Never mind that compounding as naively as you did implies the guard 10,000 years from now is receiving about $6e43 per hour.

Me:

1 kW⋅h = 3600 J

Obviously wrong!

1 kW⋅h = 3.6e06 J (3600 kJ)

10 cents / kW&sdoth; = 2.778e-8 USD / J
3.945e15 J @ 2.778e-8 USD / J = 1.096e8 USD ($110 million)

These I got right, althought it should be “kW⋅h” rather than “kW&sdoth;”. Character-order typo. No preview. Blinding glare of background whiteness. Those are my only excuses.

[Aside: on OS X you can do a sort of preview by command-a (to highlight everything in your edit box) command-c (to copy) then at the shell prompt (everyone runs Terminal, right? ) run "/usr/bin/pbpaste > /tmp/a.html" then "/usr/bin/open /tmp/a.html" which should cause your default browser to show you a formatted version so you can at least check your links and see dangling markup tags that cause half your comment to be italicized...]

… and this is why we normalize to SI units.

(Okay, admittedly we can expect other normalizations on a blog dominated by qc-gr topics, but I’m almost tempted to argue that geometrized or Planck units are less confusing to deal with than W⋅h).

Now it’s my turn to make errors!

How many joules do we get from 25 megawatts over 5a? Let’s assume the usual mean calendar year, since there are so many years to choose from.

1 a = 3.156e07 s [from NIST]
5 a = 1.578e08 s
2.5e07 W * 1.578e08s = 3.945e15 J

Normalizing bills, which are almost always for energy rather than power:
1 kW⋅h = 3600 J
10 cents / kW&sdoth; = 2.778e-8 USD / J

3.945e15 J @ 2.778e-8 USD / J = 1.096e8 USD ($110 million)

So, $25 million vs $110 million for almost 4 PJ of energy @ 25 MW of electrical power.

This ignores additional costs not included in the $25 million price, which might include things like insurance.

This also ignores additonal savings from the additional thermal energy doing work that might otherwise be done by electric, gas or oil boilers.

Finally, a question: what’s the power decay curves (electrical and thermal) of these small plants? Apart from the issue of isotope half-life, these piles are unmanaged, sot therefore they can develop unfavourable arrangements with respect to neutron economy, right? Five years is an unusually long duty cycle for a working nuclear pile.

Maybe this solution is better than giant multi-gigawatt installations ?

That’s a hard question to answer! Transmission losses from the giant installations are a large factor, but so are economies of scale — much hotter rectors lead to much more efficient electrical power generation per unit of fuel; alternatively bigger piles gain economies of scale with respect to on-line refuelling and other reactor pile geometry management (e.g. CANFLEX) which leads to less downtime and greater fuel efficiencies. These are unlikely attributes for a “no maintenance” small reactor.

In either case, the really rare resource, engineering and operational expertise, remains highly centralized, which is why the idea of large numbers of “non-field-repairable units” is tenable.

The bigger practical risk to the users of these reactors, I think, is not one of these reactors failing dangerously, but rather failing safely as designed, but taking a long time to be replaced because of production and delivery backlogs.

However, if there are a mix of large and small power generators, and a grid that can cope with dynamically distributing energy from supply to demand, the overall energy economy is more resilient in the face of plant outages (including planned maintenance and construction delays). Whether such a grid is realistic is an open question. At present, “selling excess power back to the grid” does not work in the way you probably think.

Mr Paul, you estimated the storage cost of spent fuel by compounding the guardian’s minimum wage over 10,000 years. In doing so, you ignored a gigantic factor.

Namely, you assume that the 25 MW of energy generated by the mini-nuke is worthless. The economic benefit of all that energy is difficult to estimate but should be several orders of magnitude greater than your guardian’s salary of $57,378 per year. This economic activity, like all economic activity, should be compounded too, and should by itself greatly overwhelm your FV calculation above.

Check this particular section which, to some extent, answers the concerns mr Paul as been talking about:

SHOULD WE ADD UP EFFECTS OVER MILLIONS OF YEARS?

I haven’t read the entire book yet, but this chapter and the one about comparing risks from various sources seems very interesting. The book seems a bit technical and is full of references to calculations in the appendix, but I strongly recommend everyone to take a good look at this.

http://www.phyast.pitt.edu/~blc/book/chapter11.html

This is the 11th chapter of a book entitled “THE NUCLEAR ENERGY OPTION” which was written by Bernard Cohen who is Professor Emeritus of Physics at the University of Pittsburgh. You can check his Wikipedia Page here:

http://en.wikipedia.org/wiki/Bernard_Cohen

Take a look at these quotes from the beginning of Chapter 11:

“As an initial perspective, it is interesting to compare nuclear waste with the analogous waste from a single large coal-burning power plant… For example, if all the air pollution emitted from a coal plant in one day were inhaled by people, 15 million people could die from it (3), which is 10 times the number that could be killed by ingesting or inhaling the waste produced in one day by a nuclear plant.(4)”

http://www.phyast.pitt.edu/~blc/book/chapter11.html

This is the 11th chapter of a book entitled “THE NUCLEAR ENERGY OPTION” which was written by Bernard Cohen who is Professor Emeritus of Physics at the University of Pittsburgh. You can check his Wikipedia Page here:

http://en.wikipedia.org/wiki/Bernard_Cohen

Take a look at these quotes from the beginning of Chapter 11:

“As an initial perspective, it is interesting to compare nuclear waste with the analogous waste from a single large coal-burning power plant… For example, if all the air pollution emitted from a coal plant in one day were inhaled by people, 15 million people could die from it (3), which is 10 times the number that could be killed by ingesting or inhaling the waste produced in one day by a nuclear plant.(4)”

“For nuclear waste, a simple, quick, and easy disposal method would be to convert the waste into a glass — a technology that is well in hand — and simply drop it into the ocean at random locations(5). No one can claim that we don’t know how to do that! With this disposal, the waste produced by one power plant in one year would eventually cause an average total of 0.6 fatalities, spread out over many millions of years, by contaminating seafood. Incidentally, this disposal technique would do no harm to ocean ecology. In fact, if all the world’s electricity were produced by nuclear power and all the waste generated for the next hundred years were dumped in the ocean, the radiation dose to sea animals would never be increased by as much as 1% above its present level from natural radioactivity.”

Check this particular section which, to some extent, answers the concerns mr Paul as been talking about:

SHOULD WE ADD UP EFFECTS OVER MILLIONS OF YEARS?

I haven’t read the entire book yet, but this chapter and the one about comparing risks from various sources seems very interesting. The book seems a bit technical and is full of references to calculations in the appendix, but I strongly recommend everyone to take a good look at this.