Prediction of Relative Permeability of Unsaturated Porous Media Based on Fractal Theory and Monte Carlo Simulation

Abstract

Mass transport through porous media is an important subject to engineers and scientists in various areas including oil engineering, fuel cells, soil science, textile engineering, etc. The relative permeability and capillary pressure are the key parameters that affect liquid transport through porous media. In this paper, the Monte Carlo technique is applied to predict the relative permeability of unsaturated porous media, considering the effect of capillary pressure and tortuosity of capillaries. The relative permeability is expressed as a function of porosity, area fractal dimension of pores, fractal dimension of tortuous capillaries, degree of saturation, and capillary pressure. It is found that the phase fractal dimensions (D f,w and D f,g ) strongly depend on porosity. Besides, it is shown that the capillary pressure increases with the decrease of saturation, and at low saturation the capillary pressure increases sharply with the decrease of saturation. There is no empirical constant in the proposed model, and each parameter in the model has a clear physical meaning. The predicted relative permeability obtained by the present Monte Carlo simulation is shown to have a good agreement with the experimental results reported in the literature. The proposed model improved the understanding of the physical mechanisms of liquid transport through porous media.

Fractal analysis of directional permeability of gas shale fracture networks: A numerical study

“…The fracture networks are comprised by hundreds/thousands of fractures with different lengths, apertures, and orientations, and it is difficult to accurately describe them of each fracture (Zhang and Nemcik 2013;Liu et al 2016aLiu et al , 2016bLi et al 2016). Fortunately, these parameters (i.e., fracture length and aperture) show fractal properties, and the fractal analysis of thermal conductivity (Li et al 2014;Xu 2015), permeability (Xiao et al 2012;Liu et al 2015;Xu et al 2016) and spontaneous imbibition (Cai et al 2014(Cai et al , 2015 is believed to be effective and has developed rapidly in the recent years. Jafari and Babadagli (2013) presented that the percolation-fractal properties are closely related with the permeability of 2-D fracture networks.…”

Assessment of steady state diffusion of volatile organic compounds in unsaturated building materials based on fractal diffusion model

“…Based on fractal features, these two fractal dimensions for pore tortuosity D tw and D tg in Eqs. (3) and (4) can be calculated from a serial of empirical equations below [38]:…”

A Fractal Model for Water Flow Through Unsaturated Porous Rocks

“…1,2,4,7,8,11,13,[18][19][20] This means that the fractal theory can be used to predict the capillary pressure and water relative permeability of porous media. Besides, the pore size distribution and tortuosity of capillaries have also been proven to follow the fractal scaling laws, 2,4,8,18 i.e. The transfer routes of water in unsaturated porous rocks have fractal characteristics and can be described as random fractal curves.…”