Estimation of the fast neutron fluence at control rod tips using a 3-D diffusion/2-D transport multi-step calculation scheme H. Ferroukhi a, * , J.-M. Hollard a , M.A. Zimmermann a , R. Chawla a,b a Laboratory for Reactor Physics and Systems Behaviour, Paul Scherrer Institute, CH-5232 Villigen, Switzerland b Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland article info Article history: Received 7 October 2008 Received in revised form 30 November 2008 Accepted 2 December 2008 Available online 29 January 2009 abstract This paper presents the development and application of a methodology to estimate, using conventional deterministic lattice/core analysis methods, the fast neutron fluence at the tips of control rods inserted during operation in PWR reactors. The developed methodology is based on a 3-D Nodal Diffusion/2-D Lat- tice Transport multi-step calculation scheme, in which the operating history of the nuclear environment around the tip is tracked in 3-D core follow analyses and used thereafter to provide boundary conditions for 2-D transport calculations to compute the fast neutron flux. In subsequent steps, radial and axial cor- rection factors, both based on fast flux results from the 3-D core simulator, are applied to the calculated 2-D transport flux in order to take into account radial leakage effects as well as axial flux gradients around the tip. The fluence is finally estimated through a time-integration of the corrected 2-D transport fast flux. The developed methodology has been applied to estimate the fluence for a total of 15 control rods, over 21 operating cycles of a Swiss nuclear power plant. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction For PWR operation, Rod Cluster Control Assemblies (RCCAs), consisting of several individual absorber rods, are employed for both short-term reactivity control and reactor shutdown. Referring to the RCCA as Control Rods (CR) in this paper, the CRs in a PWR are usually partially inserted or fully withdrawn during operation. Depending on the core/cycle design, the lower extremity of a fully withdrawn CR is located either just above the top of the active core or actually inside the active core region. Moreover, a given CR is normally employed during several operating cycles and might also be reshuffled between cycles. A CR, and particularly its lower parts, can thus be subject to a considerable amount of neutron fluence during its lifetime. This can affect the CR integrity through princi- pally two phenomena. Firstly, cladding material degradation can occur due to irradiation induced embrittlement (OECD, 1996) of the CR steel components. Secondly, cladding stresses due to absor- ber-clad interactions can result from the swelling of the absorbing material caused by neutron captures (Heins et al., 1992; Bourgoin et al., 1999; Matsuoka et al., 1999). For these reasons, increased rod diameters and cladding cracks/fissures may develop and eventu- ally lead to deformations that could result in control rod obstruc- tion/blockage. This enforces a limitation upon the maximum allowed residence time of a CR for reactor operation and, since this is related to the irradiation to which the CR has been subjected, an accurate method to determine the fast neutron fluence (FNF) is necessary. Another important reason to estimate the CR tip fluence is that the processing of used control rods, prior to their final dis- posal after removal from the reactor, depends partly upon the assessment of irradiation effects on the rod materials. In the above context, and upon request from a Swiss PWR oper- ator, a methodology to estimate the CR tip fluence has been devel- oped at PSI. As primary goal, the procedure is aimed at estimating, for any given CR, the fluence accumulated over several cycles of operation and to compare the results with the procedure currently applied by the plant operator. 2. Methodology 2.1. Scope The use of a higher-order transport method as basis for the methodology was considered more appropriate in terms of accu- racy than, for instance, applying a 2-group diffusion approach (Theiss and Riekert, 2002) for two reasons. Firstly, the neutron flux in the vicinity of a strong absorber region (i.e. with strong flux gra- dients and high flux anisotropy), is of primary interest. Secondly, taking into account the fact that the neutron flux above a certain energy threshold (>0.5 or 1 MeV) needs to be considered, a suffi- ciently fine group structure in the high-energy range is required. In this context, both stochastic methods (e.g. MCNPX) and deter- ministic methods could be used. However, since an accurate full 3-D core depletion analysis over several cycles is called for, an 0306-4549/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2008.12.010 * Corresponding author. E-mail address: Hakim.Ferroukhi@psi.ch (H. Ferroukhi). Annals of Nuclear Energy 36 (2009) 286–291 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene