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Bernard L. Cohen*
Abstract
The oral ingestion toxicities of buried high level radioactive waste from nuclear power plants and of the natural radioactivity in the ground are calculated and expressed as cancer doses (CD), the number of fatal cancers predicted by the linear-no threshold theory if all of the material were fed to people. Unless the size of the U.S. nuclear power industry is greatly expanded, there will probably never be more than 2 trillion CD in U.S. repositories, as compared with 31 trillion CD in the ground above them. Measurements of the U, Th, and Ra in human bodies indicate that the latter cause 500 deaths per year in U.S. The great majority of this material is derived from the top few meters of soil that are penetrated by plant roots. It is concluded that the annual number of U.S. deaths from buried nuclear wastes will be about 1.0 (or less), orders of magnitude less than the number from coal burning electricity generation, the principal competitor of nuclear power.
*Dept. of Physics, University of Pittsburgh, Pittsburgh, PA 15260
Key words: radioactive waste, natural radioactivity, risk analysis, toxicity
Introduction
One of the most difficult problems in public understanding of nuclear power is the health hazard from buried radioactive high level waste (HLW).The purpose of this paper is to present an approach to easing that problem by developing comparisons with naturally occurring uranium and thorium (and their decay products) in the ground. For HLW, the danger comes from ingesting radioactivity with food or drink, so we will consider that source of risk from the natural radioactivity. Radiation doses from the latter can be determined from direct measurements of the amounts of these materials in human bodies. This has the advantage of avoiding modeling procedures used in other approaches to estimating effects (Cohen 1986).
The end point of our calculations is the number of cancer doses, CD, in the HLW and in the naturally occurring materials in the ground. The number of CD is the number of cancer deaths expected according to linear-no threshold theory, if all of the material were fed to people. It is calculated on the basis of 0.05 deaths per person-Sv of whole body equivalent radiation exposure (ICRP 1991).
CD in HLW buried as spent fuel
A report by Croff and Alexander (1980) based on the ORNL ORIGEN code lists the radioactivity in spent fuel (including the cladding and other fuel assembly structural materials) from a pressurized water reactor (PWR) at various times after producing 33,000 MW-days (thermal) per metric tonne (te); with 90% capacity factor and 33% efficiency, this converts to 30 te/GWe-y. The radioactivity, R, is listed in Ci/te, which can be converted to CD/GWe-y as
CD/GWe-y = R Ci/te x 30 te/GWe-y x 3.7 x 1010 Bq/Ci x D Sv/Bq x .05CD/Sv
= 5.6 x 1010 x R x D
where D is the sum of the weighted committed dose equivalents to all target body organs and tissues, obtained from ICRP Publication 30 (ICRP 1979). Values of D for the principal contributors are listed in the second column of Table 1. As an example, for Am-241, ICRP 30 gives, for oral ingestion, 3.4 x 10-8, 1.0 x 10-7, 3.2 x 10-7, and 1.4 x 10-7 Sv/Bq respectively to the gonads, R-marrow, bone surfaces, and liver, which sums to 5.9 x 10-7 Sv/Bq weighted committed whole body dose equivalent. The CD/GWe-y calculated in that way are listed in Table 1 for various times after fuel discharge from the reactor.
The bottom row of Table 1 gives the total CD, the sum of the CD from all radioactive isotopes. Contributions from all radioactive isotopes not included in the Table give a negligible contribution to these sums. For reactors operating continuously for T years with their HLW buried in repositories, the number of CD in repositories is obtained by adding the number of CD each year (interpolated from the bottom row) up to time T. For T=100 years, this is 1.9 x 1010 CD/GWe; for T=300 years, it is 3.1 x 1010, and for T=1000 years it is 8.0 x 1010.
It is difficult to conceive of a policy of burying spent fuel without reprocessing for more than 100 years, or at most 300 years; raw uranium will be quite scarce and expensive by that time, and fossil fuel supplies will probably be in even shorter supply. It therefore seems reasonable to expect that after 100-300 years, we will be dealing with reprocessed HLW. The CD/GWe-y from the important contributors to this waste are listed in Table 2, the sums are shown in the bottom row, and the number of CD in repositories from this material up to time t is obtained by adding the year after year contributions, as was done for Table 1, up to time t. For t=100 years this is 8.6 x 109 CD/GWe; for t=300 years it is 1.1 x 1010 , and for t=1000 years it is 1.3 x 1010 .
