Overview

Serpent is a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, developed at VTT Technical Research Centre of Finland since 2004. The code is specialized in two-dimensional lattice physics calculations, but the geometry description allows the modeling of complicated three-dimensional geometries as well. The suggested applications of Serpent include:

The main features of the code, including the major limitations, are introduced below. This website covers the capabilities of publicly distributed Serpent 1. Most of the on-going development work is focused on Serpent 2, which is currently in a beta-testing phase, with public release scheduled for 2013-2014.

Geometry and neutron tracking

Serpent uses a universe-based CSG geometry model (similar to MCNP and Keno-VI), which allows the description of practically any two- or three-dimensional fuel or reactor configuration. The geometry consists of material cells, defined by elementary and derived surface types.

The code also provides some additional geometry features specifically for fuel design. These features include simplified definition of cylindrical fuel pins and spherical fuel particles, square and hexagonal lattices for LWR geometries and circular cluster arrays for CANDU fuels. The random dispersion of microscopic fuel particles in high-temperature gas-cooled reactor fuels and pebble distributions in pebble-bed type HTGR cores can be modeled using geometry types specifically designed for the task (see below).

Woodcock delta-tracking method

An analog Monte Carlo game and the k-eigenvalue criticality source method are used for simulating a self-sustaining chain reaction, and an external source mode is available for sub-critical and non-multiplying systems. Neutron transport is based on a combination of conventional surface-to-surface ray-tracing and the Woodcock delta-tracking method (Woodcock, 1965). The tracking routine has proven efficient and well suited for geometries where the neutron mean-free-path is long compared to the dimensions, which is typically the case in fuel assemblies, and especially in HTGR particle fuels. The combination of two tracking methods overcomes the efficiency problems normally encountered with delta-tracking in the presence of localized heavy absorbers (Leppänen, 2010b).

The main drawback of delta-tracking is that the track-length estimate of neutron flux is not available and reaction rates have to be calculated using the potentially less-efficient collision estimator. This is usually not a problem in reactor calculations when reaction rates are scored in regions of high collision density. However, the efficiency of the collision estimator becomes poor in small or optically thin volumes located far or isolated from the active source. For this reason Serpent 1 is not particularly well suited for shielding and detector calculations.

Explicit particle and pebble-bed fuel model for HTGR calculations

High-temperature gas-cooled reactor geometries differ significantly from conventional light water reactors. The fissile material is encapsulated inside microscopic fuel particles (TRISO), randomly dispersed in fuel compacts or pebbles made of graphite. In pebble-bed type geometries the spherical fuel pebbles are piled inside the reactor core, which brings another level of random heterogeneity in the calculation.

The explicit HTGR geometry model in Serpent reads the coordinates of fuel particles or pebbles from a separate input file, and generates the geometry as it is defined, without any approximations. The model works on several levels (particles inside a pebble and pebbles inside the core) and it has been tested in realistic double-heterogeneous reactor configurations consisting of over 60 million randomly positioned units (Suikkanen, 2010). The computational overhead from handling the unstructured configuration is typically 20-50% compared to a similar regular-lattice model. The routine also enables the calculation of pebble-wise power distributions over the reactor core without defining additional tallies.

To simplify the construction of HTGR geometries, Serpent provides a separate command line routine that generates random particle distribution files for the explicit geometry model.

Interaction physics

Serpent reads continuous-energy cross sections from ACE format data libraries. The interaction physics is based on classical collision kinematics, ENDF reaction laws and probability table sampling in the unresolved resonance region. Improved treatment for the free-gas scattering kernel near resonances is also available, based on the DBRC Doppler-broadening rejection correction method (Becker, 2009).

ACE format cross section libraries based on JEF-2.2, JEFF-3.1, JEFF-3.1.1, ENDF/B-VI.8 and ENDFB/B-VII evaluated data files are included in the Serpent installation package. Data is available for 432 nuclides at 6 temperatures between 300 and 1800K. Thermal bound-atom scattering data is included for light and heavy water and graphite. The data format is shared with the widely-used Los Alamos MCNP code and any continuous-energy MCNP data library can be used with Serpent as well.

Unionized energy grid format

Continuous-energy cross sections in the library files are reconstructed on a unionized energy grid, used for all reaction modes. The use of a single energy grid results in a major speed-up in calculation, as the number of CPU time consuming grid search iterations is reduced to minimum. If all original grid points are preserved, there is no loss of data or accuracy in the process. Macroscopic cross sections for each material are pre-generated before the transport simulation. Instead of calculating the cross sections by summing over the constituent nuclides, the value can be read from a pre-generated table, which is another effective way of improving the performance of the tracking routine.

