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mix in the primary coolant. This weighted mean ppc value can then be compared with the gross activity resulting from the mix of the signifi- cant isotopes listed. In computing the weighted mean ppc value for coastal waters, and the gross activity, which are included in Table 3 for the SAVANNAH primary coolant and in Table 5 for the NAUTILUS primary coolant, only the isotopes listed in these Tables have been con- sidered. Very short lived isotopes are not included in the calculation. BASIS FOR EVALUATING SAFE DISCHARGE RATES The partial permissible concentrations in the various subdivisions of the marine environment given in Table 2, and utilized by this working panel in the computations which follow, are based on long time exposure of a selected segment of the population. After release of a given volume of liquid wastes or of spent ion exchange resin to the sea water, proces- ses of diffusion will continually reduce the concentration of activity in the water. There will occur a certain period of time during which the activity in a restricted volume of the sea water may possibly exceed the environmental limits which are based on long term exposure. The pur- pose of the following development is to provide criteria which would in- sure that no significant volume of a given marine locale would have an average activity exceeding the ppc value for that locale over a signifi- cant period of time. Let A designate the area of a particular marine region within which E discharges of radioactive materials are made during the time period T. Further, designate by t\/2 the time interval required to re- place 50% of the water in the area A. with "new" water from an adjacent, uncontaminated area. The area A must be chosen such that the N. con- taminated volumes are randomly distributed throughout the area, as a result both of variations in the discharge site and of the movement of the contaminated volumes by currents. The time period T_ must be short compared to a man's lifetime, but long compared to the time required for the maximum concentration of activity from a point source discharge to be reduced by processes of dispersion to less than ppc values for the environment. The concentration of activity at a given position and a given time which results from a single discharge is designated by Â£, and the incre- ment of area within which the concentration varies from s ' 1/2 ds to to s + 1/ 2 ds during the increment of time dt is designated by dA. Further, let the total area within which the concentration at any time Â£ exceeds the ppc values for the environment be designated by Appc , *nd let the time required to reduce the concentrations everywhere in the area to less than ppc values be designated by tppc. 27
The double integral A 0 0 ppc sdAdt then represents the total activity, per unit of depth, which occurs in the area having concentrations exceeding ppc values, times the time interval during which the concentration exceeds that critical value. The area of "new" water available for dilution each time period .T is given by Hence the relationship ppc /â¢ PPc 2 N ppc /â¢ / / I I J J A x T2 0 0 then defines a mean concentration for the total area A^ during the time period T, resulting from N discharges, each having the same amount of activity. This relationship serves to establish the criteria for eval- uating the suitability of any particular marine area as a receiver of radioactive wastes from nuclear-powered ships. If the distribution of contaminated volumes within the area were truly random at all times, and if the processes of biological concen- tration of radioisotopes were instantly reversible, then a suitable cri- terion for safe discharge to the marine environment would be the re- quirement that the mean concentration defined by the above relationship be less than the ppc value (here designated as s Ppc ) for that environ- ment. Unfortunately, marine organisms which take up radioisotopes when in contact with sea water of a given concentration of activity, do not reach a new equilibrium readily when exposed to water of much lower activity. Also, it 'would be difficult to assure a completely uni- form distribution of the contaminated volumes within the subject area. Finally, and perhaps most important, the condition discussed in the previous section entitled "Restrictions on the Application of ppc Values in Seafood and in the Marine Environment" must be satisfied. There- fore, the criterion employed here is that the mean concentration de- fined by the above relationship be 1/100th of the ppc value for the en- vironment; that is, the number of releases N in the area A. during the time period T. must satisfy the relationship 28