that this limiting collective dose will be exceeded by 50% at particular nuclear plants in specific years is equal to only 4%. Analogously, for the individual dose an arithmetic mean value of 5.5 mSv can be taken as a monitoring value, which has a probability of being exceeded by 60% in specific years at particular nuclear plants of not more than 4%.

It can be seen from Table 1 that the mean individual and collective dose values for a single unit VV~R-1000 plant for the first few years of operation do not exceed the monitoring values already mentioned for a nuclear plant with two VVER-440 units.

The average value of the normalized collective dose for a VVER-440 reactor [9.2 man-Sv/ (MW-yr)] exceeds the analogous dose for new WER-1000 reactors by more than a factor of two. The values cited are close to Western data for PWRs [5, 6].

LITERATURE CITED

i. United Nations Scientific Committee on the Effects of Atomic Radiation, 1982, Report, p. 372.

2. N. V. Beskrestnov, E. S. Vasil'ev, V. F. Kozlov, et al., "Radiation doses to WER-440 nu- clear plant staff," in: Radiation Safety and Nuclear Plant Shielding [in Russian], ~ner- goatomizdat, No. 8, Moscow (1984), p. 41.

3. G. Diehev, G. Khitov, R. Fisher, et al., in: Radiation Safety in VVER-440 Serial Nuclear Plants, 2nd Conference of Comecon Member Nations on Radiation Safety in Connection with Nuclear Plant Operation [in Russian], ~nergoatomizdat, Bk. i, Moscow (1983), pp. 47-51.

4. K. P. Shirokov (ed.), Methods for Processing the Results of Measurement Observations [in Russian], Izd-vo Standartov, Moscow-Leningrad (1972).

5. M. Plews, M. Wakerley, and R. Winyard, "Comparing PWR exposures world-wide," Nucl. Eng. Intern., 31, No. 381, 46-48 (1986).

6. UN SCEAD, Present-day Radiation Exposure Associated with Nuclear Power Production [Rus- sian translation], A/AC, 82/R, 443 (1986).

PARADOX WITH THE DISCHARGE OF RADIOACTIVELY CONTAMINATED WATER

A. L. Kononovich UDC 621.039

The operation of a nuclear reactor-driven power plant entails the use of flowthrough vessels for the treatment of radioactive waste products discharged into rivers, streams, and canals. Modern standards for the control of such aqueous discharges are based on the restric- tion of the individual dose for a representative of the critical group of persons to the pres- ently accepted value of 5 mrem per year for the first group of critical organs [I], taking into account both internal and external irradiation.

Calculations show that the dose to which a human being is exposed is proportional to the concentration of the radionuclide in control objects placed in the surroundings. From this point of view, it would appear that for waste water discharged into flowing basins, such as rivers or canals, the level of radioactivity could be reduced by simply diluting the waste

water with uncontaminated water up to the limits set by the carrying capacity of the canal and the uncontaminated water reserves. However, pronounced dilution intensifies the natural processes of concentration, so that the necessity to comply with radiation safety provisions limits the use of dilution. The aim of the present paper is to consider the accumulation of radioactive contamination along the bottom of the body of water through undissolved particles and to show that an increase in the amount of waste water discharged leads to an increase in the concentration of radionuclides in certain parts of the river.

The transport of radionuclides by the current and the contaminants from the bottom of the river are examined within the framework of the following model:

Translated from Atomnaya Energiya, Vol. 67, No. 4, pp. 269-271, October, 1989. Original article submitted November 18, 1988.

756 0038-531X/89/6704-0756512.50 �9 1990 Plenum Publishing Corporation

S 10

J

H, a ,

20 la

JO ~-

Fig. 1

.r4

A Ul

Z

U3

I

ZO z#O EO ~, m 3 tsec

Fig. 2 Fig. 3

Fig. i. Profile of a canal (a) and schematic of the canal plan (b): x is the distance from the site of discharge, and L represents the coordinates of the banks (with the horizontal axis coincident with the center of the canal for b).

Fig. 2. Longitudinal distribution of the radionuclide concen- tration p in the contaminant along the canal bottom. The curve represents particles with sinking velocity u = 2"10 -3 m/sec.

