Methods of Analysis

General Concepts for Various Models

The image of the damage and the pathways of the radioactive materials are shown schematically in Fig. 3.1. These events, together with the leakage of the primary containment vessels (PCVs), caused significant release of radionuclides to the environment.

The real situation was far more complicated. Thermally damaged top-head flanges, cracks in pipe inlets in the PCV, and vent pipes between the PCV and the

Fig. 3.1 Schematic drawing of the reactor damage and behavior of radioactive materials

suppression chamber (SC) have been regarded as possible leak paths. Indeed, three units exhibited different features of cooling failure (see Chap. 2 of this volume).

Figure 3.2 shows schematically the behavior of radioactive materials in the environment after their release from the reactor facility. In order to assess the direct effects of the radioactive release to the environment, we must make use of the inventory of radionuclides and chemical elements in the fuel just before the accident; release from the fuel at the accident; existence states of radionuclides in the RPV, PCV, and reactor building; release from the stack or reactor building; migration in the atmosphere; contamination of soil; and ambient dose rate from radionuclides in the soil and in the atmosphere.

There are basically two approaches to evaluating the amount of environmental release of radionuclides. One is based on analysis of the physical and chemical conditions of the core fuel. In this approach, a fraction of the released amount is approximated with certain plausible values. The other is based on “radiation mapping” made by monitoring the excess ambient dose rate and/or radioactivity measurement of the contaminated soils. The former is an indirect method because

Fig. 3.2 Radioactive materials in the environment

the radioactive species need to be assumed from other information or knowledge. However, in the early stages of the accident it is more convenient than the latter.

Model 1: Release from Fuel with Known/Assumed Inventory

Amounts of radionuclides, such as fission products (FPs), uranium (U), plutonium (Pu), and minor actinides (MAs) in the reactor fuel need to be evaluated. Information about the chemical elements is also important for the stoichiometric estimation of the chemical forms of released fission products. This can be calculated with the help of the ORIGEN code [1], which is based on the theory of production and the following radioactive decay of FPs and MAs.

A cause for release of radioactive materials at all reactors was that decay heat of fission products had not been eliminated due to loss of the cooling function. Consequently, the fuel rods were exposed to steam and the fuel and cladding were heated up, which resulted in generation of hydrogen gas by chemical reaction between zirconium and steam above 900 °C. The reaction

Zr + 2H2O → ZrO2 + 2H2 produces hydrogen, which caused the subsequent hydrogen explosions. It also produces heat because this reaction is exothermic.

This heat accelerates the heating of the fuel combined with decay heat. At high temperatures uranium made an eutectic compound with zirconium. The melting point of this eutectic is lower than uranium oxide. Figure 3.3 shows high temperature phenomena of the fuel relating to the core-melt progression [2, 3]. Some radioactive materials in the fuel soluble in UO2 were released following heating and melting of the fuel. The fraction of released radioactive materials from the heated

Fig. 3.3 High temperature phenomena in the core [2, 3]

fuel depends on the vapor pressure (i.e., melting point) and diffusivity in the fuel. These behaviors are strongly dependent on the temperature. A release rate constant k [min−1] as a function of the temperature T [K] is given by

k = k0 exp(−Q/RT ), (3.1)

where Q is the activation energy [kcal/mol], and R = 0.001987 kcal/mol K the universal gas constant.

Although Q depends on the chemical species, Oak Ridge National Laboratory (ORNL) and others proposed, in their CORSOR-O model [4], to use the common Q of 55 kcal/mol for all species and the dependence on the species is represented by the empirically corrected k0. For example, k0 = 12,000 min−1 for Cs and Kr while it is 9,600 min−1[= 0.8 × k0 (Cs)] for I and Te. The results are shown in Fig. 3.4.

Using the CORSOR-O model, the fraction of inventory released from the fuel at time t is obtainable. Taking Cs as an example for calculation, the fractions of inventory released at 1,800 °C are: F = 90 % at t = 2 h; and F = 100 % at t = 4 h.

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