**4.1.1 Effect of noise**

Visualisations of flow speed field of four hexagonal arrays of cylinders having different levels of noise are shown in Fig. 4. The noise levels are defined as percentage of the faulty voxels of the total volume of the sample.

Fig. 4. Visualisation of flow speed field of four hexagonal arrays of cylinders having different levels of noise: (a) 0 %, (b) 0.05 %, (c) 0.3 % and (d) 5 %. Flow direction is in these cases from top to bottom. Red and yellow colours represent high flow speed and green and blue low flow speed.

We proceeded in two steps. First, we used a numerical method to find values of permeability for fibrous porous media based on regular hexagonal array of cylinders. The numerical results thus obtained were compared with the analytical results found in the literature. In the second step, we used the numerical method to find values of permeability coefficient for the wool fibre web, packaging board and sandstone samples. These results were compared with the experimental results obtained by using the PMD (Koivu et al.,

Artificial sample geometries of hexagonal arrays of cylinders were prepared to test and demonstrate the effect of different imaging artefacts on structure and numerical fluid flow analysis. The volume size of the simulation geometries were 693 x 400 x 100 pixels and the

Visualisations of flow speed field of four hexagonal arrays of cylinders having different levels of noise are shown in Fig. 4. The noise levels are defined as percentage of the faulty

**4. Results** 

2009a; Koivu et al., 2009b).

porosity of the cylinder arrays was selected to be 50 %.

(a) (b)

(c) (d)

Fig. 4. Visualisation of flow speed field of four hexagonal arrays of cylinders having different levels of noise: (a) 0 %, (b) 0.05 %, (c) 0.3 % and (d) 5 %. Flow direction is in these cases from top to bottom. Red and yellow colours represent high flow speed and green and

voxels of the total volume of the sample.

**4.1 Regular arrays** 

**4.1.1 Effect of noise** 

blue low flow speed.

Numerically analysed permeability values and corresponding (noise free) analytical value by Drummont & Tahir (1984) are shown in Fig. 5. According to the results, even a small amount of noise has a drastic influence on fluid flow permeability.

Fig. 5. Numerically solved permeability values for the hexagonal array of cylinders as a function of noise level. For comparison, analytical value for noise free geometry is also given (Drummont & Tahir, 1984).

The effect of noise on specific surface area was evaluated as a function of noise level, see Fig. 6. The specific surface areas were analysed utilising the marching cubes algorithm (Lorensen & Clive, 1987a; Lorensen & Clive, 1987b). Increase in the amount of noise increases the specific surface area of the simulation geometry and thus decreases the permeability value, see Eq. (3).

Fig. 6. Dimensionless specific surface area as a function of noise level for the hexagonal array of cylinders.

The Effect of Tomography Imaging Artefacts on

image processing methods (b).

(Drummont & Tahir, 1984).

small effect on the pore size distribution, see Fig. 11.

Structural Analysis and Numerical Permeability Simulations 479

Fig. 8. Visualisations of artificially generated edge roughness on the hexagonal array of cylinders (a) and edge roughness on reconstruction of wool fibre web caused by CXµT and

Fig. 9. Numerically solved permeability values for the hexagonal array of cylinders as a function of edge roughness level. Analytical value for noise free geometry is also given

Edge roughness on solid-void boundary increases the specific surface area of the sample and therefore decreases the permeability value, see Figs 9 and 10. Edge roughness has only

The effect of noise on pore size distribution was evaluated as a function of noise level, see Fig. 7. The pore size distributions were determined with the so-called sphere fitting algorithm. In the sphere fitting method, the pore space is filled by non-overlapping spheres. The distribution of the radii gives estimation for the pore size distribution (Wu et al., 2007). The pore size distribution was found to change dramatically as a function of noise level. The mode value of the distribution of the geometry with the noise level of 0.01 % was approximately one third of the mode value for the noise free geometry.

Fig. 7. Normalized pore size distribution for the hexagonal array of cylinders as a function of pore size in pixels with different noise levels.
