**5. Conclusions**

Approximate factors of how certain levels of noise and edge roughness effect on permeability value, mode value of pore size distribution and specific surface area of the hexagonal array of cylinders are summarised in Table 1. According to the results, even a small amount (0.01 % of sample volume) of noise in the void space has a drastic influence on the permeability values. The noise level of few percent caused magnitudes decrease in the permeability values. Increase in the amount of noise increases the specific surface area of the simulation geometry and thus decreases the permeability value. Also the pore size

The Effect of Tomography Imaging Artefacts on

decreased approximately by a factor of 0.5.

mode value for the noise free geometry.

the forest fire method.

Mode value of pore

Mode value of pore

the forest fire segmented geometry.

Structural Analysis and Numerical Permeability Simulations 489

Pore size distributions of the tomographic geometries were analysed as a function of threshold value. Although fluid flow analyses based on geometries segmented by grey value -based segmentation method might result in approximately correct permeability values, the structure of the pore geometry does not necessarily correspond with the realistic case. According to the results, the pore size distributions based on the grey value segmented geometries differ from the distributions based on geometries which were segmented using

The forest fire segmented tomographic reconstructions were used in studying the effect of noise on tomographic geometries. Results in these cases indicate that the permeability results of tomographic geometries are not as sensitive to noise as in the case of regular hexagonal cylinder arrays. By increasing the noise level to 2 %, the permeability results

The effect of noise level on pore size distribution was analysed. The effect of added noise on tomographic reconstructions is not as drastic as in the case of the hexagonal cylinder arrays. With the noise level of 2 %, the mode value of the distribution is approximately a half of the

The results indicate that effective methods for handling imaging artefact removal and segmentation are essential for obtaining reliable results for structural and transport properties by means of direct numerical analyses based on CXµT reconstructions of the 3D structure of complex porous materials. According to our studies, the most essential factor for successful structural analysis and flow simulation is the quality of the tomographic reconstruction, i.e. noiseless and realistic structure. To achieve this requirement, a well controlled image acquisition and a good segmentation algorithm together with a verification based on a characteristic parameter, e.g. the mode value of pore size distribution measured by an independent method like mercury intrusion porosimetry or average characteristic

> Error in threshold value + 20 grey values

Noise level 2 % Noise level 5 % Noise level 10 %

Error in threshold value + 30 grey values

dimension from a 2D microscopic image of the material, is required.

Error in threshold value + 10 grey values

Permeability 2 3 5

size distribution 1.1 1.4 2 Specific surface area 0.9 0.8 0.7

Permeability 0.5 0.3 0.2

size distribution 0.5 0.2 0.1 Specific surface area 1.2 1.2 2

Table 2. Approximate factors of how certain levels of threshold value and noise effect on permeability values, mode value of pore size distribution and specific surface area of the wool fibre web. The factors are given as values compared to the analysis results based on

distributions of the simulation geometries were found to change dramatically as a function of noise level. The mode value of the pore size distribution with the noise level of 0.01 % is approximately one third of the mode value of the noise free geometry.

Edge roughness on solid-void boundaries increases the specific surface area of the hexagonal cylinder geometry and therefore decreases the flow permeability value. The effect is, however, moderate compared to the effect of noise. Edge roughness was found to have only a small effect on the pore size distribution of the geometry.

Approximate factors of how certain levels of threshold value and noise effect on permeability value, mode value of pore size distribution and specific surface area of the wool fibre web sample are given in Table 2. The factors are given as values compared to the analysis results based on the forest fire segmented geometry that gives values very close to the experimental results. The results obtained using the forest fire method were compared to the data obtained from the scanning electron microscope images. Agreement with the sizes of characteristic solid objects was found to be good. The numerical permeability analyses for the sample geometries segmented using the forest fire method provided good agreement with the experimental results. The difference between the experimental results and the numerical permeability values found by using the forest fire segmented simulation geometries was less than 6.5 % for all the sample types.


Table 1. Approximate factors of how certain levels of noise and edge roughness effect on permeability value, mode value of pore size distribution and specific surface area of the hexagonal array of cylinders. Factors are given as values compared to the results for the noise free geometry.

