Nuclear Engineering and Design 236 (2006) 669–676 Investigation of bounds on particle packing in pebble-bed high temperature reactors Abderrafi M. Ougouag a,∗ , Jan Leen Kloosterman b,∗ , Wilfred F.G. van Rooijen b , Hans D. Gougar a , William K. Terry a a Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-3885, USA b Delft University of Technology, Faculty of Applied Sciences, Physics of Nuclear Reactors, Mekelweg 15, 2629 JB Delft, The Netherlands Received 6 October 2004; received in revised form 18 December 2005; accepted 19 December 2005 Abstract Models and methods are presented for determining practical limits of the packing density of TRISO particles in fuel pebbles for a pebble-bed reactor (PBR). These models are devised for designing and interpreting fuel testing experiments. Two processes for particle failure are accounted for: failure of touching particles at the pressing stage in the pebble manufacturing process and failure due to inner pressure buildup during irradiation. The second process gains importance with increasing fuel temperature, which limits the particle packing density and the corresponding fuel enrichment. Suggestions for improvements to the models are presented. © 2006 Elsevier B.V. All rights reserved. 1. Introduction The packing fraction of fuel particles within a pebble is an important factor in predicting the performance of the fuel dur- ing normal operation. Determining which packing fraction and which particle size would result in the best performance is an interesting and, so far, unsolved, problem. Yet, it must be tackled before an optimal design can be devised and before a rational testing program can be planned for the fuel from that optimal design. This paper is a first attempt at determining the influence of the packing fraction on the impact of failures of TRISO par- ticles in the 2.5-cm radius fuel zone of a pebble with overall diameter of 6 cm. The upper limit for the packing of TRISO particles in a fuel pebble is dictated by the particle failure rate and the effect of the packing on that failure rate. The performance (i.e., failure or retention of integrity) of fuel particles depends on many factors. The first is the proximity of particles within the pebble. This is because particles that are too close to one another could be damaged during the isostatic pressing stage of the pebble manu- facturing process. The second is the burnup level expected to be ∗ Corresponding authors. E-mail addresses: Abderrafi.Ougouag@inl.gov (A.M. Ougouag), J.L.Kloosterman@tudelft.nl (J.L. Kloosterman). achieved by the fuel within the particle. This factor correlates to the pressure exerted on the silicon carbide (SiC) shell by gaseous fission products and CO. This factor also correlates with the irra- diation damage that invariably accumulates in the SiC layer and with the irradiation-induced shrinkage of the pyrolytic carbon (PyC) layers. See for an extensive descriptions of these effects references Nabielek et al. (2004), Wang et al. (2004), Petti et al. (2004) and Martin (2001). Because of weakening of the SiC (i.e., lowering of its mechanical strength) when subjected to fast neu- tron irradiation at temperatures above 1000 ◦ C, this factor (i.e., the effect of burnup) is sensitive to the fuel temperature history during irradiation. All these artifacts contribute to the failure of the particle. The burnup also correlates to the radiological haz- ard, which in turn enters the definition of the impact of particle failure. The models developed in this work incorporate all of these considerations. In the next section, a proper qualification for the impact of fuel particle failures is discussed and a quantitative measure for it, the “effective impact” of failure, is defined. In Section 3, the models and programs used to calculate the failure rate from proximity are discussed. Section 4 describes a model that relates the packing fraction to the fuel enrichment needed in order to preserve the reactivity of the fuel. Subsequently, the fuel enrichment is related to the final discharge burnup, from which the expected failure rate due to burnup can be derived. 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.12.006