Analysis of the Beirut explosion?!

[kerbiloid]

10 minutes ago, Meecrob said:

But the blast clearly was kilotons in energy.

There was 2 700 t of AN at all, 7 years ago, and AN is much weaker than TNT. Where would those kilotons get from?

[DDE]

4 hours ago, RCgothic said:

I find conspiracy theorising about this disaster to be in extremely poor taste. It was an industrial accident involving a warehouse full of improperly stored confiscated ammonium nitrate, an adjacent warehouse full of fireworks, and a welding accident.

There's nothing more to it than that.

'Ere we go, time to start selling tin foil hats.

[Guest]

1 hour ago, kerbiloid said:

There was 2 700 t of AN at all, 7 years ago, and AN is much weaker than TNT. Where would those kilotons get from?

It has all been explained already, AN mixed with a little combustible material like bags and pallets in the warehouse. It does not degrade significantly with time, and judging from what happened, it had no significant water contamination. Such a mix is not as good as real ANFO, and certainly less predictable, but it will have similar yield.

Look at this mushroom cloud. This is an explosion with 10T yield:

Now look at the videos from Beirut. Completely different and much, much larger. 2750T of ANFO-like mix+an industrial quantity of fireworks+grain dust mixed in would easily account for an explosion in the neighborhood of 3kT, with the former component being responsible for the vast majority of the yield. That's how this stuff works, plain and simple. Thinking of things that could have lessened the effects is pointless, because they quite obviously didn't, unless you want to argue that the explosion devastated the majority of a large port city was much smaller than it actually was.

[sevenperforce]

1 hour ago, kerbiloid said:

There was 2 700 t of AN at all, 7 years ago, and AN is much weaker than TNT. Where would those kilotons get from?

2750 tonnes of pure ammonium nitrate, detonated properly and completely, will produce a 1.15 kiloton blast with a detonation velocity of Mach 8.

If you have a raging warehouse fire with lots of flammables, you can reach autoignition temperature for ammonium nitrate fairly easily, at which point you do not even need a primary shockwave to trigger detonation. That is what happened in the Texas City disaster.

2 minutes ago, kerbiloid said:

4 minutes ago, Dragon01 said:

AN mixed with a little combustible material

I don't discuss conspiracy theories in this thread.

Indoor fires tend to be oxygen-limited. They burn up all available oxygen pretty quickly and have to suck more in through convection. As a result, they produce a superheated fuel-rich atmospheric environment. Mach 8 is FAST. Anything flammable, from plastic bins to wooden pallets to particulate matter in the superheated fuel-rich air itself, is going to be pulverized and mixed very efficiently by a detonation wave moving at Mach 8. It might seem odd to imagine a wooden crate being part of the fuel for a bomb, but hypersonic detonation waves do funny things.

Spoiler

The TNT energy equivalence of pure ammonium nitrate is 0.42, and some impure ammonium nitrate can be as low as 0.15, but we don't know what sort of impurities were involved here. Hydrocarbon impurities from a shoddy manufacturing process can increase the energy equivalence and increase the detonation velocity. We don't know what happened to the stuff over seven years. Sure, some things could cause breakdown and a loss of energy; other things could cause any exposed AN to pick up soot or grease or particulate matter. Ordinary city smog contains high levels of volatile organic compounds which bind readily with ammonium nitrate. There are more adsorpable (note: that is not a misspelling) chemicals that would increase AN's yield than would decrease it. The Texas City disaster involved less than 3000 tonnes of ammonium nitrate but has been estimated at 2.7-3.2 kt yield.

Estimating that the blast could only have been a few tens of tonnes TNT equivalent because of the damage to the grain silo seems like a very poor way of estimating anything. That silo was EXTREMELY thick steel-reinforced concrete in multiple frangible layers, with gaps filled by grain. That's practically the most rugged kind of nonmetallic blast shield imaginable. And yet the first layer of concrete was almost completely obliterated. The Genbaku Dome was left standing despite being less than 400 meters from the edge of the nuclear fireball caused by Little Boy.

