A Simple Correlation Between Permeabilities and Mercury Capillary Pressures
Authors: Swanson B.F. 
Published: December 2007

Summary
A new correlation is developed between brine and air permeabilities with capillary pressure data. The relation is simple to use in that it is expressed easily as a nomograph. it offers ready application to improved estimation of permeability from capillary pressure measurements on small portions of sidewall core samples and drill cuttings.

Introduction
Purcell showed that mercury capillary pressures could be related empirically to permeability through the graphical integral of the curve of mercury saturation vs. reciprocal capillary pressure squared. This approach was indicated by consideration of a model comprised of tortuous, parallel capillaries of various sizes.A decade later, Thomeer observed that a log-log plot of capillary pressure data approximated a hyperbola and developed a mathematical expression for capillary pressure data. He empirically related the hyperbolic functions to permeability. The result was a further improvement over the earlier methods.We are seeking improvements that would enhance our ability to estimate permeability of small rock samples such as portions of sidewall core samples or drill cuttings. Capillary pressure curves measured on drill cuttings usually present a very gradual, poorly defined plateau as shown in Fig. 1a. The depressed plateau leads to optimistic estimates of permeability using the Purcell approach. Also, cuttings capillary pressure data are not well represented by a hyperbola. This results in poor fits of Thomeer parameters to cuttings data (Fig. 1b). In Fig. 1, the "cuttings" data are measurements on rocks of known permeability that were crushed to the size of drill cuttings.In seeking a new correlation, we try to avoid the lower plateau of the capillary pressure curve and to introduce an effective porosity or saturation that contributes most to fluid flow. We also seek a method that is easy to use.

A New Correlation
To develop a concept of our approach to a new correlation, let us infer aspects of single-phase flow from two-phase relations. Consider a common shape for an air/liquid residual-initial saturation (CCI) curves (Fig. 2). There is a region of the CCI curve normally found to be linear as initial saturation increases from zero. Also observe the corresponding capillary pressure curve of Fig. 2.As the nonwetting phase enters, it first distributes itself in a tortuous and spotty spatial distribution in some manner, as shown two-dimensionally in Fig. 3. The saturation may be high locally, but its areal distribution is spotty. This feature is demonstrated very nicely in scanning electron microphotographs of Wood's metal pore impregnations. At these lower bulk saturations, the corresponding mercury pressure is not representative of pore sizes controlling bulk flow through the total cross section of the rock, since it applies only to the connection of these large-scale tortuous paths.As capillary pressure increases slightly, a greater proportion of the pore space is entered and mercury becomes distributed more widely. It is not until some capillary pressure is reached such that a broad spatial distribution of mercury exists that we arrive at the desired effective saturation. This capillary pressure corresponds to pore sizes effectively interconnecting the total major pore system and, thus, those that dominate fluid flow.
JPT
P. 2498^