Compartmental multivariate population balances based on Monte Carlo methods

基于蒙特卡罗方法的区室多元总体平衡

• 批准号: 238540741
• 负责人: Professor Dr.-Ing. Frank Einar Kruis
• 金额: --
• 依托单位: Fachgebiet Nanostrukturtechnik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/238540741?language=en
• 关键词: Compartmental; multivariate; population; balances; based

The size evolution of particles is relevant for many fields of science and engineering such as gas-to-particle conversion processes, combustion processes, material synthesis, flue gas cleaning technology, process engineering etc. The dynamic solution of the particle size distribution can be performed by means of Population Balance Equations (PBEs). The Monte Carlo (MC) method is a stochastic simulation method which solves the PBEs. Its stochastic and discrete nature makes it ideally suited to handle discrete events. In contrast to other methods (like moments method), the MC methods do not require any a priori information of the PSD, such as the shape of the distribution. The MC methods allow the inclusion of other particle properties such as diameter, charge, composition, morphology, etc. (multivariate properties) without additional computational costs - in contrast to sectional methods. The goal of this work is to develop stochastic numerical methods for the simulation of a multivariate disperse phase in the framework of a flowsheet-oriented simulation system based on the sequential modular approach. A compartmental system will be set up in which each compartment contains a large number of simulation particles and in which the MC intercompartmental particle exchange will be done in a probabilistic way, using hopping constraints. Mechanisms which change particle properties in a dynamic flowsheet simulation are nucleation, growth/dissolution, coagulation and breakage. Transport as well as equipment functions such as sieving, mixing, sorting etc. can be simply converted in probability functions modeling the particle flow from one compartment to the other. The MC description of these functions leads to a change in the number of simulation particles, so that strategies are required which readjust the number of simulation particles guaranteeing the desired accuracy. In the first period we concentrated on MC simulation of nucleation in combination with coagulation, whereas in the second period we also included growth/dissolution coupled to the continuous phase. Furthermore, a MC formulation for breakage has been developed and benchmarked. The parallel merging and splitting algorithms developed will be essential for dealing with transport between compartments, planned for the 3rd period. Also a compartmental model of a stirred media mill and crystallization processes will be set up, based on the MC description of the simultaneous coagulation, nucleation, breakage and growth (resp. evaporation). Exemplary flowsheet simulations will be set up for these processes.

颗粒的尺寸演变与许多科学和工程领域相关，例如气体到颗粒的转化过程、燃烧过程、材料合成、烟气净化技术、工艺工程等。颗粒尺寸分布的动态求解可以通过群体平衡方程（PBE）进行。蒙特卡罗（MC）方法是一种求解 PBE 的随机模拟方法。其随机性和离散性使其非常适合处理离散事件。与其他方法（如矩量法）相比，MC 方法不需要任何 PSD 的先验信息，例如分布的形状。与截面方法相比，MC 方法允许包含其他颗粒属性，例如直径、电荷、成分、形态等（多变量属性），而无需额外的计算成本。这项工作的目标是开发随机数值方法，用于在基于顺序模块化方法的面向流程图的模拟系统框架中模拟多元分散相。 将建立一个隔室系统，其中每个隔室包含大量模拟粒子，并且使用跳跃约束以概率方式完成 MC 隔室间粒子交换。在动态流程图模拟中改变颗粒特性的机制是成核、生长/溶解、凝结和破碎。运输以及设备功能（例如筛分、混合、分选等）可以简单地转换为概率函数，对从一个隔室到另一隔室的颗粒流进行建模。这些函数的 MC 描述会导致模拟粒子数量的变化，因此需要重新调整模拟粒子数量的策略来保证所需的精度。在第一阶段，我们专注于成核与凝固相结合的 MC 模拟，而在第二阶段，我们还包括与连续相耦合的生长/溶解。此外，还开发了 MC 破损配方并进行了基准测试。开发的并行合并和分裂算法对于处理第三阶段计划的隔间之间的运输至关重要。此外，基于同时凝结、成核、破碎和生长（或蒸发）的 MC 描述，还将建立搅拌介质磨机和结晶过程的隔室模型。将为这些过程建立示例性流程图模拟。