Actually, Yucca is still needed, but yes reprocessing will minimize how much.
In the reprocessing of “spent” fuel rods, the remaining “most useful elements are extracted (as much as possible) particularly plutonium and uranium. But that actually does not make what is left NOT radioactive (due to other radioactive elements). The “left overs” from the reprocessing process remain VERY radioactive.
And what do they do with it. They vitrify it, as is intended for storage at Yucca as well.
The reprocessing will (a) add a costly step but obtain material that can still be used, and (b) still require a long term storage site for what remains after reprocessing has extracted what it could.
Using reprocessing will extend the life of Yucca, however, at the current rate of power plant’s creating more spent fuel, we will need to locate additional long term storage sites, like Yucca (deep natural underground sites), within 25 to 50 years depending on how much is removed by reprocessing before the rest is vitrified.
The big deal is that when these solutions are put to work, the power industry will have a clearer sight towards increasing the use of nuclear power. The storage problem is part of the what has been holding everyone back (in addition to the greenie weenies legal attacks).
I understand that and agree, but U.S. policy put in place by Jimmy Carter forbids the reprocessing of nuclear fuel in the U.S. It is patently against the law at this time to do so. The only way Yucca Mt. can be utilized now is to vitrify un-reprocessed spent fuel, which is not only wasteful of the nuclear material but will also be wasteful of the square footage in the repository.