Burning the Rocks?

One cubic meter of “average continental crust” has a mass of about 2700 kg, based on an assumed density of 2700 kg/m3. Depending on who you ask, thorium comprises various fraction of the Earth’s crust. If we take the CRC handbook value of 0.0000096 kg Th/kg crust, there would be (0.0000096)*(2700) = 0.026 kg or 26 grams of thorium in each cubic meter of the average crust of the Earth, and (0.0000027)*(2700) = 7 grams of uranium in each cubic meter. If the thorium and uranium were in the form of metal, then there would be about two cubic centimeters of thorium and about half of a cubic centimeter of uranium in each cubic meter of the Earth’s crust.

Assuming an energy content for thorium of 11 MW*hr/g in a LFTR and an energy content for uranium of 0.035 MW*hr/g in a light-water reactor,

(26 g thorium)*(11 MW*hr/g thorium) = 286 MW*hr of electricity
(7 g uranium)*(0.035 MW*hr/g uranium) = 0.245 MW*hr of electricity

At an electricity price of $40 to 60/MW*hr of electricity, the value of the energy that would be produced from this material is

(286 MW*hr)*($40 to 60/MW*hr) = $11,000 to 17,000 per cubic meter of crust
(0.245 MW*hr)*($40 to 60/MW*hr) = $10 to 15 per cubic meter of crust

One cubic meter is 6.3 barrels, and a barrel of Texas light sweet crude oil fetches about $100 (on or about 3/7/2012), thus an equivalent volume of crude oil would be worth $630.

At these prices the value of the energy produced by the thorium in an average cubic meter of the Earth’s crust in a LFTR is worth (11000 to 17000)/(630) = 17 to 27 cubic meters of Texas light sweet crude.

The highest grade of coal is anthracite coal, and one cubic meter of anthracite would have a mass of 1300 to 1400 kg. In June 2008 anthracite was priced at $150/short ton (short ton = 2000 lb) or $0.165/kg. This would imply a value of $215 – 230/m3 of anthracite coal.

At these prices the value of the energy produced by the thorium is an average cubic meter of the Earth’s crust in a LFTR is worth (11000 to 17000)/(220) = 50 to 77 cubic meters of anthracite coal.

By comparison, the value of the electricity produced by the uranium in a cubic meter of crust, if used in a light-water reactor, is one-fiftieth the value of the equivalent volume of crude and one-seventeenth the value of anthracite coal. It would be much better to “burn the rocks” for crude or coal than for uranium, but far more valuable to get thorium than crude or coal.