The permeability results were found to be very sensitive for the threshold value used in segmenting the 3D geometries. Faulty selection of the threshold value can cause an error for the permeability value by a factor of approximately 2-5. By using grey value -based threshold method, the permeability value might by chance have approximately correct values (compared to the experimental results). However, the permeability value with selected threshold value would not necessarily be result of the realistic sample geometry, but combination of noise causing higher specific surface area and too thin fibres increasing the porosity value of the geometry. This result was found to be qualitatively similar for all the three sample types and the imaging methods used here.

distributions of the simulation geometries were found to change dramatically as a function of noise level. The mode value of the pore size distribution with the noise level of 0.01 % is

Edge roughness on solid-void boundaries increases the specific surface area of the hexagonal cylinder geometry and therefore decreases the flow permeability value. The effect is, however, moderate compared to the effect of noise. Edge roughness was found to have

Approximate factors of how certain levels of threshold value and noise effect on permeability value, mode value of pore size distribution and specific surface area of the wool fibre web sample are given in Table 2. The factors are given as values compared to the analysis results based on the forest fire segmented geometry that gives values very close to the experimental results. The results obtained using the forest fire method were compared to the data obtained from the scanning electron microscope images. Agreement with the sizes of characteristic solid objects was found to be good. The numerical permeability analyses for the sample geometries segmented using the forest fire method provided good agreement with the experimental results. The difference between the experimental results and the numerical permeability values found by using the forest fire segmented simulation

Permeability 0.5 0.01 0.001

size distribution 0.3 0.2 0.1 Specific surface area 1.1 3 30

Permeability 1 0.9 0.5

size distribution 1 0.9 0.8 Specific surface area 1.2 2.5 9

Table 1. Approximate factors of how certain levels of noise and edge roughness effect on permeability value, mode value of pore size distribution and specific surface area of the hexagonal array of cylinders. Factors are given as values compared to the results for the

The permeability results were found to be very sensitive for the threshold value used in segmenting the 3D geometries. Faulty selection of the threshold value can cause an error for the permeability value by a factor of approximately 2-5. By using grey value -based threshold method, the permeability value might by chance have approximately correct values (compared to the experimental results). However, the permeability value with selected threshold value would not necessarily be result of the realistic sample geometry, but combination of noise causing higher specific surface area and too thin fibres increasing the porosity value of the geometry. This result was found to be qualitatively similar for all

Edge roughness level 10

the three sample types and the imaging methods used here.

Noise level 0.01 % Noise level 1 % Noise level 10 %

Edge roughness level 50

Edge roughness level 120

approximately one third of the mode value of the noise free geometry.

only a small effect on the pore size distribution of the geometry.

geometries was less than 6.5 % for all the sample types.

Mode value of pore

Mode value of pore

noise free geometry.

Pore size distributions of the tomographic geometries were analysed as a function of threshold value. Although fluid flow analyses based on geometries segmented by grey value -based segmentation method might result in approximately correct permeability values, the structure of the pore geometry does not necessarily correspond with the realistic case. According to the results, the pore size distributions based on the grey value segmented geometries differ from the distributions based on geometries which were segmented using the forest fire method.

The forest fire segmented tomographic reconstructions were used in studying the effect of noise on tomographic geometries. Results in these cases indicate that the permeability results of tomographic geometries are not as sensitive to noise as in the case of regular hexagonal cylinder arrays. By increasing the noise level to 2 %, the permeability results decreased approximately by a factor of 0.5.

The effect of noise level on pore size distribution was analysed. The effect of added noise on tomographic reconstructions is not as drastic as in the case of the hexagonal cylinder arrays. With the noise level of 2 %, the mode value of the distribution is approximately a half of the mode value for the noise free geometry.

The results indicate that effective methods for handling imaging artefact removal and segmentation are essential for obtaining reliable results for structural and transport properties by means of direct numerical analyses based on CXµT reconstructions of the 3D structure of complex porous materials. According to our studies, the most essential factor for successful structural analysis and flow simulation is the quality of the tomographic reconstruction, i.e. noiseless and realistic structure. To achieve this requirement, a well controlled image acquisition and a good segmentation algorithm together with a verification based on a characteristic parameter, e.g. the mode value of pore size distribution measured by an independent method like mercury intrusion porosimetry or average characteristic dimension from a 2D microscopic image of the material, is required.


