Burnup

This model computes the local fuel burnup from the fission rate density. The specific power is derived from the fission rate and fuel density and is then time-integrated to obtain the burnup expressed in \(\mathrm{MWd/kg}\). The model also updates related irradiation quantities, including the irradiation time and the fraction of initial metal atoms (FIMA).

The implementation follows the steps used in Simulation::Burnup().

Inputs

The model uses the following variables:

Fission rate (history variable): fission rate density.
Fuel density (sciantix variable): fuel density used to convert to specific power.
Time step (physics variable): integration time step.

Specific power and burnup rate

The specific power is computed from the fission rate density using a constant conversion factor:

\[P_{\mathrm{spec}} = \frac{\dot{F}\,C}{\rho_f}\]

where - \(\dot{F}\) is the fission rate density (Fission rate), - \(\rho_f\) is the fuel density (Fuel density), - \(C = 3.12 \times 10^{-17}\) is the conversion constant used in the code.

The burnup rate is then defined as:

\[\dot{B} = \frac{P_{\mathrm{spec}}}{86400}\]

so that burnup is expressed in \(\mathrm{MWd/kg}\).

Time integration

The burnup value is updated by time integration:

\[B^{n+1} = B^{n} + \dot{B}\,\Delta t\]

where \(\Delta t\) is the current time step (Time step). In the code, this operation is performed using solver.Integrator.

Irradiation time

When the fission rate density is positive, the irradiation time is updated consistently with the burnup increment:

\[t_{\mathrm{irr}}^{n+1} = t_{\mathrm{irr}}^{n} + \frac{24}{P_{\mathrm{spec}}}\,\Delta B\]

where \(\Delta B\) is the burnup increment over the current step. If the fission rate is zero, the irradiation time is kept constant.

FIMA

The Fraction of Initial Metal Atoms (FIMA) is updated as:

\[\mathrm{FIMA}^{n+1} = \mathrm{FIMA}^{n} + \left(\frac{\dot{F}\,3.6 \times 10^{5}}{U}\right)\Delta t_{\mathrm{irr}}\]

where - \(U\) is the uranium inventory variable (U), - \(\Delta t_{\mathrm{irr}}\) is the irradiation time increment.

Implementation note

In the source code, the model reference is reported as:

“The local burnup is calculated from the fission rate density.”