclides that escape from the pit after water enters. This concentration is used to calculate the contamination of the aquifer under the pit and to determine the individual effective dose to a person using water from the contaminated source.Here we describe a mathematical model and give a numerical algorithm for determining the concentration of radionuclides that reach the surface of an underlying aquifer from a radioactive-waste storage pit when precipitation leaks through it. It is assumed that the pit design has all the above-mentioned main features. Our approach to solving this problem is to determine alternately the percolation rate of water and the migration of radionuclides in the saturated-unsaturated region, which consists of an aeration zone and an underlying aquifer. As opposed to other models for calculating percolation in the aquifer ([1] and [2], for example), this model has time-varying moisture-transport coefficients that depend on the saturation of the medium, and thus can consider how changes in the amount of precipitation and the level of the ground water affect the escape of radionuclides from the pit.Based on this solution method, we can calculate the escape of specific radionuclides that occur in different chemical states. The state of a radionuclides is considered by choosing the appropriate retention coefficient. In general, it depends not only on the porosity of the medium and the absorptive properties of the soil and the nuclide, but also on the chemical form of the nuclide, pH, the ground water, etc. Therefore, in order to obtain the desired results, the calculations must use input data that correspond to the specific pit location and the specific chemical form of the migrating nuclide.The initial radionuclide concentrations in the interstitial water inside the pit are assumed to be known. The best method for estimating the initial concentration for a similar type of heterogeneous sources is still an experiment to determ...
A mathematical model for estimating the escape of radionuclides from storage sites for radioactive wastes with an irregular arrangement of sources of contamination, for example, sources of ionizing radiation, piled on one another, is described. The model is tested for a particular case where the problem can be solved analytically. An example of the regularization of a heterogeneous medium with a complicated structure is given. Regularization makes it possible to simplify the initial problem and calculate the flow of radionuclides out of the volume containing the irregularly arranged sources of contamination.When analyzing the safety of storage and burial of radioactive wastes, storage sites not only with a regular arrangement of sources of radioactive contamination (concrete and reinforced concrete containers, steel barrels, and others) but also an irregular arrangement are studied. These include storage sites containing radioactive garbage, soil contaminated with radioactive fallout, sources of ionizing radiation piled in containers, debris from metal structures with induced activity, and others. To simulate the propagation of radionuclides along such irregular heterogeneous media, the internal structure of the storage site must be simulated in each specific case. The simplest method of simulation is regularization of a heterogeneous medium.In the present paper, an example of such regularization is studied. It makes it possible to simplify the initial problem and to calculate the flow of radionuclides out of a volume containing irregularly arranged sources of contamination. The calculations are based on the mathematical model of [1], which makes it possible to find the distribution of the radionuclide concentration in a volume filled in a regular manner with sources of contamination in the form of a square parallelepiped, a straight circular cylinder and a sphere, as well as outside the volume with sources.The criteria for assessing the radiation safety of storage sites could be the maximum concentration of radionuclides inside and outside the storage site (for monofactor contamination), which is compared with a normative quantity -the intervention level when individual radionuclides are ingested for the population (IL water ) [2]. For simultaneous contamination with several radionuclides, the safety criterion could be the effective equivalent irradiation dose to an individual person ingesting contaminated water, calculated according to the specific concentration of radionuclides in the water.Mathematical Formulation of the Problem. A regular, uniform block-type medium with voids (channels) between the blocks is studied. The blocks in such a medium are sources of contamination. The voids between the blocks can be free or filled with a filler material -gravel, sand, bentonite. This medium can be filled with standing water or ground or infiltrating waters with filtration rate U 0 can pass through the medium. In the absence of water in the voids between the blocks the radionuclides can be transfered along the mediu...
We obtained densified chemically fixed silicon nitride (DCFSN) by pressureless sintering of the Si3N~-Y203-MgO system maintaining the sintering temperature up to 1800~The specimens having a density of 2.4-2.5 g/cm 3 were obtained in advance by synthesizing compact silicon powders containing certain sintering-activators in nitrogen atmosphere and were subjected to densification. In order to avoid dissociation of silicon nitride, the specimens were densified according to the technique of Giachello and Popper [I]: the specimens were placed in a particulate charge consisting of silicon nitride, boron nitride, and the oxides similar to the additives present in the material requiring densification.The KPS-type silicon of semiconductor-purity having an average dispersion of 5 ~m was used as the raw material. In this case, during nitriding, the degree of transformation of silicon into nitride was found to be 100%.The densification processes begin to occur even at 1450~ and their maximum rate is observed in the 1600-1700~ range. Initially, densification of the material occurs according to the liquid-phase diffusion mechanism. As the temperature increases, additional mechanisms begin to operate (dissolution and recondensation of silicon nitride in the glass phase to form elongated B-Si3N 4 grains).The microstructure of the synthesized ceramic consists of silicon nitride crystals having a diameter of 0.1-0.5 ~m in the transverse section (Fig. i). The phase composition of the ceramic is represented by the following crystalline phases: ~-and ~-Si3N~, yttrium silicates and Si3N4.Y203. Magnesium compounds are present in the form of a small quantity of MgSiOs. An analysis of the regions of coherent scattering showed the presence of elongated grains of the crystalline ~-Si3N~ phase [at (hks = (I01), the size is 0.5 ~m and at (hks = (202), it is 15.7 ~m].* After densification, the microstructure is represented by the ~-SisN~ grains having a hexagonal cross section; they are in the form of columnar crystals having a diameter of 0.7 ~m and different degrees of elongation (Fig. 2). Grains measuring 15-17 ~m in length are encountered.An analysis of the microstructure shows that in spite of the sufficiently high content of the activating agents in the original powder, glass phase is virtually absent at the grain boundaries and the fracture of the ceramic is transcrystalline in nature.At a heat treatment temperature of 1750-1800~ the density of the ceramic approaches the theoretical density and amounts to 3.2-3.3 g/cm s and its linear shrinkage attains a value of 6.0-6.5% (Fig. 3a). The increase of the density in the 1750-1800~ range (that is not related to the densification processes and the linear dimensional changes) owes to the diffusion of magnesium oxide from the particulate charge into the specimen. During the densification process, the particulate charge containing the oxide additives creates a specific gaseous atmosphere that hinders not only the dissociation of Si3N~, but also the diffusion of MgO or other magnesium compounds ...
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