Abstract—For a quick and accurate calculation of spatial neutron distribution in nuclear power reactors 3D nodal codes are usually used aiming at solving the neutron diffusion equation for a given reactor core geometry and material composition. These codes use a second order polynomial to represent the transverse leakage term. In this work, a nodal method based on the well known nodal expansion method (NEM), developed at COPPE, making use of this polynomial expansion was modified to treat the transverse leakage term for the external surfaces of peripheral reflector nodes. The proposed method was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of this modified treatment of peripheral nodes for practical purposes in PWR reactors. Keywords—Transverse leakage, nodal expansion method, power density, PWR reactors I. INTRODUCTION HE neutron distribution has to be frequently calculated in PWR reactors. This calculation is validated with measured values of reactor parameters. Even the neutron population varies along the reactor operation period depending on time variation of the nuclide distribution, which in turn varies with the spatial distribution of the depletion rate, one is fully justified to use a quasi-static approximation [1], in which the reactor cycle is divided into certain time intervals, during which the neutron fluxes are held constant. Therefore, in this case, the steady state diffusion equation and the depletion equations are solved, for each of the defined time intervals for the reactor operation period.There are a lot of methods to solve the neutron diffusion equation for a given reactor core, but determining factors that affect the quality of a system for calculating the neutronic parameters of the reactor core are the accuracy and speed with which the operational performance of the reactor is predicted. For power reactors, the most popular method is the nodal expansion method (NEM) [2]. An example of application of this method is the CNFR code (Portuguese acronym for National Reactor Physics Code) [3] that consists of three main modules, which generate nuclear data for fuel elements, 3D nuclear power distributions and characteristic parameter calculations of the nuclear reactor. The majority of nodal diffusion codes employ the diffusion equation integrated in a transverse area for given direction. From this integration, the transverse leakage is obtained. Antonio Carlos Marques Alvim, Fernando Carvalho da Silva and Aquilino Senra Martinez are all with Programa de Engenharia Nuclear, COPPE/UFRJ, Av. Horácio Macedo, 2030, Bloco G - Sala 206 - Centro de Tecnologia, Cidade Universitária, Ilha do Fundão, 21941-914 - Rio de Janeiro, RJ - Brazil aalvim@gmail.com, phone:+552125628441,fax:+552125628444 These codes use a second order polynomial to represent the transverse leakage term. CNFR code has also made use of this polynomial expansion for all nodes so far. But there was a motivation to better represent the transverse leakage for the external surface of nodes in the reflector periphery, so that this paper presents a modified treatment of the transverse leakage for these nodes. In section 2, a brief comment on the nodal expansion method (NEM) is presented. Section 3 presents the modified procedure. Section 4 shows results obtained with this modification. Conclusions are presented in section 5. II. NODAL EXPANSION METHOD The reactor core is divided, in space, into contiguous parallelepipeds called nodes. Since NEM requires that the nodes be homogeneous, special models are adopted to deal with cross-sections that are no longer uniform inside the node, due to burnup and control rod motion [4]. With these special models, nodes remain homogeneous and core nodalization, which was previously established, is maintained. The NEM uses partial interface currents and has as its starting point the neutron continuity equation and Fick's Law. The nodal balance equation, from which one obtains average nodal fluxes ) t ( n g ℓ φ for each time ℓ t , results from integration of the continuity equation in the volume n z n y n x n a a a V = of a node n, shown in Figure 1, and subsequent division of the integrated equation by this volume, i.e. ∑ = = φ Σ + - z , y , x u n g n tg n gul n gur n u ) t ( ) t ( )] t ( J ) t ( J [ a 1 ℓ ℓ ℓ ℓ ∑ = ′ ′ ′ ′ φ Σ + Σ ν χ 2 1 g n g n g g n g f eff g ) t ( )} t ( ) t ( k { ℓ ℓ ℓ (1) where the cross sections involving capture and fission, which because of the burnup gradient [5] vary spatially within the node, are given by: ∫ φ Σ φ ≡ Σ n V g xg n g n n xg dV ) t , z , y , x ( ) t , z , y , x ( ) t ( V 1 ) t ( ℓ ℓ ℓ ℓ . (2) Antonio Carlos Marques Alvim, Fernando Carvalho da Silva, Aquilino Senra Martinez Improved Neutron Leakage Treatment on Nodal Expansion Method for PWR Reactors T World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:6, No:3, 2012 228 International Scholarly and Scientific Research & Innovation 6(3) 2012 ISNI:0000000091950263 Open Science Index, Physical and Mathematical Sciences Vol:6, No:3, 2012 publications.waset.org/12424/pdf