Japan Earthquake: Nuclear Plants at Fukushima Daiichi

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The Fukushima Daiichi nuclear plant is facing significant challenges following the earthquake, with reports indicating that reactor pressure has reached dangerous levels, potentially 2.1 times capacity. TEPCO has lost control of pressure at a second unit, raising concerns about safety and management accountability. The reactor is currently off but continues to produce decay heat, necessitating cooling to prevent a meltdown. There are conflicting reports about an explosion, with indications that it may have originated from a buildup of hydrogen around the containment vessel. The situation remains serious, and TEPCO plans to flood the containment vessel with seawater as a cooling measure.
  • #11,851
tsutsuji said:
http://www3.nhk.or.jp/news/genpatsu-fukushima/20111206/index.html According to Tepco, about 150 litres of water contaminated with beta-radiating substances such as strontium flowed to the sea. A maximum of 300 litres flowed through the cracks in the building's foundation. The 150 litre figure is the result of an estimate based on data such as leaking time.

The density of radioactive materials contained in the water leaked is 2.6 x 10^10 Becquerel (provisional) in total, calculating from
the density of strontium 89, 90, cesium 134, and 137.

Strontium 89: 7.4 x 10^4 Bq/cm3 (1.1 x 10^10 Bq)
Strontium 90: 1.0 x 10^5 Bq/cm3 (1.5 x 10^10 Bq)
Cesium 134: 1.6 x 10^1 Bq/cm3 (2.4 x 10^6 Bq)
Cesium 137: 2.9 x 10^1 Bq/cm3 (4.4 x 10^6 Bq)
(Water collected on Dec 4, 2011. Amount of strontium estimated from the density of all-beta radioactive materials.)

Why is there so much strontium relative to cesium there, when there is so little strontium relative to cesium seen outside the plant? Strontium doesn't become airborne as easily, I presume?
 
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  • #11,852
The leakage afaik is from the residual water left over after treatment by the Kurion and Toshiba ion exchange lines, as well as the AREVA line, if that is still in use. That water is then desalinated and the brine left over, which contains the unrecovered nucleotides such as strontium, is stored pending an evaporation process to reduce the residual volume.
It is interesting to see the relatively minimal cesium content of this residue. It seems the water clean up process is pretty effective, with cesium down to about one millionth of the starting contamination.
 
  • #11,853
Ah, of course, silly me.
 
  • #11,855
  • #11,856
Can somebody please link a press release/report/something about PCV gas contents? Not about the nuclides but about all the components.

I've just noticed that 'no CO2' and 'no sign of CCI' are stated sometimes, but I could not find any detailed report about regular measurements.
 
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  • #11,857
Rive said:
Can somebody please link a press release/report/something about PCV gas contents? Not about the nuclides but about all the components.

I've just noticed that 'no CO2' and 'no sign of CCI' are stated sometimes, but I could not find any detailed report about regular measurements.

On http://www.tepco.co.jp/nu/fukushima-np/images/handouts_111130_09-j.pdf page 13 (17/207), table 4.4-1 provides some hydrogen, carbon monoxide and carbon dioxide concentrations in unit 1 and unit 2 PCVs. (key: 1号: unit 1 2号: unit 2 8月: August 9月:September). This table is commented on page 8 (12/207) where they say that these amounts of carbon dioxide are nothing more than the part which is naturally carried by water, and they conclude that the core-concrete reaction had been stopped at the time of those measurements. They provide more detailed explanations in attachment 14 (pages 194/207 to 199/207) and attachment 15 (page 200/207 to 206/207). Attachment 14 is named "Results of analysis of gasses compositions inside PCVs". It concerns the following samples :

No.1,2,3 : three gas samples taken on 29 July at unit 1
No.4,5,6 : three gas samples taken on 9 August at unit 2
No.7,8,9 : three gas samples taken on 14 September at unit 1
No.10 : an air sample from outside

There is also an estimate of the CO2 levels that should be expected in case of core-concrete reaction.

Attachment 15 is named "Residual gasses remaining from early accident"
 
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  • #11,858
tsutsuji said:
they say that these amounts of carbon dioxide are nothing more than the part which is naturally carried by water, and they conclude that the core-concrete reaction had been stopped at the time of those measurements.

One of the assumptions here is that significant amounts of gas from a corium-concrete reaction would necessarily end up in the cooling water. Is this true, I wonder?
 
