Correlations of Physical Properties of Porous Media
Authors: Von Gonten W. Douglas , Whiting R.L. 
Published: December 2007

Abstract
Regression analysis was used to correlate the physical properties of 478 sandstone and 90 carbonate core samples. Porosity, permeability, electrical formation resistivity factor, capillary pressure and the sonic velocity of the shear and compressional waves were measured. Prediction equations for porosity, permeability and electrical formation resistivity factor were found which should be useful in understanding the relationships between the physical properties of porous media in formation evaluation.

Introduction
The physical properties of porous media are important to the petroleum engineer and geologist. To evaluate fully the potential and behavior of a subsurface formation such as a petroleum reservoir, certain physical properties of the porous medium must be known. The problem of accurately determining physical properties of subsurface formations has not been solved because many determinations must be made by indirect measurements and because of the difficulties caused by complex pore structure and presence of clays in most naturally occurring porous media. Due to the difficulty in measuring some of the physical properties of porous media, it would be advantageous to be able to predict a certain physical property of a rock from other physical properties of the rock which could be measured more easily and more accurately. Since most potential reservoir rocks are heterogeneous, relationships between the physical properties are very complex and thus far no satisfactory correlations based on theory or laboratory models have been developed. It appears that empirical relationships obtained by measuring the physical properties of a large number of samples of naturally occurring porous media and applying regression analysis to develop for one physical property in terms of other rock properties is the best approach.

REVIEW LITERATURE
The three physical properties used as dependent variables for correlating purposes were porosity, permeability and formation factor. Since formation factor is more difficult to determine, a brief review of the literature is provided on this property. The first work on determining formation factors was published by Archie in 1942. He defined this property of a porous medium as
Ro ...............................(1) F =RW
where Ro is the resistivity of the porous medium when completely saturated with a brine of resistivity Rw. Archie found the best correlation between formation factor and porosity was the following equation,
F = - m..................................... (2)
where is the porosity fraction and m is the constant characteristic of the rock. The value of m was 1.3 for unconsolidated sand packs, and ranged from 1.8 to 2.0 for consolidated sandstones. In 1950 Patnode and Wyllie and De Witte observed that the formation factor as determined by Eq. 1 was valid only when the porous medium contained no conductive solids such as clay or shale. When conductive solids are -present the formation factor is also dependent on the resistivity of the saturating fluid. Therefore, in samples containing conductive solids the formation factor decreased as resistivity of the saturating fluid increased. Because of this, the measured formation factor was called the apparent formation factor and was designated Fa. Patnode and Wyllie proposed the following equation.
SPEJ
P. 266ˆ