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Quantitative image analysis of finite porous media
Author(s) -
Macdonald I. F.,
Kaufmann P.,
Dullien F. A. L.
Publication year - 1986
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1986.tb02808.x
Subject(s) - sample (material) , genus , volume (thermodynamics) , homogeneous , lattice (music) , porous medium , mathematics , porosity , geology , physics , combinatorics , biology , geotechnical engineering , zoology , thermodynamics , acoustics
SUMMARY Software for the reconstruction of branch‐node charts from serial sections is tested with a simple cubic lattice, and is applied to determine the genus per unit volume (specific genus) of a Berea sandstone sample from seventy‐eight serial sections. The genus is found analytically for the cubic lattice as a function of depth, cross‐section and volume. These results enable us to draw conclusions about the relative importance of depth and cross‐section and provide useful information on how to treat finite sample data to obtain the specific genus of an infinite homogeneous porous medium. It is shown that it is more important to have a deep sample (many serial sections) than a sample of large cross‐section. For samples which are too small in the direction of sectioning, the genus and the rate of change of genus with volume are too low because some of the large loops are not completed within the sample boundaries. For the Berea sample, this ‘shallow‐sample depth’ is about 2·2 grain diameters (forty‐five serial sections). Only data points at depths in excess of this value are used in determining the genus per unit volume. The slope of the genus versus volume curve is the better predictor of the genus per unit volume of the unbounded medium, of which the sample is a small part, than the value of genus/volume of the sample. For samples of finite cross‐section, the G min and G max versus volume curves are divergent and they only become essentially parallel when the dimensions in the plane of sectioning are large multiples of the grain size. It is shown that it is reasonable to assume that the arithmetic mean slope found for a small cross‐sectional area is a good estimate of the common slope that would be attained at high cross‐sectional areas. Therefore, samples of small cross‐section can be used, resulting in a reduction in the amount of data to be processed and an enhancement of the resolution of small features. The Berea sample data, beyond the ‘shallow‐sample’ region, show the same qualitative features as predicted analytically for the cubic lattice. The ratio of the slopes of the G max and G min curves is 1·22 and the genus per unit volume from the mean slope is 52·6 × 10 −8 μm −3 .