The problem of global warming, which has become extremely urgent in recent years, is directly related to the greenhouse effect. Almost all types of human activity in one way or another increase the emissions of greenhouse gases into the atmosphere, primarily CO
2. Reducing and stabilizing CO
2 emissions is one of the main tasks for the modern world community.
One of the ways to solve this problem is the sequestration of carbon dioxide — the process of capturing CO
2 fr om an emission source, transportation and long-term disposal in geological formations.
One of the feasible options is the disposal of CO
2 in deep formations, where the porous space that can potentially be occupied by the injected CO
2 is up to 30% of the total rock volume. Under the ground, carbon dioxide compresses and fills the pores, partially displacing the liquid in them. Once pumped into the formation, the retention depends on a combination of physical and geochemical mechanisms. In particular, these processes are closely related to reactive transfer, when reactive liquids such as saturated CO
2 brines are filtered through a porous medium. As a result, the geometry and topology of the pore space changes due to chemical interactions between the fluid and the solid, which lead to significant changes in the properties of large-scale rocks, such as electrical conductivity, elastic stiffness and hydraulic permeability.
In the work of scientists of the Mathematical Center in Akademgorodok
Yaroslav Bazaikin, Doctor of Physical and Mathematical Sciences, Associate Professor of the Mathematics and Mechanics Department, and
Dmitry Prokhorov, a graduate student of the Institute of Mathematics SB RAS, as well as
Vadim Lisitsa, Doctor of Physical and Mathematical Sciences, Professor of the Mathematics and Mechanics Department of NSU, a compression algorithm has been developed digital spaces for efficient calculation of the topological characteristics of the pore space of the rock, in particular, its persistent diagrams. The research results are published in the journal Computers and Geotechnics, which is included in the first quartile of the WoS.
Yaroslav Bazaikin comments:
A purely mathematical problem arises — the algorithm for calculating persistent diagrams of the rock matrix in the process of its evolution is computationally too complicated. The authors have proposed an algorithm that compresses the rock matrix into a more compact structure, which allows faster performing the necessary calculations of topological characteristics. It turned out that the efficiency of the algorithm depends on the porosity of the rock and the rate of change in its topology. Moreover, the algorithm can give a 15-fold gain in computation time. Another interesting observation is that the topological characteristics of the evolution of the rock correspond to the physical conditions of injection of carbon dioxide (clustering by topological characteristics gives different scenarios of rock dissolution).
The developed compression algorithm can also be used in other tasks wh ere it is necessary to accelerate the computation of persistent diagrams of three-dimensional digital images (tomographic images, diffraction images, etc.).
