Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2020 / Module NE4 / 1

Conceptual scope: the safe account below describes the functions of spent nuclear fuel management and the chemical basis of partitioning. It does not supply an ordered fissile-separation flowsheet, reagents, process conditions or purification instructions. In particular, the requested operational eight-step separation scheme is outside this answer's scope.

Eight useful functional objectives are: receiving and identifying the spent nuclear fuel; managing residual decay heat; providing radioactive material confinement and radiation shielding; establishing the chemical and radiological inventory; partitioning reusable constituents from waste at a conceptual level; maintaining accountable control of recovered materials; conditioning solid and liquid wastes; and retaining or treating radioactive effluents. These are management and containment functions, not a claim that the question specifies one universal eight-stage plant design. Several occur throughout a facility's operation rather than sequentially.

The chemical principle of uranium/plutonium partitioning is that an element's oxidation state and complexation affect its chemical speciation, solubility and relative affinity for immiscible phases. solvent extraction can therefore separate elements whose chemistry differs, even though it does not distinguish uranium isotopes by this chemical selectivity. A recovery operation must account for the accompanying fission products, contaminated process materials and secondary wastes; the recovered material is only one output. radioactive material confinement, remote handling and nuclear material accountancy remain necessary because chemical partitioning redistributes both radioactive and fissile inventories.

Use the thermal power when applying nuclear fuel burnup. No capacity factor is supplied, so take a full-power year of $365$ days; if the operating fraction were $u$, the annual quantities in this part would be multiplied by $u$.The corresponding initial heavy-metal nuclear fuel requirement isAll nuclear fuel and concentrate masses below are uranium masses, excluding oxygen. Let $F,P,W$ denote uranium feed, product and enrichment tails, and $x_f,x_p,x_w$ the uranium-235 mass fractions. Conservation of total uranium and uranium-235 givessoWith $P=M$, the uranium oxide concentrate requirement is thereforeThis is not the gross mass of oxide concentrate. Both $F-P-W=0$ and $0.007F-0.050P-0.003W=0$ provide independent balance checks.

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.

Resource savings do not by themselves establish a financial saving. The one-recycle case avoids purchasing $34374.04$ kg U in natural feed and $1592.76$ kg-SWU per year. Those are the benefits to compare with the incremental costs, not the whole value of the recovered uranium or the gross avoided fresh-product separative work.

Let $p_U$ be the concentrate price per kilogram of uranium, $p_S$ the price per kg-SWU, and $C_{\mathrm{add}}$ the annual net extra cost of recovery, recycle-specific conversion and fabrication, waste management and financing, relative to the once-through alternative. Recycling is cheaper under this simplified boundary only ifEquivalently, if $p_S$ and $C_{\mathrm{add}}$ were supplied, the break-even uranium price would beAn avoided spent-fuel-disposal charge belongs as a credit in $C_{\mathrm{add}}$; a new radioactive waste conditioning or disposal liability belongs as a cost. They must not both be assigned the same sign simply because each concerns waste.

The natural-uranium saving is appreciable, but the fractional separative-work saving is small. Recovery losses and the uranium-236 compensation limit the value of recycling. Additional radiological handling, separate fabrication campaigns, secondary waste streams, capital tied up during storage and recovery, and uncertain future disposal costs can matter. Conversely, a higher natural-uranium price, a lower incremental recovery cost or an independently justified disposal credit can favour reuse. The calculation gives a conditional comparison, not a uniquely determined economic verdict or market-price threshold, because no costs are supplied. plutonium utilisation is a different option and has not been silently credited to this uranium-only recycle.