We have developed, implemented and validated 1D and 2D population balance models (PBMs) in the open-source process simulator CADET. 1D PBMs incorporate the particle size as an internal coordinate and are associated with dynamic mass balances to describe particle-based processes in batch and continuous stirred tank reactors. 2D PBMs include the spatial position as an additional external coordinate to describe particulate systems in dispersive plug flow reactors. Along with particle nucleation and growth, growth rate dispersion is considered. Using the finite volume method, cell face fluxes are reconstructed by upwind, Koren and two weighted essentially non-oscillatory (WENO) schemes. Analytical Jacobians are derived to reduce runtime. The implementations utilize arbitrary grids in the internal coordinate. The implementations are validated and benchmarked using seven test cases. The L1 error norm, L1 error convergence rate, and moments up to sixth order are analyzed. Runtime and approximation errors are reported and discussed in detail.

我们在开源流程模拟器 CADET 中开发、实施并验证了 1D 和 2D 群体平衡模型 (PBM)。一维 PBM 将颗粒尺寸作为内坐标，并与动态质量平衡相关联，以描述间歇式和连续搅拌釜反应器中基于颗粒的过程。 2D PBM 包括空间位置作为附加外部坐标来描述分散活塞流反应器中的颗粒系统。除了颗粒成核和生长之外，还考虑生长速率分散。使用有限体积法，通过逆风、Koren 和两个加权基本非振荡 (WENO) 方案重建单元面通量。派生分析雅可比行列式是为了减少运行时间。该实现利用内部坐标中的任意网格。使用七个测试用例对实现进行了验证和基准测试。分析了 L1 误差范数、L1 误差收敛率和六阶矩。详细报告并讨论了运行时和近似误差。