Estimated ^{234}U content in DUThe depletion of ^{234}U can be estimated from the depletion of ^{235}U in the following way (credit to Jiri Kolafa): D(^{234}U) = (1 - 4e)^{n} ® exp(-4ne) for large n D(^{235}U) = (1 - 3e)^{n} ® exp(-3ne) for large n where e is the single stage enrichment efficiency per 1 kg/kmol mass number difference and n is the number of stages. In justifying these limit transitions, it is helpful to relize that D(^{235}U) = 1 - 3ne + O(n^{2}e^{2}) = 0.28 Therefore, whatever values the efficiency e and the number of stages n might have, they are related approximately as e µ 1 / n Eliminating the product ne from the above two equations (by taking their logarithm and dividing the results) yields D(^{234}U) = D(^{235}U)^{(4/3)} = 0.18 for D(^{235}U) = 0.28 If we actually calculate the efficiency e from the first equation for the depletion of D(^{235}U) = 0.28 assuming the number of stages n = 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, we obtain the depletion of D(^{234}U) = 0.040, 0.139, 0.157, 0.165, 0.169, 0.172, 0.173, 0.174, 0.175, and 0.176. The above value of D(^{234}U) = 0.18 for a large number of stages obviously represents the upper limit. From the most accurate measured value of D(^{234}U) = 0.15, we can conclude that the natural uranium is processed in at least 2, most likely 3 stages, before the depleted uranium is disposed of. |