Mavlyutov Institute of Mechanics

In this paper, the process of methane replacement in gas hydrate with carbon dioxide during CO2 injection into a porous medium is studied. A model that takes into account both the heat and mass transfer in a porous medium and the diffusion kinetics of the replacement process is constructed. The influences of the diffusion coefficient, the permeability and extent of a reservoir on the time of full gas replacement in the hydrate are analyzed. It was established that at high values of the diffusion coefficient in hydrate, low values of the reservoir permeability, and with the growth of the reservoir length, the process of the CH4-CO2 replacement in CH4 hydrate will take place in the frontal regime and be limited, generally, by the filtration mass transfer. Otherwise, the replacement will limited by the diffusion of gas in the hydrate.

The paper presents the implementation of the high-level decentralized control system for a group of mobile robots (MR), which provides a common information space in a group, and performs decomposition of the main task (task from operator) and generates subgroups on the basis of agents’ functional purpose.

The distributed lateral load on a plate located in a gas medium has been determined. The difference in the gas pressures of the plate surfaces results in a pressure drop and a lateral force, which depends on the middle surface curvature. It is shown that both these components of the lateral force must be taken into account in the general case. The influence of the second load component is small at a small ratio of the average pressure to the elastic modulus of the plate material and at a large relative thickness of the plate. At a small relative plate thickness and a large ratio of the average pressure of the medium to the elastic modulus of the plate material, the influence of the second component of the lateral load on the bending becomes significant. Cases of both linear and nonlinear plate bending are considered.

A mathematical model is proposed to describe methane–carbon dioxide replacement in gas hydrate by injecting liquid carbon dioxide into a porous medium initially saturated with methane and its hydrate. Self-similar solutions of the axisymmetric problems are constructed that describe the distribution of the main parameters of the reservoir. It is shown that there exist solutions according to which the process can occur both with and without boiling of carbon dioxide. Diagrams of the existence of each type of solution are constructed.

Seepage pressure waves in fractures in a porous permeable medium are studied. The effects of the reservoir and fracture porosity and permeability, the fracture width, and the rheological properties of the saturating fluid on the perturbation dynamics in the fracture are analyzed. It is shown that in porous permeable reservoirs, fractures are wave channels through which low-frequency fluctuations of borehole pressure propagate. Accurate solutions are obtained which describe the evolution of pressure fields in a fracture with an instantaneous change in the borehole pressure by a constant value. Based on these solutions, dependences of the fluid flow rate on time and interface pressure are determined.

The characteristics of the reflection and refraction of harmonic waves at its normal incidence on an interface between a “pure” liquid and liquid with bubbles filled with a vapor–gas mixture have been studied. The influence of variations of equilibrium temperature $${{T}_{0}}$$ of a system in the range $$300 \leqslant {{T}_{0}} \leqslant 373\,\,{\text{K}}$$ for two initial bubble sizes $${{a}_{0}} = {{10}^{{ - 6}}}$$ and $${{10}^{{ - 3}}}$$ m has been numerically analyzed. The effect of the perturbation frequencies on the reflection coefficient and refraction index at normal incidence has been studied. We have shown that the condition of total internal reflection can be fulfilled by the incidence of a wave from a bubbly liquid at the interface.

ПРОСТРАНСТВЕННОЕ МОДЕЛИРОВАНИЕ НЕСТАЦИОНАРНОЙ СТАДИИ ИСТЕЧЕНИЯ ВСКИПАЮЩЕЙ ЖИДКОСТИ ИЗ КАМЕР ВЫСОКОГО ДАВЛЕНИЯР.Х

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The cavitation tensile strength of a liquid for simple materials by the example of argon has been studied using molecular dynamics methods. Results on the negative tensile pressure have been obtained within the temperature range from 85 to 135 K. The tensile strength of liquid argon organization has been studied theoretically using the Redlich-Kwong equation of state. These approaches are in good agreement. Comparison with the earlier results of other authors has been performed. The test of the determination of the tensile pressure by molecular dynamics methods for homogeneous systems will make it possible to analyze qualitatively the cavitation strength in multicomponent systems as well as during consideration of heterogeneous nucleation, where the theoretical studies are extremely troublesome.

The equations of state for benzene, tetradecane, and their deuterated counterparts are derived on the basis of the original method of constructing the wide-range equations of state for hydrocarbon liquids in an analytical form. The equations describe gas and liquid phases at intensive gas-dynamic processes with consideration of evaporation and condensation and include dissociation and ionization processes associated with super-high pressures and temperatures.

A theoretical model of the development of a high-viscosity oil reservoir using the technology of paired horizontal wells is presented. The problem was solved numerically assuming that the two-well system is replaced by one hypothetical well through which simultaneous heating of the reservoir and oil recovery are performed. The heat consumption for heating the reservoir, the change in flow rate, and the mass of extracted oil for a certain period of time were analyzed for different values of the heating temperature, pressure difference, and induction period of the well. The obtained solutions can be used to determine heating conditions optimal in energy consumption.

The problem of injecting a hydrate-forming gas into a snow massif in the initial state saturated with the same gas are solved. Self-similar solutions describing the temperature and pressure fields, the distribution of snow, water, hydrate and gas saturation in the massif are constructed. It is shown that when forming a hydrate, depending on the initial thermobaric state of the ice-gas system, as well as the intensity of gas injection, it is possible to distinguish various characteristic zones in the filtration region that differ in their structure and length. It has been established that with an increase in the gas injection pressure and a decrease in the initial snow-saturation of the massif, the volume formation zone of the hydrate increases.

