**4.2.1 Effect of artefacts on fluid flow permeability**

Visualisations of wool fibre web sample with different threshold values are shown in Fig. 12. The sample geometries in (a) – (c) were denoised and then binarised using grey value based threshold (Gonzales & Woods, 2002). At the lowest threshold levels (a) and (b), the noise is clearly visible in the void space. While threshold value was gradually increased, the noise became less evident and the thickness of the fibres (or size of the solid particles) diminished. The sample geometry in Fig. 12d was segmented utilising the forest fire method. The forest fire method was found to give noise free pore space and a fibre radius that corresponded well with the mean value obtained from scanning electron microscope images, 20 µm.

Fig. 12. Visualisation of segmented wool fibre web sample at different threshold values: (a) 20, (b) 30 and (c) 40, and with the forest fire method (d).

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Structural Analysis and Numerical Permeability Simulations 483

Fig. 13. (b)

(c)

Fig. 13. Numerically solved permeability coefficients for the wool fibre web (a), the packaging board (b) and the sand stone (c) as a function of threshold value. Experimental

results are given as an average of the five measurements for each sample types.

Grey value -based thresholding procedure with different threshold values were conducted for all the three tomographic sample types. Numerical fluid flow permeability analyses were conducted for all the geometries and the obtained values were compared with experimental results, see Fig. 13.

As an example, for the wool fibre web, the "optimal" threshold value would have been between 20 and 30, see Fig. 13a. By visually examining the corresponding images, it was found that there was still noise left in flow channels at threshold value 30. Permeability at the optimal threshold value would not have been result of the realistic sample geometry, but combination of noise causing higher specific surface area and thinner fibres increasing the porosity of the geometry. The results were found qualitatively similar for the packaging board and the sand stone samples.

The forest fire method was found to be efficient tool for segmentation procedure. Numerical permeability values for the geometries segmented by the forest fire method were 2.5E-11 m2, 4.8E-14 m2 and 2.5E-12 m2 for the wool fibre web, the packaging board and the sand stone samples, respectively. Corresponding experimental measurement results for the samples were 2.5E-11 m2, 5.1E-14 m2 and 2.5E-12 m2. The maximum difference between the experimental results and the numerical permeability values found by using the forest fire segmented sample geometries was in these cases less than 6.5 %. The statistical uncertainty of the experimental results was 20%.

The numerical permeability results for the samples with different added noise levels (proportion of false voxels) are shown in Fig. 14. Artificial noise levels were generated into the sample geometries which were segmented by the forest fire method. The effect of noise on permeability was found to be qualitatively similar as for the hexagonal cylinder array. Increase in noise level caused decrease in fluid flow permeability value.

Grey value -based thresholding procedure with different threshold values were conducted for all the three tomographic sample types. Numerical fluid flow permeability analyses were conducted for all the geometries and the obtained values were compared with experimental

As an example, for the wool fibre web, the "optimal" threshold value would have been between 20 and 30, see Fig. 13a. By visually examining the corresponding images, it was found that there was still noise left in flow channels at threshold value 30. Permeability at the optimal threshold value would not have been result of the realistic sample geometry, but combination of noise causing higher specific surface area and thinner fibres increasing the porosity of the geometry. The results were found qualitatively similar for the packaging

The forest fire method was found to be efficient tool for segmentation procedure. Numerical permeability values for the geometries segmented by the forest fire method were 2.5E-11 m2, 4.8E-14 m2 and 2.5E-12 m2 for the wool fibre web, the packaging board and the sand stone samples, respectively. Corresponding experimental measurement results for the samples were 2.5E-11 m2, 5.1E-14 m2 and 2.5E-12 m2. The maximum difference between the experimental results and the numerical permeability values found by using the forest fire segmented sample geometries was in these cases less than 6.5 %. The statistical uncertainty

The numerical permeability results for the samples with different added noise levels (proportion of false voxels) are shown in Fig. 14. Artificial noise levels were generated into the sample geometries which were segmented by the forest fire method. The effect of noise on permeability was found to be qualitatively similar as for the hexagonal cylinder array.

Fig. 13. (a)

Increase in noise level caused decrease in fluid flow permeability value.

results, see Fig. 13.

board and the sand stone samples.

of the experimental results was 20%.

Fig. 13. Numerically solved permeability coefficients for the wool fibre web (a), the packaging board (b) and the sand stone (c) as a function of threshold value. Experimental results are given as an average of the five measurements for each sample types.

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Structural Analysis and Numerical Permeability Simulations 485

(c)

packaging board (b) and the sand stone (c) as a function of noise level. Experimental results

Specific surface area of the wool fibre web sample was analysed as a function of threshold value and noise level, see the results in Fig. 15. The specific surface area of the geometry thresholded by the forest fire method had a value of 0.175 m-1. The value of specific surface area of the sample geometry decreased as a function of increasing threshold value and increased as a function of increasing noise level. According to Eq. (3), when a sample geometry has a high specific surface area, it has a small permeability value. This could also

Pore size distribution of the wool fibre web sample geometry was analysed as a function of threshold value, see the results in Fig. 16a. When compared to the experimental permeability results, the optimal threshold value was found to be between 20 and 30, see Fig. 13a. The results in Fig. 16a clearly show that with the threshold values of 20 or 30 the pore size distribution differs highly from the pore size distribution of the geometry that was segmented using the forest fire method. These results support the interpretation related to the permeability values obtained using the geometries segmented by conventional grey value -based thresholding. Combination of too high specific surface area and too thin fibres (high porosity) resulted to the permeability values very close to the experimental results. These interpretations were found to be similar for the packaging board and for the sand

Pore size distribution as a function of noise level for the wool fibre web sample is presented in Fig. 16b. The effect of added noise was found to be not as high as for the hexagonal array of cylinders, see Fig. 7. For noise level of 2 %, the mode value of the distribution was

Fig. 14. Numerically solved permeability coefficients for the wool fibre web (a), the

**4.2.2 Effect of artefacts on specific surface area and pore size distribution** 

are given as an average of the five measurements for each sample types.

be seen from the results in Fig. 15 and in Figs 13a and 14a.

approximately a half of the mode value of the noise free geometry.

stone samples also.

Fig. 14. (a)

Fig. 14. (b)

Fig. 14. (a)

Fig. 14. (b)

Fig. 14. Numerically solved permeability coefficients for the wool fibre web (a), the packaging board (b) and the sand stone (c) as a function of noise level. Experimental results are given as an average of the five measurements for each sample types.
