Some numbers: energy and disasters

2010 and 2011 may not have been unusual in terms of the number of energy-related disasters, but I suspect they have at least been unusual in terms of the quantity of headline-grabbing material and TV news attention, and the ongoing disaster stemming from the earthquake and tsunami in Japan is only the most dramatic of them. With the 1-year anniversaries of the Upper Big Branch and Deepwater Horizon disasters running past along with the 25th anniversary of Chernobyl, I felt a need for some sort of quantitative comparison of these various events...

An explosion or earthquake or other disaster of that sort involves the almost instantaneous release of a large quantity of energy. For earthquakes we have a convenient measure in the Richter scale, which measures the shaking amplitude. The Richter scale increases logarithmically, so that an increase in magnitude by 1 means a shaking amplitude 10 times as large. The quantity of energy involved scales as the 3/2 power of that amplitude, so 2 magnitudes on the Richter scale corresponds to an increase in energy release by a factor of 1000. Converting energy to standard metric notation in terms of joules (1 J = 1 kg m^2/s^2), the Richter scale magnitudes come to:

Magnitude 3: 2 GJ (2x10^9 J)
Magnitude 5: 2 TJ (2x10^12 J)
Magnitude 7: 2 PJ (2x10^15 J)
Magnitude 9: 2 EJ (2x10^18 J)

Nuclear explosions are typically measured in units of kilotons of TNT, where 1 kt TNT = 4.2 TJ, i.e. a 1 kiloton explosion should be about double the energy release of a magnitude-5 earthquake, and a 1 MT (megaton) explosion around double the energy release of a magnitude-7 earthquake.

Also worth thinking about in comparison is the non-explosive use of energy, as it runs through the natural world and as we use it for our own purposes. Since a year consists of just over 3x10^7 seconds, a 1 GW power plant over the course of a year produces 3x10^16 J or 30 PJ of electrical energy. That's about 7 times the energy release of the 1 MT explosion, about 15 times the energy release of a magnitude-7 earthquake. That energy release is spread over tens of millions of seconds, not just the few seconds of an explosion, but it's good to remember it is a large quantity of energy.

Human society currently uses about 15 TW of primary energy, or 450 EJ per year. That's over 200 magnitude-9 earthquakes, almost 1 per day. That's a lot of energy.

Earth receives energy from our Sun at a rate of about 174 PW. In a year that's about 5x10^24 J, 5 YJ (yottajoules) or 5 million EJ. That's a magnitude-9 earthquake worth of energy every 12 seconds! Luckily it's spread out over the whole (day-lit) surface of the Earth, so we don't normally experience the magnitude of that energy flow in any dramatic fashion. Still, it's worth remembering how natural energy scales like this tend to dwarf whatever humans do.

So, how do our recent collection of energy-related explosions and disasters compare?

On February 7, 2010, 6 people were killed and at least 50 injured at the Kleen energy plant explosion in Connecticut. Workers were blasting natural gas through pipes at the plant in an effort to clean them of debris, with the procedure repeated about 15 times over 4 hours, with the natural gas leaving pipes for the out-door area of the plant from openings less than 20 feet off the ground. The natural gas pressure at the input end was 650 psi, over 40 atmospheres. Overall 2 million (standard) cubic feet of natural gas were used in the day, with 480,000 cubic feet released in the last 10 minutes before the explosion. 1 standard cubic foot of natural gas has an energy content of 1028 BTU or 1.08 MJ (1 BTU = 1055 J). So the energy of the explosion at the Kleen energy plant that day, if it consumed all 480,000 cubic feet most recently released, would have been about 520 GJ. That's about 1/4 of the energy release of a magnitude-5 earthquake, although in this case the explosion was entirely above ground and there was very little seismic motion involved.

