On an algorithm for generating inhomogeneous porous media

Abstract

In the article, the results of the development of an algorithm for creating inhomogeneous three-dimensional porous media based on stochastic fractals are presented. The issues of estimating the parameters of porosity of the media are considered. It has been shown that the fractal dimension of porous media is preserved for any slice scales and the size of the fractal grid used to build porous media, as well as the fractal dimension of matrices and porous media depends on the binary filtration parameter that forms the given porosity by changing the ratio of matrices, open and closed pores, to the total sample volume.

Catastrophes, fractals and chaos in geoengineering and water treatment systems

“…It is also should be noted that the activity of microorganisms that ultimately cause the corrosion is carried out cyclically, and since the initial conditions for each cycle, as a rule, are not the same, there are opportunities for the emergence of "chaos", that is, unpredictable development of events [1], which is very typical for biological treatment systems. In other words, in such systems it is only possible to predict the boundaries within which the processes can occur.…”

“…; and finally, the behavior of individual components of treatment facilities, pipelines and collectors under the conditions of a manmade disaster emerging in their depths. All these problems can be successfully solved only when we turn to the use of a new mathematical apparatus based on the results of the theories of fuzzy sets, catastrophes, fractals and chaos [1][2][3][4][5].…”