The basic methods of constructing a hexagonal mesh in Cartesian coordinates for a three-dimensional cylindrical region are considered. Several variants of grids, describing the inner region of the vortex tube, are presented. Advantages and disadvantages of presented meshes are discussed. The gas dynamics in a vortex tube is described by the mathematical model, which consists of Navier-Stokes equations for compressible viscous fluid, and the perfect gas law. The solution is done with the usage of the PIMPLE algirithm in OpenFOAM. The simulation results on different grids, including the result with the inversion of the temperature field, and their discussion are presented.

In this paper, we compare the features of the shock compression of 1-mm vapor bubbles and the nonsphericity growth during their collapse in hydrocarbon (acetone, benzol, and tetradecane) liquids. At the beginning of compression, the vapor is in a saturation state at 1.03 MPa, and the bubble collapse is caused by a liquid pressure of 5 MPa. It has been found that, during the collapse of the bubble in acetone, only weak compression waves occur in its cavity, while intense, radially convergent compression waves that transform into shock waves arise in the bubbles in benzol and tetradecane, which have a significantly greater molecular weight and, consequently, a lower speed of sound in the vapor. This leads to an extreme focusing of energy at the bubble center. A shock wave in tetradecane appears shortly after the onset of collapse, whereas a shock wave in benzol forms only during the reconvergence of the unstressed compression wave to the center of the bubble after its reflections from the center and the interface. As a result, the highest values ​​of thermodynamic parameters are achieved in tetradecane, while the lowest values are attained in acetone. The bubble nonsphericity is shown to increase by two orders of magnitude less in tetradecane than in acetone and benzol by the time it reaches the extreme values ​​of the thermodynamic parameters.

This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3, ... with the wavelength λ = 2πR/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.

The characteristics of the reflection and refraction of harmonic waves at its "oblique" incidence on an interface between a "pure" liquid and liquid with bubbles filled with a vapor–gas mixture have been studied. For the considered problem, we have obtained the dispersion equation and carried out a numerical analysis of the effect of the perturbation frequencies in the range 102–107 s–1 on the dependence of the angle of refraction on that of incidence for three equilibrium temperatures $${{T}_{0}}.$$ The dependence of the critical angle of incidence on the parameters of a two-phase system and the perturbation frequencies has been studied for the same reflection.

We propose a complex sealing compound for increasing the efficiency of shutoff operations based on natural materials processing for materials such as sand, peat, rice, and husks. We studied the influence of mechanical activation processes on the mechanical and rheological properties of the developed sealants. Through mechanochemical activation, sand dissolution in a low-concentrated alkali solution was possible, and gelling the resulting sodium silicate while reinforcing it with undissolved sand particles to obtain a sealant composition. We used this approach to produce a hybrid sealing compound based on activated rice husks with up to 20% biogenic silicon dioxide combined with mechanically activated peat: the maximum shear strain of the hybrid sealant was 27.7 ± 1.7 Pa. We produced hydrogels based on sodium silicate, polyacrylamide, and chromium acetate, reinforced with mechanically activated rice husks. We studied the sealants’ rheological and filtration properties and observed the respective viscoplastic and viscoelastic properties. An increase in the dispersion concentration from 0 to 0.5% increased the maximum strain value of undestroyed hydrogel’s structure in the range 50–91 Pa and the maximum shear strain from 104 to 128 Pa. The high residual resistance factor values of the ideal fracture model make the natural and plant-renewable raw materials very promising for repair and sealing work.

Eigenfrequencies of bending oscillations are determined for a resonator with rectangular cross-sections mounted on hinged supports. Consideration is given to the surface effect caused by the interaction between gas pressure and the difference in the areas of the resonator’s convex and concave surfaces. Changes in the frequency spectrum are examined at the presence of both concentrated and uniformly distributed masses attached to the resonator’s surface. The solution of the inverse problem enables the identification of attached masses using changes of eigenfrequencies.

A complex numerical and experimental method is proposed for studying 3D dynamics of a bubble contacting with a surface in the presence of an acoustic field. The numerical approach is based on the boundary element method for potential flows, which is most efficient for solving the problems in a 3D formulation. The use of heterogeneous computer architectures consisting of central graphic processors and becoming more and more popular makes it possible to increase the scale of the problem and sufficiently reduce the calculation time. The mesh destabilization problems are solved using a spherical filter. To describe the contact line dynamics, a semi-empirical law of motion is used. The experimental method is based on high-speed recording and optical microscopy. An air bubble contacts with the inner surface of an experimental cell made from acrylic glass and filled with distilled water. The acoustic field in the cell generated by a disk-shaped acoustic radiator is measured using a hydrophone. The behavior of the bubble contacting with a hydrophillic surface is considered for the cases of a fixed or moving contact line. The shape and volume oscillations of the bubble are investigated. The results of numerical simulations agree qualitatively with the experimental data.

The influence of the average value and amplitude of the transient internal pressure in the pipelines on the spatial vibrations of the latter has been assessed. The graphic dependences of the spatial vibrations, their phase patterns, Fourier spectra, and Poincare maps have been presented. The latter have been analyzed depending on the input parameters and time. Brief conclusions have been formulated.