  In this article we investigate the permeability of a porous medium as given
in Darcy's law. The permeability is described by an effective hydraulic pore
radius in the porous medium, the fluctuation in local hydraulic pore radii, the
length of streamlines, and the fractional volume conducting flow. The effective
hydraulic pore radius is related to a characteristic hydraulic length, the
fluctuation in local hydraulic radii is related to a constriction factor, the
length of streamlines is characterized by a tortuosity, and the fractional
volume conducting flow from inlet to outlet is described by an effective
porosity. The characteristic length, the constriction factor, the tortuosity
and the effective porosity are thus intrinsic descriptors of the pore structure
relative to direction. We show that the combined effect of our pore structure
description fully describes the permeability of a porous medium. The theory is
applied to idealized porous media, where it reproduces Darcy's law for fluid
flow derived from the Hagen-Poiseuille equation. We also apply this theory to
full network models of Fontainebleau sandstone, where we show how the pore
structure and permeability correlate with porosity for such natural porous
media. This work establishes how the permeability can be related to porosity,
in the sense of Kozeny-Carman, through fundamental and well-defined pore
structure parameters: characteristic length, constriction, and tortuosity.
