Permeability Description by Characteristic Length, Tortuosity, Constriction and Porosity

TL;DR

This paper develops a comprehensive pore structure-based model to describe and predict permeability in porous media, linking it to intrinsic parameters like characteristic length, constriction, tortuosity, and porosity, validated on idealized and real samples.

Contribution

It introduces a unified pore structure framework that fully characterizes permeability using well-defined parameters, advancing beyond empirical models.

Findings

The model reproduces Darcy's law from fundamental pore parameters.

Permeability correlates with porosity and pore structure in sandstone.

Intrinsic pore descriptors effectively predict permeability.

Abstract

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.