On April 5, 2010 an explosion in the Upper Big Branch mine at Montcoal, West Virginia killed 29 miners (for further references on the following calculation, see note 1 below). This is believed to to have involved a combination of natural gas (methane) and coal dust. The explosion is said to have spread through over 2 miles of mine tunnels "in an instant". The mine face was known to release roughly 2 million cubic feet of methane every 24 hours; ventilation systems in the mine were supposed to sweep this away to keep the gas below the 5.1% minimal explosive level. There was also evidence of considerable coal dust within the mine; that dust is explosive at concentrations of 0.055 ounces of coal per cubic ft, and efforts were made to keep that dust also below the dangerous explosive level. If the 2 miles of mine tunnel involved a cross section roughly 6 ft square, that would amount to around 360,000 cubic feet of air. At 5.1% methane, that's about 18,000 standard cubic feet of natural gas, or close to 20 GJ of energy release. If the explosive element was coal dust, at 0.055 oz/cubic ft that amounts to about 560 kg of coal, with an energy content of 24 MJ/kg that would mean at least 13 GJ of energy in the explosion. If there had been a full day's worth of gas in the explosion, on the other had, at 2 million cubic feet that would amount to over 2 TJ. This should have registered as somewhere between a magnitude 3.6 and magnitude 5 earthquake - the strange thing is I cannot find any information on the internet that documents the actual magnitude of the event, which should certainly have been recorded (2 smaller tremors from the previous day in the area, one natural and the other man-made, are noted in several online accounts).

On April 20, 2010 the BP Deepwater Horizon oil rig in the Gulf of Mexico suffered an explosion and subsequent fire, killing 11 people and injuring 17. The subsequent flow of oil and natural gas from the well was terrible - initially flow is thought to have been about 62,000 barrels of oil per day, along with millions of (standard) cubic feet of natural gas. But what were the dimensions of the initial explosion? The oil rig platform was 396 ft by 256 or close to 100,000 square feet in size. The explosion was again believed to be caused by methane, natural gas, blowing through the seals and onto the rig. If it filled the rig area up to 20 ft height, at the 5.1% explosive level that would be about 100,000 cubic ft of natural gas, or around 100 GJ of energy in the explosion, somewhere around a magnitude-4 earthquake. The continuing flow of oil and natural gas fed the subsequent fire. With one barrel of oil equivalent to 6.1 GJ that would have been (at the 62,000 bpd rate) about 400 TJ of energy per day (4000 times the initial explosion) contributing to the destruction of the rig.

On September 9, 2010 in the California suburb of San Bruno, a 30-foot section of PG&E natural gas transmission line ruptured. The resulting explosion and fires killed 8 people and destroyed 37 homes (see note 2 for references). The pipeline diameter was 30 inches, with a maximum allowed operating pressure of about 400 psi, or 27 atmospheres. Assuming the instantaneous gas content of the pipeline fairly represents what exploded, that would be close to 4000 standard cubic feet of natural gas, or about 4.3 GJ. That's double the energy release of a magnitude-3 earthquake, or the equivalent of blowing up about 1 metric ton of TNT - relatively small compared to the other events I've described here. The actual seismic event only registered as magnitude 1.2 on local USGS monitors - since the explosion was at or near the surface and into the air the seismic portion would be expected to have been only a small fraction of the full energy. The continued release of gas from the pipeline fueled the subsequent fires, likely involving several hundred times as much energy until gas flow into the pipeline was cut off.

And then in March 2011 we had the earthquake off the coast of Japan. The actual event, at magnitude 9 and releasing roughly 2 EJ of energy, was enormous; substantial portions of the main island of Japan were relocated by meters. Of concern in the energy realm, though, has been the continuing problems at the Fukuishima Daiichi nuclear complex, where 6 reactors and apparently a large quantity of spent fuel have been suffering from loss of coolant since the earthquake. A typical reactor holds on the order of 100 tons of uranium fuel; reports indicate close to 900 tons in the Fukushima reactors, plus thousands of additional tons in the spent fuel pools. The full energy content of close to 1000 tons of uranium is of course far larger than the same mass of TNT. Reactor-grade uranium isn't likely to explode in a nuclear chain reaction, but the dangers it poses come entirely from that latent energy content, which is the source of all the radiation and dangerous fission-product isotopes that continue to be released, reportedly at levels rivaling Chernobyl.

