Fuk-D: what happened to the reactors?

It will probably be some years before we get the full story of what happened at the Fukushima Daiichi reactor complex after the earthquake.
Information has not exactly been put out coherently or comprehensively, but we can make some inferences from the data that is out there.

It is likely that one or two reactor vessels were breached with release of fuel and radioactive ash into the containment vessel.

There are a lot of nuclear agencies in Japan:
the JAEA - Japan Atomic Energy Agency - whose online environmental radiation monitors are now online (Oarai is the interesting one, between Fukushima and Tokyo)
Tokyo Electric Power Company (TEPCO) with its minimalist press releases
NISA - Nuclear and Industrial Safety Agency - I don't know what they do. They have a press release saying TEPCO found Iodine and Cesium radioisotopes at Fuk-D - well, duh (ok, they include actual quantitative info on concentrations).

JAIF - Japan Atomic Industrial Forum - they have actual hard information, in particular, their daily status report includes timelines of reactor events, and pressure, temperature and water levels for the reactors.

Just to recap: there are six Boiling Water Reactors (BWRs) at Fukushima Daiichi.
Useful IAEA document on BWRs (pdf) - 1-5 are Mark I reactors (old and crude) the 6th is a Mark II I believe.
The reactors use Low Enriched Uranium, at 2-3% enrichment, except reactor 3 which has some plutonium oxide (mixed oxide fuel) mixed in. The fuel is in oxide pellets inside zirconium fuel rods.
Each rod is a little over 3 m long and the core is assembled as a grid of these rods held vertically, with support structure and control rods in between, and water coolant and moderator circulating through the grid of rods.

The magnitude 9 earthquake caused a bit of an accident, as you know.

Three of the reactors: 4,5 and 5, were offline for scheduled refueling.
The operating reactors were scram'd when earthquake warning was given and started shutdown.
The ensuing tsunami wiped out a lot of the plant infrastructure, including electrical switching rooms and generators, but not the reactors or containment buildings.
The recovery has been brutal, the workers heroic, and the management not.

Who is in charge of the Fukushima-Daiichi site?
Anyone know? Engineer? Manager?
No, I don't know either...

However, with power out and rapid successive failure of power the primary cooling circulation in the reactors shut down.
Boiling Water Reactors of this generation rely on active circulating of water, the core boils water from the pool it is embedded in, and the overpressured steam goes to condensers which drives the electricity generating turbines, and the cool water returns to the reactor vessel. Later designs can stay cool using passive circulation, but these need several MWe turbopumps to keep the primary coolant circulating.

The cores stay hot, initially due to residual fission, and just pure heat capacity, each core is a few hundred tons of fuel, cladding and control rods.

So this is where the problem began.

The hot reactor core boils the water, the water level drops exposing the tops of the fuel rods, reducing cooling.
If the rods get hot enough, the zirconium cladding oxidises: Zr + 2 H₂O -> ZrO₂ + 2 H₂
This is an exothermic reaction, which increases the heating of the rods which can accelerate the oxidation.
ZrO₂ does not have the structural properties of zirconium metal, so the fuel rod cladding integrity is compromised, and the fuel rods can crack or split spilling fuel.

The steam, and any hydroen generated, raises the pressure in the (airtight) reactor vessel.
Excess pressure in the reactor is bad, and the pressure is measured.
So, if the pressure gets too high it is vented into the containment building.
The reactor vessels is a steel flask, it is vented into a water torus inside a massive concrete and steel containment vessel, surrounded by a secondary containment building.
The roof and top two floors of the outer building are deliberately flimsy with "blowout panels", so any explosion is vented.
The reactor vessel atmosphere should have no oxygen; the containment usually is low oxygen air; the outer building normal atmosphere.

Now, when the steam is vented any hydrogen generated is also released.
Hydrogen detonates in air over a very wide range of non-stoichiometric mixing ratios with a fast shock.

Boom.
That is what happened to reactor 1 - it was vented, hydrogen had been generated and promptly detonated.
Now, these are big buildings, it take some explosion to knock out the top floor panels.
Certainly tens of kg of H₂, if not more.
That hydrogen must have come from fuel rod cladding oxidation.
Many tons of fuel rod cladding must have been oxidised, so we conclude that significant fraction of the fuel rods are damaged and possible spilling fuel.
The fuel rod cracking also releases the highly radioactive ash inside the fuel rods, including short and medium halflife isotopes.

