Japan Earthquake: Nuclear Plants at Fukushima Daiichi

[Bioengineer01]

I am suggesting that the best thing to do right now is to stop pouring water into the nuclide pile. Until the water flow out of the high radiation area is halted, we remain in the expansion of the problem mode, not the cleanup mode.



Can you describe that?

Hahahaha, sorry guys, but you made me laugh, thankfull for that, there is no way in hell that you can get a molten pile of corium into cold shutdown, not even the equivalent of it... Hahahaha

 

[turi]

Hahahaha, sorry guys, but you made me laugh, thankfull for that, there is no way in hell that you can get a molten pile of corium into cold shutdown, not even the equivalent of it... Hahahaha

The equivalent would be having it submerged in water and keeping the water below boling point.

 

[SteveElbows]

I am suggesting that the best thing to do right now is to stop pouring water into the nuclide pile. Until the water flow out of the high radiation area is halted, we remain in the expansion of the problem mode, not the cleanup mode.

Can you describe that?

Letting the cores and their surroundings heat up is likely considered a recipe for hideous new problems. There is heat to be dealt with as well as escaping radioactive material, and clearly at the moment they worry more about the heat than the buildup of radioactive water. Its not fair to focus only on problems they are creating without acknowledging the problems their current actions are preventing.

I describe the cold shutdown they seek as being wrecked-reactor type because I cannot bring myself to describe what will hopefully happen to these reactors at some point as normal cold shutdown, that term is just too connected in my mind to the standard shutdowns that undamaged reactors go into routinely.

They are seeking to get proper cooling systems in place, which will keep the remains at stable temperatures below boiling point, and will enable them to reuse the water instead of ending up with ever more bad water to deal with. Thats the main thrust of the roadmap they aim to complete at some point, that will be declared a major milestone in dealing with the plant, etc etc. It clearly won't be the end of matters, but it will represent the end of the dramatic first chapters, and at that point we'll be better placed to argue what the medium and long term cleanups consist of.

There is always the chance they will be forced to change plans into something more crude & final, and perhaps more along the lines of what you would like to see happen. If for example they utterly fail to improve key working conditions inside reactor buildings, then they will have to think again.

And on that very topic, right now I wait nervously to see what their latest survey of reactor 2 building will reveal. Seeing as they have apparently succeeded in cooling its pool properly in recent days, they are hoping humidity levels have fallen, so that they may they try to deal with radioactive substances in the air in the building. Assuming that works, they can then carry out other work they have planned inside the building as per the roadmaps.

 

[jim hardy]

Unfortunately, after they discover that two water sensors and two pressure sensors in unit 1 were wrong we can't trust any data

i have faith in thermocouples so long as they're dry . Especially if they're wired right to the computer with no electronic doodads in between.

Pressures i have suspected ever since the explosions for when you drastically overrange a sense element you give it a "set" and it'll read high ever after.
Jorge's plots were real useful for trending but i expected pressures to be found reading high.
next couple days should tell about units 2 & 3.

Levels are subject to losing water in their sense lines, as when drywell gets real hot and instrument sense line heats up driving dissolved gas out of solution. So the gage reads in error by the height of any gas bubbles in its sense lines. They became unreliable IMHO as soon as depressurization began with no ventilation to drywell. Ever open a hot Coke?


that's why i spent so many hours staring at photographs looking for reactor parts..

Most computer electronics will start to act up after several thousand R which would be scores of Sv.
It'll be interesting to see how the Packbots hold up.

Time will tell.

 

[Jorge Stolfi]

i want to personally extend thanks to you for your work in making hose graphs. Curious, whatever happened to 3 on 21st accompanied high water injection through "fire line"? i don't know what fire line is - does it go into vessel(core spray perhaps) or does it spray down the drywell?

Thanks for the compliment. "Fire line" should have been "fire extinguisher line", the other plot being the flow through the "feedwater line". AFAIK, in an intact reactor both lines lead into the RPV; the former through a ring of spray nozzles near the top of the fuel, the second one through pipes on the turbine side, near the bottom of the fuel.

 

[SteveElbows]

Unfortunately, after they discover that two water sensors and two pressure sensors in unit 1 were wrong we can't trust any data

To be fair they always made it pretty clear that quite a lot of the data could be wrong. We know for a long time that some numbers must be totally wrong, where 2 indicators disagree with each other a lot, or where values go up and down in crazy ways or show - values.

