SERPENT Guide

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Burnup Calculations

Introduction to Burnup Analysis

Burnup calculations track the time evolution of nuclear fuel composition during reactor operation. Serpent excels at coupled neutron transport and depletion analysis, making it ideal for fuel cycle studies, reactor core design, and spent fuel characterization.

Serpent's Advantage: Unlike many Monte Carlo codes that require external coupling, Serpent includes built-in burnup capability with sophisticated depletion chains and automatic cross section updates during irradiation.

Key Burnup Concepts

Fundamental Processes:

  • Neutron absorption: Converts fertile isotopes to fissile
  • Fission: Destroys fissile material, creates fission products
  • Radioactive decay: Changes isotopic composition over time
  • Neutron capture: Creates heavier isotopes and transmutation

The mathematical foundation involves solving the Bateman equations coupled with the neutron transport equation, accounting for flux spectrum changes as fuel composition evolves.

Setting Up Burnup Calculations

Burnup calculations require defining burnable materials, power levels, and time steps. Serpent handles the complexity of flux-dependent cross sections and composition updates automatically.

Basic Burnup Configuration

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% Enable burnup calculation mode
set power 3400E6        % Reactor thermal power (3400 MW in watts)
set powdens 1 fuel      % Power density in fuel material

% 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 60.0

% Or use step size in flux-time (neutron flux × time)
dep flustep
1E14 2E14 5E14 1E15 2E15 5E15 1E16

Time Step Selection: Use smaller steps early in irradiation when composition changes rapidly, then larger steps as the system approaches equilibrium. Typical PWR fuel reaches 60 GWd/tU over 4-6 years.

Burnable Material Definition

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% 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
mat fuel_middle -10.4 burn 2  
mat fuel_outer -10.4 burn 3

Advanced Burnup Features

Depletion Chains

Serpent includes comprehensive depletion chains covering actinides, fission products, and activation products. The default chains are optimized for reactor applications.

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% 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 depcut 1E-12            % Density cutoff for tracking
set inventory all           % Track all isotopes  
set nuclides all            % Include all nuclides in output

% Fission yield treatment
set fisyield 0              % 0=independent, 1=cumulative yields
set yieldsens 1E-10         % Yield sensitivity cutoff

Performance Note: Tracking all isotopes provides complete information but increases memory usage and computation time. For production calculations, consider using predefined chains optimized for your application.

Spatial Burnup Resolution

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% Pin-by-pin burnup tracking
mat fuel_pin1 -10.4 burn 1
mat fuel_pin2 -10.4 burn 2
mat fuel_pin3 -10.4 burn 3
% ... continue for each fuel pin

% Axial burnup zones  
mat fuel_bottom -10.4 burn 1
mat fuel_middle -10.4 burn 2
mat fuel_top -10.4 burn 3

% Radial fuel zones for detailed analysis
mat fuel_center -10.4 burn 1    % Central pellet region
mat fuel_rim -10.4 burn 2       % Outer rim (high burnup)

% Universe-based burnup (for lattice structures)
set bu_universe 1 1 1 1         % Burnup universe mapping

Control Rod Modeling

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% Control rod movement during burnup
dep bank_position
% Step   Pos(cm)  Bank  
1        0.0      in     % Rods fully inserted  
5        50.0     mid    % Partial withdrawal
10       100.0    out    % Rods fully withdrawn
15       75.0     mid    % Reinsert partially

% Soluble boron concentration (ppm)
dep boron_conc
0 1200    % Beginning of cycle: 1200 ppm
5 800     % Mid-cycle: 800 ppm  
10 400    % End of cycle: 400 ppm

Practical Burnup Examples

PWR Assembly Burnup

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% 17x17 PWR assembly burnup calculation
set title "PWR Assembly Burnup to 60 GWd/tU"

% Assembly power and geometry
set power 15.0          % Assembly power (MW)
set powdens 1 fuel      % Uniform power in fuel

% 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 outp 1              % Detailed output
set his 1               % History output

Fast Reactor Burnup

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% Sodium-cooled fast reactor burnup
set title "SFR Assembly Burnup Analysis"

% Fast reactor characteristics
set power 25.0          % Higher power density
set powdens 1 fuel_inner fuel_outer  % Multiple fuel types

% 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               % Natural uranium
8016.09c  -2.0

% Fast reactor time scale (longer cycles)
dep daystep
50 50 100 100 200 200 365 365 365 365

Spent Fuel Cooling

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% Post-irradiation decay calculation
set title "Spent Fuel Decay Heat Analysis"

% No neutron flux during cooling
set pop 0 0 0           % No active neutron transport
dep decaystep           % Pure decay calculation
30 90 180 365           % Days
2 5 10 20 50 100        % Years

% Track decay heat contributors
set inventory
54135 55137 90090 38090 % Short-lived FPs
60144 61147 62151       % Medium-lived FPs  
55137 90090 93237       % Long-lived isotopes

% Decay heat output
set his 1               % Detailed decay history
set repro 1             % Reproduction factor tracking

Burnup Output and Analysis

Understanding Burnup Output

Serpent generates comprehensive burnup output including isotopic inventories, reaction rates, decay heat, and neutron multiplication factor evolution.

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% Key output files generated:
% [input]_dep.m        - Main burnup results (MATLAB format)  
% [input]_his.m        - History file with k-eff vs time
% [input]_mat.m        - Material compositions vs time
% [input].coe          - Coefficient file for restart

% Typical MATLAB analysis:
% dep = load('[input]_dep.m');
% plot(dep.BURNUP, dep.INF_KEFF);  % k-infinity vs burnup
% plot(dep.DAYS, dep.TOT_POWER);   % Power vs time

Critical Burnup Parameters

Key Burnup Metrics:

  • Burnup (GWd/tU): Energy released per unit heavy metal
  • k-infinity: Neutron multiplication factor evolution
  • Conversion ratio: Fertile-to-fissile conversion rate
  • Fissile fraction: Percentage of fissile isotopes
  • Decay heat: Post-shutdown heat generation
  • Neutron poison buildup: Xe-135, Sm-149 concentrations

Restart and Continuation

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% Restart from previous calculation
set restart "[previous_input].coe"

% Continue burnup from specific step
dep restart 15          % Restart from step 15

% Branch calculations from burnup state
dep branch
% Condition    Value
temp_fuel      1200     % Increase fuel temperature  
boron_ppm      500      % Change boron concentration
ctrl_rod       out      % Withdraw control rods

% Perturbation analysis
set perturb 1           % Enable perturbation calculations
set kpert 0.01          % 1% reactivity perturbation

Branch Calculations: Use branch calculations to study the effects of parameter changes (temperature, poison concentration, control rod position) at specific burnup points without recalculating the entire depletion history.

Related Topics

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