Radioactive contamination of bottom sediments in the upper reaches of the Techa river: analysis of the data obtained in 1950 and 1951

Abstract

A stationary sorption model has been developed for re-evaluating and analysing archive data from 1950–1951 on the radioactive contamination of Techa river bottom sediments close to the site of liquid radioactive waste discharge. In general, good agreement was obtained between calculations and measurements, which substantiates further the assumptions and conclusions in two preceding articles, on the radionuclide composition of discharged liquid radioactive waste. Estimates on the effective liquid radioactive waste discharges given here are significantly different from those deduced in the 1950s, i.e. in summer 1950 and October 1951. The results are discussed in relation to the Techa River Dosimetry System 2000 (TRDS-2000) that has recently been presented to serve as a means for estimating doses to the Techa river residents. Parameter values describing the exponential decrease of bottom sediment contamination along the river due to short-lived radionuclides, such as ¹⁰⁶Ru, and ¹⁴⁴Ce, agree reasonably with those used in TRDS-2000. However, for other radionuclides, such as ⁹⁵Zr, ⁹⁵Nb, ⁹¹Y, ⁹⁰Sr and ¹³⁷Cs, substantial differences are found. It is demonstrated that water flow rate, width of the river, and surface area of bottom sediments are important parameters which were not adequately taken into account in TRDS-2000. Also, the stirring-up of contaminated bottom sediments and their subsequent transport by the water flow are seen to be an important mechanism that governs the radionuclide transport downstream. This mechanism was not included in the TRDS-2000 model. It is concluded that the sorption model used in TRDS-2000 for the reconstruction of radioactive contamination of water and bottom sediments of the Techa river in 1949–1951, is subject to considerable errors. While the present paper is focussed on details of the dosimetric modelling, the implications for the Techa river dosimetry are major. They will be further elucidated in a forthcoming paper.

Appendix

Assume that at the location x=0 of the river there is a stationary (i.e. time-constant) LRW discharge of activity into the river system. The activity is subsequently distributed between water and bottom sediments of the river, the remaining activity being transported downstream with the flow. After a certain time the river system will, along its entire length, reach a stationary distribution of specific activity in exchange layer of the bottom sediments, i.e. in the layer that is involved in the sorption/desorption processes. Given this stationary pattern in the sediment surface, the rate of radioactive decay of any of the radionuclides will be proportional to the rate of change of the activity flow D(x), i.e. the activity transported by the river through the position x per unit time.

Consider a differential volume element in the exchange layer of the bottom sediments:

$$ dV = w \cdot h \cdot dx $$

where w is the width of the river (taken to be constant along its entire length), h is the thickness of the exchange layer of the bottom sediments, and dx is the extension of the considered volume element in the direction of the river flow. The change of the activity due to radioactive decay in the considered diffential volume element of the bottom sediment can then be represented as follows:

$$ dR{\left( x \right)} = \lambda \cdot A{\left( x \right)} \cdot \rho \cdot dV $$

where λ is a decay constant, А(х) is the specific activity of bottom sediments in the river section (activity per dry weight) and ρ is the density (dry weight per total volume of wet sediments) of the bottom sediment exchange layer.

Assume that the activity per unit volume in the river water, С(х), is in dynamic equilibrium with the activity in the exchange layer of the bottom sediment in any river section. The change of the radioactive outflow D(x) from the elementary section can be expressed as follows:

$$ dD{\left( x \right)} = Q \cdot dC{\left( x \right)} = Q \cdot dA{\left( x \right)}/K_{d} $$

where Q is the water outflow rate (taken to be constant along the entire length of the river), К _d is the distribution coefficient for the radionuclide of interest in the “water-bottom sediment” system (scaled to dry weight).

The activity balance in the system that is being considered is expressed by the following equation:

$$ \begin{aligned} & dD{\left( x \right)} = - dR{\left( x \right)} \\ & {\text{or}} \\ & \frac{{dA{\left( x \right)}}} {A} = - \sigma \cdot dx \\ \end{aligned} $$

with the constant:

$$ \sigma = \lambda \cdot w \cdot h \cdot \rho \cdot \frac{{K_{d} }} {Q} $$

The solution of this equation is:

$$ A{\left( x \right)} = A_{0} \cdot e^{{ - \sigma x}} $$

where А ₀ is the specific activity of the bottom sediments at the LRW discharge site (х=0).