To assess the combined effects of buried spent fuel for the first 100 years and reprocessed HLW thereafter, we recognize that the contributions from Sr-90 and Cs-137 remain at their saturation level, 2.0 x 108 CD/MWe, times their average lifetime, (30y/ln2 =)43 y, which is 8.6 x 109 CD/MWe. The contribution of Am-241 from Table 2 eventually saturates at 6.4 x 106 times its average lifetime, (432y/ln 2 =)630y, or 4.0 x 109 CD/ GWe; its contribution from spent fuel (Table 1) is initially 1.2 x 1010 and the two contributions become equal, 3.0 x 109 each, at t = 870y. During this time period the contributions from the other actinides remain unimportant, so the total inventory of material in repositories at that time is (8.6 x 109 + 3.0 x 109 +3.0 x 109 =) 1.5 x 1010 CD/GWe, still less than the 1.9 x 1010 at T=100 y for buried spent fuel.
Going beyond a few hundred years would require considerations of breeder reactors which burn actinides, but that is beyond the scope of this work. In summary, these calculations indicate that if reprocessing begins after 100 years, at no time in the next few thousand years will the quantity of radioactive material in repositories exceed 1.9 x 1010 CD/GWe. If reprocessing is delayed for 300 years, this will increase to 3.1 x 1010 CD/GWe; availability of raw uranium very probably precludes going beyond 300 years before reprocessing. To simplify further discussion we will use 2.0 x 1010 CD/GWe as the maximum toxicity in repositories for the next several thousand years.
CD in the ground from natural U, Th, and their decay products
The area of U.S. (contiguous 48 states) is 8.0 x 1012 m2, rock has an average density of 2.5 te/m3, and on average this includes 1.7 g/te of uranium. The quantity of uranium per meter of depth is the product of these three numbers, 3.4 x 1013 g/m which converts to 4.2 x 1017 Bq/m. All U-238 decay products have this same activity. The average thorium content of rock is 5.8 g/te; an analogous calculation to the above gives the thorium content to be 11.6 x 1013 g/m which converts to 4.9 x 1017 Bq/m; this applies to each of the Th-232 decay products.
For the U-238 decay chain, application of ICRP-30 (as in the previous section) gives whole body equivalent committed doses in Sv/Bq of 0.6 x 10-7 for U-238, 0.7 x 10-7 for U-234, 1.5 x 10-7 for Th-230, 3.0 x 10-7 for Ra-226, and 4.4 x 10-7 for Po-210, a total of 10.2 x 10-7 Sv/Bq. For the Th-232 decay chain this is 7.4 x 10-7 for Th-232, 3.3 x 10-7 for Ra-228, 1.0 x 10-7 for Th-228, and 0.9 x 10-7 for Ra-224, a total of 12.6 x 10-7 Sv/Bq. Multiplying these totals by the Bq/m from the last paragraph and the conversion factor 0.05 CD/Sv, gives
For U-238, 4.2 x 1017 x 10.2 x 10-7 x 0.05 = 2.1 x 1010 CD/m,
For Th-232, 4.9 x 1017 x 12.6 x 10-7 x 0.05 = 3.1 x 1010 CD/m
The sum of these, 5.2 x 1010, is the number of cancer doses per meter of rock depth in the ground under U.S. .
From measurements on human corpses, the amounts of U, Th, and their decay products in human bodies is well known, and from these it is reasonably straightforward to estimate average whole body dose equivalents (UNSCEAR 1988). In microsieverts per year from the U-238 decay chain, these are 5 from U-238 ( U-234, 7 from Th-230, and 7 from Ra-226, for a total of 19. For the Th-232 decay chain these are 3 from Th-232, and 13 from Ra-228 ( Ra-224 for a total of 16. Oral ingestion of all of these materials combined thus gives us an annual dose of (19 +16 =) 35 x 10-6 Sv/y. The number of deaths these presumably cause is then (35 x 10-6 Sv/y x 0.05 deaths/Sv x 280 x 106 population =) 500 deaths per year in U.S.
