 Solution

ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2020/paper-ne4/1/b/solution

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

P_{th} = \frac{1650}{0.37} = 4459.459 MW, E_{th} = 4459.459 (365) = 1.627703 \times 1 0^{6} MW d y r^{- 1} .

The corresponding initial heavy-metal nuclear fuel requirement is

M = \frac{E _{th}}{55000} = 29.5946 t U y r^{- 1} .

All 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}

F = P + W, F x_{f} = P x_{p} + W x_{w},

\frac{F}{P} = \frac{x _{p} - x _{w}}{x _{f} - x _{w}} = \frac{0.050 - 0.003}{0.007 - 0.003} = 11.75.

With

P = M

, the uranium oxide concentrate requirement is therefore

F = 11.75 M = 347.7365 t U y r^{- 1}, W = 318.1419 t U y r^{- 1} .

This is not the gross mass of oxide concentrate. Both

F - P - W = 0

and

0.007 F - 0.050 P - 0.003 W = 0

provide independent balance checks.

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