Regarding the contaminated water in turbine buildings

Two days ago we first got the report that there is highly radioactive water in the turbine building basement of reactor 1. NISA released this list of isotopes found in the water and its activity per cubic centimeter. I added half lives to the list to make it more understandable.

       
nuclide activity(Bq/cm³) half life Q value (keV)
Cl-38 1,60E+006 37,24 min 4916,53
As-74 3,90E+002 17,77 days 2151
Y-91 5,20E+004 58,51 days 1544,82
I-131 2,10E+005 8,025 days 970,86
Cs-134 1,60E+005 2,065 days 1233,38
Cs-136 1,70E+004 13,04 days 2548,22
Cs-137 1,80E+006 30,08 years 1175,63
La-140 3,40E+002 1,679 days 3762,22



We see that there is one peculiar things, a high activity of Chloride-38. The only way for Chloride-38 to be created is by Chloride-37 in seawater absorbing a neutron and turning into Cl-38. This would indicate there is still a considerable neutron flux in the core. Forum discussions have been going on about it. The other peculiar thing is the activity levels, the activity per cm³ is just crazily high. I suspect they are really measuring activity per liter and mistakenly report it as cubic centimeter and I will give 2 arguments for that.

1. The activity of the water
They reported that 3 workers had been working in the water for more than an hour, their dosimeters showed a dosage close to 200 mSv and two of the workers didn't wear rubber boots so they got a large surface dose on their ankles and feet from beta radiation(some reports say up to 6 gray). But this does not match with the activity levels seen in the table I pasted above. If one multiplies the activity in Bq/cm³ with the Q value, i.e the energy released in the decay of one atom, and massage the numbers a bit to get the numbers in joules instead of keV and in cubic meters instead of cubic centimeters. Then one finds that the water is putting out 1.68 Watts per cubic meter of water. Something like 20% of that energy is from gamma rays, the rest is beta rays and recoil energy in the decaying nuclei.

1.68 Watts doesn't sound like a lot given that a normal water kettle can have a power of 1000 W. But in terms of ionizing radiation 1.68 W is just crazy. Radiation dose is measured in Grays, one Gray is equal to one joule absorbed by one kg of tissue and a Watt is as we know one Joule per second. A one Gray whole body dosage is enough to get radiation sickness, 10 Grays will kill you slowly(over a few days) and 100 Grays kills you instantly.

These workers where working in water that is putting out watts of radiation, that means they should have gotten hundreds of Grays in an hour. It was stated they where knee deep in this water! Now if we instead consider that perhaps they mean activity per liter, misstakenly reported as cubic centimeters, then everything goes down by a factor of 1000(there are one thousand cubic centimeters in a liter). Instead of hundreds of Gray the workers would have gotten hundres of milligray, that is consistent with their dosimeter readings.

2. The neutron flux needed to create Cl-38
The probability that a Cl-37 atom will absorb a neutron and turn into Cl-38 is quite low, 1 barn(this probability is measured in a unit called barns, one barn=10^-24 cm², uranium has as comparison a fission probability of  about 600 barns). So one needs a lot of neutrons to create any significant quantity of Cl-38. If one assumes the water concentration of Cl-38 has dropped by a factor 1000 when traveling from the reactor vessel to the water in the turbine hall basement(dilution, decay etc).  Then one can make a rough approximation of the neutron flux needed in the core in order to create the Cl-38 concentration seen in the turbine hall(technically solving the Bateman equation for a equilibrium case with one group cross sections).

Neutron flux ends up being around 10¹²  neutrons per square centimeter and second. A reactor running at full power produces on the order of 10^14 n/cm²*s. The core would have to be running at about 1% of its full power(10-20 MW thermal) to produce that flux, but I might as well be off by a factor of 10 in my estimate of dilution, which would put the power in the rage from 1-100 MW. We can exclude 100 MW since we have not seen a pressure and temperature spike that high in reactor number 1. We can not exclude 1-10 MW power levels because it is on the same order as the decay energy. But if we also again here assume they mean Bq/liter instead of Bq/cm³ then the needed flux to produce the Cl-38 goes down to something around 1*10^9 neutrons/cm²*s. That kind of neutron flux could plausibly be around from radioactive decay or a very very low power level.

Those 2 factors together makes me believe they are reporting activity levels wrongly. Lets see if I will have to change my opinion when new information arrives.

Notes for the interested.

To convert from the unit eV(electron volt) to joule one multiplies 1 eV with 1.602*10^-19

The Bateman equation describes the time dependent concentration of radionuclides. For the case of a nuclide created by a neutron flux and destroyed by decay one gets this equation

dN/dT= N_37*sigma_37*flux - N_38*lambda_38
Where:
N_37=number of Cl37 atoms per cubic centimeter(I assumed saturated salt water at 100 degres, which gives 0.39 grams of salt per cm² which gives 9,74*10^20 Cl37 atoms per cm³)
sigma_37=neutron capture cross section, around 1*10^-24 cm²
flux=neutron flux in neutrons per cm² and second
N_38= Number of Cl-38 atoms per cm³.
lambda_38 = decay constant for Cl-38(equals to Ln(2)/half life)

If one assumes equilibrium then dN/dT=0 and one gets that

flux=N_38*lambda_38/(N_37*sigma_37)

One get N_38 from dividing activity with decay constant and then multiplying by a dilution factor.
Here are all the numbers I plugged in in case someone can spot an error.

Find flux
           
Avogadros number 6,02E+023        
Salt density(gram per cm3) 3,90E-001     Dilution factor(from vessel to puddle) 1000
Molar mass sodium 2,30E+001     Cl37 capture cross section 1,00E-024
Molar mass chlorine 3,55E+001     Cl37 number density (per cm³) 9,74E+020
Moles of NaCl 6,67E-003     Cl38 lambda 3,10E-004
Fraction Cl-37 2,42E-001     Cl38 number density (per cm³) 5,16E+009
Moles Cl-37 1,62E-003        
Number of Cl-37 per cm³ 9,74E+020     Flux 1,64E+012

 

Links(english)

Kyodo News Woes deepen over radioactive waters at nuke plant, sea contamination
Reuters Soaring radioactivity deals blow to Japan’s plant
BBC Radiation soars at japan reactor
NHK extreme radiation detected at number 2 reactor

Links(swedish):
DN Arbetare evakueras efter akut strålning
SvD Fler svenskar misstror kärnkraft
SVD Nya bakslag vid Fukushima
Aftonbladet tio miljoner gånger högre strålning
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