# Total Fukushima radiation releases compared to total core inventories

• Fukushima
I'd like to start a new thread regarding the technical and numerical aspects of the radiation releases of Fukushima Daiichi.

Does anyone know how big the iodine and cesium core- and SFP inventories were before the accident happened?
I'd like to compare the released amount to the amount which was originally there.

Furthermore I'd like to conclude from which of the units most of the releases came and why. I hope you'll be able to help. :)

http://www.nisa.meti.go.jp/english/files/en20110412-4.pdf" [Broken]
http://www.tepco.co.jp/en/press/corp-com/release/betu11_e/images/110421e2.pdf"
http://fukushima.grs.de/sites/default/files/Messwerte_ODL_Fukushima_Daiichi_110421-1230_Gesamt.pdf"

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## Answers and Replies

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NUCENG
Science Advisor
I'd like to start a new thread regarding the technical and numerical aspects of the radiation releases of Fukushima Daiichi.

Does anyone know how big the iodine and cesium core- and SFP inventories were before the accident happened?
I'd like to compare the released amount to the amount which was originally there.

Furthermore I'd like to conclude from which of the units most of the releases came and why. I hope you'll be able to help. :)

http://www.nisa.meti.go.jp/english/files/en20110412-4.pdf" [Broken]
http://www.tepco.co.jp/en/press/corp-com/release/betu11_e/images/110421e2.pdf"
http://fukushima.grs.de/sites/default/files/Messwerte_ODL_Fukushima_Daiichi_110421-1230_Gesamt.pdf"
I'll pull some numbers together. Your inteest is probably just Cs-137 and I-131 because they are the only isotopes we can compare to Fukushima measurements. Since the damage is only to units 1,2 ,3, and 4, can we ignore the share fuel storage pond and units 5 and 6?

Start thinking about a few things:

How much of the core will be retained in vessel?
How much airborne release or leakage from containment?
How much liquid release from containment?
What age will you assume for spent fuel in fuel pools?

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Since the damage is only to units 1,2 ,3, and 4, can we ignore the share fuel storage pond and units 5 and 6?
Good question . Bit odd that power has been restored to reactor control room for reactors 5+6 for over a month and yet it's operational status according to the JAIF updates continues to be "Estimated"?

I'll pull some numbers together. Your inteest is probably just Cs-137 and I-131 because they are the only isotopes we can compare to Fukushima measurements. Since the damage is only to units 1,2 ,3, and 4, can we ignore the share fuel storage pond and units 5 and 6?

Start thinking about a few things:

How much of the core will be retained in vessel?
How much airborne release or leakage from containment?
How much liquid release from containment?
What age will you assume for spent fuel in fuel pools?

Thanks for your answer.

Interest: Yes, mainly I131 and C137. Other isotopes are not of concern. I played a little with the Chernobyl radioactive materials and IAEOs I131 conversion table. In Chernobyl, I131 and C137 alone were responsible for over 80% of the converted I131 activity. Other isotopes won't change the "danger"-math.

Ignoring: Yeah, of course.

Core retaining: I skimmed through your documents but didn't find charts for core releases based on partial meltdowns and containment venting. I have to admit that I was hoping for your response when I created this thread. There's only a german source which calculated core releases based on different accident scenarios:
http://www.biu-hannover.de/atom/unsicher/teil2.htm#4
I think in our case it's something between "Heizrohrleck im Dampferzeuger" (don't know how to translate this - probably a leak in the condenser) and "Kleines Leck im Sicherheitsbehälter (Niederdruckpfad)" (Containment leakage)
Overall I'd think that 1-10% of the core inventory of I131 and C137 has escaped.

Airborne release: Well, that's the only thing we know for sure, since there are the NISA numbers they used for INES-7

Liquid release: That's a good question... I think all damaged or broken fuel rods have probably released most of their fission products into the basement. The constant waterflow should have washed it out.

