Question

Estimate the volume of spent fuel generated annually by a 1 GW if the fuel is UO2 enriched to 3.0% 235 and the density of the fuel is 3000 kg/m3.

Answer 1

0.03 kg of U²³⁵ per kg of loaded uranium will undergo fission, producing something like the

(183.6 MeV * 1.6022 *10^-19 MJ ) / 235.04 amu / 0.03 Kg = 4.171*10^{6 MJ/Kg}

Thus, on the basis of uranium loaded, the fission produces (0.03)( 4.17x10⁶) = 1.25x10⁶ MJ/kg.

A 1000 MWe power plant, operating at an efficiency of 33% requires a heat input of (1000 MW)/33% = 3000 MW = 3000 MJ/s. If the plant operates at a 95% capacity factor, the total heat energy input during the year will be (95%)(3000 MJ/s)(3600 s/h)(24 h/day)(365 d/yr) = 9.08x10¹⁰ MJ. The mass of uranium required then is (9.08x10¹⁰ MJ/yr) / (1.25x10⁶ MJ/kg) = 5.47x10⁴ kg/yr of uranium. The amount of UO₂ is found by multiplying by the molar mass ratio of UO₂ to U which is (238 + 32)/238 = 1.143.

Thus the required amount of UO₂ is (1.143)(5.47x10⁴ kg/yr) = 6.21x10⁴ kg/yr of UO₂.