Nuclear power wastes vs natural radioactivity in the ground
Typical depths proposed for HLW repositories are about 600 meters. The toxicity of the natural radioactivity in the ground closer to the surface than these repositories would then be (5.2 x 1010 x 600 =) 3.1 x 1013 CD. It gives some perspective to compare this with the wastes from nuclear power buried in these repositories. There are now about 88 GWe operating in U.S. and little prospect that this number will grow to more than 100 GWe in the next few decades. Using that number as the average until reprocessing begins, and our estimate of 2.0 x 1010 CD/GWe leads to a maximum of 2.0 x 1012 CD eventually in repositories. Thus there will probably always be at least 15 times as many CD of natural radioactivity in the ground above the repositories as there are CD of HLW in the repositories. If we assume that an atom of nuclear power HLW has the same probability for human ingestion as an atom of radioactivity in the ground above it , the 500 deaths/y from the latter would lead us to expect (500/15 =) 33 deaths per year from the HLW. This is far less than one percent of the deaths we now experience from air pollution due to coal burning (EPA 1996, Wilson and Spengler 1995), the principal competitor to nuclear power for generating electricity.
But this comparison is grossly unfair to nuclear power. The vast majority of U and Th in our food comes from the top few meters of soil which is penetrated by plant roots. About half of our dietary intake of Uranium comes from drinking water (NCRP 1984), about half of our drinking water derives from ground water, and it has been shown that rock at 600 m depth is only 1/7 as likely to encounter ground water as the average rock above it (Cohen 1985a). Thus the 33 deaths per year derived above should be multiplied by x x 1/7, which gives about 1.0 death per year due to HLW.
One obvious question about this comparison between natural radioactivity in the ground under U.S. and buried HLW arises from the fact that the latter is much more concentrated. But this does not matter! According to the linear-no threshold theory, the number of deaths expected is just the total number of CD ingested by humans, and this does not depend on the variations in local concentrations. In fact the high concentration of radioactivity in the HLW makes it practical to monitor for escaping radioactivity, and to take other measures which improve its security. Of course, the localized high concentrations mean that only the populations near HLW repositories would experience this 1.0 death per year (assuming it is not averted by monitoring for escaping radioactivity or by progress in curing cancer over the next thousands of years), while the entire U.S. population benefits from the electricity. But that unfairness applies to every segment of our economy. For example, the harmful effects of air pollution from the steel industry are experienced mostly by people in the Pittsburgh, PA and Gary, IN areas and from the oil refining industry by people in the Houston, TX area, whereas the products of these industries benefit the entire nation. In these examples, the harmful effects are hundreds of times more serious than those from the buried HLW.
As another perspective on this issue, the many thousands of years delay between use of the electricity today and the deaths caused by its waste products, combined with population mobility, means that people harmed by the waste because of living near a repository are equally likely to be the distant progeny of any one of todays users.
An interesting application of Tables 1 and 2 is to compare the toxicity of buried HLW with that of the uranium originally mined to fuel the reactors that produced the wastes. Raw uranium requirements for current reactors are about 160 te/GWe-y which converts to 2.0 x 1012 Bq/GWe-y. Multiplying this by 10.2 x 10-7 Sv/Bq and 0.05 CD/Sv gives the toxicity of the uranium originally mined, assuming it is in equilibrium with its decay products, to be 1.0 x 105 CD/GWe-y. From interpolation of the bottom rows of Fig. 1 and 2, this is equal to the toxicity of spent fuel after 110,000 y and of reprocessed HLW after 21,000 y.
Questionable aspects of this analysis
One obviously questionable part of the above analysis is our assumption that materials in HLW, principally Am and Pu according to Table 1, are no more easily transferred from the ground into our food than the naturally radioactive materials in the ground, U, Th, and Ra. A review of data on these (Cohen 1984, Fig. 1) indicates that this condition is well satisfied. Am and Pu are among the least transferable of elements, whereas U and Ra are roughly average in this respect. The Cs and Sr in HLW are somewhat more transportable but their effects in Tables 1 and 2 are grossly exaggerated because our analysis ignores the very substantial time delays for escaping radioactivity to reach the environment due to the time required for ground water to penetrate the casings and dissolve the HLW, the slow movement of ground water combined with the long distance that it must travel to reach the surface, and ion exchange hold-up of Cs and Sr in passing through rock normally each of these three factors independently delays release by hundreds of years or more.
