Tuesday, May 10, 2016

Ask a Physicist: Nuke the Sun?

Sharon from Pittsburgh, PA wants to know:

Would it be a bad thing to shoot our nuclear waste into the sun?


It's a fun idea, and at first blush you might think it'd be a great way to get rid of something toxic—after all, what's more "gone" than something incinerated in a giant fusion reactor, ninety million miles away? But let's dig a little into how such a proposal could work, along with some potential pitfalls.
First off it's important to note that, while disposing of nuclear waste is still a challenge, managing it isn't actually as much of a problem as most people believe. XKCD did a fantastic What if? on "wet storage", which is how most of the nuclear fuel in the US is currently stored. It turns out that keeping spent fuel rods at the bottom of a pool of ordinary water (albeit a well-maintained and heavily guarded one) is enough to ensure they don't do any harm.  Currently, the plan involves letting the rods cool down in wet storage for a long time, until they can be transferred to a more permanent home—known as "dry storage". While this would be preferable since it requires fewer resources and less active maintenance, there's nothing explicitly wrong with leaving the rods in wet storage indefinitely. But let's say once we decide to take our fuel out of wet storage, we go way beyond "dry storage" to "metal-vaporizingly-hot-storage", and send it into the sun to be rid of it entirely.

Right out of the gate, the first issue you'd run into with this plan would be the price tag. Currently, it costs about $10,000 per pound of material that you want to send to space, and that's just to put it in low-Earth orbit, where most satellites and the International Space Station reside. Sending something to the sun would probably be even more expensive, since you've got to pack the fuel necessary to get all the way out of the earth's potential well, rather than just zooming around the rim fast enough to avoid falling back in, as in the low Earth orbit case. Only a few manmade objects have ever left Earth's potential well—even the trip to the moon didn't count! (Which makes sense when you consider that the moon is orbiting the earth.)

But let's be generous here and stick with the $10,000/lb figure, assuming that economies of scale take care of the extra fuel costs and that our payload doesn't have to reach the sun in a particularly timely manner. Since there's no friction to slow it down in space, once it's out of Earth's potential well even a slight push in the exact right direction could set an object on a collision course with the sun.

So just how much space-waste are we talking about here? This GAO report indicates that spent nuclear fuel is accumulating at a rate of roughly 2,000 metric tons per year. Since a metric ton is 2205 pounds, that means it'd cost roughly $22,050,000 to send a metric ton of material to space. Multiply that by 2,000, and we find a cost estimate around $44 billion—just over twice NASA's annual budget.

While that's a lot, I was actually surprised to see it so affordable; I was expecting something orders of magnitude more than what we currently spend. Compared to the military's annual budget, it's practically a drop in the bucket!

However, there are other issues here, not the least of which is the possibility of a mishap. A program like this would involve rockets leaving every few days, to keep up with the 2000 metric tons per year we'd need to ship off and, while we're pretty good at getting things to space in one piece, miscalculations and accidents do happen. The Challenger shuttle disaster was bad enough, and a national embarrassment to boot—the possibility of a similar occurrence scattering nuclear waste across the land is more than enough to make sure this proposal stays on the ground.

All in all, it seems like it's probably not worth it to try, especially when there are so many other options for disposing of nuclear waste. However, out of curiosity, I thought it'd be interesting to do a rough calculation and see if this process would even be energy-positive—that is: do UNspent nuclear fuel rods contain enough energy to get themselves to space, or do the laws of physics guarantee that this would be a waste of time?

According to Wikipedia, the USA uses 4,686,400,000 Megawatt-hours of electricity per year, roughly 20% of which comes from nuclear power. This tells us that the 2,000 metric tons of spent fuel accumulating each year provide 20% of that number, or 937,300,000 Megawatt-hours.

Now, a watt is a unit of power, or energy per unit time. A lightbulb might be rated at 60 watts, meaning it uses 60 joules of energy every second. A Megawatt, then, is a million joules of energy per second, and a Megawatt-hour is the number of joules that get used up by a Megawatt-powered device running for a full hour. Since there are 3600 seconds in an hour, we can conclude that a Megawatt-hour is 3600 Megajoules. Multiplying the above number by this figure, we find that nuclear fuel annually provides the US with roughly 3.4*10^18 J of energy.

