Katz Thompson Relationship in Bricks

The data set generated for the bricks allows us to quantitatively evaluate the use of the Katz-Thompson relationship for predicting the permeability of these porous materials. The basic Katz-Thompson relationship is given by [18]:

$$k=\frac{{\frac{D}{D_0}}*D_c^2}{226}$$ (2)

where k is the permeability, D/D ₀ is the relative diffusivity, and D_c is the critical pore diameter evaluated from a mercury intrusion experiment and corresponding to the largest pore size for which there exists a connected pathway through the microstructure when considering only pores of this size and larger.

Experimentally, permeability has been measured and the relative diffusivity can be obtained by dividing the measured value by the value for water vapor in air (0.0922 m²/h). However, a measure of D_c is lacking. But, computationally, the 3-D microstructural binary images can be evaluated to provide an estimate of D_c in the following manner. First, the connectivity of the systems can be examined using a "burning" algorithm [19] to determine the fraction of the overall porosity which is part of a connected pathway through the microstructure for a "diameter" of one pixel. For the clinker brick and lime silica bricks, we find percolated fractions of 0.78 and 0.85, respectively. In addition, a program which simulates the 3-D intrusion of spherical particles of various sizes can be used as a coarse simulation of the mercury intrusion process (coarse because in three dimensions, the intruding mercury surface is characterized by two radii of curvature and may not be spherical) [4]. For a D_c=3 pixels (about 20 µm), the pores in the clinker brick are virtually inaccessible, while about 25 % of those in the lime silica brick are accessible when intruding from one surface of the 3-D system. Thus, reasonable estimates of D_c might be 1 pixel (6.65 µm) and 2 pixels (13.3 µm) for the clinker and lime silica bricks, respectively. These values are in good agreement with mercury intrusion porosimetry curves presented previously [1]. Substituting these values into equation 2 along with the measured relative diffusivities, one computes estimated permeabilities of 0.004 µm² for the clinker brick and 0.034 µm² for the lime silica brick, in good agreement with the experimentally determined values. This preliminary analysis indicates that the Katz-Thompson relationship very likely holds for these bricks, as well as for the porous rocks to which it was originally applied [18]. Here again, the analysis for the clinker brick would benefit from having a data set obtained at a higher resolution to allow a more accurate determination of D_c for this material.