Aside from slowly getting a few more bits of accurate data as they install new instruments, there isn't all that much more that I am expecting in terms of quality data that will give us a clear picture. Personally the most illuminating thing I can hope for in the weeks ahead is the english translation of TEPCOs long analysis document. The one that contains the estimates of core damage that we already know about in detail, but also estimates for containment damage, where we have only seen a few internet & press reports & a couple of paragraphs of the document that I machine translated. Although I can't speak Japanese I can tell by looking at it that it seems to contain some interesting graphs showing not just actual pressure & temperature data that we know already, but also what they think the temperatures & pressures really were at various times early on. Sometimes this differs considerably from the actual data, and there are handy events labelled on many of these graphs, such as the moments they think core, RPV and D/W or S/C damage happened.

 

[Astronuc]

Each of the situations at #s 1,2 and 3 are far worse than TMI.

Quite true. TMI-2 was operating in its first cycle with only ~62EFPD of production. The fission product inventory was quite low compared to the mature operation of the the Fukushima cores.

The way I see it, although the site around the containment structures can and should be cleaned up, the corium blobs themselves should not be disturbed.

There is nothing to be gained from mucking about with the corium.

There is no confirmation of corium. Only visual inspection can confirm corium.

It was thought that the fuel in SFP #4 had grossly failed, yet the visual evidence show little sign of melting or gross failure. Instead it appears that the spent fuel is largely intact. If so, it can be removed and placed in casks, which is the ideal situation.

The cooling of the fuel in the cores is necessary in order to mitigate/prevent further degradation of the cladding and the consequent release of fission products to the coolant.

Ideally, a closed loop cooling system would be established. Such as system would also include a processing system to collect any fission products, and the fission products would be solidified in order to preclude their transportation into the environment.

The fuel and core components will have to be removed eventually in order to decomission the reactor. Decomissioning has been accomplished at various sites in the US and Europe, so the process is well understood. The complication at Fukushima is the degradation of the cores, which could very well be comparable to TMI-2's core.

 

[hbjon]

I am sure we all remember the guy who went in and tried manhandle and wrestle around with a devil ray in his own elements. It is the unknow that overloads the analizer and becomes an unmanageable catastrophe. Since a lot of people have spent over 2 months agonizing over readings from faulty gauges and misinformation, why not take that advice and step back, take a deep breath, and find out where the sharp pointy sides of these devil rays are?

 

[jim hardy]

"""I am suggesting that the best thing to do right now is to stop pouring water into the nuclide pile. Until the water flow out of the high radiation area is halted, we remain in the expansion of the problem mode, not the cleanup mode.""

Many people don't appreciate what energy is.

To put it simply, think of the energy in that core as just another fluid. Early physicists called it "Caloric". The core is making it, that's the Decay Heat..

The "Caloric" will by hook or crook get out of that "Corium".
The "Corium" is most likely a crumbly debris bed that's still in the vessel.
If you bury the "Corium" the "Caloric" will i guarantee tunnel its way out and its radioactive friends will tag along.
They must continue to actively remove the decay heat.

Should the unthinkable happen the core will very quickly produce an unthinkably large amount of "Caloric" which will exit the area with pyrotechnics.

Water prevents fast unthinkable.
Boron prevents thermal unthinkable.
So it is important they continue applying borated water.

That they have done so is why the vessels are still able to make steam.
Wherever the steam is being made is where the cores are.

All they have to do is move heat and contain radiation.
Water is best stuff around for moving heat.
Their problem is containing the waterborne radiation.
If you know of a better substance than water please advise. Sand is no good for moving heat because it just doesn't pump worth a darn.

Kind of a Catch-22, ain't it?

 

[MadderDoc]

Thanks for the compliment. "Fire line" should have been "fire extinguisher line", the other plot being the flow through the "feedwater line". AFAIK, in an intact reactor both lines lead into the RPV; the former through a ring of spray nozzles near the top of the fuel, the second one through pipes on the turbine side, near the bottom of the fuel.

In an BWR, I believe, the feedwater line also enters above the top of the fuel.

 

[Quim]

They must continue to actively remove the decay heat.

Why?
Why not let it reach its own equilibrium?
Hot sand, gravel, concrete or dirt is no threat to anything or anyone.

Should the unthinkable happen the core will very quickly produce an unthinkably large amount of "Caloric" which will exit the area with pyrotechnics.

Water prevents fast unthinkable.
Boron prevents thermal unthinkable.

Those days are over, without a moderator a (blob, hunk of, or puddle of) corium can't go critical with thermal reaction.

And a fast reaction is out of the question with 5% (or whatever) enrichment.

