Wednesday, November 29, 2006

A Back-Of-The-Envelope Calculation

I was reading Ron Bailey's comments on world energy which cites Daniel G. Nocera's Daedalus article in estimating global energy consumption at 102 TW in 2050. After paying the $10 for the full text, it turns out that Nocera gets his figure from the UNDP World Energy Assessment. Since a terawatt is a measure of energy per unit time (specifically, watts per second) that should come in at 3.22x1021 Joules, or 3.22 zetajoules, but the 2000 report suggests something more like 1.041 ZJ, which may be because of the confusion over peak versus average capacity.

Anyway, as a thought exercise, I figured it might be interesting to calculate how much boron such a scenario might be required to fuel all that consumption. From the Wikipedia entry on terrestrial fusion reactions:

8.6x106 eV/atom • 6.02x1023 atom/mol / 10.811x10-3 kg/mol •
1.602x10-19 J/eV = 76.7x1012 J/kg
So that's almost eighty terajoules per kilogram of boron. Pretty sweet. Now, take a look at this:
1.041x1021 J / 76.7x1012 J/kg = 13.6x106 kg
or about 13,500 tonnes of boron annually. (Of course, this doesn't adjust for inefficiencies in the process; just as a guess, assume the whole process is something like 25% efficient, so consumption is more like 54 kt.) According to Roskill, the world is lately using 1.6 Mt of boron annually, which would make this figure well within reach hardly put a dent in world production.

Update 12/1/06: corrected for the error in Avogadro's number, which makes this look even more obscenely desirable. For a 1 GW power plant running at full capacity all year, that means

86400 s/day • 365.24 day/year • 1x109 W = 31x1015 J


31x1015 J / 76.7x1012 J/kg / .25 = 1.6 t

One and a half metric tonnes per year. Now I'm all full of boron-lust... can we just get to fusion... please?