Uranium consumption in a nuclear reactor
A typical thermal reactor contains about 100 tons of uranium with an average enrichment of 2% (do not confuse it with the enrichment of the fresh fuel, that is about 4%). For the reactor of power of 3000MWth determine the consumption of 235U that must undergo fission each day to provide this thermal power.
This problem can be solved very simply. The average recoverable energy per 235U fission is about Er = 200.7 MeV/fission. Since we know that each second we need 3000 MJ of energy, the required reaction rate can be determined directly as:
Since each atom of 235U has a mass of 235u x 1.66 x 10-27 kg/u = 3.9 x 10-25 kg, the daily consumption of a reactor is:
9.33 x 1019 fissions/sec x 3.9 x 10-25 kg x 86400 sec/day = 3.14 kg/day
For comparison, a 1000 MWe coal-fired power plant burns about 10 000 tons (about 10 million kg) of coal per day.
Since a typical fuel cycle takes about 320 days (12 month fuel cycle), the annual fuel consumption is about:
3.14 kg/day x 320 days = 1 005 kg of 235U