# openmc.deplete – Depletion¶

## Primary API¶

The two primary requirements to perform depletion with openmc.deplete are:

1. A transport operator

2. A time-integration scheme

The former is responsible for calculating and retaining important information required for depletion. The most common examples are reaction rates and power normalization data. The latter is responsible for projecting reaction rates and compositions forward in calendar time across some step size $$\Delta t$$, and obtaining new compositions given a power or power density. The CoupledOperator class is provided to obtain reaction rates via tallies through OpenMC’s transport solver, and the IndependentOperator class is provided to obtain reaction rates from cross-section data. Several classes are provided that implement different time-integration algorithms for depletion calculations, which are described in detail in Colin Josey’s thesis, Development and analysis of high order neutron transport-depletion coupling algorithms.

 PredictorIntegrator Deplete using a first-order predictor algorithm. CECMIntegrator Deplete using the CE/CM algorithm. CELIIntegrator Deplete using the CE/LI CFQ4 algorithm. CF4Integrator Deplete using the CF4 algorithm. EPCRK4Integrator Deplete using the EPC-RK4 algorithm. LEQIIntegrator Deplete using the LE/QI CFQ4 algorithm. SICELIIntegrator Deplete using the SI-CE/LI CFQ4 algorithm. SILEQIIntegrator Deplete using the SI-LE/QI CFQ4 algorithm.

Each of these classes expects a “transport operator” to be passed. OpenMC provides the following transport operator classes:

 CoupledOperator Transport-coupled transport operator. IndependentOperator Transport-independent transport operator that uses one-group cross sections to calculate reaction rates.

The CoupledOperator and IndependentOperator classes must also have some knowledge of how nuclides transmute and decay. This is handled by the Chain class.

## Minimal Example¶

A minimal example for performing depletion would be:

>>> import openmc
>>> import openmc.deplete
>>> geometry = openmc.Geometry.from_xml()
>>> settings = openmc.Settings.from_xml()
>>> model = openmc.model.Model(geometry, settings)

# Representation of a depletion chain
>>> chain_file = "chain_casl.xml"
>>> operator = openmc.deplete.CoupledOperator(
...     model, chain_file)

# Set up 5 time steps of one day each
>>> dt = [24 * 60 * 60] * 5
>>> power = 1e6  # constant power of 1 MW

# Deplete using mid-point predictor-corrector
>>> cecm = openmc.deplete.CECMIntegrator(
...     operator, dt, power)
>>> cecm.integrate()


## Internal Classes and Functions¶

When running in parallel using mpi4py, the MPI intercommunicator used can be changed by modifying the following module variable. If it is not explicitly modified, it defaults to mpi4py.MPI.COMM_WORLD.

openmc.deplete.comm

MPI intercommunicator used to call OpenMC library

Type

mpi4py.MPI.Comm

During a depletion calculation, the depletion chain, reaction rates, and number densities are managed through a series of internal classes that are not normally visible to a user. However, should you find yourself wondering about these classes (e.g., if you want to know what decay modes or reactions are present in a depletion chain), they are documented here. The following classes store data for a depletion chain:

 Chain Full representation of a depletion chain. DecayTuple Decay mode information Nuclide Decay modes, reactions, and fission yields for a single nuclide. ReactionTuple Transmutation reaction information FissionYieldDistribution Energy-dependent fission product yields for a single nuclide FissionYield Mapping for fission yields of a parent at a specific energy

The Chain class uses information from the following module variable:

chain.REACTIONS

Dictionary that maps transmutation reaction names to information needed when a chain is being generated: MT values, the change in atomic/mass numbers resulting from the reaction, and what secondaries are produced.

Type

dict

The following classes are used during a depletion simulation and store auxiliary data, such as number densities and reaction rates for each material.

 AtomNumber Stores local material compositions (atoms of each nuclide). MicroXS Microscopic cross section data for use in transport-independent depletion. OperatorResult Result of applying transport operator ReactionRates Reaction rates resulting from a transport operator call Results Results from a depletion simulation StepResult Result of a single depletion timestep

The following class and functions are used to solve the depletion equations, with cram.CRAM48() being the default.

 cram.IPFCramSolver CRAM depletion solver that uses incomplete partial factorization
 cram.CRAM16 Solve depletion equations using IPF CRAM cram.CRAM48 Solve depletion equations using IPF CRAM pool.deplete Deplete materials using given reaction rates for a specified time
pool.USE_MULTIPROCESSING

Boolean switch to enable or disable the use of multiprocessing when solving the Bateman equations. The default is to use multiprocessing, but can cause the simulation to hang in some computing environments, namely due to MPI and networking restrictions. Disabling this option will result in only a single CPU core being used for depletion.

Type

bool

pool.NUM_PROCESSES

Number of worker processes used for depletion calculations, which rely on the multiprocessing.pool.Pool class. If set to None (default), the number returned by os.cpu_count() is used.

The following classes are used to help the openmc.deplete.CoupledOperator compute quantities like effective fission yields, reaction rates, and total system energy.

 helpers.AveragedFissionYieldHelper Class that computes fission yields based on average fission energy helpers.ChainFissionHelper Computes normalization using fission Q values from depletion chain helpers.ConstantFissionYieldHelper Class that uses a single set of fission yields on each isotope helpers.DirectReactionRateHelper Class for generating one-group reaction rates with direct tallies helpers.EnergyScoreHelper Class responsible for obtaining system energy via a tally score helpers.FissionYieldCutoffHelper Helper that computes fission yields based on a cutoff energy helpers.FluxCollapseHelper Class that generates one-group reaction rates using multigroup flux

The openmc.deplete.IndependentOperator uses inner classes subclassed from those listed above to perform similar calculations.

## Intermediate Classes¶

Specific implementations of abstract base classes may utilize some of the same methods and data structures. These methods and data are stored in intermediate classes.

Methods common to tally-based implementation of FissionYieldHelper are stored in helpers.TalliedFissionYieldHelper

 helpers.TalliedFissionYieldHelper Abstract class for computing fission yields with tallies

Methods common to OpenMC-specific implementations of TransportOperator are stored in openmc_operator.OpenMCOperator

 openmc_operator.OpenMCOperator Abstract class holding OpenMC-specific functions for running depletion calculations.

## Abstract Base Classes¶

A good starting point for extending capabilities in openmc.deplete is to examine the following abstract base classes. Custom classes can inherit from abc.TransportOperator to implement alternative schemes for collecting reaction rates and other data prior to depleting materials

 abc.TransportOperator Abstract class defining a transport operator

The following classes are abstract classes used to pass information from transport simulations (in the case of transport-coupled depletion) or to simply calculate these quantities directly (in the case of transport-independent depletion) back on to the abc.TransportOperator

 abc.NormalizationHelper Abstract class for obtaining normalization factor on tallies abc.FissionYieldHelper Abstract class for processing energy dependent fission yields abc.ReactionRateHelper Abstract class for generating reaction rates for operators

Custom integrators or depletion solvers can be developed by subclassing from the following abstract base classes:

 abc.Integrator Abstract class for solving the time-integration for depletion abc.SIIntegrator Abstract class for the Stochastic Implicit Euler integrators abc.DepSystemSolver Abstract class for solving depletion equations