**2.2.1 Sample geometry preparation**

470 Computational Simulations and Applications

numerical permeability studies are based on analysis made for computationally generated models of porous media (Rasi et al., 1999; Aaltosalmi et. al., 2004; Belov et al., 2004; Holmstad et al. 2005; Lundstrom et al., 2004; Verleye et al., 2005; Verleye et al., 2007). Tomographic reconstructions are increasingly utilised in combination with numerical methods to analyse permeability of porous materials (Manwart et al., 2002; Martys & Hagedorn, 2002; Aaltosalmi et al., 2004; Kutay et al., 2006; Fourie et al., 2007). According to our knowledge, only a few studies are based on analysing the effect of tomographic image properties on numerical permeability results (Aaltosalmi et al., 2004; Holmstad, 2005) The effects of imaging noise, imaging artefacts and the quality of image segmentation on flow permeability found by using direct numerical flow simulation by a specific implementation of finite-difference method (FDM) (Wiegmann, 2007) are studied. The specific surface area of the samples and the features of pore geometry are also analysed. The analyses are done for four different sample types. First, an artificial sample geometry, comprised of hexagonal array of cylinders with known analytical permeability result, is used to analyse the effect of added random noise and edge blurring on the analysis results. Second, CXµT reconstructions of wool fibre web, packaging board and sandstone samples are used to illustrate the effects of different artefact removal and image segmentation methods on permeability results. Finally, the numerically simulated values of flow

permeability are compared with experimental results for the same material.

CXµT is a non-destructive technique for analysing interior features within solid objects and for obtaining digital information of their 3D structure and properties. During the recent decade, the precision of x-ray tomographic imaging techniques have reached the submicrometre resolution and enables analyses of statistical properties of various materials.

Authentic simulation geometries were obtained by utilising CXµT. Both synchrotron -based x-ray beams and conventional x-ray tubes were used as the radiation sources. The adequate resolution and the overall quality of the images depend on the techniques used. In this study, two laboratory scale devices (Sky-Scan 1172 and Xradia Micro XCT-400) based on xray tubes, and a tomographic imaging facility ID19 of the European Synchrotron Radiation

The voxel resolution of the laboratory scale devices can be varied from a few micrometres up to few tens of micrometres. The wool fibre web sample was imaged by SkyScan 1172 device with the voxel resolution of 4.48 µm and the sand stone sample with Xradia Micro XCT-400 with the voxel resolution of 2.10 µm. The packaging board sample was scanned at ESRF beam-line ID19. The imaging set-up used at ID19 facility had the voxel resolution

CXµT imaging is a two phased process. First, a tomographic scanner is utilised to acquire a series of 2D shadowgraphs of a sample from multiple angles. Then, the 3D reconstruction of the sample is computed from the shadowgraphs using special algorithms (Kak & Slaney,

Typical CXµT imaging system is comprised of a light source, optical elements and a camera which all pose certain imaging artefacts (Gonzales & Woods, 2002). Basically, the main

**2. Tomography and image processing** 

**2.1 Tomography imaging of porous samples** 

**2.2 Imaging artefacts and image processing** 

1988). The process involves many sources of artefacts.

Facility (ESRF) were used.

fixed to 0.7 µm.

Representative elementary volumes (REVs) of the sample geometries were cropped out of the full CXµT reconstructions. In this study the REVs were determined in a deterministic way by evaluating the porosity of larger and larger sample volumes always centred on the same image voxel (Drugan & Willis, 1996; Rolland du Roscoat et al., 2007). A REV size thus obtained for the wool fibre web sample was (in XxYxZ -directions, see Fig. 1) 300x300x360 voxels, for the sand stone sample 500x500x500 voxels and for the packaging board sample 450x450x420 voxels.

The sample REVs were filtered by variance-weighted mean filter (Gonzales & Woods, 2002) and later thresholded to yield binary images including the solid material and the pore space. Visualisations of the REVs are presented in Fig. 1.

Fig. 1. Tomographic reconstructions of (a) the wool fibre web, (b) the packaging board and (c) the sandstone samples.
