SERPENT Guide
Burnup Calculations
Coupled neutron transport and depletion analysis for fuel cycle studies, core design, and spent fuel characterization.
Introduction to Burnup Analysis
Burnup calculations track the time evolution of nuclear fuel composition during reactor operation by solving the Bateman equations coupled with the neutron transport equation. As the reactor operates, fissile material is consumed through fission, fertile isotopes are converted to fissile species through neutron capture, and fission products accumulate in the fuel. These compositional changes alter the neutron flux spectrum, which in turn affects the reaction rates that drive further transmutation.
Unlike many Monte Carlo codes that require external coupling scripts to link the transport solver with a separate depletion module, Serpent includes built-in burnup capability with sophisticated depletion chains and automatic cross section updates during irradiation. The code solves the coupled problem by alternating between transport calculations (to determine the flux spectrum and one-group reaction rates) and depletion calculations (to update material compositions).
Setting Up Burnup Calculations
A burnup calculation requires three inputs: burnable materials, a reactor power level, and a depletion time step schedule.
Basic Burnup Configuration
The burnup mode is activated by specifying a power level and a depletion schedule. Serpent supports three approaches for defining the depletion schedule: time-based steps in days, burnup-based steps in MWd/kgU, and flux-time steps. Time step selection is critical: smaller steps should be used early in irradiation when composition changes are most rapid, with progressively larger steps as the system approaches quasi-equilibrium. A typical PWR fuel assembly reaches approximately 60 GWd/tU over four to six years of operation.
% Enable burnup calculation mode
set power 3400E6 % Reactor thermal power (3400 MW in watts)
% set powdens 40.0 % Alternative: power density in W/g
% Burnup time steps (days)
dep daystep
1.0 2.0 5.0 10.0 20.0 50.0 100.0 200.0 365.0
365.0 365.0 365.0 % Three annual cycles
% Alternative: step size in burnup (MWd/kgU)
dep bustep
1.0 2.0 5.0 10.0 20.0 30.0 40.0 50.0 60.0Burnable Material Definition
Materials that undergo depletion must be flagged with the burn keyword in their definition. The burn index allows Serpent to track each material zone independently, which is essential for capturing spatial variations in burnup across the fuel. When volume information is needed for proper power normalization, the vol keyword specifies the physical volume of the material region in cubic centimeters. For detailed spatial resolution, multiple burnable material zones can be defined with distinct burn indices, enabling pin-by-pin or even radial-within-pin tracking of isotopic evolution.
% Fuel material with burnup tracking
mat fuel -10.4 burn 1 % Density with burn flag
92235.09c 0.045 % 4.5 at% U-235
92238.09c 0.955 % Depleted U-238
8016.09c 2.0 % Stoichiometric oxygen
% Alternative: volume-based power distribution
mat fuel -10.4 vol 1500.0 burn 1 % Volume in cm³
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% Multiple burnable zones (for spatial resolution)
mat fuel_inner -10.4 burn 1
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_middle -10.4 burn 2
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_outer -10.4 burn 3
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0Advanced Burnup Features
Serpent includes depletion chains covering actinides, fission products, and activation products. The default chains are optimized for LWR applications, but isotope tracking, density cutoffs, and fission yield treatment can be customized. Tracking all isotopes maximizes completeness but increases memory and computation time; predefined chains optimized for specific applications are more efficient for production runs.
Depletion Chain Configuration
% Depletion chain selection
set declib "endfb71_dec" % ENDF/B-VII.1 decay data
set nfylib "endfb71_nfy" % Fission yield data
% Custom depletion chain (advanced)
set inventory all % Track all isotopesSpatial Burnup Resolution
Spatial resolution in burnup calculations is achieved by defining multiple burnable material zones, each with a unique burn index. This approach can be applied at the pin level for assembly-wide burnup distributions, along the axial direction to capture the characteristic cosine-shaped power profile, or even radially within individual fuel pellets to model the enhanced burnup at the pellet rim. For lattice-based geometries, the universe-based burnup mapping provides an efficient means of assigning burn indices to periodic structures without manually defining each material zone.
% Pin-by-pin burnup tracking
mat fuel_pin1 -10.4 burn 1
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_pin2 -10.4 burn 2
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_pin3 -10.4 burn 3
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% ... continue for each fuel pin
% Axial burnup zones
mat fuel_bottom -10.4 burn 1
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_middle -10.4 burn 2
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_top -10.4 burn 3
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
% Radial fuel zones for detailed analysis
mat fuel_center -10.4 burn 1 % Central pellet region
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
mat fuel_rim -10.4 burn 2 % Outer rim (high burnup)
92235.09c 0.045
92238.09c 0.955
8016.09c 2.0
Control Rod and Soluble Boron Modeling
Control rod positions and soluble boron concentrations vary over the cycle to maintain criticality and shape the power distribution. Serpent's branch card defines parametric perturbation states (different temperatures, boron concentrations, rod positions) that are evaluated at each burnup step to generate parameterized few-group cross sections for downstream nodal diffusion codes. The actual cycle-to-cycle operational modeling occurs in the nodal code, not in Serpent.
% Time-dependent operating conditions (control rod positions,
% boron concentration, temperatures) are handled through the
% branch card, which defines a set of perturbation states.
% At each burnup step, Serpent can evaluate multiple branch
% conditions to generate parameterized cross section data.
