Investigation on 3D Fractal Dimension as Complexity Parameter of Interconnected Pore in 3D Porous Media

3D Fractal dimension as a complexity parameter of interconnected pore in 3D porous media is investigated. Four sets of 3D digital porous media with the size of 150×150×150 pixels are constructed by randomly depositing spherical grains with radius in the range of 10-20 pixels in an empty cube. Fractal dimension is obtained by means of the box counting method. Interconnected pore in 3D porous media are identified by applying cubical random walk in three different directions. The complexity of the interconnected pore is then described means of tortuosity, which is defined as the ratio between geodesic lengths of the interconnected pore to the sidelength of the medium. To observe the consistency of 3D fractal dimension as complexity parameter of 3D porous media structure, the four sets of samples of 3D porous media were generated with four different porosity. The correlation coefficient obtained from the samples are 0.1999, 0.3962, 0.9012 and 0.5682. Based on the results 3D fractal dimension shows a positive correlation with average tortuosity for each different porosity. It indicates that the higher 3D fractal dimension for 3D porous media, the interconnected pore of the porous media is more complex.