The drawback of the unionized energy grid approach is that computer memory is wasted for storing redundant data points. The grid size may become prohibitively large in burnup calculations, often involving over 250 actinide and fission product nuclides. To overcome this problem the code uses two methods for reducing the memory demand (Leppänen, 2009b). Excessive memory usage can still be considered one of the main limitations for the Serpent code, and it was one of the reasons for starting the development of Serpent 2 in September 2010.

Built-in Doppler broadening routine

A built-in Doppler broadening preprocessor routine allows the conversion of ACE format cross sections into a higher temperature. This capability results in a more accurate description of the interaction physics in temperature-sensitive applications, as the data in the cross section libraries is available only in 300K intervals. The method has been validated with good results and the routine works efficiently without a major increase in the overall calculation time (Viitanen, 2009).

Burnup calculation

The burnup capability in Serpent is entirely based on built-in calculation routines, without any external coupling. The number of depletion zones is not restricted, although memory usage may become a limiting factor when the number of burnable materials is large.

Fission products and actinide daughter nuclides are selected for the calculation without additional user effort and fuel rods and burnable absorber pins can be divided into annular sub-regions to account for the rim-effects. The irradiation history is defined in units of time or burnup. Reaction rates are normalized to total power, specific power density, flux or fission rate and the normalization can be changed by dividing the irradiation cycle into a number of separate depletion intervals. Volumes and masses needed for the normalization are calculated automatically for simple geometries, such as fuel pin lattices, or the values can be defined by the user. Predictor-corrector calculation is optional and used by default for each burnup step.

Radioactive decay and fission yield data used in the calculation is read from standard ENDF format data libraries. The decay libraries may contain data for almost 4000 nuclides and meta-stable states, all of which is available for the calculation. The total number of different nuclides produced from fission, transmutation and decay reactions is generally lower, in the order of 1500. The concentrations of all included nuclides with decay data are tracked in the burnup calculation, and the number of nuclides with cross sections typically ranges between 200 and 280. Energy-dependent fission yields are available for all main actinides (31 nuclides in ENDF/B-VII data).

Integral one-group transmutation cross sections are calculated either within the transport cycle, or by collapsing the continuous-energy reaction cross sections after the cycle using a flux spectrum collected on the unionized energy grid. The spectrum collapse method speeds up the calculation by a factor of 3-4, and due to the high energy resolution of the flux spectrum, the errors in the results are practically negligible. Similar methodology has been successfully used with coupled Monte Carlo burnup calculation codes (Haeck, 2007; Fridman, 2008) before it was implemented in Serpent.

Serpent has two fundamentally different options for solving the Bateman depletion equations. The first method is the Transmutation Trajectory Analysis (TTA) method (Cetnar, 2006), based on the analytical solution of linearized depletion chains. The second option is the Chebyshev Rational Approximation Method (CRAM), an advanced matrix exponential solution developed for Serpent at VTT (Pusa, 2010; 2011; 2012). The two methods have shown to yield consistent results, both when used with Serpent (Leppänen, 2010a) and in separate methodological studies (Isotalo, 2010).

Fission product poison Xe-135 can be handled separately from the other nuclides, and iterated to its equilibrium concentration during the transport simulation. The equilibrium calculation is independent of the depletion routine, and the iteration can also be performed in transport mode without burnup calculation.

Parallelization

Serpent 1 uses the Message Passing Interface (MPI) for parallel calculation. Parallelization of the transport routine is implemented by dividing the neutron histories to several tasks and combining the results after the simulation has been completed. This approach is simple and efficient, but it lacks error tolerance and dynamic load sharing. The overall calculation time is dependent on the slowest task, which is why the method is best applied in a symmetric parallel environment.

In addition to the neutronics simulation, parallelization in the burnup calculation mode divides also the preprocessing and depletion routines into several tasks. Each task handles a different material and the speed-up may become significant if the number of depletion zones is large. The extensive memory demand due to unionized energy grid approach may become a limiting factor in parallel burnup calculation, if several MPI tasks are sharing the same memory space.

Results and output

Serpent can be used for producing homogenized multi-group constants for deterministic reactor simulator calculations. The standard output includes:

All result estimates are accompanied by the associated relative statistical errors.

Homogenization can be carried out for multiple universes simultaneously, which allows the production of group constant data for several fuel assemblies or zones within a single run.

The effective delayed neutron parameters are calculated using a forward Monte Carlo method developed at the NRG (Meulekamp, 2006). The few-energy group structure for group constant generation is arbitrary and defined by the user. The code also calculates fission source entropies for convergence studies. The total entropy is divided into x-, y- and z-components to monitor source convergence separately in each direction.

