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Analysis of seepage characters in fractal porous media. (English) Zbl 1167.76046

Summary: We analyze plane-radial and plane-parallel flows of Newtonian fluid in fractal porous media. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and using fractal characteristics of pore size distributions in porous media, we develop expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows. The obtained expressions are functions of tortuosity, fractal dimension, maximum and minimum pore diameters, there are no empirical constants, and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.

MSC:

76S05 Flows in porous media; filtration; seepage
86A05 Hydrology, hydrography, oceanography
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