Improvement of fractal model for porosity and permeability in porous materials

Abstract

The investigation of porosity and permeability of porous materials is a challenge due to its complex pore microstructures. In this paper, an improved model of porosity is proposed based on the pore filling method, in which the facts of microscopic observation are considered that the smaller pores will be found with the decreasing observation scale or increasing magnification. The model is verified by two-dimensional and three-dimensional experiments, and the results show that the improved model can accurately describe the porosity and the pore volume distribution of fractal porous materials. Besides, a probability density function of pore size without conventional restrictions is also proposed based on the improved model of porosity, which makes the scope of application of the model of tortuosity fractal dimension much wider. Moreover, an improved model of permeability is finally proposed based on the improved model of porosity and the probability density function. By comparing the predicted values of the new permeability model with the experimental data, it is confirmed that the permeability model proposed in this paper could accurately predict the permeability of fractal porous materials.