Table 2. Approximate factors of how certain levels of threshold value and noise effect on permeability values, mode value of pore size distribution and specific surface area of the wool fibre web. The factors are given as values compared to the analysis results based on the forest fire segmented geometry.

The Effect of Tomography Imaging Artefacts on

Oxford, pp. 437–454.

pp. 1137–1149

169

582-585

*Physics,* Vol.79, pp. 12–49

*Fluid Dynamics*, Vol. 23, No.10, pp. 713–721

*Geotechnics*, Vol.33, No.8, pp. 381–395

*and interactive techniques*, New York, USA

and Structures, Vol.35, No.10, pp. 650–659

media, *Physical Review. E.,* Vol.66, No.1, 016702.

Structural Analysis and Numerical Permeability Simulations 491

Kak, A. C. & Slaney, M. (1988). *Principles of Computerized Tomographic Imaging,* IEEE Press

Koivu V.; Mattila K. & Kataja M. (2009a). A method for measuring Darcian flow permeability. *Nordic Pulp and Paper Research Journal*, Vol.24, No.4, pp. 395–402 Koivu V.; Decain M.; Geindreau C.; Mattila K., Alaraudanjoki, J.; Bloch J.-F. & Kataja M.

Koivu V.; Decain M.; Geindreau C.; Mattila K.; Bloch J.-F. & Kataja M. (2010) Transport

Kutay, M. E.; Aydilek, A. H. & Masad, E. (2006). Laboratory validation of lattice Boltzmann

Leskelä, M. and Simula, S. (1998). *Papermaking Science and Technology, Paper Physics, Transport* 

Liakopoulos, A. C. (1965). Darcy's coefficient of permeability as symmetric tensor of second

Lundström, T. S.; Frishfelds, V. & Jakovics, A. (2004). A statistical approach to permeability

Lorensen, W. E. & Clive H. E. (1987a). Marching cubes: A high resolution 3D surface

Lorensen, W. E. & Clive H. E. (1987b). Marching cubes: A high resolution 3D surface

Manwart, C.; Aaltosalmi, U.; Koponen, A.; Hilfer, R. & Timonen, J. (2002). Lattice-Boltzmann

Martys, N. S. & Hagedorn, J. G. (2002). Multiscale modeling of fluid transport in

Ojala, T.; Pietikäinen, M. & Harwood, D. (1994). Performance evaluation of texture measures

Osher, S.; Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed:

Perona, P. & Malik J. (1987). Scale-space and edge detection using anisotropic diffusion. *Proceedings of IEEE Computer Society Workshop on Computer Vision*, pp. 16–22.

*phenomena*, ISBN952-5216-16-0, Fapet Oy, Helsinki, pp. 284–317

rank. *Hydrolocical Sciences Journal*, Vol.10, No.3, pp.41–48

*International Journal of Computer Vision*, Vol.1, No.4, pp.321-331

Kass, M; Witkin, A. & Terzopoulos, D. (1987). Snakes - Active Contour Models*.* 

(2009b). Flow permeability of fibrous porous materials. Micro-tomography and numerical simulations. *Proceedings in the 14th Fundamental Research Symposium*,

properties of heterogeneous materials. Combining computerised X-ray microtomography and direct numerical simulations, *International Journal of Computational* 

method for modeling pore-scale flow in granular materials. *Computers and* 

of clustered fibre reinforcements, *Journal of Composite and Materials,* Vol.38, No.13,

construction algorithm, *ACM SIGGRAPH Computer Graphics*, Vol.21, No.4, pp. 163-

construction algorithm, *Proceedings of the 14th annual conference on computer graphics* 

and finite-difference simulations for the permeability for three-dimensional porous

heterogeneous materials using discrete Boltzmann methods, Journal of Materials

with classification based on Kullback discrimination of distributions, *Proceedings of the 12th IAPR International Conference on Pattern Recognition (ICPR 1994)*, vol.1, pp.

Algorithms based on Hamilton-Jacobi formulations, *Journal of Computational* 
