The formation of compressible filter cakes under constant pressure has been the subject of many studies, as it is important for the determination of filtration resistances for use in scale-up calculations. Often, the model equations of Tiller et al. are used that describe the relationship between cake resistance, compressive stress, and porosity as a power law model.

In this talk, we argue that the Tiller equations may not be the most appropriate ones for the description of cake filtration experiments. First, a curious case of filtration experiments is shown in which filter cakes expand at higher pressures in the common constant-pressure laboratory setup.

Secondly, several approaches for the description of compressible cake behavior are described, resulting in a set of possible simulation models for the filtrate flow curve over time. One of these approaches is that of Tiller, with two more models describing the decrease of pressure drop in newly formed cake layers over time and the decrease in filtrate flow as physical reasons for the compression of cake layers over time.

Finally, simulation results are shown, which were fit to experimental filtrate flow curves. It is explained that several different physical processes can lead to an uneven build-up of porosity over the length of the filter cake...