10. Depletion and Transmutation — OpenMC Documentation (2024)

10.1.2.1. Energy Deposition¶

The default energy deposition mode, "fission-q", instructs theCoupledOperator to normalize reaction rates using theproduct of fission reaction rates and fission Q values taken from the depletionchain. This approach does not consider indirect contributions to energydeposition, such as neutron heating and energy from secondary photons. In doingthis, the energy deposited during a transport calculation will be lower thanexpected. This causes the reaction rates to be over-adjusted to hit theuser-specific power, or power density, leading to an over-depletion of burnablematerials.

There are some remedies. First, the fission Q values can be directly set in avariety of ways. This requires knowing what the total fission energy releaseshould be, including indirect components. Some examples are provided below:

# use a dictionary of fission_q valuesfission_q = {"U235": 202e+6} # energy in eV# create a Model objectmodel = openmc.Model(geometry, settings)# create a modified chain and write it to a new filechain = openmc.deplete.Chain.from_xml("chain.xml", fission_q)chain.export_to_xml("chain_mod_q.xml")op = openmc.deplete.CoupledOperator(model, "chain_mod_q.xml")# alternatively, pass the modified fission Q directly to the operatorop = openmc.deplete.CoupledOperator(model, "chain.xml", fission_q=fission_q)

A more complete way to model the energy deposition is to use the modifiedheating reactions described in Heating and Energy Deposition. These values can be usedto normalize reaction rates instead of using the fission reaction rates with:

op = openmc.deplete.CoupledOperator(model, "chain.xml", normalization_mode="energy-deposition")

These modified heating libraries can be generated by running the latest versionof openmc.data.IncidentNeutron.from_njoy(), and will eventually be bundledinto the distributed libraries.

10.1.2.2. Local Spectra and Repeated Materials¶

It is not uncommon to explicitly create a single burnable material across manylocations. From a pure transport perspective, there is nothing wrong withcreating a single 3.5 wt.% enriched fuel fuel_3, and placing that fuel inevery fuel pin in an assembly or even full core problem. This certainlyexpedites the model making process, but can pose issues with depletion. Underthis setup, openmc.deplete will deplete a single fuel_3 materialusing a single set of reaction rates, and produce a single new composition forthe next time step. This can be problematic if the same fuel_3 is used invery different regions of the problem.

As an example, consider a full-scale power reactor core with vacuum boundaryconditions, and with fuel pins solely composed of the same fuel_3 material.The fuel pins towards the center of the problem will surely experience a moreintense neutron flux and greater reaction rates than those towards the edge ofthe domain. This indicates that the fuel in the center should be at a moredepleted state than periphery pins, at least for the fist depletion step.However, without any other instructions, OpenMC will deplete fuel_3 as asingle material, and all of the fuel pins will have an identical composition atthe next transport step.

This can be countered by instructing the operator to treat repeated instancesof the same material as a unique material definition with:

op = openmc.deplete.CoupledOperator(model, chain_file, diff_burnable_mats=True)

For our example problem, this would deplete fuel on the outer region of theproblem with different reaction rates than those in the center. Materials willbe depleted corresponding to their local neutron spectra, and have uniquecompositions at each transport step. The volume of the original fuel_3material must represent the volume of all the fuel_3 in the problem.When creating the unique materials, this volume will be equally distributedacross all material instances.

10.2.2.1. Reaction Rate Normalization¶

The IndependentOperator class supports two methods fornormalizing reaction rates:

1. source-rate normalization, which assumes the source_rate provided bythe time integrator is a flux, and obtains the reaction rates by multiplyingthe cross sections by the source-rate.

2. fission-q normalization, which uses the power or power_densityprovided by the time integrator to obtain normalized reaction rates bycomputing a normalization factor as the ratio of the user-specified power tothe “observed” power based on fission reaction rates. The equation for thenormalization factor is

   (1)¶\[f = \frac{P}{\sum\limits_m \sum\limits_i \left(Q_i N_{i,m} \sum\limits_g\sigma^f_{i,g,m} \phi_{g,m} \right)}\]

   where \(P\) is the power, \(Q_i\) is the fission Q value for nuclide\(i\), \(\sigma_{i,g,m}^f\) is the microscopic fission cross sectionfor nuclide \(i\) in energy group \(g\) for material \(m\),\(\phi_{g,m}\) is the neutron flux in group \(g\) for material\(m\), and \(N_{i,m}\) is the number of atoms of nuclide \(i\)for material \(m\). Reaction rates are then multiplied by \(f\) sothat the total fission power matches \(P\). This equation makes the sameassumptions and issues as discussed in Energy Deposition.Unfortunately, the proposed solution in that section does not apply heresince we are decoupled from transport code. However, there is a method toconverge to a more accurate value for flux by using substeps during timeintegration. This paperprovides a good discussion of this method.

10.2.2.2. Multiple Materials¶

A transport-independent depletion simulation using source-rate normalizationwill calculate reaction rates for each material independently. This can beuseful for running many different cases of a particular scenario. Atransport-independent depletion simulation using fission-q normalizationwill sum the fission energy values across all materials into \(Q_i\) inEquation (1), and Equation (1)provides the normalization factor applied to reaction rates in each material.This can be useful for running a scenario with multiple depletable materialsthat are part of the same reactor. This behavior may change in the future.

10.2.2.3. Time integration¶

The values of the microscopic cross sections passed toopenmc.deplete.IndependentOperator are fixed for the entire depletionsimulation. This implicit assumption may produce inaccurate results for certainscenarios.