There are a lot of reasons to think the Beirut explosion was roughly one kiloton.

• In addition to the raw amount of ammonium nitrate involved (comparable to the Texas City disaster), we have a known seismic magnitude of 3.3, which would not be possible unless it was at least in the 1.3-kiloton range.
• We also can see from visual inspection of footage that the instantaneous fireball was between 60 and 110 meters, comparable to a one-kiloton nuclear blast.
• That instantaneous fireball appeared in less than one thirtieth of a second, meaning that the LOWER bound of detonation velocity was Mach 7 (and likely much higher) so the AN could not have degraded substantially.
• Dimensional analysis of the exponential fireball growth using the G. I. Taylor method suggests 1-2 kilotons.
• Broken glass was reported at distances of 7-10 kilometers, which simply is not possible for a blast lower than 100 tonnes TNT equivalent and actually points to it likely being well over a kiloton.

So we have lots of reasons to think the blast was least one kiloton and just misplaced speculation about AN impurities and degradation to say otherwise.

[K^2]

3 hours ago, Meecrob said:

But the blast clearly was kilotons in energy.

Can be sub-kT, but in high hundreds of tons. Estimares based on established methods place it in 100T-3kT range. The big spread is due to simplest of these being based on rate of fireball exansion, and that one is 5th power in radius, second in time. So error due to estimate of size is high, especially with granary in the way. As usual, real number is probably closer to the middle. The relevant estimate formula, famously used in Trinity test to get very early estimate is E = k*rho*R^5/t^2, with k very close to 1 for air, so it's often just omitted. Here, rho is density of air, and R is radius of fireball some time t since explosion. For best results, fit this to several frames of video from multiple sources.

Other methods have much larger errors inherently, but also fall well within this range. I'm yet to see an established method produce something wildly different.

The most reliable measure will be from analysis of destruction. Matching photos to simple models used to estimate damage from nukes shows that it has to be at least in hundreds of tons, and can't be more than a few kT, but that's still a huge spread. There are some online tools that will overlay damage zones over map that you can try different numbers with, and I encourage you to try these out, rather than blindly take someone's word. Problem is, these are approximate - granary certainly made a difference, and it's hard to tell with some buildings, how hard they were hit from pictures alone. Simulations of the blast wave and experts on the ground will be able to get data you'd need to make a precise call. That will take time.

But even with error bars being what they are, you can be confident that it's no less than hundreds of tons and not more than a few kT. Insisting on anything else at this point is on par with insisting Saturn V did not have carrying capacity for Apollo missions and for similar reasons. It's inherently conspiratorial, assuming hundreds of people are incompetent or lying, in conjunction with bad math and/or total lack of understanding estimate methods used.

[sevenperforce]

20 minutes ago, K^2 said:

Can be sub-kT, but in high hundreds of tons. Estimares based on established methods place it in 100T-3kT range. The big spread is due to simplest of these being based on rate of fireball exansion, and that one is 5th power in radius, second in time. So error due to estimate of size is high, especially with granary in the way. As usual, real number is probably closer to the middle. The relevant estimate formula, famously used in Trinity test to get very early estimate is E = k*rho*R^5/t^2, with k very close to 1 for air, so it's often just omitted. Here, rho is density of air, and R is radius of fireball some time t since explosion. For best results, fit this to several frames of video from multiple sources.

Other methods have much larger errors inherently, but also fall well within this range. I'm yet to see an established method produce something wildly different.

The most reliable measure will be from analysis of destruction. Matching photos to simple models used to estimate damage from nukes shows that it has to be at least in hundreds of tons, and can't be more than a few kT, but that's still a huge spread. There are some online tools that will overlay damage zones over map that you can try different numbers with, and I encourage you to try these out, rather than blindly take someone's word. Problem is, these are approximate - granary certainly made a difference, and it's hard to tell with some buildings, how hard they were hit from pictures alone. Simulations of the blast wave and experts on the ground will be able to get data you'd need to make a precise call. That will take time.

