The fractal menger sponge and Sierpinski carpet as models for reservoir rock/pore systems: I. ; Theory and image analysis of Sierpinski carpets
James R. Garrison, W. C. Pearn, D. W. von Rosenberg · InSitu · 1992
In this paper reservoir rock/pore systems are considered natural fractal objects and modeled as and compared to the regular fractal Menger Sponge and Sierpinski Carpet. The physical properties of a porous rock are, in part, controlled by the geometry of the pore system. The rate at which a fluid or electrical current can travel through the pore system of a rock is controlled by the path along which it must travel. This path is a subset of the overall geometry of the pore system. Reservoir rocks exhibit self-similarity over a range of length scales suggesting that fractal geometry offers a means of characterizing these complex objects. The overall geometry of a rock/pore system can be described, conveniently and concisely, in terms of effective fractal dimensions. The rock/pore system is modeled as the fractal Menger Sponge. A cross section through the rock/pore system, such as an image of a thin-section of a rock, is modeled as the fractal Sierpinski Carpet, which is equivalent to the face of the Menger Sponge.