  • #11,859
tsutsuji said:
...
Thanks.

I wonder how often they are checking the levels.
 
  • #11,860
The strontium leak:

http://www.tepco.co.jp/en/press/corp-com/release/11120806-e.html Report on response to the accident due to the leakage of water containing radioactive materials at the water desalination (evaporative concentration apparatus) of Fukushima Daiichi Nuclear Power Station to NISA. (24 pages, English) ("it will take nearly one month to obtain result of the analysis of Strontium in the leaked water")

"Concept of Securing the Mid-Term Safety":

http://www3.nhk.or.jp/news/genpatsu-fukushima/20111209/1700_hoanin.html The NISA has approved Tepco's mid term safety plan for the next 3 years. The NISA heard the opinions of specialists at a meeting on 9 December. Some specialists expressed the view that more should be done to find out the fuel condition "such as using infrared measurements", but the NISA said that as an urgent response, the plan was valid. Kazuhiko Kudo of Kyushu university said "only minimal safety countermeasures are implemented, and more efforts should be done to secure safety ". The NISA must then report the plan to the NSC, and upon NSC approval, all the conditions for completion of "step 2" are met. http://www.tepco.co.jp/en/press/corp-com/release/11120814-e.html Report with regards to "Policy on the mid term security" for the Units 1 to 4 of Fukushima Daiichi Nuclear Power Station to Nuclear and Industrial Safety Agency at the Ministry of Economy, Trade and Industry (part 2) (8 December 2011, English press release linking to a 159 page Japanese report)

http://www.tepco.co.jp/en/press/corp-com/release/11120701-e.html Report with regards to "Policy on the mid term security" for the Units 1 to 4 of Fukushima Daiichi Nuclear Power Station to Nuclear and Industrial Safety Agency at the Ministry of Economy, Trade and Industry (part 1) (revision 2) (7 December, English press release linking to Japanese report)

http://www.tepco.co.jp/en/press/corp-com/release/11110912-e.html Report with regard to "Policy on the mid term security" for the Units 1 to 4 of Fukushima Daiichi Nuclear Power Station to Nuclear and Industrial Safety Agency at the Ministry of Economy, Trade and Industry (part 1) (revision 1) (9 November, English press release linking to Japanese report)

http://www.tepco.co.jp/cc/press/11101702-j.html Report with regard to "Policy on the mid term security" for the Units 1 to 4 of Fukushima Daiichi Nuclear Power Station to Nuclear and Industrial Safety Agency at the Ministry of Economy, Trade and Industry (part 1) (17 October, Japanese)

http://www.nisa.meti.go.jp/english/press/2011/10/en20111020-2.pdf Regarding the Receipt of Report from TEPCO and Holding Hearings on “The Concept of Securing the Mid-Term Safety” for Units 1 to 4 at Fukushima Dai-ichi Nuclear Power Station, Tokyo Electric Power Co., Inc.(October 17, 2011, English)

http://www.nisa.meti.go.jp/english/press/2011/10/en20111019-2.html Regarding the Direction on “The Concept of Securing the Mid-Term Safety” for Units 1 to 4 at Fukushima Dai-ichi Nuclear Power Station, Tokyo Electric Power Co., Inc. (October 3, 2011, English)
 
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  • #11,861
zapperzero said:
One of the assumptions here is that significant amounts of gas from a corium-concrete reaction would necessarily end up in the cooling water. Is this true, I wonder?

I also wonder how much extra CO2 would be released from concrete melted by corium once it's gone much beyond penetrating the concrete surface.

It was under the impression that CO2 from air reacts with concrete mostly at the surface exposed to air and that deeper inside there would be far less CaCO3. Partly this is because it was mentioned in one of the threads here before that broken concrete (as in shattered bits that fell into spent fuel pools at unit 3 or 4) is highly alkaline because deep inside it still contains a lot of alkaline CaO.

When CaCO3 gets heated to be white hot (~1000C) it releases CO2, but how much CaCO3 is there 65 cm below the surface? Is it at all valid to deduct from CO2 levels that the reaction stopped at that depth?
 
