Estimated 234U content in DU
The depletion of 234U can be estimated from the depletion of 235U in the following way (credit to Jiri Kolafa):
D(234U) = (1 - 4e)n ® exp(-4ne) for large n
D(235U) = (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(235U) = 1 - 3ne + O(n2e2) = 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(234U) = D(235U)(4/3) = 0.18 for D(235U) = 0.28
If we actually calculate the efficiency e from the first equation for the depletion of D(235U) = 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(234U) = 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(234U) = 0.18 for a large number of stages obviously represents the upper limit. From the most accurate measured value of D(234U) = 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.