A fractal permeability model for bi-dispersed porous media

Abstract

In this paper a fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the media. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. An analytical expression for the pore area fractal dimension is presented by approximating the unit cell by the Sierpinski-type gasket. The pore area fractal dimension and the tortuosity fractal dimension of the porous samples are determined by the box counting method. This fractal model for permeability does not contain any empirical constants. To verify the validity of the model, the predicted permeability data based on the present fractal model are compared with those of measurements. A good agreement between the fractal model prediction of permeability and experimental data is found. This verifies the validity of the present fractal permeability model for bi-dispersed porous media.