  • #11,862
joewein said:
When CaCO3 gets heated to be white hot (~1000C) it releases CO2, but how much CaCO3 is there 65 cm below the surface? Is it at all valid to deduct from CO2 levels that the reaction stopped at that depth?

http://koti.welho.com/tsevon/mcci.pdf

Siliceous concrete releases mainly water vapor, while calcareous concrete releases also substantial amounts of carbon dioxide.
 
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  • #11,863
I see what I missed. Concrete is made from a mix of cement, aggregate, sand and water. I was only thinking about the chemistry of cement and water (plus air), but the aggregate may contain carbonate rocks (such as limestone or dolomite) too.
 
  • #11,864
http://www3.nhk.or.jp/news/genpatsu-fukushima/20111212/index.html While commenting that "the reactors are still in the the way towards stable condition, and the possibility of troubles is remaining", and that "[the effort] shall expand over a long duration, and the durability of the equipment must be inspected", the NSC (Nuclear Safety Commission of Japan) approved Tepco's mid term safety plan. The "cold shutdown" status is expected to be announced by the Japanese government on 16 December.

http://www.nsc.go.jp/info/20111212_dis.pdf The main lines of the NSC's examination of Tepco's mid-term safety plan (Japanese)
 
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  • #11,865
Has anyone seriously considered creating small reservoirs next to our many piles of stored spent rods in the event that the power in the United States fails, and we need to cool them by a gravity-fed system until generators to power pumps are working?
 
  • #11,866
falcon32 said:
Has anyone seriously considered creating small reservoirs next to our many piles of stored spent rods in the event that the power in the United States fails, and we need to cool them by a gravity-fed system until generators to power pumps are working?

The pool itself is supposed to work as such a reservoir, with typically enough water to cope at least a week or so before new water needs to be added.
 
  • #11,867
http://www3.nhk.or.jp/news/genpatsu-fukushima/20111214/0400_osensui.html Another leak of 30 litres of water, that remained indoors and was stopped by closing a valve, was found at the same evaporative concentration equipment on 12 December. The NISA is issuing a "severe reprimand" to Tepco. It is the first time the NISA issues such a reprimand since the one that concerned the identity checks at the site entrance in August.

http://www.tepco.co.jp/en/nu/fukushima-np/images/handouts_111213_03-e.pdf Leakage from Sampling Line of Evaporative Concentration System 3 C
 
  • #11,868
http://www3.nhk.or.jp/news/genpatsu-fukushima/20111203/0735_reikyoku.html (3 December) Tepco's internal investigation report says that the suitability of the mechanism which makes the IC's valves automatically close when battery power is lost must be investigated. The mechanism is intended to prevent radioactive substances to be released outside of the plant in case of emergency, but in this case, it prevented the emergency cooling function from being performed.

http://www3.nhk.or.jp/news/html/20111209/t10014537511000.html (9 December) A JNES study was presented at a hearing of specialists organised by the NISA on 9 December. According to the JNES study, if unit 1's IC had been started at 4:15 PM (which is 45 minutes after the tsunami), cooling could have started before fuel exposure takes place, the water level could have been kept stable, and meltdown would not have occurred. But that would have required replenishing the IC with water. If the IC had been started at 6:15 PM (which is 2 hours 45 minutes after the tsunami), the fuel would be already exposed and it would not have been possible to restore the water level. A Hokkaido university professor who attended the meeting commented that "If the cooling equipment had been continuously used, the situation would not have been so severe. Retrospectively, unit 1's hydrogen explosion had consequences on unit 2 and unit 3. The complacency of the early response is an important soul searching item. How much the cooling equipment was in people's mind and how much the response had been prepared must be investigated". Tepco's Junichi Matsumoto commented that "searching one's way in the dark with a flashlight, and given the fact than only a limited number of valves can be manually operated from outside the PCV, recovering the cooling equipment's function was difficult. (...) The equipment is designed so that the valves are automatically closed when battery power is lost, so it was a situation where operation is impossible. Assuming that it had been possible to recover cooling function within the time mentioned in the [JNES] study, perhaps the water level could have been maintained, but wasn't it realistically difficult given the design of the equipment ?"

http://www.tepco.co.jp/en/news/topics/11120901-e.html "The isolation condenser was out of control and lost its function via the automatic isolation interlock operation due to the blackout caused by the tsunami."

