Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE4 / 1

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.

burnup refers to thermal energy per initial heavy-metal mass. Correct the electrical rating for thermal efficiency before using it, and apply the capacity factor once:Consequently the annual initial heavy-metal fuel requirement isLet $F,P,W$ be feed, enriched product and enrichment tails masses, all measured as uranium, and $x_f,x_p,x_w$ the corresponding uranium-235 mass fractions. The isotopic mass balance givesWith $P=M$, the uranium oxide concentrate requirement is thereforeThese are uranium or heavy-metal masses, not tonnes of uranium oxide. The check $327.394(0.007)=35.394(0.040)+292.000(0.003)$ closes the uranium-235 balance as well as the total mass balance.

Use the recovered uranium inventory, rather than the initial fuel mass, as the recycle feed. Its available mass isAssuming the same enrichment tails assay and the specified higher recycled-fuel assay, the isotopic mass balance givesTreat this fuel as replacing the same heavy-metal mass of ordinary fresh fuel: the stipulated higher uranium-235 content compensates for uranium-236. The displaced natural feed isabout 12.63% of the once-through natural-uranium requirement. The residual natural feed demand is $286.052\mathrm{t}\mathrm{U}\mathrm{y}{\mathrm{r}}^{-1}$.

For separative work accounting defineUsing kilograms in this expression gives kg-SWU. For ordinary fresh fuel the work per product kilogram isThe fresh work avoided by substituting $P_r$ is $23896.3\mathrm{kg}\text{-}\mathrm{SWU}\mathrm{y}{\mathrm{r}}^{-1}$, but producing that recycled product still requiresHence the net saving isThe work saving is only about 0.786% of the original annual separative work. Crediting the whole avoided fresh-fuel work without charging the recycle work would substantially overstate the saving. This is an annual resource account at the supplied assays, with no isotope-separation equipment model.

An economic threshold requires all unit costs to have an explicit mass basis. Let $p_U$ be the concentrate price per kilogram of uranium, and let $C_{\mathrm{net}}$ denote the annual incremental fabrication-and-disposal cost of the closed cycle relative to the open cycle. The break-even annual cash balance iswhere $M_{\mathrm{rep}}$ is the charged nuclear fuel reprocessing throughput in kilograms of initial heavy metal. Use $M_{\mathrm{rep}}=35393.9394$: the stated $33$ tonnes is the remaining uranium inventory, not the whole initial heavy-metal throughput. ThusIf the quoted combined $400$ dollars per kilogram is a net additional charge on that same reprocessed-HM basis, $C_{\mathrm{net}}=400M_{\mathrm{rep}}$, giving 1,196.77 dollars per kg U. Under this explicit convention, the saving in purchased separative work is small and the resource saving must pay nearly all the additional nuclear fuel reprocessing cost.

The wording does not identify the mass basis or counterfactual sign of the combined recycled-fuel and spent-fuel-disposal term. If instead $400$ dollars is a net charge per kilogram of the $4469.4375$ kg recycled product, the same balance gives 897.56 dollars per kg U. If it denotes a net avoided charge of $400$ dollars per kilogram of discharged HM, the threshold is 511.87 dollars per kg U. These are alternative accounting conventions, not three simultaneous economic thresholds; the general balance makes the ambiguity visible.

All prices here are per uranium mass, not per gross concentrate mass. This simplified comparison assigns no plutonium credit, financing, conversion-cost difference or change in repository liability, and takes the quoted charges as incremental. A closed fuel cycle can save natural uranium without being the cheaper option: at a price below the threshold under the chosen cost convention, the additional charges exceed the resource credit. No contemporary uranium-market price is needed for that conclusion.