Age for spent fuel: I think if we're only concentrating on C137 then age should be of no concern. We could say that all iodine is effectively gone, but that nearly all of the original C137 is still there. I don't think that the rods are older than five years.

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Astronuc
Staff Emeritus
Science Advisor
Based on the following, I'd expect rank of source strength: Units 3, 2, 1. Unit 4 would have a higher Cs/I ratio due to its shutdown on Nov 30, 2010, and lower source strength than the other units.

Code:
             ------- Capacity Factors % ------   Startup
Unit Assys   Sep  Oct  Nov  Dec  Jan  Feb  Mar  Current Cy  (TEPCO)
1    400   10.9   99  100  100  100  100   34    Sep 27   (Sep 27)
2    548   49.2    0   38  100  100  100   34    Nov 20   (Nov 18)
3    548   21.3  100  100  100  100  100   34    Sep 24   (Sep 23)
JAIF - http://www.jaif.or.jp/english/aij/index2.html [Broken]

Assembly in Unit 1 = 173 kgU
Assemblies in Units 2, 3 and 4 = 175 kgU

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Assembly in Unit 1 = 173 kgU
Assemblies in Units 2, 3 and 4 = 175 kgU
What's kgU?

Astronuc
Staff Emeritus
Science Advisor
What's kgU?
kgU = kilograms of uranium.

Fuel burnup (exposure) is measured in terms of energy/unit mass, e.g., MWd/kgU or GWd/MTU. 1 MTU = 1000 kgU.

Knowing the plant rating (MWt), days of operation (d) and kgU in the core, one can estimate a cycle burnup/exposure. That gives the average exposure added to each batch of fuel during a cycle. Obviously some fuel runs above average, and some below.

I expect the units load about 1/4 of the core each cycle, but it's probably a bit more than 1/4 and less than 1/3.

Units 1 and 3 had about 5.5 months of operation, and unit 2 about 3.7 months.

Knowing the plant rating (MWt), days of operation (d) and kgU in the core, one can estimate a cycle burnup/exposure. That gives the average exposure added to each batch of fuel during a cycle. Obviously some fuel runs above average, and some below.
So the overall uranium mass in core #1 would be 173 * 400 ~ 70tons? But the actual, fissionable material is less, isn't it? Only 4% of these 70tons would account for U-235, and only those 4% could be fissured into such elements as C137 or I134, or am I wrong?

Let's take Unit 1:

(1380MWt * 5.5m * 30d) / 173 kgU ~ 1320 MWd/kgU. In dimensions that's energy per kg, allright. So that's the energy one kg uranium ore has produced over a specific time frame. But how do I get the isotopes such as I131 and C137? If I remember correctly, 6% of all fission products were C137 and 3% I131...

NUCENG
Science Advisor
From ORIGEN2 for a US BWR

Cs-137 4.644E3 Ci/MWt 53.37 g/MWt
I-131 2.780E4 Ci/MWt 0.2193 g/MWt

From Nuclide Tables

Cs-137 half life 30.07 y
I-131 half life 8.0207 d

From JAIF
Unit 1 400 assemblies in core 292 assemblies in SFP Rated 1380 MWt
Unit 2 548 assemblies in core 587 assemblies in SFP rated 2381 MWt
Unit 3 548 assemblies in core 514 assemblies in SFP Rated 2381 MWt
Unit 4 0 assemblies in core 1331 assemblies in SFP Rated 2381 MWt

1 Ci = 3.7E10 Bq
Use the rated thermal power and core size to estimate per bundle source term when fresh (assume 548 bundles for a core in Unit 4).

Use exponential decay exp(0.693*t/T') to account for decay. T' is half life, Remember to match units for t and T'. You will have to assume some age for fuel in SFP. For Unit 4 assume 548 bundles dischareged in October.

Fuel over 10 years is probably in dry fuel storage or in reprocessing. So I recommend assumed age from 5 to 10 years in SFP as an average.

