Development of multivariant structure and process models for filter cakes, combining experimental methods of process engineering with digital computer based methods.

过滤过程设计中的一个核心问题仍然是：给定粒子系统的过滤特性是什么？目前的技术水平，如已建立的卡门-科泽尼方程，不能以技术上足够的精度计算特定的饼阻力或毛细压力分布形成给定的粒度分布。这就是为什么在这个领域中仍然有一些经验的相关性，这些相关性只在一个小的定义领域中有效，因此不能被视为普遍有效。因此，在过程模拟的背景下，不可能实现从颗粒属性到相应孔隙系统（即相应滤饼）属性的步骤。该项目的目的是多维颗粒特性分布的相关性，其中颗粒大小和颗粒形状都被视为分布特性，以及由这些颗粒构建的滤饼的3D形态的特性分布。弯曲度和孔隙大小是分布饼性质的例子。为此，实验过程工程的方法与基于数字计算机的方法相结合。分析颗粒表征以及所研究的颗粒系统和所得滤饼结构的层析成像数据可作为使用参数随机模型表征颗粒特性和两相或三相滤饼结构的三维形态的基础。一方面，采用参数耦合方法对多相滤饼系统的颗粒性质向量（如粒径和形状特征）的多维分布和特性进行建模；另一方面，参数化3D结构模型经过校准，然后可以生成虚拟3D粒子或多相滤饼结构，即所谓的数字双胞胎，在统计意义上等同于层析图像数据。copula模型和3D结构模型的描述都只有几个参数，这可以有效地表征潜在的颗粒和孔隙系统。然后使用回归技术确定传递函数，将描述粒子系统的模型参数映射到描述滤饼结构的模型参数上。通过这种方式，仅从多维颗粒特性的潜在（多元）概率分布的知识就可以预测滤饼的过程行为（例如脱水，滤饼洗涤，分散）。

A central question in the design of filtration processes still is: what are the filtration properties of a given particle system? The state of the art, like the established Carman-Kozeny-equation, is not capable to calculate with technically sufficient accuracy the specific cake resistance or the capillary pressure distribution form a given particle size distribution. That is why there are still several empirical correlations in this field, which are only valid in a small field of definition and which therefore cannot be seen as universally valid. In the context of process simulation it is therefore not possible to implement the step from particle properties to the properties of the corresponding pore system, i.e. the corresponding filter cake. The aim of this project is the correlation of the distribution of multi-dimensional particle properties, where both the particle size and the particle shape are regarded as distributed properties, with the distribution of properties of the 3D morphology of the filter cake built up from these particles. Tortuosity and pore size are examples for distributed cake properties. For this purpose, methods from experimental process engineering are combined with digital computer-based methods. Analytical particle characterization as well as tomographic image data of the investigated particle systems and of the resulting filter cake structures serve as the basis for characterizing the particle properties and the 3D morphology of two- or three-phase filter cake structures using parametric stochastic models. On the one hand, the multi-dimensional distribution of particle property vectors (e.g. particle size and shape characteristics) and the properties of the resulting multi-phase filter cake system are modeled with parametric copula approaches. On the other hand, parametric 3D structure models are calibrated, which can then generate virtual 3D particles or multi-phase filter cake structures, so-called digital twins, that are equivalent in a statistical sense to the tomographic image data. Both copula models and 3D structure models are described with only a few parameters, which enables efficient characterization of the underlying particle and pore systems. Then regression techniques are used to determine transfer functions, which map parameters of the models describing the particle systems onto the model parameters describing the filter cake structure. In this way, it will become possible to predict the process behavior (e.g. de-watering, cake washing, dispersion) of a filter cake, solely from the knowledge of the underlying (multivariate) probability distribution of multi-dimensional particle properties.