The mass-238 isotope of uranium (most of what is in a reactor) actually weighs in at 238.0507826 atomic masses, slightly above 238. The mass-235 isotope (enriched to a few percent typically) comes in at 235.0439299, also slightly above 235. The mass-56 isotope of iron, in contrast weighs in at 55.9349375 atomic masses, a fraction below 56. If U-235 was as strongly bound as the iron nucleus, it would weigh 234.727 atomic masses rather than 235.044, a difference of 0.317, or 0.135%. Similarly, U-238 is 0.327 atomic masses or 0.137% heavier than it would be if it were as strongly bound as iron. So 1000 tons of uranium has a mass excess of about 1.37 tons that could in principle be obtained by fission and nuclear decays and other rearrangements of the nuclei. Given Einstein's famous E=mc^2 formula, multiplying that 1.37 tons by the speed of light squared gives a total nuclear energy content of 1370 x 9 x 10^16 J = 123 EJ.

That is - the total energy represented by the roughly 1000 tons of nuclear fuel in the Fukushima reactor cores is over 50 times the energy release of the magnitude-9 earthquake that caused the disaster in the first place. Including the spent fuel in the complex multiplies this factor several times over. There was very good reason to expend enormous effort to control that vast store of energy; unfortunately even so, much has been released to the environment, and things still don't seem to be fully under control.

We can reflect back on the Chernobyl disaster for a bit of context. On April 26, 1986 while conducting some experiments ironically to improve the reliability of safety systems at that plant, the core became unstable and reached a power level at least 10 times its intended operating rate of 3.2 GW (thermal). The result was two explosions seconds apart. The first is believed to have been a steam explosion, from the pressure resulting from conversion of thousands of tons of cooling water into steam. The second explosion has long been claimed to have been a hydrogen explosion similar to the explosions seen at several of the Fukushima reactors, but there is some evidence that it may have been a nuclear criticality incident (Pakhomov, Sergey A; Yuri V. Dubasov (2009). "Estimation of Explosion Energy Yield at Chernobyl NPP Accident". Pure and Applied Geophysics 167: 575). If that was the case, between 0.01% and 0.1% of the nuclear fuel may have been involved. Either way, the energy release in the second explosion was about 40 GJ, comparable to some of the natural-gas explosions we've discussed here previously. The Chernobyl explosion resulted in the fragmentation and expulsion of significant portions of the core into the surrounding area; parts of the core also melted and formed lava-like masses within the structure. Around 1000 metric tons of graphite moderator caught fire, adding to the energy release and the flow of core materials into the environment.

The Chernobyl accident killed 2 workers immediately in the explosions, and 64 are believed to have died directly from radiation exposure. Estimates of deaths from the increment in background radiation it gave to world populations vary widely, but are likely at least in the thousands. Nevertheless, given the total energy potentially involved, the consequences seem to have been relatively small. Total uranium mass in the core and affected spent fuel pool before the accident was around 200 tons, or about 1/5 or less of the possible problem scale at Fukushima. That potential nuclear energy content at Chernobyl then amounted to about 25 EJ, almost a billion times the scale of the initial explosions there, over ten times the energy content of a magnitude-9 earthquake, around 10,000 MT of TNT. That energy content is still there, sitting under the sarcophagus, gradually releasing itself as heat as it may do for many millions of years to come.

It is that huge energy content in nuclear facilities that makes them so potentially dangerous, even though so far we have never had anything close to a full release of that energy on a short time scale. As mentioned earlier, 1 GW over the course of a year comes to 30 PJ; a 3.2 GW thermal reactor like Chernobyl then produces about 0.1 EJ of energy in a year just in its normal course of running. The fact that nuclear reactors are run with essentially the same fuel over a period of 1 to several years is what necessarily makes their energy content so high - a single core has to provide a good fraction of an EJ to be able to give you the GW of electrical output steadily over those years. But even then, we're only using a small fraction of the core energy content; Chernobyl would have had to run for about 250 years using the same fuel to actually consume all the fission energy it contained.

It seems clear to me that our current technologies for turning nuclear fuel into energy are far too primitive; the dangers come inherently from the tiny fraction of the energy content we are able to extract in a reasonable period of time. It is similar to the early days of the industrial age, when steam power was highly inefficient and dangerous. At least with fossil fuel technologies, as the examples above discuss, we generally are in the 10s to 100s of GJ energy range when accidents happen. With nuclear power, in principle, we have millions or billions of times more at stake. Carlo Rubia's accelerator-based fission idea may be a real solution; I don't think any other type of reactor currently proposed can possibly really be safe given the necessary large energy content in every other design.

