Permeation properties of three-dimensional self-affine reconstructions of porous materials

A binary medium generation method is presented, which is capable of producing three-dimensional reconstructions of porous solids. The method is based on the midpoint displacement and successive random addition technique, which is, essentially, a graphical reproduction technique for the generation of self-affine media that follow fractional Brownian motion (FBM) statistics. Thresholding of the site values at the desired porosity value leads to three-dimensional porous constructions, the correlation degree of which is defined by the preselected value of the Hurst exponent. The correlation length of such single-cell media is comparable to the size of the working cell and, therefore, this approach would be of local use only. To remedy this problem, a method for producing multicell FBM media is presented, which is capable of generating media with size considerably larger than the correlation length and, as such, they can be employed to simulate a variety of actual porous solids. The percolation properties of these reconstructions are investigated and the specific surface area is calculated as a function of the porosity, the number of interwoven cells, and the Hurst exponent value. Furthermore, the flow equations are solved numerically within the void space of the three-dimensional FBM media and the effects of structure porosity and correlation degree on the permeability are studied. Application of the methodology to a sandstone sample as a case study showed a very good agreement of the numerical predictions for the permeability with actual permeability measurements and with the permeability estimate using a serial sectioning technique.