But even with error bars being what they are, you can be confident that it's no less than hundreds of tons and not more than a few kT. Insisting on anything else at this point is on par with insisting Saturn V did not have carrying capacity for Apollo missions and for similar reasons. It's inherently conspiratorial, assuming hundreds of people are incompetent or lying, in conjunction with bad math and/or total lack of understanding estimate methods used.

My prediction remains at 0.8-1.5 kilotons. Would be very surprised if it is not somewhere in that range.

[K^2]

3 minutes ago, sevenperforce said:

My prediction remains at 0.8-1.5 kilotons. Would be very surprised if it is not somewhere in that range.

Having taken a better look at aftermath footage, me too, but I can't find any one estimate whose error bars I can bring in this tight.

What did you use for seismic estimate to get 1.3kT from mag 3.3? I was fitting to known points from N. Korean tests, and ended up with a lower number, but also extrapolating 2 magnitudes, I wasn't expecting stellar precision.

[sevenperforce]

1 hour ago, K^2 said:

Having taken a better look at aftermath footage, me too, but I can't find any one estimate whose error bars I can bring in this tight.

There is no one estimate -- that's more the result of overlapping methods. From the perspective of the available energy and the instantaneous fireball size, I can't imaging it being more than 1.5 kilotons. Yet in terms of the extent of damage and the observable detonation velocity, I can't imagine it being under 0.8 kilotons. So that's where I'm getting my boundaries. 

Quote

What did you use for seismic estimate to get 1.3kT from mag 3.3? I was fitting to known points from N. Korean tests, and ended up with a lower number, but also extrapolating 2 magnitudes, I wasn't expecting stellar precision.

Oh, I used the actual equation.

log₁₀J = 4.8 + 1.5M

A 3.3 on the Richter scale is 5.62e9 J or 1,344 tonnes TNT equivalent.

EDIT: Well that was useless

Edited August 7, 2020 by sevenperforce

[K^2]

8 minutes ago, sevenperforce said:

Oh, I used the actual equation.

log₁₀J = 4.8 + 1.5M

A 3.3 on the Richter scale is 5.62e9 J or 1.34 tonnes TNT equivalent.

 

Yeah, but that's tons and not kT, and assuming 100% transfer. Of course, the transfer is actually known to be very, very poor. So while 1.3T equivalent transferred into ground waves is not inconsistent with anything, it doesn't really narrow things down for the actual yield.

That's why I was trying to use known nuclear tests as baseline. That landed me at something like 0.4kT, but that's a very rough estimate, essentially assuming that transfer is about the same at all energies, which isn't quite true, and I don't have any data points at low kT or sub-kT ranges to fill in gaps and make it a better estimate. Still in the right ballpark, though, so I was pretty happy with that.

Edited August 7, 2020 by K^2
Reducing quoted section to relevant.

[K^2]

11 minutes ago, sevenperforce said:

Sorry, I meant 1.34 kilotonnes, not 1.34 tonnes. Just a typo.

That energy equation is for the total energy of the event, not the amount of energy transferred into ground waves.

4.5 + 3.3 * 1.5 = 9.75, so the result is going to be in GJ. Your figure of 5.62GJ follows from it. A ton of TNT is 4.2GJ. To get to kT, you need 3 more orders of magnitude, 4.2e12J or 4.2TJ per kT.

And yeah, normally the energy is released underground in an earthquake, which is why these formulae simply mention energy. When shock wave originating above ground impacts ground, most of the energy is reflected. Which is why in explosion, the transfer fraction is important to estimate the earthquake potential. Details are way outside of my expertise beyond these basics, so I have no way to actually estimate any of it. Just extrapolating from known data.

[sevenperforce]

2 minutes ago, K^2 said:

4.5 + 3.3 * 1.5 = 9.75, so the result is going to be in GJ. Your figure of 5.62GJ follows from it. A ton of TNT is 4.2GJ. To get to kT, you need 3 more orders of magnitude, 4.2e12J or 4.2TJ per kT.

