# Supplementary data to publication 'Sensitivity of Filter Cake Permeability to Systematic Variations in Particle Shape and Size: A Bottom-Up Stochastic Analysis'

## General Remark ##
This dataset is connected to the a scientific publication with the following **abstract**:
A key question in filtration process design is understanding the filtration properties of a specific particle system. Current methods, like the Carman-Kozeny equation, struggle to accurately predict specific cake resistance and capillary pressure from a given particle size distribution, leading to reliance on limited empirical correlations. This poses challenges for process simulation, as the transition from particle characteristics to filter cake properties remains unclear. 
This work aims to correlate the distribution of multi-dimensional particle properties—both size and shape—with the properties of the resulting 3D filter cake morphology. We use tomographic image data of filter cakes to validate a stochastic 3D model which describes the relationship between particle properties and multi-phase filter cake characteristics using generated virtual particles that statistically resemble the actual data.
These particles are utilized to construct virtual filter cake structures using a forced bias algorithm, which statistically represent actual cake structures. The generated virtual cake structures allow for deriving trends in permeability by systematically varying particle properties virtually.

## X-ray CT Equipment
All X-ray tomography scans were performed using a **Zeiss Xradia Versa 510 micro-CT system**. Voxel size was 3.93 µm, acquired at 4× magnification. Detailed measurement parameter description is given below (**Dataset Structure**). Raw CT gray values are normalized to an 8-bit grayscale range (0–255), representing increasing X-ray attenuation. The normalization is referenced to the global maximum gray value across all measurements to ensure consistent scaling between datasets. A higher bit depth (e.g., 16-bit) is not appropriate, as most particles contain insufficient voxel counts to justify a larger number of classes. Excessive binning leads to over-binning, causing fragmented bins, increased noise, and reduced interpretability of the gray value distribution.

## Sample Material
The feed materials for the filtration experiments are (datasheets in dataset included):
- glass beads, commercially available from Sigmund Lidner GmbH (datasheet: https://www.sili.eu/wp-content/uploads/2025/03/9001-2-F-SiLibeads-Glas-AIR-Hohlglaskugel-Online-2025-02-05.pdf).
- quartz sand BCS211, commercially available from Strobel Quarzsand GmbH (datasheet: https://www.strobel-quarzsand.de/media/BCS211.pdf).

## Dataset Structure
The dataset includes nine different measurements of filter cake samples: 

- **quartz_system1_sample1** (quartz particles)
  - filter cake built from feed particle size distribution of quartz particles 40...315 µm

- **quartz_system1_sample2** (quartz particles)
  - filter cake built from feed particle size distribution of quartz particles 40...315 µm

- **quartz_system2_sample1** (quartz particles)  
  - filter cake built from monomodal particle size distribution of quartz particles 90...125 µm

- **quartz_system2_sample2** (quartz particles)
  - filter cake built from monomodal particle size distribution of quartz particles 90...125 µm

- **quartz_system3_sample1** (quartz particles) 
  - filter cake built from bimodal particle size distribution of quartz particles 40...90 µm and 160...315 µm

- **quartz_system3_sample2** (quartz particles)
  - filter cake built from bimodal particle size distribution of quartz particles 40...90 µm and 160...315 µm

- **glass_system1_sample1** (glass beads) 
  - filter cake built from feed particle size distribution of glass particles 40...230 µm

- **glass_system2_sample1** (glass beads) 
  - filter cake built from monomodal particle size distribution of glass particles 90...100 µm

- **glass_system3_sample1** (glass beads) 
  - filter cake built from bimodal particle size distribution of glass particles 40...75 µm and 125...230 µm

These samples were created by an in-situ filtration unit with 5 mm diameter. More information about the in-situ unit can be found here: https://doi.org/10.1016/j.powtec.2019.12.054.

## Reconstructed raw tomograms
For each filter cake, the dataset contains reconstructed image stacks:
- **Files for each measurement:**  
  - `image_stack.h5` – HDF5-file of image stack
  - `parameters.PNG` – screenshot of acquisition and reconstruction parameters  
  - `insitu.PNG` – screenshot of one projection of sample  
  - `overview.PNG` – representative slice and rendered 3D visualisation of sample for quick overview  

These datasets provide the basis for particle segmentation and artifical filter cake modelling.

## Artifical cake structures
Additionally, the generated and analyzed artificial structures of the filter cakes are also attached in the folder 'variation_study_artifical_cake_structures.zip'.
The structures are grouped into folders that specify the grid point on the 5-dimensional parameter grid, with four realizations each for the different packing densities or porosities. The image data consists of 16-bit images, with each particle having its own label.