How large would the steam explosion at Chernobyl have been?

I had the exact same question when I saw the episode. Building on user1476176's answer, I have thoughts as to how someone might have derived a much higher upper bound, though until someone pulls the actual source they used we won't know. They did explicitly say in the episode that other reactors would be engulfed, presumably with their water. That only multiplies the amount of useful fluid a few times, but then there is the exterior reservoir that is itself connected to internal pumps that might also be part of someone else's calculation, since that reservoir would have had nearly 10^6 tons of water judging from Wikipedia's map, which would make the yield upper bound 150 kT TNT. Of course it's not like an open reservoir would magically behave like a steam vessel when lava touches it, but it might be the source of this worst-case calculation.

Another possibility is that our unknown source made the common mistake of assuming that the material in these nuclear reactors can explode like an atomic bomb. If the mass of fuel in a core is about 200 tons (for RBMK reactor) and the yield/weight ratio for the earliest fission bombs is about .05 MT/ton, then we're getting close. I really hope a show as good as this didn't source this datum from somewhere that would make so bad a mistake though.

I had the same question and found an old Guardian articla from 2005 saying that the explosion would come from:

"There was a moment when there was the danger of a nuclear explosion, and they had to get the water out from under the reactor, so that a mixture of uranium and graphite wouldn't get into it - with the water, they would have formed a critical mass. The explosion would have been between three and five megatons. This would have meant that not only Kiev and Minsk, but a large part of Europe would have been uninhabitable. Can you imagine it? A European catastrophe."

https://www.theguardian.com/environment/2005/apr/25/energy.ukraine

The top accepted post (user1476176) has already done a thorough job of calculating the thermodynamics for a steam explosion (spoiler: nowhere near the megaton scale -- they were only off by 10,000X to 100,000X).

To compliment that, here's some intuition for what it takes to achieve a megaton-scale explosion, and why it is so laughably unrealistic to think that could happen by accident in even the worst-possible reactor disaster (i.e., Chernobyl):

1. It took our top scientists and engineers multiple years to achieve kiloton-scale bombs, and years more to achieve megaton-scale bombs using fusion. It was not easy, and they were working with billions to trillions of dollars of government resources at their disposal. If you could just drop some melted corium into water ... they would have done that at least once -- the first H-bomb test involved vaporizing a building-scale cryogenic chilling plant that was keeping the liquid deuterium from boiling away.

Making even kiloton-scale explosions requires precision.

Making megaton-scale explosions requires extreme precision, beyond the capabilities of many nation states. And fusion.

2. The largest pure-fission bomb ever tested was on the order of 0.5 megatons. They used huge quantities of weapon grade $^{235}U$ (>95% enrichment), surrounded by a neutron reflecting tamper, and almost instantaneously compressed to super-criticality by two different high-explosives precision engineered to produce a perfectly spherical shock wave. Chernobyl used fuel that was less than 2% enriched, meaning that 98% of it was non-fissile $^{238}U$, and that is before you account for contamination by fission byproducts, melted concrete, and melted steel.

3. Fusion is the only way that weapons engineers have been able to create megaton-scale explosions. And fusion is completely out of the picture here for at least two reasons:

• Bombs depend on fusing rare hydrogen isotopes like deuterium ($^2H$) and tritium ($^3H$) that weren't present at Chernobyl; for deliverable bombs, they use lithium-deuteride which contains deuterium and forms tritium under neutron bombardment (by cracking the lithium). The random fire-hose water that was seeping through Chernobyl was almost entirely (99.98%) composed of normal hydrogen ($^1H$), which is so hard to fuse that we don't / can't use it in bombs.
• Even to fuse $^2H$ and $^3H$, they have to use kiloton-scale fission bombs, combined with precision engineering that uses the fission bomb's x-rays to generate compression that's way beyond what's achievable with conventional explosives. This drives the $^2H$ and $^3H$ atoms together at extreme pressures and temperatures. It's extremely hard to do and, unlike with fission criticality accidents, fusion will never happen by accident. For example, if you moved the tritium from the center of the plutonium pit and just set it next to the bomb, it wouldn't fuse. Fusion is exceedingly difficult to achieve, on a level that's hard to put into words.