http://www.tepco.co.jp/en/press/corp-com/release/11121513-e.html Report with regards to "Policy on the mid term security" for the Units 1 to 4 of Fukushima Daiichi Nuclear Power Station to Nuclear and Industrial Safety Agency at the Ministry of Economy, Trade and Industry (part 3) (15 December 2011, English press release linking to a 125 page Japanese report)

http://www.nisa.meti.go.jp/english/press/2011/12/en20111214-2.html "Regarding Evaluation of the Report from Tokyo Electric Power Co., Inc. (TEPCO) on Leakage of Water Containing Radioactive Materials from Evaporation Concentration Device"

http://www3.nhk.or.jp/news/genpatsu-fukushima/20111215/0825_hairo.html The decommissioning of Fukushima Daiichi will take a maximum of 40 years. Tepco and the Ministry of Economy and Industry have prepared a middle and long term schedule based on a report by the NSC. Fuel removal from unit 4 will start within two years, which is one year earlier than the NSC's report was recommending. The removal of melted fuel from units 1, 2, and 3 will be performed within 25 years, and the dismantling of the reactors and buildings will take until a maximum of 40 years from now. It implies difficult operations without precedent in the world and the design of new robots for remote operations is included in the plan. The "cold shutdown" and completion of step 2 will be announced by the government on 16 December. The middle and long term schedule will be released at the end of December.
 
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  • #11,869
tsutsuji said:
http://www.tepco.co.jp/en/news/topics/11120901-e.html "Comments concerning the page 2 article in the December 9 morning edition of the Mainichi Newspaper titled, "Had the reactor condenser begun running within an hour following the tsunami, the Unit 1 reactor meltdown would not have occurred. (Japan Nuclear Energy Safety Organization (JNES) analysis)" "

Thank you, Tsutsuji-san for this piece of information! Behind the link, there's a statement by TEPCO that the isolation condensor at unit 1 was out of order because of an "automatic isolation interlock operation due to the blackout caused by the tsunami". My understanding of neither the Japanese nor the English language is not sufficient to be able to say for certain, but to me this appears to be an explanation that it would not have been possible to open the IC valve between the tsunami and 18:18. At 18:25, the steam production by the IC is said to have stopped, which may be due to the hydrogen blocking the IC pipes.

Two questions to those more familiar with the GE design:

How is the valve in the IC return line operated? Is it just motor operated or would it be possible to open it manually in case of loss of DC?

Is there a way to release non-condensible gases from the IC?

As far as I'm aware, so far TEPCO has blamed the loss of measurements for the inability to engage the IC. This is the first time I've seen them suggesting "it would have been done if only it was possible".

Clearly, the control room personnel did what they were instructed to do and it would not be fair to put blame on them, but this yet another version of "why the IC was not used" seems somewhat confusing.
 
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  • #11,870
zapperzero said:
One of the assumptions here is that significant amounts of gas from a corium-concrete reaction would necessarily end up in the cooling water. Is this true, I wonder?

I used http://www.scienceaccelerator.gov/ advanced search with keywords “corium” and “concrete” to search for references. Here is a summary of what I found.

Gaseous products of Corium/Limestone Concrete Interaction:

http://www.osti.gov/bridge/servlets/purl/6439801-y4LnD0/6439801.pdf

Similar, but includes Basaltic Concrete and lots of math details:

http://www.osti.gov/bridge/servlets/purl/5080398-ulvUFv/5080398.pdf

Experimental Results

http://www.osti.gov/bridge/servlets/purl/5073998-ELWgMT/5073998.pdf

Mk I BWR specific:

http://www.osti.gov/bridge/servlets/purl/6572846-bJT5Ss/6572846.pdf

Theoretical model with crust and overlaying water pool

http://www.osti.gov/bridge/servlets/purl/10136693-iaggOp/10136693.pdf

Discussion of DW Liner Failure (beyond what has been discussed at Fukushima reactors):

http://www.osti.gov/bridge/servlets/purl/6476557-e9NERk/6476557.pdf

Experimental Heat transfer to liquid layers with entrainment of gases:

http://www.osti.gov/bridge/servlets/purl/7100357-d83aw9/7100357.pdf

NUREG /CR-5978 Probably best answers are in this document for aerosols retained in water including corium/concrete interactions in a BWR:

http://www.osti.gov/bridge/servlets/purl/10186838-I0dgvH/native/10186838.pdf

I have skimmed these documents and the NUREG seems to quantify the gas retention in the watter pool best. Bon Apetit! (BTW, There are lots more references in the search described above.)
 