The critical spectrum calculation is based on a semi-deterministic approach, in which homogenized multi-group cross sections from the Monte Carlo simulation are used to form B₁ equations, which are then solved outside the main transport loop. The solution yields a leakage-corrected flux spectrum, which is used to re-homogenize the group constants. The procedure is very similar to the methods used in various deterministic codes, and comparisons to HELIOS calculations (Fridman, 2011; 2012) have shown good results.

User-defined detectors (tallies) can be set up for calculating various integral reaction rates. The spatial integration domain can be defined by a combination of cells, universes, lattices and materials, or using a three-dimensional super-imposed mesh. The number and structure of detector energy bins is unrestricted. Various response functions are available for the calculation, including material-wise macroscopic and isotopic microscopic cross sections and ACE format dosimetry data.

Output for burnup calculation consists of isotopic compositions, transmutation cross sections, activities, spontaneous fission rates and decay heat data. The results are given both as material-wise and total values. Group constants and all the other output parameters are calculated and printed for each burnup step.

All numerical output is written in Matlab m-format files to simplify the post-processing of the results. The code also has a geometry plotter feature and a reaction rate plotter, which is convenient for visualizing the neutronics in thermal systems (see the gallery for examples).

Results and validity

Serpent has been extensively validated for assembly-level group constant calculations. Effective multiplication factors and homogenized few-group reaction cross sections are within the statistical accuracy from reference MCNP results, when the same ACE libraries are used in the calculations. Validation against MCNP has also been carried out with equally good results for individual nuclides, by comparing flux spectra produced by the two codes. Differences to other Monte Carlo codes (Keno-VI) are small, but statistically significant discrepancies can be observed in some cases. Differences to deterministic lattice codes are generally larger, mainly due to the fundamental differences between the calculation methods.

Validation of burnup calculation routines is considerably more difficult, due to the lack of a perfect reference code. In addition to the transport simulation, there are additional uncertainties coming from decay and fission yield data, methods used for solving the Bateman equations, number of nuclide concentrations tracked for each burnable material, depletion algorithms used to iterate between the two solutions, and so on. The results are generally good compared to other burnup calculation codes, but there are some significant discrepancies as well. Comparisons to CASMO-4E (Leppänen, 2009a), for example, show a consistent few-percent over-prediction in the build-up of Pu-239 and noticeable differences in the concentrations of the main fission product poisons, Xe-135 and Sm-149. The differences most like originate from several factors relating to the methods used by the two codes, but the root cause is yet to be discovered.

Serpent 1 lacks any statistical tests performed on the calculated results. The standard assumption is that Monte Carlo result estimates, which are essentially random variables, follow the normal distribution according to the central limit theorem. If this is not the case, the confidence intervals of the normal distribution do not apply, which may lead to the over-estimation of statistical accuracy. Some analysis based on a series of independent test calculations have confirmed the statistics for the main integral parameters (multiplication factors, homogenized group constants, etc.), but there is no guarantee that the same conclusion applies to all results and calculation cases.

Performance

Serpent 1 is optimized for performance in infinite lattice calculations. The typical single-CPU running time on a 2.6 GHz AMD Opteron PC varies from 5 to 20 minutes, when 3 million neutron histories are simulated. Owing to the unionized energy grid approach, the running time is not strongly dependent on the complexity of the material compositions. Compared to fresh fuel calculations, the transport cycle usually slows down by less than a factor of 1.5 when modeling irradiated fuels consisting of 100-250 nuclides.

The situation becomes more complicated in burnup calculation. If the number of depletion zones is large, a significant fraction of CPU time is contributed to data processing between the burnup steps. An LWR assembly burnup calculation involving 65 depleted material regions, 40 burnup steps with predictor-corrector calculation and a total of 3 million active neutron histories per Monte Carlo simulation can be completed in less than 12 hours on a standard single-processor PC workstation. Of this time, about 60% is contributed to the Monte Carlo transport simulation and the remaining part to data processing. The fraction of CPU time spent for solving the depletion equations using the CRAM matrix exponential method is practically negligible.

Parallelization using MPI is an efficient way of reducing the overall calculation time, and the speed-up factor increases almost linearly as a function parallel tasks. It should be noted, however, that the excessive memory usage due to the unionized energy grid approach, together with distributed-memory parallelization using MPI seriously limits the capability to run burnup calculations in parallel mode. This limitation has been overcome in Serpent 2, in which the parallelization is based on hybrid OpenMP / MPI techniques.

Serpent Discussion Forum

Serpent User's Manual
(March 6, 2013)

Base version:

Serpent 1.1.7

Current update:

1.1.19 (April 2, 2013)

Important updates: