ABSTRACT

The Kozeny equation for fluid flow through isotropic unconsolidated porous media is developed. It is shown that the utility and application of this equation to consolidated and non-isotropic porous media hinge on the derivation of appropriate values for the Kozeny constant, k. It is postulated on the basis of a dichotomy originally suggested by Carman that the Kozeny constant for any porous system having a random distribution of pores is obtainable if the tortuosity of the porous system can be measured. Electrical methods to determine tortuosity in isotropic, non-isotropic, and partially saturated porous media are outlined and experimental data bearing on the validity of these methods are examined.

By combining the fundamental postulates of the Kozeny equation with the properties of the capillary pressure desaturation curve of a porous medium, a new expression for permeability is obtained:
K=γ2F2ϕ2.501.0dSw/Pc2. 
Similarly, the wetting phase relative permeability is shown to be,
Krw=II2Sw 20SwdSw/Pc 201.0dSw/Pc 2.

Here K is permeability, γ interfacial tension, F formation factor, ϕ porosity, Sw fractional wetting phase saturation, and Pc capillary pressure.

It is noted that the principal difference between unconsolidated and consolidated porous media lies in the higher tortuosities applicable to the latter. By the preparation of thin sections and the use of a statistical method for determining surface area, it is shown that the Kozeny equation appears to give valid surface areas for consolidated porous media. Such measurements make possible an estimate of the average grain sizes of many consolidated porous media.

First Page Preview

First page PDF preview
You do not currently have access to this article.