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  • #11,871
NUCENG said:
I have skimmed these documents and the NUREG seems to quantify the gas retention in the watter pool best. Bon Apetit! (BTW, There are lots more references in the search described above.)

Oh this is good stuff, thanks a bunch.

one early catch (I'm still skimming through this stuff):

http://www.osti.gov/bridge/servlets/purl/10136693-iaggOp/10136693.pdf
efficient bulk cooling of melt will occur as long as the concrete
decomposition gas velocity lies above 6 cm/s. When the gas velocity falls below
this value, an interstitial crust is predicted to form: Thereafter, heat
transfer from the MCCI zone to the coolant will be crust-limited.

iow, it appears to be possible for MCCI-produced gasses to stop going into the cooling water, as the melt cools somewhat and crusts over.
 
  • #11,872
zapperzero said:
Oh this is good stuff, thanks a bunch.

one early catch (I'm still skimming through this stuff):

http://www.osti.gov/bridge/servlets/purl/10136693-iaggOp/10136693.pdf


iow, it appears to be possible for MCCI-produced gasses to stop going into the cooling water, as the melt cools somewhat and crusts over.

Correct, if you assume the crust is stable. Gases are still generated and tend to build up in the liquid corium which cold cause ruptures in the crust. It may be a iterative process of formation and rupture of crust for some period until the heat removal stabilizes the crust. Also consider that the presence of a water pool overlaying the corium. may be periodic due to boiling and makeup cycles. If the water has boiled off. crust may remelt. This appears to be an extremely dynamic process with a lot of variables.
 
  • #11,873
NUCENG said:
This appears to be an extremely dynamic process with a lot of variables.

I don't see how I could extract values for many of those variables using only the data that TEPCO is releasing.
 
  • #11,874
zapperzero said:
I don't see how I could extract values for many of those variables using only the data that TEPCO is releasing.

True, but what does that matter? They are measuring offgassing, and temperatures and indications are that the plants are reasonably stable now. It will be quire some time before they start to disassemble and remove core debris. I have asked this question before: What would we do differently if we had all the parameters you feel are missing? The original question you asked was whether water retention of gasses was a reasonable assumption. The information I provided indicates that the assumption is theoretically and experimentally valid. It seems that TEPCOs measurements (limited thogh they may be) also are consistent.

I guess the point is that if the current behavior is consistent with theory and experiment, the conclusion that the plants are stabilizing is reasonable. That is progress. We should continue to watch for divergence from the expected behavior, but lack of divergence is good news.
 
  • #11,875
NUCENG said:
True, but what does that matter? They are measuring offgassing, and temperatures and indications are that the plants are reasonably stable now.

Their thinking is "the corium concrete melt must have crusted over because we are seeing no CO2 gas in the water, therefore it must be at so-and-so temperature, therefore MCCI ceased and all is well".

But the models are more complex than that, are they not? Lots and lots of variables. Maybe there is a "stable" crust, but it will break again tomorrow? Maybe a stable crust formed earlier than the models suggest, for some reason (such as insufficient/unreliable data), so the melt is way hotter than TEPCO believes?

Maybe there wasn't any crust at all, ever, because fuel was sprayed under pressure from the RPV and is now laying in the form of small flakes and powder on the floor of the PCV, amply cooled but in danger of going critical again because there is so much water around?

They have temp sensors in places where there certainly is no corium now, and they are estimating the corium temp based on that. They are measuring the gas content of the cooling water and inferring stuff about how MCCI is proceeding, but have no explanation for the continued production of hydrogen and its presence in the PCV. They know of breached containments in three reactors, have zero information as to the shape and position of the corium yet work is proceeding as if a new major release of radioactive gasses and dust is impossible.

I have very little faith in their modelling and how it represents the physical reality. I suppose that makes me a skeptic? Or paranoid, perhaps?
 