Fig. 3. Dependence of contamination along the bottom of the canal on discharge rate of waste water: A is the ratio of con- tamination along the bottom of the canal at the critical point for the given rate of waste water discharge to contamination along the bottom of the canal at the critical point for a dis- charge rate of 16 m3/sec; B is the flow rate of water into the canal. The curves represent particles with sinking velocities u I = 2"10 -2 m/sec, u 2 = 2"10 -3 m/sec, and u 3 = 2"10 -4 m/sec.

- two contaminant phases are present - particles in suspension and particles along the bottom of the river;

- between these phases an exchange takes place, during which the influx of radionuclides in suspension is proportional to the concentration of the contaminant along the bottom;

- it is assumed that there are no whirlpools present at fixed positions;

- globally seen, consumption of contaminants through tributaries is negligibly small, compared with that in the main part of the river;

- migration processes in the longitudinal and transverse directions are independent of one another.

From this last condition, it follows that the distribution functions for the radionu- clides found along the bottom of the river can be represented in the form of the product of

757

these two independent factors. The first of these describes the longitudinal transport and the exchange between phases, and the second describes the process of transverse turbulent diffusion and the dilution owing to the influx of uncontaminated water, such as from ground- water and tributaries. In the present paper, we assume that the accumulation time for the contaminants described by the first factor is infinite, corresponding to the most hazardous case possible.

The balance of radioactive material then leads to the following system of equations for the stationary function describing the longitudinal contaminant distribution:

V H (Oq/Ox) -- ~O - ~q - - ~Hq; ( 1 ) P(Op/Ox)~ - - ~ p + ~ q - - k 6 p .

Here, x is the coordinate directed along the river, q and p are the concentrations of the radionuclide in the suspended phase (the average value over the vertical direction) and along the bottom of the river, V is the velocity of the current, H is the depth of the river, X is the decay constant for the radionuclide, P is the amount of contaminant from the river bottom swept along, 6 is the "thickness" of the migrating layer of contaminant from the river bot- tom, and ~ and $ are kinetic parameters describing the mass exchange rate between the phases.

Owing to the stochastic character of the transport of the river bottom contaminant, the quantity ~ is statistically characterized as a random process with the dimension of length and is not defined by concrete geometric dimensions.

To determine the kinetic parameters, it is necessary to make use of a specific model of dynamic transport, a consideration which goes beyond simple material balance. The kinetic parameter ~ depends on the diffusion model employed for the vertical redistribution of con- taminant particles within the body of water. At the boundaries of the turbulent layer, with thickness HT, the time necessary to reach an equilibrium distribution is ~i = HT2/D, where D is the vertical component of the turbulent diffusion coefficient. At the boundaries of the transitional layer, the Prandtl thickness 6pr is reached and the time required to reach equi- librium is T 2 = ~pr/U, where u is the sinking velocity of the particles. The resulting equa- tion for the kinetic parameter is

The quantity ~/~ is determined by the ratio of the carrying capacities of the river to the density of the contaminant along the river bottom. The carrying capacity of the river can be calculated from the formula

S~ILISNP(V~/H),

and the specific amount of contaminant particles swept along, by the relation

where

P~O,~)2 (v/]/~,~) ~ ( v - v i ) (d/~)o,'~,

V. --1,4 ~ ln(H/7d)(dmax/d)I /7; 1

N and F a r e p a r a m e t e r s in t h e L e v i - K a r a u s h e v model [2 , 3 ] , g i s t h e a c c e l e r a t i o n o f a f r e e l y f a l l i n g body, d and dma x a r e t h e mean and maximum d i a m e t e r s o f t h e c o n t a m i n a n t p a r t i c l e s along the river bottom, and V i is the initial velocity with which the contaminant particles are swept along.

For the light-weight fraction, as long as the relation SP << ~VH is satisfied, the sys- tem of equations (i) can be replaced by the simpler system

{ vH(oq/Ox)=~p-~q_~q~; (2) P--~q/(~+~).

The solutions to the systems of equations (i) and (2) are found numerically by an itera- tive method with the aid of a computer.

As an example, we consider the contaminant distribution along the bottom of a canal, for which the profile is illustrated in Fig. I. The results are shown in Fig. 2. It can be seen

758

that, at greater depths, an increase is predicted in the amount of contaminants along the bottom of the canal. Such an effect was in fact observed by these authors in [4].

