[page 228, §1]

[228.1.1] Table 2 gives an overview of several
geometric properties for the four microstructures
discussed in the previous section.
[228.1.2] Samples GF and SA were constructed to have the same
correlation function as sample EX.
[228.1.3] Figure 7 shows the directionally averaged
correlation functions

[228.2.1] The Gaussian field reconstruction

[page 229, §1] [229.1.1] If two samples have the same correlation function they are expected to have also the same specific internal surface as calculated from

(67) |

[229.1.2] The specific internal surface area calculated from this formula is given in Table 2 for all four microstructures.

[229.2.1] If one defines a decay length by the first zero
of the correlation function then the decay length
is roughly

[229.3.1] In summary, the samples

[229.3.8] The differences in visual appearance of the four
microstructures can be quantified using the geometric
observables

[229.4.1] The figures show that the original sample exhibits stronger
porosity fluctuations than the three model samples except for
sample SA which comes close.
[229.4.2] Sample DM has the narrowest distribution which
indicates that it is most homogeneous.
[229.4.3] Figures 8a–8d show also that the

[page 230, §0]

[page 231, §0]

[page 232, §0]
fluctuations which will be studied below.
[232.0.1] The conclusion is also consistent with the results for

[232.1.2] Figure 9 shows the variance of the local
porosity fluctuations, defined in (40) as function
of

[page 233, §1]
[233.1.1] At

[233.1.5] Visual inspection of Figures 1 through 4 does not reveal the degree of connectivity of the various samples. [233.1.6] A quantitative characterization of connectivity is provided by local percolation probabilities [27, 10], and it is here that the samples differ most dramatically.

[233.2.1] The samples EX, DM , GF and SA are globally connected in all
three directions.
[233.2.2] This, however, does not imply that they have similar
connectivity.
[233.2.3] The last line in Table 2 gives the fraction of blocking
cells at the porosity

[233.3.1] Figures 8a through 8d give a more complete
account of the situation by exhibiting

[page 234, §0]
in the

[234.1.1] The absence of spikes in

[234.2.1] The insets in Figures 8a through 8d show the
functions

[page 235, §0] suggests that reconstruction methods [1, 70] based on correlation functions do not reproduce the connectivity properties of porous media. [235.0.1] As a consequence, one expects that also the physical transport properties will differ from the experimental sample, and it appears questionable whether a pure correlation function reconstruction can produce reliable models for the prediction of transport.

[235.1.1] Preliminary results [42] indicate that these conclusions remain unaltered if the linear and/or spherical contact distribution are incorporated into the simulated annealing reconstruction. [235.1.2] It was suggested in [70] that the linear contact distribution should improve the connectivity properties of the reconstruction, but the reconstructions performed by [42] seem not to confirm this expectation.