Analysis of the permeability tensor and the correlation length of heterogeneities in paper using X-ray microtomography

A technique to determine the permeability from X-ray microtomographic images was developed and applied to paper structures. The images are thresholded and a skeleton of the pore space is obtained from the images. The skeleton is represented by means of a network of resistances. The total resistance of the network along the principal directions is now determined both in the in-plane (X, Y) as well as through the plane (Z) directions. The network resistance for structures at each section is determined. From this data, a correlation length for the network resistance is obtained. Correlation length data are used for determining the effect of heterogeneities on transport properties of paper structures. From this analysis, it is possible to analyze and simulate the moisture transport processes such as wicking and drying in paper, reproducing smaller-scale variations. Permeabilities in the thickness direction were calculated from the X-ray microtomographic reconstructions of the pore space. A set of paper samples prepared with different amounts of fines but with similar porosity and density was analyzed. The permeabilities of the X-ray reconstructions were reduced significantly in papers with fines in agreement with macroscopic measurements of flow through the same sheets. This demonstrated the higher tortuosities of the papers and their increased flow resistance, although the macroscopic porosity and density were relatively unchanged. The same analysis was repeated for a set of pilot machine sample papers to demonstrate variations in permeability predicted by X-ray microtomographic analyses in agreement with expected increases due to refining of pulps.