[ RadSafe ] Fukushima and the Pacific - some calculations

Mon Jan 6 10:28:27 CST 2014

OK - so let's do some math!

According to a report put out by PNNL the total radionuclide inventory of Units 1 and 3 was about 2.30 x 10^17 Bq about three months (100 days) post-shutdown (I will have to post the URL for this report later - can't find it at the moment). If we assume that this is for each reactor then the total fission product inventory of the three affected reactors is about 7x10^17 Bq. This is based on the ORIGEN computer code, although I can't remember if it was based on the actual or the worst-case power history for these reactors.

The volume of the Pacific Ocean is about 7x10^17 cubic meters (http://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html). This means that if the entire fission product inventory of all three Fukushima reactors were to magically dissolve into the Pacific Ocean the average activity concentration would be about 1 Bq/cubic meter or about 1 mBq/liter (there are 1000 liters per cubic meter).

The concentration of natural radioactivity in seawater is about 12 Bq/liter (http://www.physics.isu.edu/radinf/natural.htm), primarily K-40. This suggests that the worst-case event - complete dissolution of all three reactor cores into the Pacific Ocean - would add insignificantly to the amount of radioactivity naturally present in the seawater.

If we take this a little further and assume (to make things easy) that ALL of the radioactivity is Cs-137 then we can calculate the radiation dose to someone immersed in the water. According to Federal Guidance Report 12 (http://www.epa.gov/radiation/docs/federal/402-r-93-081.pdf) the dose conversion factor for immersion in water containing dissolved Cs-137 is about 1.5x10^-20 Sv/sec for every Bq/cubic meter. Doing the unit conversions (3.15x10^7 seconds per year) shows us that living continuously in water with 1 Bq/cubic meter of Cs-137 would give a radiation dose of about 5x10^-13 Sv annually. I'd suggest that this is a radiation dose not worth worrying about, and it certainly falls into the category of what the ICRP calls a "trivial" dose of radiation. And even if the spent fuel pools contain 100 times as much radioactivity as the operating reactors (which is almost certainly not the case) the radiation dose is still incredibly low.

This is a VERY quick and dirty calculation that is highly conservative. The conservative parts are:

-Assumes the entire fission product inventory dissolves into the seawater
-Does not account for decay since the 100 day point
-Assumes continuous exposure to the radionuclide-containing seawater
-Assumes all of the dose comes from gamma-emitting Cs-137 (as opposed to alpha and beta emitters)

And, to keep everyone honest, here are the parts of this that are not subject to much conjecture:

-Fission product inventory is based on the physics of nuclear fission and was calculated by a tried-and-true computer code
-The Law of Radioactive Decay seems to operate consistently across the universe (we can see evidence of this in the spectra of supernovae at great distance)
-The volume of the Pacific Ocean is fairly non-controversial
-The dose conversion factor for various nuclides is based on energy deposition per unit mass and these are also fairly non-controversial

Thus, barring a math mistake (always possible) there shouldn't be much argument about the calculated radiation dose. And I know I can count on all of you to let me know if I had a keystroke error!

So - barring some freak concentration of radionuclides by a factor of many orders of magnitude - there seems to be no plausible mechanism for the reactor cores to cause death and destruction across the Pacific. So residents of our Pacific Coast states (plus Hawaii) would seem to be safe.


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