On global asymptotic stability of solutions of a system of ordinary differential equations

To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system. © 2017 Author(s).Russian Foundation for Basic Research, RFBR: 16–01–00401The work was supported by Russian Foundation for Basic Research 16–01–00401

Formation of phase structure in the system Ti-3Al at the stage of secondary structurization at synthesis in the mode of thermal explosion

Features of phase formation processes in the system Ti-3Al at realization of self-extending synthesis in the mode of thermal explosion have been established with use of technological reactor enabling instant switching-off of the heating source. The analysis of synthesis finished products allows to draw a conclusion that phase structure of charge is abnormally depends on sizes of titanium particles. The single-phase product corresponding to initial stoichiometry is synthesized on fine and large fractions for the induction period. On intermediate fraction the product of synthesis is multiphas

Formation of phase structure in the system Ti-3Al at the stage of secondary structurization at synthesis in the mode of thermal explosion

Features of phase formation processes in the system Ti-3Al at realization of self-extending synthesis in the mode of thermal explosion have been established with use of technological reactor enabling instant switching-off of the heating source. The analysis of synthesis finished products allows to draw a conclusion that phase structure of charge is abnormally depends on sizes of titanium particles. The single-phase product corresponding to initial stoichiometry is synthesized on fine and large fractions for the induction period. On intermediate fraction the product of synthesis is multiphas

Simulation of Optimal Operation of a Multiple Wells Open Geothermal System

Geothermal energy is a promising type of renewable energy. To analyze and improve the efficiency of the system, a three-dimensional mathematical model of an open geothermal loop system is developed. The proposed model takes into account thermophysical characteristics of the geothermal aquifer and the most important technical parameters of the wells. The pump pressures in producing and injection wells, as well as the distances between these wells are considered as parameters to be optimized in terms of achieving the longest period of effective operation of the geothermal loop. The results of numerical calculations are discussed. © 2018 Institute of Physics Publishing. All rights reserved.This work was supported by RFBR (projects No. 16-01-00401 and by Program of UB RAS (project No. 18-1-1-8).Russian Foundation for Basic Research (RFBR

A general model of an open geothermal system

Geothermal aquifers may be considered as a renewable resource of heat and energy. Internal earth heat may be transported with underground water to the surface by wells, and to not overexploit the aquifer, this water should be returned back. As a rule such systems consist of two wells. Hot water from the producing well is used, as example, for greenhouse complex or other buildings needs, which cools the water, and the injection well returns the cold water into the aquifer. To simulate this open geothermal system a three-dimensional nonstationary mathematical model and numerical algorithms are developed taking into account the most important physical and technical parameters of the wells to describe the heat distribution and thermal water transportation in the aquifer. Results of numerical calculations are presented. © Published under licence by IOP Publishing Ltd

Representation of solutions of boundary value problems for nonlinear evolution equations by special series with recurrently calculated coefficients

One of the analytical methods of presenting solutions of nonlinear partial differential equations is the method of special series in powers of specially selected functions called basic functions. The coefficients of such series are found successively as solutions of linear differential equations. The basic functions can also contain arbitrary functions. By using such functional arbitrariness allows in some cases, to prove the global convergence of the corresponding constructed series, and also allows us to prove the solvability of the boundary value problem for the Korteweg-de Vries equation. In the paper for a nonlinear wave equation a theorem on the possibility of satisfying a given boundary condition using an arbitrary function contained in the basic function is proved. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 19–07–00435The work was supported by Russian Foundation for Basic Research 19–07–00435

Thawing of Permafrost During the Operation of Wells of North-Mukerkamyl Oil and Gas Field

Thawing of ice-saturated rocks due to climate change or various technological impacts will be accompanied by subsidence of the earth’s surface and development of dangerous permafrost geological processes called thermokarst, leading to accidents, which may destruct the wells. Currently, the investment programs of the development of new northern oil and gas fields are restricted. In this regard, reducing the cost of developing the oil and gas fields is an urgent problem. For example, diminishing the area of well pads and maintaining efficiency in the northern oil and gas fields can significantly reduce the costs, in particular, during the design stage. A model of unsteady thermal fields propagation in frozen soil from new well construction for the North Mukerkamyl oil and gas field is developed, taking into account the construction features, the annulus, and the complex lithology of the soil surrounding the well. It is planned to take into account climatic and technological factors, in particular, an annual rest period of well operation, which held from several hours to two weeks. The paper discusses the computational features of the thermal fields calculating in frozen ground from wells and explores the influence of various parameters, which in the computations may lead to a significant increasing of thawing area in the well pads. © Siberian Federal University. All rights reserved.The work was supported by Russian Foundation for Basic Research 19–07–00435

Simulation of operation of an open geothermal system with seasonal variations

A mathematical model for the operation of an open geothermal cyclic system for two wells is presented. The production well is supposed to pump hot water from an underground geothermal reservoir. After the use for heating purposes the cooled water is pumped back into the aquifer through the injection well. Various options related to the seasonal needs for hot water are investigated for operating such a system. During the summer months hot water is required in less quantitites. The results of numerical calculations show that it is possible to choose such modes for greater efficiency and increase the time of operation of such a system. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 19-07-00435This work was supported by RFBR (project No. 19-07-00435)