A more substantial question is whether ground water can more easily dissolve an atom of HLW, as spent fuel or as a product of reprocessing, than an atom of ordinary rock. With all the debates about the security of HLW burial, there has been little consideration of this question, which perhaps implies that it is not a problem. I have raised the issue in some of my papers (Cohen 1985b, 1986), but there has been no response. If it is decided that this is a serious problem, there are solutions available for making the HLW chemically similar to ordinary rock, and it is important for these to be pursued. If it is not a problem, the conclusion from the calculations presented here is that fears of buried HLW are grossly overblown.
References:
Cohen BL. A generic probabilistic risk assessment for low level waste burial grounds. Nuclear and Chemical Waste Management 5:39-47;1984
Cohen, BL, A simple probabilistic risk analysis for high level waste repositories, Nuclear Technology 68:73-76;1985a
Cohen BL. Critique of the National Academy of Sciences study of the isolation system for geologic disposal of radioactive waste. Nuclear Technology 70:433-440; 1985b
Cohen BL. Risk analysis of buried waste from electricity generation. Am J Phys 54:38-45;1986
Croff AG and Alexander CW. Decay characteristics of once through LWR and LMFBR spent fuels, high level wastes, and structural material wastes. Oak Ridge,TN: Oak Ridge National Laboratory Report ORNL/TM-7431;1980
EPA(U.S. Environmental Protection Agency), Air quality criteria for particulate matter, Washington, DC: U.S. EPA;Report EPA/600/P95-/001CF;1996
ICRP (International Commission on Radiological Protection). Limits for Intakes of Radionuclides by Workers, Oxford: Pergamon Press; ICRP Publication 30. Annals of the ICRP 3; No. 1-4;1979
ICRP (International Commission on Radiological Protection). 1990 Recommendations of the International Commission on Radiological Protection, Oxford: Pergamon Press; ICRP Publication 60. Annals of ICRP 21: No. 1-3 (p.153);1991
NCRP (National Council on Radiation Protection and Measurements), Exposures from the Uranium Series with Emphasis on Radon and its Daughters, Bethesda, MD: NCRP Report No.77; 1984
UNSCEAR (United Nations Scientific Committee on Effect of Atomic Radiation). Sources, Effects, and Risks of Ionizing Radiation. New York: United Nations;1988
Wilson R and Spengler J. Particles in Air: Concentrations and Health Effects, Cambridge, MA: Harvard University Press;1995
Table 1: CD/GWe-y in buried spent fuel due to the principal radioactive isotopes, vs time after removal of fuel from the reactor. The second column lists the whole body equivalent dose in Sv/Bq used in their calculation.
______________Years out of reactor______________
Isotope Sv/Bq 10y 30y 100y 300y 1000y 10,000y 100,000y
Sr-90 3.6x10-8 1.2x108 7.2x107 1.2x107 1.2x105 6.0x10-3
Cs-137 1.4x10-8 6.5x107 4.1x107 7.8x106 7.8x104 7.8x10-3
Am-241 5.9x10-7 5.6x107 1.1x108 1.3x108 8.9x107 2.9x107 3.2x102
Pu-239 1.2x10-7 2.1x106 2.1x106 2.1x106 2.1x106 2.0x106 1.6x106 1.2x105
Pu-240 1.2x10-7 3.6x106 3.6x106 3.5x106 3.4x106 3.2x106 1.2x106 8.7x101
Am-243 5.9x10-7 5.6x105 5.6x105 5.6x105 5.6x105 5.3x105 2.2x105 5.0x101
Sums 2.4x108 2.2x108 1.4x108 9.4x107 3.4x107 3.0x106 1.2x105
Table 2: CD/GWe-y in reprocessed HLW due to principal radioactive isotopes, vs time since removal of fuel from the reactor
Years out of reactor________________
Isotope 10y 30y 100y 300y 1000y 10,000y 100,000y
Sr-90 1.1x108 7.0x107 1.3x107 1.1x105
Cs-137 6.4x107 4.1x107 7.8x106 7.8x104
Am-241 6.4x106 6.4x106 5.9x106 4.3x106 1.4x106 3.0x102
Pu-239 1.1x104 1.1x104 1.1x104 1.1x104 1.3x104 2.6x104 3.4x103
Pu-240 2.6x104 3.7x104 4.4x104 4.4x104 4.1x104 1.6x104 1.1x100
Am-243 5.6x105 5.6x105 5.6x105 5.6x105 5.3x105 2.2x105 4.6x101
Sums 1.7x108 1.1x108 2.7x107 5.1x106 1.9x106 2.6x105 3.4x103
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