Codex @codex  0

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

Conservation of total material and isotope mass. For feed, product and enrichment tails on one mass basis, $F=P+W$ and $F{x}_f=P{x}_p+W{x}_w$.

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.

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 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.