Development of burnup methods and capabilities in Monte Carlo code RMC Ding She a , Yuxuan Liu a , Kan Wang a,⇑ , Ganglin Yu a , Benoit Forget b , Paul K. Romano b , Kord Smith b a Department of Engineering Physics, Tsinghua University, Beijing 100084, China b Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA article info Article history: Received 16 April 2012 Received in revised form 25 July 2012 Accepted 29 July 2012 Available online 13 October 2012 Keywords: Monte Carlo Burnup Full-scale RMC abstract The Monte Carlo burnup calculation has always been a challenging problem because of its large time con- sumption when applied to full-scale assembly or core calculations, and thus its application in routine analysis is limited. Most existing MC burnup codes are usually external wrappers between a MC code, e.g. MCNP, and a depletion code, e.g. ORIGEN. The code RMC is a newly developed MC code with an embedded depletion module aimed at performing burnup calculations of large-scale problems with high efficiency. Several measures have been taken to strengthen the burnup capabilities of RMC. Firstly, an accurate and efficient depletion module called DEPTH has been developed and built in, which employs the rational approximation and polynomial approximation methods. Secondly, the Energy-Bin method and the Cell-Mapping method are implemented to speed up the transport calculations with large num- bers of nuclides and tally cells. Thirdly, the batch tally method and the parallelized depletion module have been utilized to better handle cases with massive amounts of burnup regions in parallel calcula- tions. Burnup cases including a PWR pin and a 5  5 assembly group are calculated, thereby demonstrat- ing the burnup capabilities of the RMC code. In addition, the computational time and memory requirements of RMC are compared with other MC burnup codes. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Owing to its advantages in modeling problems without complex meshing and generation of multi-group cross-sections, the Monte Carlo (MC) method is becoming widely used in the field of transport calculations in reactor physics. It is natural then that there is considerable interest in burnup calculations using the MC method as evidenced by the volume of recent work on this to- pic. Compared with deterministic burnup analysis, MC burnup analysis uses more accurate models of continuous energy and arbitrary geometry without resort to energy and spatial averaging of neu- tron cross-sections, but the large computational time required to obtain reasonable statistics can limit its application in practice. Fortunately, with the development of computer hardware and especially the trend towards increasing parallelism and concur- rency, it may soon be possible to perform full-scale assembly or core burnup calculations using MC transport codes as determinis- tic transport codes do currently. The MC burnup calculation couples a series of MC transport cal- culations and point-burnup (referred to as ‘‘depletion’’ in this paper for clarity) calculations. The depletion calculation uses the neutron flux and cross-sections tallied by the MC transport calcu- lation as input to generate the nuclide inventory at the next time step. Some of the MC burnup codes, such as MVP-BURN (Okumura et al., 2005), and SERPENT (Leppänen, 2012), have built-in deple- tion modules. Many others, such as MOCUP (Moore et al., 1995), MONTEBURNS (Holly, 1998), MCODE (Xu, 2003), and MCBurn (Yu, 2002), are usually external wrappers between the MC codes, e.g. MCNP (X-5 Monte Carlo Team, 2003), and the depletion codes, e.g. ORIGEN-2 (Croff, 1980). Though the explicit coupling tech- nique is convenient from an implementation standpoint, it has to spend extra time on file I/O and therefore somewhat decreases the efficiency. The RMC code (Wang et al., 2011) is a newly devel- oped MC code with a built-in depletion module aimed at the effi- cient burnup calculation of large-scale problems. To strengthen RMC’s burnup capabilities, a number of measures, which will be introduced in Sections 2–4, have been taken to improve both the MC module and the depletion module. Firstly, a new depletion module called DEPTH is developed and implemented, to replace the ORIGEN-2.1 module which was for- merly coupled (She et al., 2011) in the RMC code. The DEPTH module is able to handle detailed depletion chains containing thousands of isotopes at an extremely fast speed with accuracy owing to its advanced matrix-exponential solvers including the ra- tional approximation methods (Pusa, 2011) and the Laguerre poly- nomial approximation method (She et al., 2012). Numerical results of several depletion cases have shown that the DEPTH module is more accurate and efficient than the formerly embedded depletion module. 0306-4549/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2012.07.033 ⇑ Corresponding author. Tel.: +86 10 62783087; fax: +86 10 62782658. E-mail address: wangkan@mail.tsinghua.edu.cn (K. Wang). Annals of Nuclear Energy 51 (2013) 289–294 Contents lists available at SciVerse ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene