Cellular Automata and X-Ray Microcomputed Tomography Images for Generating Artificial Porous Media

摘要

Problems involving fluid flow in porous media are of great interest in many scientific and technological areas. The development of numerical methods at the pore level allows simulating such phenomena considering characteristics and heterogeneities of the medium normally ignored in the macroscopic approach. To achieve the computational implementation of those numerical methods, it is necessary to initially define the domain (porous media) in which the simulations will be held. In this study, a simple, yet powerful methodology of representing a porous medium by means of cellular automata (CA) and microcomputed tomography is presented. Two parameters are proposed to link the tomographic images with those generated by CA. The first one considers the porosity, whereas the second one takes into account void alignment inside the image. The methodology computes the parameters in every automata image generated in a time range and compares them with the parameters of the tomographic image until certain user-controlled precision is achieved. As an application example, two tomographic experiments with different resolutions were carried out on a soil sample. Two-dimensional (2D) outer totalistic CA rules whose evolution in time exhibits variation between the amount of black and white cells, independently from the initial condition, are considered. The calculations showed a gain of accuracy with the resolution increase. Although the implementation is presented for the 2D case, the methodology proposed is easily extendible to three-dimensional analysis.