Nuclear Reactor Basics

I had a conversation this morning with my two good friends. We're discussing Japan nuclear crisis following the 9.0 earthquake and tsunami. Radioactive materials are released into ocean and atmosphere, and I was left wondering how many kilograms of uranium material needed to power a typical nuclear reactor. Below are my estimates.

A nuclear power plant is powered by the nuclear splitting process (fission) of either natural or enriched uranium. Natural uranium has largely U-238, about 0.7% U-235 isotope, and a tiny amount of U-234. Enriched uranium has 3-5% U-235. Either natural or enriched uranium can act as nuclear fuel. The amount of heat liberated by one fissile U-235 atom is 202.5 MeV. Since 1 eV = 1.602 × 10^-19 J, 202.5 MeV = 3.2 × 10^-11 J. The atomic weight of uranium is 238 amu = 238 g/mol due to the overwhelming fractional amount of U-238. Since 1 mole = 6.02 × 10²³, the amount of energy liberated per kg of natural uranium due to U-235 fission is 134 is 566.6 GJ/kg.

A large power plant typically produces about 1 GW electrical power. Per year, this means an energy production of 31,536 TJ. Hence, the natural uranium needed to produce this much energy is 55.7 metric ton. But, this much uranium is for a 100% heat-to-electricity energy conversion efficiency. A more realistic efficiency number is 40% – as I expect the nuclear power plant will use high temperature steam to drive turbine blades – so that a more realistic estimate of natural uranium required per year for the 1 GW power is 139.3 metric ton.

The estimate amount for the enriched uranium will be 4-7 times less due to its higher U-235 composition, but the numbers of U-235 atoms required in either fuel types are the same.

Neutrons produced by the U-235 fission are also captured by the more abundant U-238 leading to the production of fissile Pu-239 (plutonium). The amount of heat released by fission of one Pu-239 atom is 207.1 MeV, which is comparable to the heat produced by fissile U-235, and is used as well for power generation. The Economist (31 March 2011) reported that Pu-239 was detected in soil samples taken from the surrounding area of Fukushima Daiichi nuclear power plant.

The Fukushima Daiichi nuclear power plant has 6 units with a combined electrical power output of 4.6 GW. They are boiling water reactor (BWR) type, where cooling water passes through the hot fuel and the steam is directly produced from the water.