%
% Example: define branches for different boron concentrations
branch boron0
stp water -0.714 574 % 0 ppm boron
branch boron1000
stp borated_water -0.7149 574 % 1000 ppmPractical Burnup Examples
PWR Assembly Burnup
A 17x17 PWR assembly burnup calculation models three 18-month operating cycles to achieve a discharge burnup of approximately 60 GWd/tU. The depletion schedule uses finer time steps at the beginning of each cycle when xenon and samarium transients are most pronounced, transitioning to coarser steps as the composition approaches equilibrium.
% 17x17 PWR assembly burnup calculation
set title "PWR Assembly Burnup to 60 GWd/tU"
% Assembly power and geometry
set power 15.0E6 % Assembly power (15 MW)
% Realistic PWR burnup schedule
dep daystep
% Cycle 1 (18 months)
10 10 10 20 20 30 30 50 50 80 80 100 100
% Cycle 2
10 10 10 20 20 30 30 50 50 80 80 100 100
% Cycle 3
10 10 10 20 20 30 30 50 50 80 80 100 100
% Track important isotopes
set inventory
92235 92238 94239 94240 94241 94242 % Actinides
54135 55133 60143 62149 63151 % Important FPs
% Output options
set his 1 % History outputFast Reactor Burnup
Sodium-cooled fast reactor burnup calculations differ from thermal reactor analyses in several important respects. The harder neutron spectrum results in different transmutation pathways, with greater production of higher actinides through successive neutron captures. MOX fuel compositions include significant plutonium fractions, and the breeding blanket regions around the driver fuel produce additional fissile material through U-238 capture. The longer operating cycles typical of fast reactors are reflected in the coarser time step schedule.
% Sodium-cooled fast reactor burnup
set title "SFR Assembly Burnup Analysis"
% Fast reactor characteristics
set power 25.0E6 % Assembly power (25 MW)
% MOX fuel burnup
mat fuel_inner -10.8 burn 1 % Inner enrichment zone
94239.09c 0.13 % 13 at% Pu-239
94240.09c 0.05 % 5 at% Pu-240
94241.09c 0.02 % 2 at% Pu-241
92238.09c 0.80 % 80 at% U-238
8016.09c 2.0 % Stoichiometric oxygen
% Breeding blanket
mat blanket -10.4 burn 2 % Depleted uranium blanket
92238.09c 1.0 % U-238 (depleted)
8016.09c 2.0 % Stoichiometric oxygen
% Fast reactor time scale (longer cycles)
dep daystep
50 50 100 100 200 200 365 365 365 365Spent Fuel Cooling
With no neutron flux present after discharge, composition changes are governed entirely by radioactive decay. These calculations support spent fuel pool thermal analysis, transportation cask design, and repository performance assessments. The time steps span from days (short-lived fission product decay) to decades (long-term activity and heat generation).
% Post-irradiation decay calculation
set title "Spent Fuel Decay Heat Analysis"
% Pure decay mode: Serpent solves only the Bateman equations
% No neutron transport is performed during decay steps
dep decstep % Decay step calculation (days)
30 90 180 365 % Short-term cooling
730 1826 3652 7305 % 2 to 20 years
% Track decay heat contributors
set inventory
54135 55137 90090 38090 % Short-lived FPs
60144 61147 62151 % Medium-lived FPs
93237 95241 94238 % Long-lived actinides
% Decay heat output
set his 1 % Detailed decay historyBurnup Output and Analysis
Serpent generates comprehensive burnup output distributed across several files. The main depletion file ([input]_dep.m) contains isotopic inventories and integral burnup parameters as a function of depletion step. The history file ([input]_his.m) records the evolution of k-effective and other neutronics parameters over time. Material compositions at each depletion step are typically included in the _dep.m file (a separate [input]_mat.m file is not standard in all Serpent 2 versions; check your output directory). The coefficient file ([input].coe) stores coefficient and branch calculation output data.
The key burnup metrics to monitor include the burnup itself in GWd/tU (energy released per unit initial heavy metal mass), the k-infinity evolution that characterizes the reactivity trajectory of the fuel, the conversion ratio measuring fertile-to-fissile conversion efficiency, the fissile mass fraction, decay heat generation rates, and the buildup of neutron poisons such as Xe-135 and Sm-149.
Output File Structure
% Key output files generated:
% [input]_dep.m - Main burnup results (MATLAB script format)
% [input]_his.m - History file with k-eff vs time
% [input].coe - Coefficient/branch output file
%
% NOTE: Material compositions at each depletion step are
% typically contained in the _dep.m file. The existence of
% a separate [input]_mat.m file is not standard in all
% Serpent 2 versions; check your output directory.
% Typical MATLAB analysis:
% run('[input]_dep.m'); % Execute the script to load variables
% plot(BURNUP, INF_KEFF); % k-infinity vs burnup
% plot(DAYS, TOT_POWER); % Power vs timeRestart and Branch Calculations
Serpent supports restarting depletion calculations from a saved state, enabling parameter perturbation studies at specific burnup points without recalculating the entire history. Branch calculations allow the analyst to systematically vary fuel temperature, boron concentration, control rod position, or other operating parameters at each burnup step, generating the lattice physics data needed for nodal diffusion codes used in full-core analysis.
% Restart from a previous calculation
set rfr 15 "previous_input.wrk" % Read restart file at step 15
% Branch calculations define parametric variations of
% operating conditions at each burnup step, generating
% the lattice physics data needed for nodal diffusion codes.
% Branches are defined using the branch card (see above)
% and are evaluated automatically at each depletion step.