Astronuc
Staff Emeritus
Science Advisor
So the overall uranium mass in core #1 would be 173 * 400 ~ 70tons? But the actual, fissionable material is less, isn't it? Only 4% of these 70tons would account for U-235, and only those 4% could be fissured into such elements as C137 or I134, or am I wrong?
The enrichment is probably about 4%.

Let's take Unit 1:

(1380MWt * 5.5m * 30d) / 173 kgU ~ 1320 MWd/kgU. In dimensions that's energy per kg, allright. So that's the energy one kg uranium ore has produced over a specific time frame. But how do I get the isotopes such as I131 and C137? If I remember correctly, 6% of all fission products were C137 and 3% I131...
(1380MWt * 5.5m * 30d) / (400 *173 kgU) ~ 1320/400 MWd/kgU ~ 3.3 GWd/tU. Some assemblies would get about 7 GWd/tU during that period, while those nearest the edge of the core get about 1 GWd/tU.

Also, 1% of initial metal atoms (U) are fission for ~9.8 GWd/tU.

(1380MWt * 5.5m * 30d) / (400 *173 kgU) ~ 1320/400 MWd/kgU ~ 3.3 GWd/tU.

Also, 1% of initial metal atoms (U) are fission for ~9.8 GWd/tU.
I knew there was something missing... okay, where do you get those 9.8 GWd/tU? Is that a constant?

And now that I have those 3.3 GWd/tU - how do I get my Cs and Is. Please throw me a bone here... ^^;

NUCENG
Science Advisor
More ideas From NUREG-1465

95% OF I-131 released as CsI particulate
5% of I released as iodine gas or HI

Gap release -clad minor damage duration 30 minutes releases 5% of Cs and I
Early in Vessel Melting duration 1.5 hours releases 25% of remaining Iodine and 20% of remaining Cs.

Above release is all in vessel. If RPV fails:
Ex Vessel Release duration 3 hours releases 35% of remaining Cs and 30% of remaining I directly into containment

And for the next bit which is core on the floor and probably into the concrete Release about another 1% of Cs and I into the vessel.

QuantumPion
Science Advisor
Gold Member
So the overall uranium mass in core #1 would be 173 * 400 ~ 70tons? But the actual, fissionable material is less, isn't it? Only 4% of these 70tons would account for U-235, and only those 4% could be fissured into such elements as C137 or I134, or am I wrong?

Let's take Unit 1:

(1380MWt * 5.5m * 30d) / 173 kgU ~ 1320 MWd/kgU. In dimensions that's energy per kg, allright. So that's the energy one kg uranium ore has produced over a specific time frame. But how do I get the isotopes such as I131 and C137? If I remember correctly, 6% of all fission products were C137 and 3% I131...
It's not that simple since I and Cs are radioactive, and I-131 can absorb a neutron when the reactor is at power, causing it to decay into stable Xe-132. The only way I know of to calculate this is using various computer codes designed to do so such as Origen-ARP.

edit: nevermind, NUCENG already calculated it with Origen heh :)

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NUCENG, I just used your numbers to calculate I131 and C137 in the cores:

#1/2/3 I131: ~1.420.000 / ~2.450.000 / 2.450.000 Tbq
#1/2/3 C137: ~240.000 / ~410.000 / ~410.000 Tbq

Are those Ci/MWt numbers specified for a specific time frame? I'd like to calculate the core inventory with Astronucs method as well, it seems to be more accurate (if I figure out how to get my Cs and Is^^)

QuantumPion
Science Advisor
Gold Member
The enrichment is probably about 4%.

(1380MWt * 5.5m * 30d) / (400 *173 kgU) ~ 1320/400 MWd/kgU ~ 3.3 GWd/tU. Some assemblies would get about 7 GWd/tU during that period, while those nearest the edge of the core get about 1 GWd/tU.