Of course, it is not just nuclear power that has a large-energy-content issue. Hydro-electric dams also intrinsically store up on the order of several month's or a year's worth of energy in the raised water level behind the dam, i.e. on the order of PJ for a 1 GW generator. So far, failures at hydroelectric generating plants have been mercifully rare (though other dams have certainly failed). The worst recorded case though was really, really bad: the 1975 failure of the Banqiao Dam in China, with 26,000 people killed in immediate floods, and tens of thousands more dying in the months after from disease. In that case, the dam was overtopped through the influx of a huge quantity of rainfall over 24 hours from Super Typhoon Nina, a "once in 2000 year" event. Total capacity of the dam reservoir was 492 million cubic meters, with a dam height of 24.5 meters, giving a total energy content on the order of 100 TJ. Much of that energy was released in the flood of water as the dam failed, for an energy equivalent to about a magnitude-6 earthquake, or about 25 kt of TNT.

On the complete opposite end of the scale are the newest renewable technologies, in solar and wind power. For solar photovoltaics there is essentially no energy stored in the system at all. Sunlight is converted to electric energy leaving the panels for the electrical system in microseconds. For wind power there is some energy stored in the motion of the blades of a wind turbine. For a recent 5 MW turbine the total mass of 3 blades is about 50 tons, and blades may be turning at a tip speed of up to 200 mph or 90 meters/second. That translates to a total energy content (1/2 m v^2) of 0.2 GJ - far less than the energy released in any of the explosions discussed here. It is only a tenth of the energy content of the gas tank of a typical car. And it represents just 40 seconds of the 5 MW production rate.

Of course, the lack of long-term energy storage associated with solar and wind is often counted as a down-side: when the sun is down and the wind stops, where do we get energy from then? In the long run we are going to need energy systems that are capable of storing at least a day's worth, and perhaps several days worth of total energy use. Whether in the form of pumped hydroelectricity, compressed air, superconducting currents, batteries, or something else, that energy storage system will intrinsically in itself have some dangers just because it is serving its purpose of storing large quantities of energy. The harder it is to release that energy quickly, the safer the system, but even so, it's a concern.

Many people have noted that the problem with nuclear power is not so much safety as economics. But it is the intrinsic dangers inherent in the enormous energy content of nuclear power that makes it so expensive. If we weren't worried (with good reason) about the possibilities of widespread radioactive contamination there would be no need for those expensive containment domes, etc. Hydro power has similar cost constraints that may well limit it in future just as for nuclear (i.e. except in countries that are able to ignore economics or safety...)

There has been much push for natural gas as a substitute for oil and coal, especially within the US - the "Pickens plan" is one example, and the Obama administration has taken steps to promote natural gas production and use. But as the last year's worth of disasters illustrate - natural gas is actually responsible for most of the big explosions associated with fossil fuel production and use, whether it's intrinsically about gas as in the San Bruno and Kleen energy cases, or about oil or coal extraction as in the other two. Natural gas should cut down on CO2 emissions relative to those alternatives, but that doesn't necessarily make it the best choice.

The future of energy I envision has no place for the natural gas explosions or nuclear disasters we have seen recently. I'm encouraged that nothing like the Banqiao Dam failure seems to have happened recently in hydroelectricity - but nevertheless, the danger may be one best limited by changing the way we use hydropower to one where a reservoir represents only a few day's need, rather than months. In the long term we should be just tapping in to that huge peta-watt flow of solar energy as we need it, bypassing the need for localized concentrations of energy and the dangers they pose. There's no reason it can't be done.

1. References on Upper Big Branch explosion:

2. References on San Bruno explosion:


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Excellent post and good point

Excellent post and good point regarding the danger of dams. I like the quotes around the "once in 2000 year".

I think that fusion is also a pretty safe option if we can get it to work. It does not seem to run by itself so easily. Like that laser fusion stuff.

The 10^3 scale on the Richter

The 10^3 scale on the Richter yields some interesting results.
Have a look at what a hurricane is energetically.