The description of intra-granular fission gas behaviour is a fundamental part of any model for the prediction of fission gas release and swelling in nuclear fuel. In this work we present a model describing the evolution of intra-granular fission gas bubbles in terms of bubble number density and average size, coupled to gas release to grain boundaries. The model considers the fundamental processes of single gas atom diffusion, gas bubble nucleation, re-solution and gas atom trapping at bubbles. The model is derived from a detailed cluster dynamics formulation, yet it consists of only three differential equations in its final form; hence, it can be efficiently applied in engineering fuel performance codes while retaining a physical basis. We discuss improvements relative to previous single-size models for intra-granular bubble evolution. We validate the model against experimental data, both in terms of bubble number density and average bubble radius. Lastly, we perform an uncertainty and sensitivity analysis by propagating the uncertainties in the parameters to model results.

颗粒内裂变气体行为的描述是预测核燃料中裂变气体释放和溶胀的任何模型的基础部分。在这项工作中，我们提出了一个模型，该模型根据气泡数密度和平均尺寸以及与气体释放到晶界之间的关系来描述颗粒内裂变气泡的演化。该模型考虑了单个气体原子扩散，气泡成核，再溶解和气泡中气泡捕获的基本过程。该模型是从详细的群集动力学公式得出的，但是它仅包含三个最终形式的微分方程。因此，它可以在保留物理基础的情况下有效地应用于工程燃料性能规范中。我们讨论了相对于以前的单一尺寸模型进行颗粒内气泡演化的改进。我们根据气泡数密度和平均气泡半径方面的实验数据验证了该模型。最后，我们通过传播参数中的不确定性以对结果进行建模来执行不确定性和敏感性分析。