Chapter 3 



DISPOSAL OF RADIOACTIVE WASTES IN THE OCEAN: THE FISSION 



PRODUCT SPECTRUM IN THE SEA AS A FUNCTION OF TIME 



AND MIXING CHARACTERISTICS ^ 



Harmon Craig, Scripps Institution of Oceanography, University of California, 



La Jolla, California 



I. Introduction: Estimated output of nuclear 

 heat and fission products at "steady state" 

 nuclear power production 



In two other papers in this report, Wooster 

 and Ketchum discuss mixing rates in the oceans 

 on the basis of oceanographic data, and the 

 present writer reviews the natural isotopic stud- 

 ies which bear on the problem. In this paper 

 we attempt to construct a detailed quantitative 

 picture of the fission product spectrum in the 

 ocean, in steady state with a given fission rate. 

 Such an attempt may well be termed premature, 

 in view of our sketchy knowledge of the in- 

 ternal mixing rate in the sea. Nevertheless, we 

 know a good deal more today than was known 

 five years ago, enough at least to make some 

 simple model calculations which may well yield 

 correct results to an order of magnitude. More- 

 over, the construction of a model and the cal- 

 culation of its characteristics are often highly 

 informative, and, at the very least, provide a 

 basis for the orientation of future studies. 



The following figures, available in various 

 sources, are pertinent to the estimation of fu- 

 ture consumption rates of nuclear power. 



Present U. S. electrical energy: 



6x 10^ mwh/yr. 



Present world electrical energy: 



10^ mwh/yr. 



Present world energy consumption (all 

 sources) is about 4.5 X lO^" mwh/yr, doubling 

 every 30 years. 



For the present calculations, we shall assume 

 a stationary world fission rate of U--^ equal to 

 1000 metric tons/yr, supplying all the fission 

 products to be disposed of in the sea. We 

 shall then attempt to construct as reasonable a 



^ Contribution from the Scripps Institution of 

 Oceanography, New Series, No. 902a. 



picture as possible of the fission product ac- 

 tivity in the sea, when this activity reaches 

 steady state with the rate of fission, i.e., when 

 the decay rate of each fission product in the sea 

 is equal to the rate at which it is being dumped 

 into the sea, so that its concentration remains 

 constant. We shall also make some calculations 

 for a linear build up to such a fission rate in 

 50 years. 



Since 1 gram of U^^^ is equivalent to 24 

 mwh, our assumed fission rate of 1000 tons of 

 U235 pej. ygar is equivalent to 2.4 x 10^° mwh/ 

 yr of nuclear heat. At 50 per cent efficiency, 

 this is equivalent to a world nuclear power 

 consumption of 1.2 xlO^** mwh/yr. If this 

 latter figure represents 10 per cent of the total 

 world energy utilization, we are then assuming 

 a world consumption of 1.2x10^^ mwh/yr, 

 which seems not unreasonable as an estimate 

 for the year 2000 A. D. 



Thus a fission rate of 1000 tons of U-^^/yr 

 represents a 2.7 fold increase in the present 

 world energy consumption, 10 per cent being 

 derived from nuclear heat with 50 per cent 

 efficiency, which should be reached in about 

 the year 2000 based on the present trend in 

 energy consumption (see above) . Our calcu- 

 lations will all be linear with the fission rate, 

 so that data for other fission rates are easily 

 derived from the present calculations. 



The build up of fission products in a reaactor 

 is given by: 



where / = fission yield (per cent of fissions 

 yielding an individual fission product, the sum 

 equalling 200 per cent) , R is the rate of fission 

 (atoms U^^Yyr) here assumed constant and 

 equivalent to 1000 tons of U^^^/yr, and N = the 



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