Energy density: a lifetime of energy in the palm of your hand

Golf ball size lifetime energy

Barry Brook got my attention in 2010 with his post that I remember as “The Golf Ball and the Soda Can”. If we generated all of our energy via fast spectrum reactors similar to the IFR, then your personal lifetime energy needs would be supplied by the golf ball-sized lump of thorium or uranium pictured at left. That’s your total energy consumption including farming, transportation, industrial uses, heating and air conditioning. Everything except the calories you derive from food. And that’s at the extravagant American energy consumption level.

This tiny amount of input fuel can be pure metallic thorium or “depleted” fertile uranium-238, fissionable uranium-235 or used PWR fuel (the dreaded “nuclear waste”). 


All your waste

What are the waste products of your lifetime energy consumption? About the size of the pictured soda can, which is a little bit bigger than the golf ball because the fission products are more atoms of lighter elements which take up more volume. In 300 years your Coke can of waste will decay to the level of the background radiation around the original mined uranium ore. No need to talk about thousands of years of storage.

George Stanford’s calculation follows: The density of metallic uranium is 19 g/cc. Thus the volume of 1 kg is 52.6 cc. That’s a sphere with a diameter of 4.6 cm (1.8 inches) — slightly bigger than a ping-pong ball (4.0 cm). The volume is proportional to what you use for the per-person average energy consumption. The “waste volume” will be larger — maybe about the size of a soda can. But remember, the waste volume calculated that way is irrelevant — for disposal on land, it’s the heat generation that has to be managed, so the volume of the disposal facility is orders of magnitude larger than a soda can.

In the U.S., the energy per person per year is given as 8.25 TOE (tonnes of oil equivalent). If a lifetime is 85 years, that’s 700 TOE. One TOE = 11,630 kilowatt hours, for a lifetime total of 8 million kW-hr. As a rule of thumb, fissioning one gram of heavy metal (uranium) releases 1 MWth-day, or roughly 8 MWe-h = 8,000 kWe-h. So 8M/8k = 1,000 grams — one kg of fissions — which, of course, means one kilogram of fission products. If the average density of the waste form were 2 g/cc, then the volume would be 0.5 liter. Ball-park calculation only, assuming all energy comes from nuclear-generated electricity.

Note that that’s total US energy consumption divided by the number of people (not counting calories derived from food). That makes it 850 grams per 85-year lifetime instead of 1 kg. Still in the soda-can range for the fission products (a very crude approximation at best, since the waste form is not defined). Note that burning 700 tonnes of oil produces about 2,000 tonnes of CO2, for a waste-weight ratio >2 million to one (for whatever that’s worth).

Energy density is critical to transition our industrial societies from fossil to zero-carbon energy. You can read more details on fast spectrum reactors and energy density in this 2011 paper Advanced Nuclear Power Systems to Mitigate Climate Change.