Half-Life of Uranium from Sea Water

Thomas L. Wayburn, PhD in chemical engineering

Today I computed how long the Uranium and Thorium would last in a nuclear economy in which the energy budget increased at the rate of 1.4% (Ann. Energy Report 2005, EIA of DOE).  This calculation needn't be very accurate.  The guess of an energy returned over energy invested of 1.5 might be wishful thinking for Uranium from seawater; but, from an anti-nuke perspective it is a "conservative" estimate.  If the ER/EI is less than 1.0 though, the lifespan is about 10 years without breeders or fusion.  Here is the result:

I got this figure of 3.0 · 10⁵ quads for world reserves of fissionable material  from the following URL:

http://www.computare.org/Support%20documents/Fora%20Input/CCC2006/Nuclear%20Paper%2006_05.htm

You might want to check that.  First I computed the time T required to exhaust it assuming that we start off with an EROEI of 10 which diminishes to 1.5; but, since most of the energy comes from Uranium in sea water, I decided to assume the EROEI was  1.5 throughout.  The delivered energy is ED = ER - EI, and ER = 3 x ED.  The delivered energy is what we consume and what true believers (in capitalism) expect to grow exponentially to prevent economic collapse.  ED for the world is about 400 quads now, and the DOE expects it to grow at the rate of 1.4% per year at least in the US.  But, let's assign that growth rate to the world.  "See Third-Worlders, things are getting better."  Thus, with growth, ED = 400 x exp(0.014t) until the Uranium, Thorium, etc. run out.  The integral of ER from 0 to time T must equal the total reserves if we forget about Peak Uranium; so,

 

Therefore, T_½ = 0.5 · ln(11.5) / 0.014 = 87.25 years.

If you want to discourage nuclear, you must look for other reasons.  Try the extremely fair and balanced report at http://www.dematerialism.net/CwC.html#_Toc149364189 followed by http://www.dematerialism.net/CwC.html#_Toc149364216, which explains what is needed for robust economic growth under capitalism.

Houston, Texas

March 15, 2007