Abstract
A statistical method, based upon the surface analysis of samples, is presented for determining simultaneously the following structural characteristics of granular porous media: porosity, mean pore width, mean grain thickness, specific surface, true sphericity of grains, number of grains per unit volume, and surface area of individual grains. per unit volume, and surface area of individual grains. Since a two-dimensional analysis is used as a means for obtaining information about three-dimensional systems, the applicability of the proposed method is restricted to homogeneous and isotropic media.
Introduction
The study of the geometrical properties of granular porous media is of importance in a variety of scientific and technological disciplines, such as fluid mechanics, soil mechanics, sedimentology, stratigraphy and petrophysics. The literature available in this field reveals that relatively little is known about the actual internal structure of granular media with a random distribution of irregular grains. When a quantitative description of the structural characteristics of these systems is required, it has become a practice to postulate idealized geometric models as representative of the real media. Thus, models consisting of packings of spheres and spheroids have been used for studying fluid flow and capillary behavior in granular media, such as soils and natural sands. Similar systems have been employed as models for filter cakes and beds of catalyst pellets. Likewise, cylindrical and parallel-plate pore models have been postulated for studying pore structure of real media. These simplified models, however, usually have the disadvantage of giving only approximate results; and sometimes large discrepancies between theory and observation are obtained. In view of the difficulty of giving a proper geometrical characterization of granular porous media by standard procedures, it is concluded that new methods of procedures, it is concluded that new methods of analysis leading to a better understanding of the anatomy of porous materials are needed. Accordingly, a method which allows a detailed structural description of granular porous media is presented in this paper. The guiding idea in the presented in this paper. The guiding idea in the development of the method has been the belief that a proper analysis of the surface of a homogeneous and isotropic porous material must provide all the basic information to characterize adequately the internal structure of the medium. The results obtained to date have shown that, if a cross-section of a granular porous sample is analyzed by means of a square grid, it is possible to determine in a simple and accurate way the following structural characteristics: porosity, mean pore width, mean grain thickness, specific surface, true sphericity of grains, number of grains per unit volume, and surface area of individual grains. To improve the consistency between the mathematical symbols and their meaning, the nomenclature employed in this paper is somewhat different from that used in the related previous papers. papers.
IMPORTANT RELATIONSHIPS
In addition to porosity, one of the most important geometrical characteristics of a porous sample is the specific surface. In the strict sense, there are two basic types of specific surface for a granular porous material: pore specific surface, Ssp, and porous material: pore specific surface, Ssp, and grain specific surface, Ssg. The former is defined as the surface area of the pore walls, Sp, per unit bulk volume, Vt, namely,
and the latter is defined as the surface area of grains Sg also per unit bulk volume; that is
If the contacts between grains were mathematical points, the two types of specific surface would have points, the two types of specific surface would have the same value. However, for a real granular medium, the contacts always have associated a given surface area, and hence these parameters are necessarily different.
SPEJ
P. 363
Waterfall Algorithm as a tool of investigation the geometrical features of granular porous media