So is this enough to propel 2,000 tons of spent nuclear fuel out into the sun? It seems like it'd be a tough thing to figure out, but physics can provide us with a bit of a shortcut! We know the escape velocity of Earth, based on its gravitational mass; it's actually equal to how fast something would be moving if it fell to Earth from an infinite distance, so to get something far enough away from Earth that it wouldn't fall back down again, it has to start out moving at about that speed—25,000 miles per hour, almost exactly. Knowing that the kinetic energy of an object is given by the formula: K=(1/2)*M*v^2 where M is mass and v is velocity, we find that 2,000 tons of spent fuel rods moving at 25,000 mph (that's 2E6 kg at 11,176 meters per second, for those of you calculating along) have a kinetic energy of 1.25*10^14 J.

While 1.25*10^14 might look like it's a significant fraction of 13.4*10^18, it's actually less than one part in twenty thousand! From that perspective, this idea isn't a bad one, but most of the trouble with things like space travel isn't in getting the energy, but converting it to the right kind of energy in a safe way. Now if only there were some way to use the nuclear power itself for spacecraft propulsion!

Thanks for writing in!

2 comments:

  1. France already recycles spent nuclear fuel. In the 1960s, we in the US recycled spent nuclear fuel.  We don't recycle nuclear fuel now for two reasons:

    1. It is valuable and people steal it. The place it went that it wasn't supposed to go to was Israel. This happened in a small town near Pittsburgh, PA circa 1970. A company called Numec was in the business of reprocessing nuclear fuel. [I almost took a job there in 1968, designing a nuclear battery for a heart pacemaker.]

    2. Virgin uranium is so cheap that it is cheaper than recycling. This will change eventually, which is why we keep the spent fuel where we can reach it. The US possesses a lot of MOX fuel made from the plutonium removed from bombs. MOX is essentially free fuel since it was paid for by the process of un-making bombs.

    Please read this Book: "Plentiful Energy, The Story of the Integral Fast Reactor" by Charles E. Till and Yoon Il Chang, 2011. You can download this book free from: http://www.thesciencecouncil.com/pdfs/PlentifulEnergy.pdf. Charles E. Till and Yoon Il Chang, are former directors of the nuclear power research lab at Argonne National Lab near Chicago. Get another free book from: http://www.thesciencecouncil.com/prescription-for-the-planet.html

    Per Till & Chang: The Integral Fast Reactor [IFR] uses "nuclear waste" as fuel and gets 100 times as much energy out of a pound of uranium as the Generation 2 reactors we are using now. The IFR is safer than the Generation 2 reactors, which are safer by far than coal. The IFR is commercially available from GEHitachiPRISM.com

    The IFR is meltdown-proof. The IFR can be turned up and down quickly and repeatably. The IFR uses metal fuel that is recycled in a system that makes it difficult to get plutonium239 out of the fuel. To make a good plutonium bomb, you must have almost pure plutonium239. 7% plutonium240 and higher isotopes or other actinides will spoil the bomb. IFR Pyro process recycled fuel is useless for bomb making.

    Elements with more protons than uranium are called trans-uranics alias actinides. Actinides are the part of so-called nuclear "waste" that makes it stay radioactive for a long time. The IFR uses up the actinides as fuel. Actinides include plutonium, neptunium, americium, curium, berkelium, californium, einsteinium, fermium, mendelevium, nobelium and all of the other "synthetic" elements.

    The IFR is the ideal source of electricity since it does not make CO2. The resultant "waste" is very small, will decay in only 300 years and is useful in medicine. The IFR is commercially available now. See: GEHitachiPRISM.com

    The following countries either already recycle spent fuel or are experimenting with a recycling process or both:
    France, Japan Russia, China, India, South Korea.
    The US recycled spent fuel in the 1960s.

    Purex process: The old one. Separates out plutonium, but does not separate the isotopes of plutonium. Any bomb made with this plutonium from a powerplant reactor would fizzle. You can't make a plutonium bomb with more than 7% Pu240.

    Pyro process: Leaves plutonium mixed with uranium and trans-uranic elements. [All fissionable elements are kept together with uranium]
    Other processes [wet] are also under development.

    By recycling nuclear fuel, we have a 30,000 [thirty thousand] year supply.

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  2. It's a fun idea, but not necessarily a wise one. We really have so little understanding of the Sun, so to set such a project into motion would be quite foolish - and possibly dangerous. Our presently accepted model of the Sun is that it is a massive body with a hydrogen-fusion core, yet no real evidence exists to verify this theory. What if we are completely wrong? What if it turns out to be something completely different? For instance, think needle pinprick in a balloon.

    https://youtu.be/2fdhyhPu6PY

    Sincerely,

    Stephen Goodfellow

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