  • #11,876
I was waiting until Tepco would provide a full translation of the document, but such a translation does not seem to be coming. So here is my question: the other day I translated a few tables :

tsutsuji said:
I attach a translation of the figures on pages 12 and 15 of http://www.tepco.co.jp/nu/fukushima-np/images/handouts_111130_09-j.pdf

In https://www.physicsforums.com/attachment.php?attachmentid=41476&d=1322928125 we have a list of assumptions made by Tepco before launching its simulations. I was disappointed to learn that the 0.81 m deposit thickness inside the sump is not a result but a mere supposition. Perhaps it is a good educated guess, but doesn't that make the 0.65 m concrete erosion depth result and the "PCV steel lining is still OK" conclusion look unsure ? Should not Tepco have simulated with a worse assumption, like assuming the sump is full with corium (which means using a 1.2 m thickness instead of 0.81 m) ? I tend to imagine liquid corium like liquid water. If enough liquid corium falls on the pedestal, the liquid would flow into the sump until the sump is completely filled, wouln't it ? So, conversely, does it mean I am wrong to imagine corium as a liquid which fills every hole like liquid bronze fills a statue mold (http://www.pbs.org/newshour/art/blog/2010/01/wednesdays-art-notes-6.html)?

I have another, most likely stupid question, but I can't find the answer myself. Why do they need that big Areva/Kurion/Sarry water purification facility in the first place ? I understand that they need to remove salt because salt and steel do not get on very well with each other. But why remove cesium ?
 
  • #11,877
tsutsuji said:
I have another, most likely stupid question, but I can't find the answer myself. Why do they need that big Areva/Kurion/Sarry water purification facility in the first place ? I understand that they need to remove salt because salt and steel do not get on very well with each other. But why remove cesium ?
The salt interferes with the collection of Cs and other isotopes. The water in the reactor building contains soluble fuel, transuranics and fission products. The objective of AREVA/Kurion/Sarry is to process the liquid, i.e., collect and concentrate in solid form the radionuclides in order to reduce the release of radionulcides. Basically, they set up a system similar to a fuel reprocessing stream. Ideally, the cleaner water is sent back to flush the reactor buildings. I would expect the goal is to remove all the soluble fission products leaving only those insoluble in containtment. However, I understand the fission products have leached into the concrete containment structures, so decontaminating them will would be virtually impossible, although the radioactivity levels would be lower than without the current processing program.
 
  • #11,878
Astronuc said:
The objective of AREVA/Kurion/Sarry is to process the liquid, i.e., collect and concentrate in solid form the radionuclides in order to reduce the release of radionulcides.

You mean that injecting the contaminated water without purification would create other clouds of contaminated steam which would then be spread into the atmosphere ? Yes that makes sense. Thank you for your answer. I was too much focused on the idea "those reactors need cooling, so all kind of water, including dirty contaminated one can do the job".
 
  • #11,879
tsutsuji said:
You mean that injecting the contaminated water without purification would create other clouds of contaminated steam which would then be spread into the atmosphere ? Yes that makes sense. Thank you for your answer. I was too much focused on the idea "those reactors need cooling, so all kind of water, including dirty contaminated one can do the job".

There's also the issue that the systems pumping water to the reactors would become extremely radioactive and impossible to approach for e.g. maintenance/repair work, and all leaks (that will eventually occur no matter what in such a temporary arrangements) would spread contamination with the site. And work would not be possible in those areas of the site where water injection lines are located.
 
  • #11,880
tsutsuji said:
You mean that injecting the contaminated water without purification would create other clouds of contaminated steam which would then be spread into the atmosphere ? Yes that makes sense. Thank you for your answer. I was too much focused on the idea "those reactors need cooling, so all kind of water, including dirty contaminated one can do the job".
There is still decay heat to remove. If the water was stagnant, it woud heat up, just like the spent fuel pool, which is cooled. The stagnant water would also dissolve radionuclides from the fuel.

So there are two objectives - cool the fuel material that is present (get to 'cold shutdown'), and extract the radioactive material (fuel, transuranics and fission products) in order to mitigate dispersion and release. At some point, the closed system would transport the mobile/soluble radionuclides to a collection vessel which can then be removed and sent to some disposal site.

I order for people to access the reactor buildings at some point, the contamination/radioactivity there has to be reduced to some level. However the complication is the fuel material that remains (which is mostly insoluble) and the radionuclides that have leached into the concrete structure. Ultimately, they have two choices - entomb the containments such that no leaching of radionuclides is possible, or demoslish the containment structures (while mitigating the release of radioacitive dust) and shipping the contaminated concrete to some final repository. I suspect there is pressure to go with the former option.
 

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