And yeah, normally the energy is released underground in an earthquake, which is why these formulae simply mention energy. When shock wave originating above ground impacts ground, most of the energy is reflected. Which is why in explosion, the transfer fraction is important to estimate the earthquake potential. Details are way outside of my expertise beyond these basics, so I have no way to actually estimate any of it. Just extrapolating from known data.

Wow, I flubbed that up royally. Thanks for the good catch.

Looking to see what else I can find.

The 1997 suspected Russian nuclear test had a seismic magnitude of 3.8-3.9 and was estimated as an 0.1-1.0 kiloton event...a factor of ten, which is not terribly helpful but tells us that we are in the ballpark. Because this was a (suspected) underground nuclear test, it would have had more efficient transmission than the blast in Beirut.

[RCgothic]

I think the fact that the blast site is strongly hemmed in by Mediterranean could account for a yield in the high hundreds still producing a seismic 3.3 from a nominal 1.1kT worth of incompletely detonated AN.

Ditto the focussing effect of the grain silo and the area of destruction opposite to that shield.

Fuel contamination - bags, pallets, fuel-rich firestorm environment, could also produce a larger magnitude.

Any combination of these could bump up the yield, even with incomplete detonation of partially degraded AN.

Or it could just have been a 1.1kT detonation purely from complete detonation of the known quantity of AN.

I don't think a yeild under the high hundreds is credible. If there'd been a photon flash instead of a red cloud of nitric acid nobody would have any trouble believing this was a small nuke.

Edited August 7, 2020 by RCgothic

[Guest]

2 hours ago, sevenperforce said:

The 1997 suspected Russian nuclear test had a seismic magnitude of 3.8-3.9 and was estimated as an 0.1-1.0 kiloton event...a factor of ten, which is not terribly helpful but tells us that we are in the ballpark. Because this was a (suspected) underground nuclear test, it would have had more efficient transmission than the blast in Beirut.

Vastly more, I would say. In, Beirut the Earth was clobbered with 50% of the energy at most, and likely much less. In Russia, it was 100%, what with it being underground.

According to Wiki, 4744T of ANFO gave a yield of about 4kT. 
https://en.wikipedia.org/wiki/Minor_Scale

Using that as a reference, 2750T of ANFO would have exploded with the force of 2.3kT. So that gives us an upper bound. 1.1kT (AN only explosion) gives us a reasonable lower bound. The actual yield will be hard to estimate much more accurately, there's a lot of variables here, and this one was far from a neat, controlled, spherical kaboom that Minor Scale was. I feel 1.something kT is a pretty good estimate, given that.

Also, I think it's a bit of an eye-opener regarding how powerful nukes actually are. 1.5kT is a nuclear warhead in the tactical artillery/air to air range. Half the city was devastated, and that only because the explosion happened next to the sea, yet in nuclear weapon terms, this blast was dinky. Each Minuteman III missile can carry three warheads, each a hundred times more powerful than that. Granted, damage doesn't scale linearly with the yield (the taller the fireball, the more energy is wasted), but it's still a terrifying amount of energy. 

Edited August 7, 2020 by Guest

[kerbiloid]

12 hours ago, sevenperforce said:

2750 tonnes of pure ammonium nitrate, detonated properly and completely

It could not detonate completely even if staying completely intact, because it was neither encased, nor properly initiated in many places.
Only a small part of it could detonate, and the question is just how much small.
It can be from tens to hundreds tonnes. My current estimation is tens, others say hundreds, doesn't matter.

The damages and casualties are far from a kiloton-range explosion, the fireball is much smaller than a kiloton
(
Nuke fireball radius (do not confuse with diameter)
ground explosion: r,m, sphere = 59 * yield,kt ^0.4
midair explosion: r,m, hemisphere = 68 * yield,kt ^0.4
)

Anyway this yield (tens or hundreds) clearly could be provided just by the declared amount of stored AN, and there is absolutely no reasons to bring any other fuel oe explosive until some known facts forrce to do this.
That's why I treat the ANFO hypothesis like a conspiracy theory until something will make to think it's ANFO rather than just AN.