4. To achieve even kiloton-scale yields, great care must be taken to assemble the super-critical mass as quickly as possible, and to avoid stray neutrons that might start the chain reaction prior to the maximum compression (i.e., maximum super-criticality). For example, the first North Korean bomb attempt "fizzled" with a sub-kiloton yield ... generally, this happens for one of two reasons: either the implosion was less than perfect, or stray neutrons started the chain reaction before the point of maximum compression. Either way, what happens is that the fissile material, which is heating at an exponential rate, physically blows itself apart before the chain-reaction can achieve kiloton yields.

• Compression, compression, compression. The art of designing a nuclear bomb involves three things: Getting the the bomb into a maximally super-critical state (implosion), starting the chain reaction precisely at the moment of maximum criticality (the polonium/gold neutron initiator), and then keeping the fissile material super-critical state for as long as possible to maximize the yield (the "tamper" material slows the expansion by tens of nanoseconds). Note that none of these components were present at Chernobyl.

• Weapons Grade. To get good bomb yields, you want to use a fissile material that's as pure as humanly possible. Both being as close to 100% fissile material as possible (compared to Chernobyl's 2% fuel), as well as not being contaminated with neutron sources that will trigger an early detonation "fizzle". The Chernobyl corium contained highly active neutron emitters and would have instantly fizzled at the moment of criticality well in advance of achieving the super-criticality required for a kiloton-scale yield.

5. The neutron chain-reactions in a reactor are very different from those used in bombs:

• Thermal Neutrons - the only way to achieve criticality with Chernobyl's 2% enriched uranium is to use a neutron moderator, like graphite, that slows the neutrons emitted by fission until they are in the "thermal" spectrum (i.e., bouncing around at similar thermal temperatures to the surrounding atoms). This increases $^{235}U$'s neutron absorption cross-section and consequently, raises the probability that any given neutron will trigger another fission event rather than leaking out of the reactor core or being absorbed into some other atom. But because they need to bounce through graphite before slowly finding more $^{235}U$, thermal neutrons have much longer "doubling times" than do fast neutrons, meaning that the bomb-scale chain reactions just aren't possible: the critical mass will thermally blow itself apart as soon as even a tiny fraction of the material fissions.

• Delayed Neutrons - in addition to using "thermal" rather than "fast" neutrons, reactors are designed to operate "prompt sub-critical", meaning that the neutrons that are emitted from $^{235}U$ fission are insufficient for sustaining a chain-reaction unless one also includes neutrons generated from secondary decay chain events that occur seconds to minutes later. This is important because it makes reactors much easier to control. One of the key questions I have about Chernobyl is whether during the sheer incompetence that led to the initial reactor explosion, they managed to take the reactor into the "prompt criticality" regime, although with thermal neutrons that have to bounce around before chain-reacting, it becomes a more subtle distinction. I'm not sure if that's globally unknown, or just unknown to me.

A steam explosion between corium at 3000 degC and water would be pretty dramatic, potentially destroying additional containment elements, ejecting highly radioactive material onto the roof and grounds, and generally complicating the already hellish clean-up challenges. So no kidding, they wanted to avoid that.

But a steam explosion is nowhere near the megaton-scale energy release described in the show.

It's highly dubious that the Chernobyl corium, stripped of its moderating graphite and contaminated by concrete, steel, and especially Boron (a potent neutron absorber), could have even assembled into a critical mass at all.

But even if, by some crazy set of coincidences that did happen, the chain reaction of thermal neutrons in a barely critical configuration would have thermally blown itself apart well before reaching even the kiloton-scale range of energy releases. Megatons is laughable.

The show (which, overall, was AWESOME), was embarrassingly unfounded on this point. Chernobyl was awful enough in reality without the need to fear-monger with ludicrous hypotheses.

I had heard this scenario many years ago and its primary source I believe was an interview with Gorbachev were he mentioned it (I cant find the source though, so take with a pint of salt).

I too considered it to be without much foundation (Given the known facts its out right impossible unless they had stored nuclear weapons hidden under the cores foundation) and given that it comes out of a man that isn't a scientist but a politician, my best guess would be that the 3 megaton figure should not be considered as the yield of an explosion event but more likely the fallout equivalent of the radiation that would have been released after the steam explosion and the subsequent destruction of the remaining 3 cores at the vicinity

Guys you need to read more papers on steam explosions. When talking about steam explosions with corium, you need to note the velocity of energy exchange between the heated mass and the water. That needs intermixing of really tiny superhot particles and water in very very short time(hard to achieve). The efficiency of this steam explosions ( ratio of thermal energy to converted mechanival eneegy) is very very low. Even below 1%.