That they have done so is why the vessels are still able to make steam.

I see steam as being very undesirable, it is the pathway for nuclides to escape into the environment.

Water is best stuff around for moving heat.

But there is no need to "move" any heat. The heat is fine where it is.
Once the water is removed from the nuclide piles, heat becomes an academic subject. Containment is achieved.



I'm glad you're responding Jim, I know you won't get your feelings hurt as some here would if they attempted to hold up your side of this discussion.

 

[sp2]

Not necessarily so. One has no evidence of 'blobs of corium'. Any reference to corium is speculation.

Those outside of industry have little credibility regarding the state of the reactor/core/fuel.

There is an appropriate engineering solution, but it is unlikely to come from outside the industry.

'SOLUTION?' "There is an appropriate engineering SOLUTION?"

With all due respect, Astronuc, you need to use a different word.
There may be a best 'response.' There may be wiser 'options.'

But a 'SOLUTION?'

Is there a 'solution' that'll magically erase the millions of terabecquerels already released?
That'll decontaminate every fish, and every piece of seaweed in 10,000 square miles of ocean?
That'll somehow neatly suck up the layer of Cs-137 over hundreds of square km of countryside, that's already heavier than that of the Exclusion Zone in Chernobyl?
That'll perfectly clean up the contaminated spinach and tea 200 miles from the site?

I'm sorry, but talk of a 'solution' to Fukushima is the kind of Orwellian language that makes reasonable people around the world so profoundly distrust the nuclear industry.

 

[Quim]

makes reasonable people around the world so profoundly distrust the nuclear industry.

That highlights a statement I made in post #8854.
"But the other side is just as bad"


Why not just let the cards fall where they may?

 

[biffvernon]

But there is no need to "move" any heat. The heat is fine where it is.
Once the water is removed from the nuclide piles, heat becomes an academic subject. Containment is achieved.

Er...I don't think heat can be contained. You might slow down it's transfer for a while but that just stores up a bigger problem for later.

 

[Quim]

Er...I don't think heat can be contained. You might slow down it's transfer for a while but that just stores up a bigger problem for later.

Where I said: " Containment is achieved" I was referring to containment of radioactive material.

Heat in itself is not a problem IMO.

I assume that the end result will be a 5 - 10 acre parcel of land which has no source of ground water and is quite hot on its upper surface and warm tapering to ambient on its perimeter.

This would be a very low maintenance site.
Also, this would be leakproof as far as radiation is concerned.


If you are trying to say that this "solution" wouldn't have an acceptable political end result, you should probably post that in the more political forum.

 

[Jorge Stolfi]

Why not let [corium] reach its own equilibrium?
Hot sand, gravel, concrete or dirt is no threat to anything or anyone.
But there is no need to "move" any heat. The heat is fine where it is.
Once the water is removed from the nuclide piles, heat becomes an academic subject.

The problem is that you don't have a fixed amount of heat (as in ordinary molten iron), but rather megawatts of heat being produced continuously. If you enclose wht remains of the fuel (in whatever form or mixture) within a poorly conducting material, the mass will keep getting hotter until the uranium oxide itself boils.

 

[biffvernon]

Indeed. It's a question of whether the heat conduction through the sand or whatever is fast enough to stop the corium boiling. If yes, that's fine. If no, then that very much not fine at all.

 

[hbjon]

Er...I don't think heat can be contained. You might slow down it's transfer for a while but that just stores up a bigger problem for later.

The quantity of fuel is an important factor to consider. Jim aint a whistling dixie when he says there is a lot of potential energy at this site. I remember reading about the Mass Defect and the conversion of matter to energy in high school. If you bury everything in sand, I believe the fuel will realize it's full potential in time. I side with Jim on this. But I am just one of the backseat drivers around here.

 

[Astronuc]

'SOLUTION?' "There is an appropriate engineering SOLUTION?"

With all due respect, Astronuc, you need to use a different word.
There may be a best 'response.' There may be wiser 'options.'

But a 'SOLUTION?'

Is there a 'solution' that'll magically erase the millions of terabecquerels already released?
That'll decontaminate every fish, and every piece of seaweed in 10,000 square miles of ocean?
That'll somehow neatly suck up the layer of Cs-137 over hundreds of square km of countryside, that's already heavier than that of the Exclusion Zone in Chernobyl?
That'll perfectly clean up the contaminated spinach and tea 200 miles from the site?

I'm sorry, but talk of a 'solution' to Fukushima is the kind of Orwellian language that makhes reasonable people around the world so profoundly distrust the nuclear industry.

