One way of solving population balance model (PBM) in a time efficient way is by means of discretisation of the population property of interest. A computational grid, for example, ( is the volume of particle in class ), could be used to classify the particles in discretisation techniques. However, there are still disagreements in the appropriate number of classes divided by the grids. In this study, the different numbers of classes for solving PBM were compared in terms of accuracy and performance to describe the particle size distribution (PSD) from the flocculation of activated sludge. It is found that the simulated PSDs are similar to the experimental data for all the geometric grids , and there is no obvious difference among the values of calibrated parameter, ratio of breakage rate coefficient and collision efficiency, for each velocity gradient. However, the simulation results with less error could be obtained with larger number of classes, and more computational times, which show exponential relationship with the number of classes, are needed. Considering numerical accuracy and efficiency, the classes 35 or a geometric grid with factor 1.6, aligning with the Fibonacci sequence , is recommended for the particles in the size range of 5.5~1086 μm.

中文翻译：

---

人口平衡模型离散求解方法中不同类数的准确性和性能比较

一种以时间高效的方式解决人口平衡模型（PBM）的方法是通过离散化感兴趣的人口属性。例如，可以使用计算网格（是类中粒子的体积）在离散化技术中对粒子进行分类。但是，在划分网格的适当数量的类上仍然存在分歧。在这项研究中，从准确性和性能方面比较了用于解决PBM的不同类别，以描述活性污泥絮凝的粒径分布（PSD）。结果发现，仿真的PSD与所有几何网格的实验数据相似。，对于每个速度梯度，标定参数值，破损率系数比和碰撞效率之间没有明显差异。然而，使用更多的类可以得到误差较小的仿真结果，并且需要更多的计算时间来显示与类的数量呈指数关系。考虑数值精度和效率，类35或与因子1.6的几何网格，与斐波那契数序列对准，被推荐用于在5.5〜1086的尺寸范围内颗粒 μ米。