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The depleted material stream in isotope uranium enrichment. enrichment tails retain uranium, so gross feed demand exceeds the enriched product mass.

The recycle feed is the recovered uranium, not the whole initial nuclear fuel charge. After the stated loss it isUsing the same enrichment tails assay and the stipulated higher recycle-product assay, the isotopic mass balance givesTreat the $5.3\%$ recycled product as replacing the same uranium mass of ordinary $5.0\%$ nuclear fuel: the additional uranium-235 compensates for the supplied uranium-236 penalty. It displaces fresh natural-uranium feed in the ratio calculated in part (b), henceThe remaining natural feed is $313.36245\mathrm{t}\mathrm{U}\mathrm{y}{\mathrm{r}}^{-1}$, a 9.885% resource saving relative to the full-power once-through requirement. This credits one uranium recycle only; it adds no second-pass recycling or plutonium credit.

Separative work must be charged for producing the recycled nuclear fuel as well as credited for displaced fresh nuclear fuel. With uranium-235 mass fraction $x$, use the separative value functionMasses in kilograms give work in kg-SWU. For ordinary fresh product the work per product kilogram isThus the fresh work avoided isThe recycled product still requiresThe net separative-work saving is consequentlyAs a whole-cycle check, the fresh route requires $215668.0851$ kg-SWU per year, while the mixed fresh-plus-recycled supply requires $214075.3261$ kg-SWU. The net saving is only 0.7385% of the original work. The recovered stream has a higher uranium-235 assay than natural feed, but the higher required product assay uses most of the work credit. These equations are resource accounting and do not specify an uranium enrichment plant or its operation.

The distinction is between partitioning reusable fuel constituents from fission-product waste, and subsequently partitioning uranium from plutonium. In the first operation, chemical selectivity transfers selected actinides into a different stream while most fission products remain in the waste stream. In the second, differences in chemical speciation allow the two recovered elements to follow different streams. Neither operation separates uranium isotopes: uranium enrichment and chemical element separation are different tasks.

At a conceptual level, solvent extraction exploits unequal affinities of dissolved species for immiscible liquid phases. complexation changes those affinities, while a change in oxidation state can change an element's preferred phase without changing its identity. This explains why a stream bearing actinides can first be separated from much of its accompanying waste, and why uranium and plutonium need not subsequently remain together. Dissolved and undissolved residues, contaminated solvents and off-gases remain waste-management obligations; a recovery percentage alone is not a complete material balance.

Equipment must provide phase contact and phase disengagement within shielded, confined systems. Remotely maintained contactors and settlers are equipment categories serving those functions; sealed transfer systems, shielded cells and monitored off-gas handling limit contamination and exposure. Cooling manages residual decay heat, and nuclear material accountancy follows inventories and losses. criticality control in radioactive waste is essential because solvent extraction can redistribute fissile constituents. Scoped limitation: this answer gives the chemical principles and equipment functions; operational fissile-separation recipes, reagent sequences, contactor design details and process conditions are intentionally not supplied.

An increase in the fraction of a specified uranium isotope. Fuel-cycle accounting tracks feed, product, enrichment tails and separative work; it does not specify an uranium enrichment plant or its operating conditions.