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In this paper, a unified model for describing the fractal characters of porous media is deduced. The theoretical predictions from the proposed unified model are compared with those from the previous models and from the box-counting method. The results from the proposed model are found to be in good agreement with both the previous models and box-counting method. The results also indicate that the proposed unified model is applicable to both the exactly and statistically self-similar fractal media. A statistical property of porous media is also described based on the basic fractal theory and technique. A criterion, for determining whether a porous medium can be characterized by fractal theory and technique or not, is proposed based on the fractal statistical property.

In the past decades, there was considerable controversy over the LucasWashburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the L s (t) ∼ t 1/2D T law is obtained (here D T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.

Spontaneous capillary imbibition is an important fundamental phenomenon existing extensively in a variety of processes such as polymer composite manufacturing, oil recovery, soil science and hydrology, etc. In this work, analytical expressions for characterizing a spontaneous co-current imbibition process of wetting fluid into gas-saturated porous media are proposed based on the fractal characters of porous media. The mass of imbibed liquid is expressed as a function of the fractal dimensions for pores and for tortuous capillaries, the minimum and maximum hydraulic diameter of pores, and the ratio for minimum to maximum hydraulic diameters, porosity, and fluid properties, as well as the fluid-solid interaction. The imbibed weight predicted by the present model is in good agreement with the available experimental data.

The flow in porous media has received a great deal of attention due to its importance and many unresolved problems in science and engineering such as geophysics, soil science, underground water resources, petroleum engineering, fibrous composite manufacturing, biophysics (tissues and organs), etc. It has been shown that natural and some synthetic porous media are fractals, and these media may be called fractal porous media. The flow and transport properties such as flow resistance and permeability for fractal porous media have steadily attracted much attention in the past decades. This review article intends to summarize the theories, methods, mathematical models, achievements, and open questions in the area of flow in fractal porous media by applying the fractal geometry theory and technique. The emphases are placed on the theoretical analysis based on the fractal geometry applied to fractal porous media. This review article shows that fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media. A few remarks are made with respect to the theoretical studies that should further be made in this area in the future. This article contains 220 references.

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