Fractal analysis of permeability of dual-porosity media embedded with random fractures

• An analytical model for permeability in dual-porosity media was derived based on fractal.
• The analytical expression for permeability of dual porous media is found to be a function of the fractal dimensions and the microstructural parameters of the media.
• The parametrical effects on the permeability were investigated.

Dual-porosity media embedded with random fractures widely exist in water and oil reservoirs, soils etc. The permeability of such media has been one of focuses in the area of mass transfer in porous media in the past decades. In this paper, analytical scheme for permeability of the media is presented by the fractal theory and technique based on the fact that the length distribution of random fractures obeys the fractal scaling law and flow in each fracture follows the cubic law. The porous matrix of the media is assumed to consist of a bundle of tortuous capillaries whose sizes also follow the fractal scaling law. The analytical expression for permeability is derived and is found to be a function of the fractal dimensions and the microstructural parameters of the media. The present results show that the proposed permeability model can reveal more mechanisms of seepage characteristics in the media than the traditional models.