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Relating permeability to pore connectivity using a power-law flow unit equation

Relating permeability to pore connectivity using a power-law flow unit equation

Petrophysics (Houston, Tex)

The effects of pore connectivity, the valve action of pore throats, and cementation are implemented into a bundle of tortuous leaky capillary-tubes macroscopic model of permeability. Practical straight-line plotting and parameter determination schemes are presented for convenient correlation of the porosity-permeability or porous media using a simplified macroscopic model. The permeability of porous media is accurately correlated by means of a single continuous function over the full range of porosity using a power-law flow unit equation. The present approach leads to a compact and simplified correlation, which can be incorporated into the modeling of porous media processes without adding appreciable complexity and computational burden. The parameters of the power-law flow unit equation, incorporating the fractal attributes of connected pore space into a bundle of tortuous leaky hydraulic tubes model of porous media, are proven to be strong functions of the coordination number of porous media and significantly different than those of the Kozeny-Carman equation. The mathematical relationships of the power-law parameters to the coordination number are also presented. The power-law flow unit model is shown to fit the porosity-permeability data successfully. The analyses of various data indicate the validity of the present approach and lead to accurate and functionally well-behaving correlations over the full range of porosity. The associated analysis also lends itself to the physical interpretation of the pore connectivity and cementation factor in terms of the relationship or permeability to porosity.

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Accession: 019885459

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