Now, IF fuel pellets fall to the bottom of the reactor, or the fuel rods became hot enough to melt and slump, THEN it is possible for a compact lump of fuel to form within the reactor within the residual water, and it may start fission reactions again, heating up.
That is bad.
In particular core melt can breach the reactor vessel causing molten core material to fall into the containment well - this is concrete/sand/steel/concrete layers, very thick, and it ought to hold most of the core indefinitely.

This did NOT happen to reactor 1: we know this because the reactor vessel in reactor 1 is holding its internal pressure. The water level is low but the core must have cooled down and is stable.
This was probably ensured by the dumping of boron and seawater (because they were out of fresh water) into the reactor.
The reactor is trashed, but probably won't do anything more.

Reactor 3 also had a hydrogen explosion: a bigger one, later, after steam venting.
So we infer its fuel rods also oxidised and its core is damaged.
The reactor vessel was holding its pressure, but with the fuel rods exposed, until march 20th when the reactor vessel pressure apparently dropped to ambient (or the gauge broke). The water level stayed about 2m below where it should be, and radiation levels around reactor 3 are high.

This suggests, strongly but indirectly, that the reactor vessel is breached - probably a crack about halfway down the core, basically where the water level is stuck.
If I understand the relative pressure measurements - they are relative, not absolute, relative to what is moderately important.
This suggests that some fuel may have escaped into the containment well, and the reactor may still be undergoing partial fission.

Now, reactor 2 also had an explosion, but it was not a hydrogen explosion at the top of the building; it was apparently a steam explosion from the water torus vent - that suggests massive overpressure in the reactor vessel driving a "steam hammer" into the torus with a shock erupting into the containment building.
The reactor has been stuck with a low water level, almost 2m below nominal, and the reactor vessel has been persistently unpressured.

Reactor 2 almost certainly has a cracked reactor vessel; it is possible the explosion was due to hot melted core material and water falling into the drywell and a lot of water flash vapourizing. Or not, but something damaged the suppression pools outside the vents.

So: it seems likely, to me as physicist working from incomplete and mildly incoherent information that one or two of the reactor vessels have breached and released fuel and ash.

Is there ongoing fission in molten bits of the core.
I had thought not, until I read the handy-dandy press release from NISA on TEPCO measurment of radionuclides at the plant.
They find I-132 and I-133 on March 19th.
Those isotopes are short lived - hours, not days - and they are fissile products.
If there is any significant amount of them at the plant a week+ after shutdown, then I start thinking there must be an ongoing source of these isotopes.
Finding other, shorter lived fission products, would be the smoking gun.

Of course, these may come from the spent fuel ponds, not breached reactors.
I'd love to know if they are seeing ¹⁶N around either reactor.
It comes from an (n,p) reaction on ¹⁶O and has halflife of seconds, so is only there is there is active neutron flux and a current leak...

The fuel ponds are a separate issue - reactor 4 is a mess because they just unloaded a quarter of a core into the spent fuel pond - the fuel ponds are there next to the reactor in open concrete pools, you need them to have some place to put the hot spent rods when you lift them out of the core, but they're not supposed to stay there indefinitely!
Unless you have no other place to put them.

The spent fuel ponds actually hold more radioisotope inventory than the cores, and they are hot. If the water drains out, like if explosions cracked the concrete pools, or if it just evaporates, the fuel rod cladding can burn releasing the fuel and ash. In principle melted spend fuel rods could also reach a geometry where they go critical and fission resumes, except this would be open air fission, not inside containment.

++Ungood.
Which is why there is so much focus on keeping the spent fuel pools cool and not on fire.
The older reactors have several cycles of spent fuel rods - up to 4 core loads!
Those rods need to be moved out to some stable less crowded storage, but the explosions destroyed the cranes and gantries.

How much radioactive material is there?
Well, if dispersed uniformly, enough to make of order 10,000 km² uninhabitable.
For real, not at the arbitarily way low standard safety limits for radiation doses.

Fortunately the inventory will not be spread uniformly, but mostly be clumped.
There is still the potential for massive radiation release, still, with a significant area closed to habitation and a larger area being unable to produce consumable agricultural products.

Radiation traces will also show up in manufacture, mostly at a harmless but scary level.
Any alpha emitters spread around could trash japanese manufacture of bleeding edge electronics - high density chips don't like hot spots on them.

This is going to be a mess.
But, hopefully just a mess, not a mass casualty event or panicked mass evacuations.