Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE4 / 2 / b / Solution

The useful mechanism is radioactive decay during retention, not chemical destruction of carbon dioxide. With the time in seconds,Here $a$ is a radioactive activity concentration; the supplied units are per volume rather than per mass. The original plot follows this concentration over four hours.

A practical illustrative choice is a three-hour guaranteed residence time, at which $a/a_0=0.00214175$, giving about a factor $467$ reduction. On a plug-flow basis, the carbon-dioxide-equivalent hold-up volume isUse a contained delay line or a validated retention arrangement that prevents early breakthrough, followed by monitored discharge. A retention bed could instead hold the radioactive carbon dioxide, but its capacity and breakthrough performance would have to be established. Gas retention and monitored discharge are waste-treatment functions, independent of the eventual use of the isotope.^[ref]

The $4.00$ L result is a flow-delay volume, not a fill-and-immediately-dump tank specification. It credits radioactive decay during the guaranteed transit time and no subsequent storage after discharge from the delay system. Gas entering a filling tank near the end of filling has not aged for the entire filling time. For a literal tank filled for $T$ and immediately emptied, the radioactive activity at emptying is insteadThat alternative must not be analysed by multiplying the whole collected inventory by $e^{-\lambda T}$. If “no post filling radioactive decay” is intended to prescribe this literal fill-and-dump arrangement, the three-hour calculation does not establish compliance for it.

The nitrogen fraction is also unspecified. If $y$ is the carbon dioxide volume fraction at the stated volume reference conditions, a gas delay line requires $V_{\mathrm{mixture}}=V_{\mathrm{C}{\mathrm{O}}_2}/y$, not necessarily $4.00$ L of physical vessel volume. The graph alone does not define a unique optimum: a cost objective, operating calendar and residence-time model are needed. Parts (c) and (d) quantify the discharge constraint for the stated guaranteed-delay design.