The continued operation of a nuclear reactor requires each fission event to yield enough free neutrons for one to escape loss or fruitless absorption and cause a further fission - the condition of criticality. In most types this can be achieved only by starting with uranium artificially enriched to a few percent in the fissile isotope U-235. With time, especially in the usual thermal regime, the proportion of fissile material declines and fission products build up, some of them very strongly absorbing neutrons to no useful effect. Eventually it is no longer practicable to maintain criticality and that fuel must be discharged.
As an example it may then contain about 3% fission products, 1% plutonium (another 2% would already have been consumed), 96% of the original uranium including a U-235 content that may still be higher than natural, and small amounts of other heavier elements ("minor actinides"). It has delivered about a hundredth of the energy that might have come from fission of all the uranium that went into its manufacture, including the depleted "tails" from the enrichment process.
The purpose of reprocessing is to separate the remaining uranium and plutonium from the 3% of genuine waste and make it available for recycling. Commercially this is done by dissolving the fuel substance in nitric acid and extracting the uranium and plutonium with a solvent that leaves the fission products and minor actinides behind, to be concentrated, evaporated and incorporated into glass blocks for storage and eventual disposal. (Incidentally, these and other waste forms are tested on the assumption of being waterlogged, so that while obviously desirable, it is not essential that a repository should remain dry.) The extracted uranium and plutonium are currently separated from each other and converted to oxide powder, but there might be advantages in leaving much of the uranium with the plutonium.
Partition and transmutation (P&T)
Besides the minor actinides, the residual solution after extraction contains about thirty elements, widely differing in chemistry, in the middle range of atomic number. The short-lived isotopes decay almost completely before reprocessing. Of the rest, some are stable; some have intermediate stability, such as strontium-90 and caesium-137 with half-lives of about 30 years; some are extremely long-lived such as neptunium-237 (two million years); and some elements such as rhodium have potentially commercial applications.
There has been considerable interest in separating (partitioning) these groups for various reasons: recovering valuable materials, removing the harmless components from the requirements for long-term management, or reducing the most durable hazards in waste disposal. The last would involve conversion (transmutation) of the isotopes concerned to stable or short-lived species by irradiation with neutrons; this could not be done with the raw fission-product mix become of some very strongly neutron-absorbing components, especially among the "rare-earth" or lanthanide group of elements which make up about a quarter of the total.
Neptunium might rather easily be diverted from waste into a product stream of the main-line process, with some interesting possibilities. Otherwise, however, the chemistry of partition would be difficult and the engineering very expensive, besides an issue of radiation dose to operators. Research on such schemes is still continuing, but few of the long-lived isotopes are really amenable to transmutation and the balance between benefit and drawback is questionable.