Catastrophes, fractals and chaos in geoengineering and water treatment systems

Igor Yeremeyev,Ievgen Khlobystov,Natalya Remez,Volodymyr Kyselov,Alina Dychko,S Semerikov,S Sakhno,H Danylchuk,A Iatsyshyn,P Nechypurenko,V Osadchyi,S Chukharev,S Klimov,T Vakaliuk,A Striuk,O Bondarenko

doi:10.1051/e3sconf/202128002009

Abstract

The present paper provides the assessing scale of the actual state of the geoengineering complexes and the model for predicting the behavior of supporting structures. To predict accidents in geoengineering and water treatment facilities it is proposed to apply the results of the theory of catastrophe theory, fuzzy sets, chaos theory and the theory of possibilities for the selection of optimal models of system behavior for a particular situation. It is shown that determination the limit boundaries in which the operation of the system can exist is impossible without the consideration of geoengineering treatment facilities and their components as fractal structures, functioning under conditions of “chaos”. To minimize risks of damages of sewage geoengineering systems the monitoring with measurement of the toxic gases concentration and comparing it with the obtained one should be provided. The use of models of internal and external corrosion which includes the elements of the theory of fuzzy sets helps to evaluate completely the state of water supply and treatment facilities network.

Highlights

In the processes of water treatment and water purification, there are very often the problems that are clearly nonlinear and, at the same time, can not be analysed with the methods used in “classical” nonlinear systems, or give the results that are far from the optimal ones. These problems include quasiperiodic changes in the states of shallow water basins, which may receive stormwater or wastewater; behavior of biological treatment systems; general behavior of the entire complex of water treatment systems in different spatial and temporal boundaries and scales, etc.; and 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 [1-5]
Result of presented research indicate that water is corrosive at 10.6%-89.4% of drinking water supply reservoirs [6]

Summary

Introduction

In the processes of water treatment and water purification, there are very often the problems that are clearly nonlinear and, at the same time, can not be analysed with the methods used in “classical” nonlinear systems, or give the results that are far from the optimal ones (and even plausible). An analysis of the results of observations and analogies suggests that the structures and functioning of natural and geoengineering water treatment systems demonstrate in a broad sense the self-similarity of water purification processes from pollution both in natural conditions and in engineering treatment facilities – the same principles are applied, the only difference is in productivity and quality of treatment In other words, both those and other systems more or less fit into a wide range of spatial, temporal and quantitative scales, which indicates the presence of a certain symmetry of the scales. The proposed approach assumes the use of catastrophe theory, fuzzy set theory and chaos theory to predict accidents in geoengineering and treatment facilities

Reliable assessment of the state of geoengineering structures

Findings

Conclusions