A Simplified Method for Determining Specific Surface
Authors: Perez-Rosales Candelario 
Published: December 2007

Abstract
A simplified method for evaluating specific surface of porous media is described. The theory takes as its point of departure a previous statistical method. Due to its simplicity, it is considered that the proposed method has certain advantages over methods currently used. By making some simplifications, the procedure for estimating specific surface is reduced to superposing, on an enlarged reproduction of a section of the sample to be analyzed, an evenly spaced grid and counting the number of intersections of the grid lines with the perimeter of pores. An indirect test of the theory is presented and the advantages of the method are discussed.

Introduction
The specific surface of a porous medium, defined as the surface area of the pores per unit bulk volume, is an important parameter with regard to flow of fluids through porous materials. In particular, it has long been recognized that specific surface is closely related to permeability. Since the internal surface of any porous material is extremely complex, the measurement of specific surface can only be accomplished by indirect means. It is considered that the best method in current use for determining specific surface is the statistical method of Chalkley, Cornfield and Park who originally applied it for estimating volume-surface ratios of morphologic components, such as cells or nuclei. This method will be outlined later. A method which has been used extensively in determining specific surface is based on the adsorption of a vapor by the internal surface of porous media. However, this method does not yield the surface pertinent to fluid flow, since it includes the tiny molecular interstices which do not influence the permeability of the porous material. This method has been employed by Brooks and Purcell to measure internal surface area of sedimentary rocks. The Kozeny equation, which relates the specific surface to the permeability of a porous medium, has found wide use in determination of specific surface. However, the Kozeny equation is not strictly correct. Large discrepancies have been found between theory and experiments. Consequently, the specific surface estimated by this method is subject to serious uncertainties. Finally, there are other methods for specific surface measurements which are based upon a variety of physical and chemical properties: the heat conduction by a gas, ionic adsorption phenomena and direct chemical reactions of the surface with other substances. This paper describes a simplified statistical method for determining specific surface of porous materials. It is considered that, due to its simplicity, it has certain advantages over the methods presently used. For its validity, it is required that the porous structure of the material under study be of a spatially random nature. This is not a serious limitation since the naturally occurring porous media have this characteristic.

THEORY
The method proposed in this paper takes as its point of departure the interesting result obtained by Chalkley et al. The method shows that if a line of length r is dropped repeatedly at random over a section of a porous medium. and counts are made of the number of times the two end points fail within pore areas (denoted by h for "hits") and the number of times the line intersects the perimeter of pores (denoted by c for "cuts"), then in a very large number of throws
................................(1)
where S is the internal surface of the sample (surface of pores) and V, the volume of the pores (Fig. 1).