I was referring only to the current state of the damaged cores and SFPs at Fukushima units 1-4. I do not include the contamination due to the release of fission products so far; this is an entirely different problem, although one rooted in the same precursor.

I appreciate the mistrust/distrust of the nuclear industry. The event at Fukushima has betrayed whatever trust had been established.

My immediate concern is the situation at hand, and the minimization of further contamination - aside from the technical considerations.

The imperative is to cool the cores in order to reduce/mitigate further release of fission products. Then, to the extent possible, a closed system for cooling and prodessing of the radwaste must be established. To the extent possible, a containment system must be established to prevent further releases into to the atmosphere. These are the technical considerations.

 

[Quim]

The problem is that you don't have a fixed amount of heat (as in ordinary molten iron), but rather megawatts of heat being produced continuously. If you enclose wht remains of the fuel (in whatever form or mixture) within a poorly conducting material, the mass will keep getting hotter until the uranium oxide itself boils.

You raise a valid concern.
Yet, these "puddles" are already three months old and they will decline in heat generation from here on out (sans criticalities.)

But you are absolutely correct that somebody needs to attempt the actual math behind the premise I am proposing.

A problem could be expected to develop if the corium is still contained in the RPVs and all the water goes away - the corium would then only have air as a heat sink. That wouldn't be acceptable for the reason you raise.

But I bet there are ways of dealing with that circumstance cheaply and without endangering anyone's health. Be it lead or sand or something else, the RPVs will need something in them other than corium and air.

I believe that can be done.

 

[Quim]

Indeed. It's a question of whether the heat conduction through the sand or whatever is fast enough to stop the corium boiling. If yes, that's fine. If no, then that very much not fine at all.

Agreed!

 

[SteveElbows]

Well as expected we now learn how the humidity has changed in reactor 2 since the successful pool cooling.

Not terribly surprisingly the news is bad, it has not changed. It was probably always wishful thinking that the pool was responsible for most of the humidity inside reactor 2 building, but they had to rule it out.

One alternative plan of action they are talking about seems to involve opening the door!

http://www3.nhk.or.jp/daily/english/06_02.html

 

[jim hardy]

""But I am just one of the backseat drivers around here.""

thanks hbjon i too am out of my league here. i do remember my high school physics though.

So did Frank Sinatra - to paraphrase:

"When an unstoppable force like (decay heat) meets an immovable object like (perfectly insulating mountain of sand), something's got to give".

not trying to start a war of words here, just we got to keep our thinkin' straight.

i appreciate when people point out my slips.

And i am not talking down to anyone. i try always to put things in simple language because it keeps my thinking straight.
Isaac Asimov was the master at explaining things, and i always try to imitate the 'one step at a time' thinking i learned from his writings. One comes to appreciate just how imprecise and inconsistent English language can be at painting accurate pictures in our mind.

old jim

 

[Borek]

But there is no need to "move" any heat. The heat is fine where it is.
Once the water is removed from the nuclide piles, heat becomes an academic subject. Containment is achieved.

Nope. There is simply too much heat produced (and will be produced). What is there is still able to get through many meters of whatever you want to put under. Note, that the fuel has very high density, so whenever it will melt substances surrounding it it will sink deeper, replacing them. Contrary to what you think it will be not contained, sooner or later it will end in the groundwater.

 

[Bioengineer01]

There is the saying: never say never. Certainly this recent tragedy is once again a testament to this philosophy and a stark reminder to all engineers and scientists.

Given that disclaimer, these civilian nuclear reactors are designed with contingency in place to ensure they (for the most parts) do not go critical when they aggregate into a lumped mass corium at the bottom of a reactor containment and beyond. This is because firstly the nuclear fuel is of low purity in terms of fissile elements. Secondly, neutrons generated directly from fission of say uranium have too high energy - this results in a low probability of causing other fission events of other uranium atoms thereby eventually freezing out a chain reaction.

These reactors are purposely designed to have neutron moderators placed between fuel rods to slow down and reduce the energy of these neutrons from fission, so that they can cause fission and sustain a chain reaction. In other words, when fuel rods are melted down into a corium, there is presumably no more neutron moderators between the fuel rods and fuel elements (that is, the water), thereby from that point on you are primarily concerned with high energy neutrons generated from fission which have low probability of sustaining a chain reaction while thermal neutrons (lower energy) that can sustain a chain reaction are reduced in a hypothetical corium configuration.

