A fractal permeability model for gas flow through dual-porosity media

Abstract

The dual-porosity medium, i.e., a matrix porous medium coupled with fractured networks, extensively exists in fissured rocks, natural gas reservoirs, and other natural underground reservoirs or in resolving subsurface contamination problems. This work investigates gas permeability through matrix porous media embedded with randomly distributed fractal-like tree networks. The analytical expression for gas permeability in dual-porosity media is derived based on both the pore size of matrix and the mother channel diameter of embedded fractal-like tree networks having fractal distribution. It is found that gas permeability is a function of structural parameters (the fractal dimensions for pore area and tortuous capillaries, porosity and the maximum diameter of matrix, the length ratio, the diameter ratio, the branching levels and angle of the embedded networks) for dual-porosity media. The proposed model does not contain any empirical constant. The model predictions are compared with the available experimental data and simulating results, a fair agreement among them is found. The influences of geometrical parameters on the gas permeability in the media are also analyzed.