A 1 gigawatt nuclear plant produces about 1 ton of fission products per year, mixed with about 22 tons of uranium. That uranium is in the form of an oxide, so there is 3 tons of oxygen in there too, and some zirconium and traces of other things. The afterheat from that 1 ton of fission products decays as follows.
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Some folks like the idea of burying the reactor underground, and allowing the afterheat to dissipate away into the surrounding rock. The trouble with this idea is that the ground is not a very good conductor. A 60 meter diameter hemisphere sunk into bedrock, with a surface 200 C hotter than the rock around it, can dissipate 75 kilowatts. It takes about 125 years for the fission products from one year's operations to decay this much. That's not much help in an emergency.
So the heat must be dissipated into the environment with a fluid, either water or air. Our 60 meter diameter hemisphere, this time poking up out of the ground, again 200 C hotter than the surroundings (air), will now dissipate around 8 megawatts. It takes about 9 hours after shutdown for the fission products to get down to that power level. That sounds like a more reasonable time frame.
In that time, the fission products have emitted 950 gigajoules of heat, which is a lot. That's enough heat to raise the hemisphere, if made of 40 cm thick concrete, to 200 C. However, containments are usually thicker than this, so it'll take a bit longer for the entire concrete dome to get up to sufficient temperature to convect away the afterheat, and the temperature it rises to will be a bit lower.
Lars, I used your decay numbers for this analysis, and I also checked against Kirk's ORIGEN results in his Java applet. Your numbers don't perfectly match, but it seems about right. If the integrated decay heat is right, why does AP1000 bother with a pool at the top of the containment? Air cooling would appear to work, so long as the heat can make it through the concrete.
The concrete itself is a bit of a challenge. The 60 meter diameter dome, made of 1 meter thick concrete, will transmit just 1.9 megawatts with a further 200 C drop across the concrete. This puts the interior surface at 400 C, which seems unreasonable. I'd want to embed heat pipes in the concrete if I were going to use it as my backup heat exchanger.
-Iain