Sustainable circular economy is introducing new industrial challenges, including recycling, to move from the cradle-to-grave paradigm to the innovative cradle-to-cradle concept. The core of several recycling systems consists of mechanical comminution, which aims at producing homogeneous mixtures of highly liberated particles. However, the complexity of comminution processes requires adequate models to control and optimize their behavior within the entire recycling system. In the literature, the so-called Population Balance Model has been proposed, which is however limited to the mining industry. In this paper, we examine the applicability of the Population Balance Models in the Waste Electrical and Electronic Equipment recycling industry. In particular, we include the homogeneity and multiplication assumptions, and analyze the impact of the comminution chamber saturation. These simplifications reduce the number of model parameters to be estimated, as the set of parameters remains the same over a wide range of working conditions. We tested our assumptions on a real system for recycling Printed Circuit Boards. Results showed the validity of the multiplication assumption and a marginal effect of saturation (p values for rotor velocity and saturation were always above 25% in an ANOVA with the Bonferroni correction). The homogeneity assumption is also tenable, with the exception of the initial transient, as the null hypothesis of constant output mass distribution under equivalent shredding times was never rejected at the 5% significance level. Outcomes of an out-of-sample validation confirmed the effectiveness of our simplified Population Balance Model (values of the Kolmogorov-Smirnov metric lower than 0.1).

可持续的循环经济正在带来包括回收在内的新的工业挑战，从而从摇篮到摇篮的范例转变为创新的摇篮到摇篮的概念。几种回收系统的核心是机械粉碎，目的是产生高释放颗粒的均匀混合物。但是，粉碎过程的复杂性要求适当的模型来控制和优化其在整个回收系统中的行为。在文献中，已经提出了所谓的人口平衡模型，但是该模型仅限于采矿业。在本文中，我们研究了人口平衡模型在废弃电气电子设备回收行业中的适用性。特别是，我们将均匀性和乘法假设，并分析粉碎室饱和度的影响。这些简化减少了要估计的模型参数的数量，因为在广泛的工作条件下，参数集保持不变。我们在一个实际的印刷电路板回收系统上测试了我们的假设。结果表明乘法假设的有效性和饱和度的边际效应（p在使用Bonferroni校正的ANOVA中，转子速度和饱和度的值始终高于25％）。除初始瞬变外，均质性假设也是成立的，因为在等效的切碎时间下恒定输出质量分布的零假设在5％的显着性水平上从未被拒绝过。样本外验证的结果证实了我们简化的“人口平衡模型”的有效性（Kolmogorov-Smirnov指标的值低于0.1）。