Enriched Uranium

Naturally-occurring uranium contains 0.72% of the 235U isotope. The remaining 99.28% is mostly the 238U isotope which  is a fissionable isotope, but is not a fissile isotope. Most reactors require uranium to be enriched from 0.7% to higher concentrations. The process of  increasing the concentration of one isotope relative to another is called “enrichment.” The level of enrichment required depends on specific reactor design (e.g.,  PWRs and BWRs require 3% – 5% of 235U) and specific requirements of the nuclear power plant operator. Without required enrichment these reactors are not able to initiate and sustain a nuclear chain reaction.

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 3000MW_th determine the consumption of ²³⁵U that must undergo fission each day to provide this thermal power.

Solution:

This problem can be solved very simply. The average recoverable energy per ²³⁵U fission is about E_r = 200.7 MeV/fission. Since we know, we need 3000 MJ of energy that each second, 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

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Uranium

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