12 hours ago, sevenperforce said:

If you have a raging warehouse fire with lots of flammables, you can reach autoignition temperature

Of autoignition. Not "autodetonation".
But the ignition is not enough. The AN should be encased and ignited in many points, otherwise most part of it would be just spread around and burn without detonation, and what we can see looks exactly like this.

12 hours ago, sevenperforce said:

Indoor fires tend to be oxygen-limited. They burn up all available oxygen

AN consists of 2 N, 3 O, 4 H.
N is nearly inert ballast, it's mostly exhausted as N.
4 H get bound with 2 O.
1 O gets released.

So, AN doesn't depend on the air at all, it can't be a fuel-air explosive. In air it just has greater surface area, that's all.

The mentioned fireworks contain nitrates of alcali metals. They don't significantly depend on external oxygen, and the presence of AN couldn't affect them and their yield. They would just burn faster.

12 hours ago, sevenperforce said:

but we don't know what sort of impurities were involved here.

In this case the impurities are an excessive entity. Nothing makes to think they were there even if they were, as the total yield of the explosion looks much less than kilotons.

12 hours ago, sevenperforce said:

The Texas City disaster involved less than 3000 tonnes of ammonium nitrate but has been estimated at 2.7-3.2 kt yield.

Texas city disaster is described in wiki very emotionally and without exact values instead of flying anchors, so it's hard to tell how close to the reality is their yield estimation.
Mentioned 2.7-3.2 kt yield from 2.3 thnd t of AN look like a pure fantasy, unless the ship was additionally carrying a thousand tonnes of TNT, as AN is several times weaker than TNT.

And even if it actually was that strong, don't compare the strong metal hull of the ship (i.e. the casing, keeping both pressure and reaction mass inside) and lightweight storage construction with windows and doors.
Of course, the storehouse walls became a cloud of flying rubbish before the AN could react completely.

12 hours ago, sevenperforce said:

In addition to the raw amount of ammonium nitrate involved (comparable to the Texas City disaster), we have a known seismic magnitude of 3.3, which would not be possible unless it was at least in the 1.3-kiloton range.

Magnitude-yeild dependence is logarithmic. Always. The released energy can be estimated only with significant error.
Also when they bring Korean numbers to Lebanese event, this is handwaving, as every region has its own rock structure, and the coefficients differ for many times.
So, such accuracy looks unclear.

12 hours ago, sevenperforce said:

We also can see from visual inspection of footage that the instantaneous fireball was between 60 and 110 meters, comparable to a one-kiloton nuclear blast.

While 1 kt nuke blast would have at least 120 m in diameter.
Also it's a chemical blast, slower than the nuclear one and having another mechanism of the air heating, so the yield could be several times lower.

12 hours ago, sevenperforce said:

That instantaneous fireball appeared in less than one thirtieth of a second

Watching the video at 1/16 speed makes to think this accuracy is overestimated.
We can see the progress of the fireball expansion, and it unlikely can be defined so precisely, so the 7 Mach is just the upper (and emotional) value.

12 hours ago, sevenperforce said:

Dimensional analysis of the exponential fireball growth using the G. I. Taylor method suggests 1-2 kilotons.

Clarification is required. What exactly do they call "dimensional analysis" and its algorithm.

12 hours ago, sevenperforce said:

Broken glass was reported at distances of 7-10 kilometers,

Broken glass is a weak shockwave area and it happens far beyond the zone of regular damages, highly depends on local landscape and shockwave reflections.

Say, the 58 Mt had broken wooden houses in a village at 700 km distance.
But this doesn't mean that it devastated a 1400 km wide area. Just trhe shockwave reflected from the upper atmosphere and produced a concentric pattern. The village appeared staying at local maximum.

So, the broken glass can indicate only one thing: that at this distance the walls are not broken. It can't be used for accurate estimations.

1 hour ago, Arugela said:

How is that a conspiracy. It's a storage area. Anything could have gotten on it an any point.

