Percolation processes and porous media: I. Geometrical and topological model of porous media using a three-dimensional joint pore size distribution

Abstract

Three-dimensional information on the pore space in porous media, generated either in a continuous or in a discrete manner, was transformed into a geometrical-topological network system of intersecting ellipsoids, using random processes for the investigation of pore size and the reconstruction of the pore structure. It was assumed that: (i) pore space and pore size can be described by an orthogonal three-dimensional system; (ii) pore unit shape can be described by an ellipsoid; (iii) the reconstruction of the medium by randomly packing ellipsoids in space and allowing them to intersect will preserve the topological-geometrical properties of the original medium. The rationale for this approach lies in our inability to describe analytically the pore space geometry and topology of a natural porous medium. Even if this feat could be accomplished, the use of such information for fluid flow studies in porous media would be impractical or impossible because of the complicated boundary conditions imposed by the irregular geometry of the pore space. Instead, the natural pore geometry has been replaced with a geometry that can be handled mathematically, even if only approximately, and the network structure of the pore space is also replaced with a network that can be handled. These concepts find applications in Part II. The results presented here confirm that the proposed concepts have a sound basis. The advantage offered by this study with respect to research of pore space geometry and topology is that it offers an automated and computerized method for obtaining a relatively simple statistical representation of a porous medium.