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

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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.