Could doesn't mean was.
Until you can't explain the observed events with known facts, you shouldn't bring additional factors arbitrarily. That's how scientific method works at all, Occam bless it.
Otherwise we should also include meteorites, antimatter, godzilla, and other things which nobody had seen, but theoretically could be.

So, while the explosion can be explained with pure AN detonation, and while nothing clearly indicates presence of an additional factor, any ANFO, antimatter, meteorite and other factors stay as pure conspiracy theory as it can be at all.

Edited August 8, 2020 by kerbiloid

[Piscator]

[snip]

It's literally impossible to make any kind of alcohol from AN unless you involve some kind of nuclear reaction to create the carbon.

Edited August 8, 2020 by Vanamonde

[Arugela]

So, was the AN isolated or did it have stuff in it to start with. I thought it was literally highly concentrated fertilizer and not pure.

[kerbiloid]

7 hours ago, Arugela said:

it was literally highly concentrated fertilizer

Officially documented fact.

7 hours ago, Arugela said:

and not pure.

[snip] presumption [snip]

Edited August 8, 2020 by Vanamonde

[Arugela]

[snip] Did it have other things in it?

Was there a way for other things to get in it over time?

[snip]

Edited August 8, 2020 by Vanamonde

[kerbiloid]

1 minute ago, Arugela said:

Did it have other things in it?

How could I know?

[Arugela]

1 minute ago, kerbiloid said:

How could I know?

Do you have any understanding of what you just said in context to your previous statements?!

Edited August 8, 2020 by Arugela

[kerbiloid]

7 hours ago, Arugela said:

Do you have any understanding of what you just said in context to your previous statements?!

It means absolutely what I'm saying: while I have no reasons to presume there were significant impurities or other explosives, and while the event can be explained without invention of facts, no such arguments should be taken into account.

[snip]

Edited August 8, 2020 by Vanamonde

[kerbiloid]

3 hours ago, Arugela said:

if it had impurities could it have become alcoholic

As it's said above, AN doesn't have any C to produce alcohol.

So, there is no recipe of AN moonshine.

[Vanamonde]

Some content has been removed. The definition of science is beyond the scope of this forum and the limits on what can be known is a whole branch of philosophy called "epistemology" which generations of geniuses have not be able to quantify, so how about we leave that out of this thread? Since it's off-topic anyway? Also, please watch the tempers and don't make the discussions personal. 

[Guest]

12 hours ago, kerbiloid said:

But the ignition is not enough. The AN should be encased and ignited in many points, otherwise most part of it would be just spread around and burn without detonation, and what we can see looks exactly like this.

AN is detonated by shock. It's a tertiary explosive, heat has nothing to do with it. In fact, as an oxidizer, it doesn't burn. You don't need to "properly initiate" AN. All you need to do is to provide a strong shockwave from another explosive material. After that, if even a small pocket explodes, it will initiate all material nearby. The shockwave travels faster than the speed of sound, so further material is detonated before it has a chance to scatter. This is common to all shock-initiated explosives. Once it gets going, all of it gets going.

12 hours ago, kerbiloid said:

It can be from tens to hundreds tonnes. My current estimation is tens, others say hundreds, doesn't matter.

Try "thousands". You're undershooting by two orders of magnitude. Others have already explained how it was calculated. I even posted a video of a real 10T bomb, which is visibly much smaller than that. It's much larger than even the FOAB test (44T).

Causalities are lower, because it happened in a port, where not many people were around it. Property damage, however, was massive. Again, the port took the most of it, so devastation in the city itself was somewhat lower. A 10T blast would almost certainly fail to overturn that cruise ship, for instance. Ever seen one of these up close? They're gigantic, and not easy to flip over, Costa Concordia notwithstanding.

[kerbiloid]

9 hours ago, Dragon01 said:

AN is detonated by shock.

It doesn't matter how. Sorry, but I'm not going to repeat same things again and again. If you wish to have another opinion, you welcome.

9 hours ago, Dragon01 said:

Try "thousands".

See above.