Also, 1% of initial metal atoms (U) are fission for ~9.8 GWd/tU.
Are you calculating GWd/t U235? I've never seen that used before myself.

My ballpark estimate came up with a core average burnup of 15 GWD/MTU based on 1400 MWt and 800 days average core exposure, 70 MTU loading.

Astronuc
Staff Emeritus
Science Advisor
Are you calculating GWd/t U235? I've never seen that used before myself.

My ballpark estimate came up with a core average burnup of 15 GWD/MTU based on 1400 MWt and 800 days average core exposure, 70 MTU loading.
I was just commenting on the enrichment. Burnup is always per total U or total HM (HM = heavy metal = U+Pu). Some institutions, e.g., Belgonucleaire and Halden do burnup in kgUO2.

The Fukushima reactors run on annual cycles - with fairly low capacity relative to the rest of the world. Figure about 300 efpd/year, and maybe less.

NUCENG
Science Advisor
NUCENG, I just used your numbers to calculate I131 and C137 in the cores:

#1/2/3 I131: ~1.420.000 / ~2.450.000 / 2.450.000 Tbq
#1/2/3 C137: ~240.000 / ~410.000 / ~410.000 Tbq

Are those Ci/MWt numbers specified for a specific time frame? I'd like to calculate the core inventory with Astronucs method as well, it seems to be more accurate (if I figure out how to get my Cs and Is^^)
These results were derived for a core-wide event near the end of a cycle that has been operating at 100% rated thermal power long enough to reach equilibrium conditions for the source term. Thus the daughtering that goes on during operation has reached steady state. It conservatively accounts for fuel enrichmnt, exposure, fuel loading (kgU/bundle), and refueling batch sizes for a modern fuel design. This is the design basis source term used for analysis of accident doses for license compliance. For localized accidents such as a fuel handling accident or control rod dro accident in a BWR a locally peaked source term can also be calculated. However at Fukushima we are talking about core wide failures.

NUCENG
Science Advisor
I was just commenting on the enrichment. Burnup is always per total U or total HM (HM = heavy metal = U+Pu). Some institutions, e.g., Belgonucleaire and Halden do burnup in kgUO2.

The Fukushima reactors run on annual cycles - with fairly low capacity relative to the rest of the world. Figure about 300 efpd/year, and maybe less.
That means my numbers will probably be very conservative as they are based on longer cycles and 100% capacity. However with the uncertainties in extent of damage you can probably still be in the ballpark with reasonable assumptions. Ir may also be possible to use NISA, JAIF and TEPCO estimates of total releases to scale these numbers back.

NUCENG
Science Advisor
I was just commenting on the enrichment. Burnup is always per total U or total HM (HM = heavy metal = U+Pu). Some institutions, e.g., Belgonucleaire and Halden do burnup in kgUO2.

The Fukushima reactors run on annual cycles - with fairly low capacity relative to the rest of the world. Figure about 300 efpd/year, and maybe less.
I think I see where your method is heading. Calculate the total fissions for the fuel and use the fission yields for I-131 and Cs-137 to predict inventories. How do you plant to adjust for equilibrium?

Your approach does allow a second method to check my numbers and the estimates from Japan.

Astronuc
Staff Emeritus
Science Advisor
I think I see where your method is heading. Calculate the total fissions for the fuel and use the fission yields for I-131 and Cs-137 to predict inventories. How do you plant to adjust for equilibrium?

Your approach does allow a second method to check my numbers and the estimates from Japan.
One would have to estimate the batch average burnup for the 1st, 2nd, 3rd and 4th cycle fuel. The discharge burnup should be high 30's. Peak assembly is probably around 40 or so. Units 1 and 3 are about half-way through their cycle, and Unit 2 about 1/3 of the way.

For units 1 and 3, I'd estimate burnup of 6, 16, 26, 33 GWd/tU for the four batches, and on unit 2, someting like 4, 14, 24, 30 GWd/tU.

