Nuclear Engineering and Design 187 (1999) 327 – 337 Simulation of isothermal fission gas release An analytical solution Martı ´n Maldova ´n 1 , Alicia Denis *, Rosa Piotrkowski 2 Unidad de Actiidad Combustibles Nucleares, Comisio ´n Nacional de Energı ´a Ato ´mica, A. del Libertador 8250, (1429) Buenos Aires, Argentina Received 20 April 1998; received in revised form 7 September 1998; accepted 6 November 1998 Abstract An analytical version of a previous diffusion model representing fission gas release during isothermal irradiation of UO 2 nuclear fuel is presented. The previous numerical version was successfully applied to a variety of experiments. The present model, although based on more restrictive assumptions, gives a quick but sufficiently accurate estimation, useful to predict experiments or more detailed calculations. The main new hypotheses are: constant fuel grain radius, constant gas generation rate and constant grain boundary gas content. The latter is met at the final stage of fuel irradiation, after grain boundary saturation, and partially met at the beginning of irradiation, when the grain boundary is nearly empty. Two analytical solutions are obtained and conveniently matched, yielding a unique solution representing the whole process. The difference between the analytical and numerical results for the fractional release is appreciable only near the matching. It is lower than 1% over 93% of the process duration for all the temperatures tested, ranging from 1250 to 2000 K and has no significant effect on the results at the end of life. © 1999 Elsevier Science S.A. All rights reserved. 1. Introduction During irradiation of UO 2 nuclear fuels, several types of fission products are born, among them different isotopes of the noble gases Xe and Kr. Their almost complete insolubility in the UO 2 matrix is responsible for the formation of small gas bubbles (in the nanometer range) within the fuel grains. Diffusion, especially significant in the hotter region of the fuel, causes accumulation of gases in the grain boundaries, where larger bub- bles (in the micrometer range) are formed. Both types of bubbles are bombarded by the highly energetic fission fragments traveling in the fuel element. The gas content of a broken intragranu- lar bubble is dispersed in the fuel matrix; the gas atoms turn back to participate in the diffusion process and consequently give origin to a dynami- cal solubility higher than that predicted by the equilibrium conditions. At the same time, the * Corresponding author. Tel.: +54-1-7547241; fax: +54-1- 7547345; e-mail: denis@cnea.edu.ar. 1 Present address. FUDETEC, Center for Industrial Re- search, L.N.Alem 1067, (1001) Buenos Aires, Argentina. 2 Present address. Escuela de Ciencia y Tecnologı ´a, Univer- sidad Nacional de Gral. San Martı ´n, Calle 91 N°3391, (1653) Villa Ballester, Pcia. de Buenos Aires, Argentina. 0029-5493/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII:S0029-5493(98)00299-4