Read steam explosions in light water reactors, swedish comité.

About criticality, i certanly doubt that it was a threat at that moment. Probably impossible to have with corium.

Considering the character making the 3 megaton steam explosion assertion, Ulana Khomyuk, was a composite of multiple Soviet scientists and the fact that the state was making every attempt to cover up, divert blame and threaten those who were trying to bring the problem out in the open, I do not think it would be amiss to consider one other option. The scientists involved in containing the accident may have exaggerated the gravity of the situation in order to make an impression on the political apparatchiks. It wouldn't be unreasonable to expect that many in the government would have understood what the meaning of a megaton was given the general knowledge of nuclear weapon yields. Telling a member of the politburo a megaton equivalent, even if it was a vast exaggeration may have been seen as a way to get the political authority to commit the type of resources required to deal with the problem. Recall that for nearly 30 hours after the accident, the operators on scene were insisting that it had not happened, that it couldn't happen, and that it was "no big deal". Were I a responsible scientist living within the culture that was the late cold war Soviet Union I think I would have done whatever was needed to get the problem under control, including exaggeration.

The upper-voted answer has the right aim, but it still doesn't give the right estimate. The true source of energy under consideration is indeed the core, not the water, but the calculation in that post is essentially assuming cooling the core from its standing temperature to normal temperature - and as Emilio Pisanty pointed out in the comments, this won't happen as the core is actually its own energy source, capable of maintaining an elevated temperature.

Hence, what you get is effectively a heater that will apply to whatever is applied against it a thermal transfer power equal to the wattage being created by the ongoing fission process within the core material. As such, it is legitimate, as that poster also mentioned, to surmise in theory that an upper limit of megatonnes of total core potential energy is available. In particular, if you have roughly (using figures floating here) 1000 Mg of nuclear fuel that is maybe 5% fissile uranium ($^{235}_{92}mathrm{U}$), that is 200 Mg of such and this fuel has an energy content of about $86 times 10^9 mathrm{MJ/Mg}$, so the total available energy is on the order of $1.3 times 10^{11} mathrm{MJ}$, while a megatonne equivalent TNT is roughly $4 times 10^9 mathrm{MJ}$, hence easily tens of megatonnes of available potential fission energy.

But this energy cannot turn into an explosion of that same size under these condition because the core is not releasing that energy fast enough. If it were, it would have already exploded in the manner of a gigantic pure-fission nuclear weapon of that yield. The rate of the fission reaction depends on the composition of the core melt mix, and to get such a reaction would require extreme concentration of the fissile $^{235}_{92} mathrm{U}$ (basically, so that the nuclei are close together and there are few to no obstacles to absorb the neutrons that are needed to propagate the chain reaction), but melting and mixing the material can only serve to dilute it at best. Increasing fissile concentration is the definition of "uranium enrichment" and as we all know, that's HARD! Dumping water on it won't change that. Instead, you a better model would be a a thermal terminal that maintains a constant temperature of 2800 C against anything that hits it, or, at least, something suitably well above the boiling point of water.

Thus, in fact, the question asker is right to imagine this instead as asking for the energy required to vaporize all the water, and this is the maximum energy that can be released in a steam explosion. Energy is contact-transferred - hence once converted to steam, it is very difficult to absorb more from the core.

And this is relatively simple to obtain. With $7000 mathrm{m^3}$ of water volume, that's $7000 mathrm{Mg}$ of water mass, and the heat of vaporization for water is $2260 mathrm{kJ/kg} = 2260 mathrm{MJ/Mg}$ (hence my use of megajoules as the unit above), but we also need to take into account the energy to heat the water to the boiling point, which means we should use $4.184 mathrm{frac{kJ}{kg cdot K}} = 4.184 mathrm{frac{MJ}{Mg cdot K}}$ times the temperature rise (75 K) which gives $314 mathrm{frac{MJ}{Mg}}$ and hence $2574 mathrm{frac{MJ}{Mg}}$ of total energy to vaporize each megagram (tonne) of water starting at the given staid temperature 25 °C. With 7000 Mg of water, thus, the total potential energy is thus about

$$1.8 times 10^7 mathrm{MJ}$$

maximum possible steam explosion energy. In terms of tonnes equivalent of TNT, it is ~4 kilotonnes TNT equivalent, and so still well below the range given (though also well in excess of the present top answer's figure).