AltSU mathematicians model natural processes in order to preserve the ecological safety of territories

2 July 2021 Department of Information and Media Communications
AltSU mathematicians solve urgent economic problems associated with filtration of liquids in porous media.

Postgraduate student of the Department of Differential Equations of the Institute of Mathematics and Information Technologies of Altai State University Rudolf Virtz under the supervision of Head of the Department, Doctor of Physical and Mathematical Sciences Alexandra Papina, is implementing the project "Numerical and analytical study of mathematical models of the flow of liquids and gases in porous media."

The tasks outlined in the project are used in various areas of human life, from engineering solutions to environmental problems. In particular, such as irrigation and drainage of agricultural fields, migration of magma in the earth's crust, forecasting the spread of pollution in the bowels of the earth, filtration near river dams and other hydraulic structures, in order to predict flooding and eliminate their consequences, preservation of carbon dioxide in the bowels of the earth, and etc.

The research of the graduate student from AltSU can also provide significant assistance in describing natural processes, such as the migration of magma in the earth's crust leading to volcanic eruptions.

Another task that the young scientist realized within the framework of the project is the modeling of certain physical processes in which carbon dioxide, after being buried in the ground, will not be able to come out to the surface.

“I got acquainted with the topic of filtration of liquids and gases in porous media while still studying for the bachelor's degree, when I chose the Department of Differential Equations in my 3rd year. I started my research with one-dimensional problems, and now I have already moved on to the problems of carbon dioxide storage and I am solving two-dimensional problems on this topic. Most of the studies in this direction are devoted to problems that do not take into account the poroelastic properties of the mountain environment where carbon dioxide is buried - only the constant porosity of the medium is considered. In my work, I take into account possible changes in the mountain environment, as a result of which the porosity may change. This is a very important point, on which sometimes the ecological safety of the territory depends,” Rudolf Wirtz clarifies.

According to Rudolf, the studies used generalizations of filtration models, which they adapted to specific tasks.

“Now I am conducting research in two laboratories. This is a laboratory for mathematical modeling in the mechanics of inhomogeneous media and a laboratory for mathematical and computer modeling in natural and industrial systems. The first one was created in 2012 together with Lavrentyev Institute of Hydrodynamics, SB RAS, and the second was opened within the framework of the project “Modern methods of hydrodynamics for problems of nature management, industrial systems and polar mechanics.” The purpose of the laboratories is to build models and study problems in the mechanics of inhomogeneous media, use the fundamental results obtained to solve applied problems of rational nature management, industrial systems and polar mechanics, and provide training for highly qualified scientific and pedagogical personnel and specialists in the field of applied mathematics and mechanics. Thanks to the capabilities of the laboratories, I manage to obtain the most accurate calculations within the framework of my project,” summed up Rudolf Wirtz.

It is worth noting that the results obtained by  scientists at AltSU can be used in the field of oil and gas production, as well as in research work, agriculture, and engineering surveys.

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