Let us consider the effect of an increase of the waste water discharge rate on the amount of contaminants along the bottom of the canal at the point of their maximum concentration

Pmax.

Near x = 0 it is assumed that there is a uniform concentration of radionuclide in the contaminated water. The volume of discharged waste water is proportional to the discharge rate, that is, to the amount of radioactive material entering the system per unit time. A change in this parameter results in a change in the flow rate of the radionuclide and in the depth at which it is found at each part of the canal. The relation between the depth and the flow rate is determined by the equation V = Cv~, where I is the inclination of the canal bed [5]. Calculations were performed for particles containing the nuclide 51Cr, for three different sinking velocities of the contaminant particles: 2"10 -2 , 2"10 -s, and 2"10 -# m/sec. From the results shown in Fig. 3, an increase can be seen in the specific activity of the contaminant along the bottom of the canal at the point with Pmax for all three particle frac- tions. However, for the particle fraction with sinking velocity 2"10 -3 m/sec, the behavior is nonmonotonic at the beginning of the curve. For the fractions with sinking velocities 2"10 -s and 2.10 -# m/sec, the point Pmax occurs at a distance of 6.5 km from the site of dis- charge. For the 2"10 -2 m/sec fraction, a change in the rate of waste water discharged into the canal influences the location of the point Pmax- This results from the fact that, for heavy particles, the residence time in the contaminant along the canal bottom is greater than that for light particles and also that the effect of radioactive decay is more significant. For this reason, the point Pmax is located closer to the site of discharge than in the deeper parts of the canal.

It is worth noting that a coarser model not properly accounting for the finiteness of the rate of equilibrium buildup between the contaminant along the bottom of the canal and the suspended contaminant particle phase does not predict an increase in the concentration of radioactive material at the point Pmax for an increase in waste water discharge rate. Let us consider this point in greater detail. According to the mechanics of turbulent flow, as was shown in [3], the contaminant carrier capacity is proportional to the square root of the ratio of flow rate to depth, which holds true for a broad class of "turbidity" models. For this kind of behavior, to a first approximation the carrying capacity varies with the canal bed characteristic, that is, with the inclination of the bottom and the Chezy coefficient, and does not depend on the rate of water influx into the canal. Consequently, such models pre- dict an increase in the size of the contaminated zone with an increase in the waste water discharge rate into the canal for canals with uniform concentrations of radioactive material in the contaminants along the bottom of the canal and in the water discharged.

But the mechanisms discussed are not the only possible causes of an increase in the con- centration of radionuclides in certain objects present in aqueous systems with an increase in the rate of waste water discharge. These processes are the consequence of changes in the flow regime and distribution of contaminants in a real system with an increase in the rate of water influx into the canal. In the general case, a consideration of this effect is very time-consuming. Therefore, for engineering calculations of the radiation content, it is ad- visable to determine this as the ratio of the amount of radioactive material in the system per unit time to the concentration at the critical point for maintaining hydraulic stability under system normal conditions [6]. In practice, such a constraint hardly affects the re- sult, but significantly simplifies the calculation.

LITERATURE CITED

i. Sanitation Principles in the Design and Operation of a Nuclear Power Plant, SPAES-79, ~nergoizdat, Moscow (1981).

2. A. V. Karaushev, Theory and Methods for the Calculation of River Deposits [in Russian], Gidrometeoizdat, Leningrad (1977).

3. I. I. Levi, Dynamics of River Currents, ~nergoizdat, Moscow (1957). 4. Yu. A. Egorov, S. V. Kazakov, and N. V. Staurin, "The influence of basin depth on the

contents of radionuclides along the bottom," in: Radiation Safety and Protection at Nu- clear Power Plants [in Russian], No. II, ~nergoizdat, Moscow (1986), pp. 75-80.

5. P. G. Kiselev, Hydraulics [in Russian], Energiya, Moscow (1980). 6. A. L. Kononovich and L. P. Kham'yanov, The Radiation Content of Objects in the Environ-

ment, in: Atomic Electrical Stations [in Russian], No. 9, ~nergoatomizdat, Moscow (1987), pp. 171-174.

759