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中心问题仍然是：给定颗粒系统的过滤特性是什么？与已建立的Carman-Kozeny方程一样，目前的技术水平不能以技术上足够的精度计算给定粒度分布的比滤饼阻力或毛细压力分布。这就是为什么在这一领域仍然有几个经验相关性，它们只在很小的定义领域内有效，因此不能被视为普遍有效。因此，在工艺模拟的背景下，不可能实现从颗粒特性到对应的孔系统的特性的步骤，即对应的滤饼。该项目的目的是将多维颗粒特性的分布与由这些颗粒构成的滤饼的三维形态的特性分布相关联，其中，颗粒大小和颗粒形状都被视为分布特性。曲折度和孔径大小是分布滤饼特性的例子。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。分析的颗粒表征以及所研究的颗粒系统和所产生的滤饼结构的层析图像数据是使用参数随机模型来表征两相或三相滤饼结构的颗粒特性和3D形态的基础。一方面，用参数Copula方法对颗粒特性向量(如颗粒大小和形状特征)的多维分布以及所得到的多相滤饼系统的特性进行建模。另一方面，校准参数3D结构模型，其然后可以生成在统计意义上等同于断层图像数据的虚拟3D颗粒或多相滤饼结构，即所谓的数字孪生。Copula模型和3D结构模型都只用几个参数来描述，这使得能够有效地表征底层的颗粒和孔隙系统。然后使用回归技术来确定传递函数，该传递函数将描述粒子系统的模型的参数映射到描述滤饼结构的模型参数。这样，仅根据多维颗粒属性的潜在(多变量)概率分布的知识，就可以预测滤饼的过程行为(例如，脱水、滤饼清洗、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.