Unit 1 would have reloads of slightly above 100, perhaps as much as 120/batch. Units 2 and 3 would have 140 assemblies or more per batch.

Those are very rough estimates. One could use the number of newly discharged fuel assemblies (new in the spent fuel pools) as a batch estimates as well.

1,600,000 TBqs of uncontained Ce137 sounds bad to me . What happens if you add in the spf material?

NUCENG
Science Advisor
NUCENG, I just used your numbers to calculate I131 and C137 in the cores:

#1/2/3 I131: ~1.420.000 / ~2.450.000 / 2.450.000 Tbq
#1/2/3 C137: ~240.000 / ~410.000 / ~410.000 Tbq

Are those Ci/MWt numbers specified for a specific time frame? I'd like to calculate the core inventory with Astronucs method as well, it seems to be more accurate (if I figure out how to get my Cs and Is^^)
Astronucs method will gice a more accurate answer as you suggest. The kind of analsis IU have done has been aimed at a bounding result under worst case conditions. Astronucs method is aimed at prducing a realistic estimate based on this event.

But I still don't know how to use Astronucs method...

Well, if I just take those C137 numbers and compare them to the 12.000 TBq release estimate by NSC it seems that only 1% of the cores went airborne. And the SFPs are not included, so it's less then 1%.
And then look what a mess those 1% generated...

NUCENG
Science Advisor
But I still don't know how to use Astronucs method...

Well, if I just take those C137 numbers and compare them to the 12.000 TBq release estimate by NSC it seems that only 1% of the cores went airborne. And the SFPs are not included, so it's less then 1%.
And then look what a mess those 1% generated...
Okay, some other numbers you will need for Astronuc's method
202.5 MeV thermal energy total per fission including fission product decay

From Table of nuclides Fission Yields: (neglect fast fissions)
http://atom.kaeri.re.kr/index.html
2.88432E-2 accumulated atoms of I-131 per thermal fission of U-235
3.84661E-2 accumulated atoms of I-131 per thermal fission of Pu-239
6.26588E-2 accumulated atoms of Cs-137 per thermal fission of U-235
6.72736E-2 accumulated atoms of Cs-137 per thermal fission of Pu-239

For added complexity, Look up the Wikipedia article on "Minor Actinide." You will probably simplify the problem by assuming only U-235 thermal fission. http://en.wikipedia.org/wiki/Minor_actinide

For both approaches:

Release events to be considered.
1. SRV operation venting RPV to the containment wetwell/torus suppression pool and torus air space.
2. Operation of torus to drywell vacuum breakers to equalize pressure and non-condensibles back to the drywell.
3. Containment venting via hardened wetwell vent per the event timeline.
4. Hydrogen explosions
5. Leakage from damaged containment. Leakage at containment cap is airborne. Leakage from suppression chamber airspace is airborne. Leakage from suppression pool is liquid.
6. Feed and Bleed for injection of seawater or freshwater and leakage.

Damage to fuel in spent fuel pool
1. Releases during zirconium fires
2. Releases due to hydrogen explosions (Maybe you can figure out Unit 4!)
3. Releases from feed and bleed from spraying and leakage or overflow.
4. Releases with vapor.

For airborne releases, see
http://pbadupws.nrc.gov/docs/ML0037/ML003740205.pdf

A daunting task indeed! If your task is to eat an elephant it is best to start with a single bite.

Don't dispair. PhD candididates willl be writing dissertations and computer models will be chewing on this event for years. You can work at this with simplifying assumptions and reasonable guestimates. Your numbers will be as good as anyone's. But I think you see why it doesn't make sense to use more than 1 significant digit in your calculations.

And just to add insult to injury, none of this will satisfy those who believe there has been recriticality.

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And just to add insult to injury, none of this will satisfy those who believe there has been recriticality.
Preemptive strike in case of Dmytry finding this thread, huh?

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