Air Permeability as a Function of Three Pore-Network Parameters
Authors: Thomeer J.H. 
Published: December 2007

A new relationship between air permeability and three parameters describing a pore network is presented. The parameters are normally derived from the mercury/air capillary-pressure curve but may also be approximated from a petrographic analysis of thin sections. petrographic analysis of thin sections. Introduction

In 1960 Thomeer showed that mercury/air capillary-pressure curves form a family. Each curve can be uniquely defined by specific values of three parameters of the equation that describe the family. The following parameters of the equation that describe the family. The following relationship between capillary pressure ( ) and bulk volume occupied by mercury ( ) was proposed:

............................(1)

This equation describes a hyperbola when plotted on log-log paper. The values of and determine the location of its asymptotes, and the value of defines its shape. An individual capillary-pressure curve is uniquely defined by specific values of the following three parameters.

= pore geometrical factor, reflecting the distribution of pore throats and their associated PV; = mercury/air extrapolated displacement pressure, indicating the pressure required for mercury to enter the largest pore throat, psia (kPa); and = percent bulk volume occupied by mercury at infinite capillary pressure, or total interconnected PV.

Methods to determine the values of these parameters for a capillary-pressure curve are given in the referenced 1960 paper. Thomeer also evaluated both the significance and accuracy of determination of these parameters. Values were determined from capillary-pressure curves on 144 parameters. Values were determined from capillary-pressure curves on 144 diverse rock samples and correlated with air permeabilities measured on the same samples. This correlation showed a good relationship between air permeability and the parameters. In this paper, we propose improvements permeability and the parameters. In this paper, we propose improvements and refinements of this relationship and also suggest a method for estimating air permeability from a petrographic rock description. This method employs conversion of petrographic observations into equivalent capillary curve parameters.

The Data Set

Laboratory-measured porosities, air permeabilities, and mercury/air capillary-pressure curves on 279 rock samples were used. The samples were obtained from reservoirs in about 54 fields and consisted of 165 siliciclastics and 114 carbonates. All three laboratory measurements were performed on the same piece of rock. Air permeabilities represent routine performed on the same piece of rock. Air permeabilities represent routine measurements-i.e., they were not corrected for the Klinkenberg effect. For each capillary curve, the parameters, and were determined using the overlay procedure. Figs. 1 through 3 show the distribution of porosities, air permeabilities, and pore geometrical factors for the 279 samples separately permeabilities, and pore geometrical factors for the 279 samples separately for the total set, the carbonates, and the siliciclastics.

JPT

p. 809