Particle systems and bulk structures, such as a filter cake, are composed of a multitude of individual particles that exhibit diverse properties. Consequently, they are described by probability distributions. However, as often only equivalent parameters are measured, only a limited number of measurement methods are able to resolve several properties simultaneously in a particle-discrete manner, i.e., to generate an information vector of its properties for each particle. In this context, three-dimensional imaging techniques offer a distinct advantage, enabling the determination of multivariate distributions. Modern optical measurement techniques, such as X-ray microscopy, are capable of generating large image data sets, which can greatly enhance the information yield for process engineering studies [1-3].

In process models, this information is often reduced to a discrete absolute value, which is only able to quantify the particle system or the resulting property function to a limited extent. A review of the literature reveals that the resulting integral parameters are not sufficient to describe or model process engineering effects in sufficient detail [4-6].

The use of distributions is also required in cake filtration, particularly given that the structure of the cake is described by parameters that are also distributed. These include pore diameter, tortuosity, number of contact points, volume of isolated liquid clusters, capillary pressure, contact angle and local porosity.

The objective is to correlate distributed multidimensional particle properties, such as particle size and shape distribution, with distributed parameters of the 3D morphology of the pore space composed of these particles. This is to be achieved by combining experimental process engineering with digital computational methods.

However, the variety of available tomographic image data is often insufficient to permit the reliable determination of transfer functions. One approach resolving this issue is to expand the database through the use of model-based simulation of virtual, yet realistic, filter cake structures.

The initial step is to utilize a stochastic modelling approach to generate the virtual filter cakes, whereby the model parameters are calibrated and validated utilizing tomographic image data. The model simulates two distinct particle systems, namely glass beads and crushed quartz particles, by generating artificial particles of irregular shape utilizing mixed Gaussian random fields on a sphere. These are then spatially arranged to form a three-dimensional artificial filter cake, which is validated with respect to geometric descriptors not used for model fitting, such as constrictivity, porosity, tortuosity and specific surface area.

A broad spectrum of virtual 3D filter cake structures will be ...