This is the best case scenario of course. If it so happens that the civil structure of the plant itself unknowingly had neutron reflecting material nearby, it may be able to sustain a reaction to a degree. Theres also the possibility that the corium achieves localized critical mass configurations within the corium that can sustain a reaction (though not likely as the fuel is purposly designed to have low purity and is assumed to be homogenous in composition). All of this is purely hypothetical of course as are any other plausible scenarios people can draw up.

That is also not the end of the story of course, as life is never that perfect: it is not just 100% fuel configuration with control rods in place or 100% corium lump mass. If it is partially melted with a corium and some spent fuel assembies, presumably with neutron moderating water inbetween, this can again lead to criticality, especially since control rods that would have otherwise prevented criticality may be ineffective to block neutrons between the corium and the fuel assemblies though they will be far away in distance and the reaction rate should not be very high.

Arm chair, I understand what you say and I don't argue with it, but what happens with Unit 3 Corium? That has MOX in it, do we know what percentage of MOX they used? And what type of Plutonium they used? 90% weapons grade? if so, what was the composition of the MOX. I am extremely concerned about the high experimental nature of the MOX as a fuel, due to the higher cross sectional area of Pu-239 for neutron absorption, and the zero data that we have on accidents of this nature involving MOX... Also, the short lived use of the reactor since it was restarted in Setember 2010 up to March's accident means that most Pu was still there...
I'd love to hear other experts comments on this topic...

 

[Quim]

Nope. There is simply too much heat produced (and will be produced). What is there is still able to get through many meters of whatever you want to put under. Note, that the fuel has very high density, so whenever it will melt substances surrounding it it will sink deeper, replacing them. Contrary to what you think it will be not contained, sooner or later it will end in the groundwater.

That's not what happened in the only other comparable circumstance.
Why would it happen here?

These core loads have had three months to bleed off nuclides.
At that other place the dried out material started out in life as a core developing full power.


Let's see some math, or are the formulas yet to be developed? (as a result of the Fukushima incident)

 

[Astronuc]

Arm chair, I understand what you say and I don't argue with it, but what happens with Unit 3 Corium? That has MOX in it, do we know what percentage of MOX they used? And what type of Plutonium they used? 90% weapons grade? if so, what was the composition of the MOX. I am extremely concerned about the high experimental nature of the MOX as a fuel, due to the higher cross sectional area of Pu-239 for neutron absorption, and the zero data that we have on accidents of this nature involving MOX... Also, the short lived use of the reactor since it was restarted in Setember 2010 up to March's accident means that most Pu was still there...
I'd love to hear other experts comments on this topic...

There has been considerable use of MOX fuel in light water reactors (LWRs).

It was reported that there were 32 MOX fuel assemblies in Unit 3, or about 6% of the core of 548 assemblies. They were operating in their first cycle, so they didn't have much operation/exposure. Ostensibly, the MOX fuel was derived from spent fuel from the Fukushima reactors, thus it was reactor grade, and the Pu isotopics would have reflected that legacy. The MOX fuel would be designed to match the enrichment of the U-235 assemblies, which is about 4% U-235. So likely the MOX would be about 6% Pu, with a mix of Pu239, 240, 241 and 242.

Spent fuel contains Pu isotopes. The use of MOX is rather insubstantial to the event and the current state of Unit 3.

 

[tsutsuji]

A new theory for unit 1 explosion :

TEPCO officials believe hydrogen gas that should have been released from the vent pipe flowed back into the reactor building through the open SGTS valve after reaching the point where the two exhaust systems converge.
http://www.asahi.com/english/TKY201106040165.html

 

[etudiant]

You raise a valid concern.
Yet, these "puddles" are already three months old and they will decline in heat generation from here on out (sans criticalities.)

But you are absolutely correct that somebody needs to attempt the actual math behind the premise I am proposing.

A problem could be expected to develop if the corium is still contained in the RPVs and all the water goes away - the corium would then only have air as a heat sink. That wouldn't be acceptable for the reason you raise.

But I bet there are ways of dealing with that circumstance cheaply and without endangering anyone's health. Be it lead or sand or something else, the RPVs will need something in them other than corium and air.

I believe that can be done.

My $0.02 is that someone did do the math and concluded that your belief is mistaken.
We are looking at 4 to 6 megawatts per core of residual heat per core, more than enough to boil that core if the heat is not removed continuously. Adding lead is useless, it may be a great shield but it melts at low temperature and emits toxic fumes. Ditto sand, no toxic fumes but no cooling either. Because it is decay heat, no outside material such as boron will help. We are lucky that water is cheap, non toxic and has a high heat capacity.. It is cooling this mess reasonably well and our only problem is that we are running out of places to store the used water. That is a high class problem relative to the question of how do you control boiling radio nucleotide vapors.

