Gas Decay

This model computes the radioactive decay of gaseous species present in the fuel matrix. The decay process follows first-order kinetics and accounts for continuous production of the radioactive gas during irradiation.

Reference

Standard radioactive decay law.

Inputs

The model uses:

  • <Gas name> decayed (sciantix variable)

  • <Gas name> produced (sciantix variable)

  • Decay rate (gas property)

  • Time step (physics variable)

Model activation

The model is applied to each gas system satisfying:

  • the decay rate is greater than zero,

  • the gas is not located in a restructured matrix.

Model formulation

For each radioactive gas species, the evolution of the decayed amount follows:

\[\frac{dN_{\mathrm{dec}}}{dt} = \lambda \, N_{\mathrm{prod}} - \lambda \, N_{\mathrm{dec}}\]

where:

  • \(\lambda\) is the decay constant,

  • \(N_{\mathrm{prod}}\) is the amount of produced gas,

  • \(N_{\mathrm{dec}}\) is the accumulated decayed amount.

Time integration

The solution over a time step \(\Delta t\) is obtained using the internal solver.Decay routine:

\[N_{\mathrm{dec}}^{n+1} = \texttt{Decay} \left( N_{\mathrm{dec}}^{n}, \lambda, \lambda N_{\mathrm{prod}}^{n+1}, \Delta t \right)\]

The updated value is stored in:

<Gas name> decayed

Outputs

  • <Gas name> decayed (updated decayed inventory stored in sciantix variables)