Use of a Two-Dimensional Stationary Radionuclide Migration Model for Predicting the 137Cs Content in the Enisei River System

A mathematical model of the transport of radioactive impurity in a two-dimensional uniform flow is examined. This model is used to predict and reconstruct the levels of radioactive contamination of water, bottom deposits, and flood plain soils of the Enisei on a 250 km long section of the river below the discharges from the Krasnoyarsk Mining and Chemical Combine. The model is based on the two-dimensional turbulent diffusion equation and takes account of the interaction of radioactive substances between the water mass (solution, suspension) and bottom deposits. The input parameters of the model are determined from in situ investigations performed on the Enisei in the period of 1990 to 2000. The Maple V R4 symbolic mathematics program package is used for the calculations.The model is verified on the basis of measurement results obtained in expedition studies of the Enisei River in 1991 (the period when the direct-flow reactors were in operation) and 1998, 2000. Comparing the computed and measured ¹³⁷Cs concentrations in the water in the top layer of the bottom deposits showed good agreement. The model is also used to estimate the contamination of flood plain soil during a flood period. Measurements obtained in model experiments with soil samples, which were performed over several years on the Berezovyi Island, are used to check the calculations.The application of the model for solving the inverse problem makes it possible to estimate from the known concentration of individual radionuclides in the flood plain soil the intensity of the discharges that produced the radioactive contamination during a flood period. The 1996 flood is examined as an example.