 

[rmattila]

In an BWR, I believe, the feedwater line also enters above the top of the fuel.

Above the top of the core, but outside the shroud (=in the downcomer region) where the cooler feedwater mixes with the recirculation flow to provide some suction head for the recirculation pumps. At least this is the case with reactors with internal recirculation pumps, which I am familiar with.

The core spray system, which I believe the fire extinguisher system at Fukushima is lined up to, ends up inside the shroud and actually sprays the water on top of the fuel, not into the downcomer (from where it may flow out of the reactor through leaking main circulation pump seals and never reach the actual core region).

 

[Quim]

My $0.02 is that someone did do the math and concluded that your belief is mistaken.

"Your assumption is that someone did the math....."I assume otherwise.Or to take the advice of Bill Gates: "assume nothing"**This is a assembly directive in the MS assembly language which exists in the form of "assume nothing."

To make a long story short, it accomplishes nothing, it would have only been included as an assembly directive because Mr. Bill was trying to tell us something.

 

[Luca Bevil]

Quick question:

Fission yield from U 235 are quite similar for Cs 134 (6,78%) and CS 137 (6,08%) according to wikipedia.

Given the shorter half life of CS134, though, activity of CS134 is much higher: 47.864 Tbq/g (CS 134) vs 3.214 Tbq/g (Cs 137).

Even after taking into account the faster decay, during the average time likely spent since fission, I would have expected CS134 contribution to water radioactivity being quite higher than CS137 contribution.

However data TEPCO released a few days ago about basement 1 contamination had estimates for CS137 bq/cc and CS 134 Bq/cc very close to each other.

How would that be explained ?

 

[rmattila]

Quick question:

Fission yield from U 235 are quite similar for Cs 134 (6,78%) and CS 137 (6,08%) according to wikipedia.

Very little Cs-134 is produced directly in fission, and most of it is produced by neutron capture of the more common (stable) fission product Cs-133. The value 6,78 % is the combined yield of Cs-133 and Cs-134. How much of Cs-133 is converted to Cs-134 depends on the burnup of the fuel.

 

[Astronuc]

Quick question:

Fission yield from U 235 are quite similar for Cs 134 (6,78%) and CS 137 (6,08%) according to wikipedia.

Those should be the cumulative yield based on the decay chains (and transmutations) leading to the respective isotopes.

Given the shorter half life of CS134, though, activity of CS134 is much higher: 47.864 Tbq/g (CS 134) vs 3.214 Tbq/g (Cs 137).

Even after taking into account the faster decay, during the average time likely spent since fission, I would have expected CS134 contribution to water radioactivity being quite higher than CS137 contribution.

However data TEPCO released a few days ago about basement 1 contamination had estimates for CS137 bq/cc and CS 134 Bq/cc very close to each other.

How would that be explained ?

The Cs-134/Cs-137 ratio depends upon burnup. In the Fukushima cores, there are perhaps four batches of fuel representing four populations of burnup, and each will have a different accumulation of the Cs-134 and Cs-137. The actual ratio of Cs in the coolant will be a weighted sum of the source terms of those assemblies that failed.

 

[etudiant]

"Your assumption is that someone did the math....."


I assume otherwise.


Or to take the advice of Bill Gates: "assume nothing"*


*This is a assembly directive in the MS assembly language which exists in the form of "assume nothing."

To make a long story short, it accomplishes nothing, it would have only been included as an assembly directive because Mr. Bill was trying to tell us something.

Excellent approach. Mr Gates is a good guide.
So we have 3 reactor cores, each dissipating about 6 megawatts of residual decay heat (4 in the case of unit 1, which is much smaller). That will continue for the next few years largely unchanged, albeit with a modest downward trend. Assume the cores are hot, but not yet melted, at around 1000 degrees Kelvin.
A reactor core is about 100 tons of uranium oxide, plus additives. Uranium oxide has a specific heat of 240 joules/kg per degree K. So we have 100,000 kg of fuel producing 6 megawatts of heat, or 6 million joules/second. Heating the fuel 1 degree will take 240 * 100,000 joules, or 24 million joules, about 4 seconds worth of heat output. So to heat the fuel to the boiling point, somewhere around 4000 degrees Kelvin, will take 3000 times that long, about 12,000 seconds, less than 4 hours.
I'd recommend sticking with the water option.