Displacement of oil by solutions of an active additive from a uniform stratum with allowance for gravity

Self-similar solutions describing the displacement of oil by solutions of an adsorbed active additive have been obtained and investigated [1–3] in the framework of a one-dimensional flow model with neglect of diffusion, capillary, and gravity effects. In the present paper, a self-similar solution is constructed for the problem of oil displacement by an aqueous solution of an active additive from a thin horizontal stratum with allowance for gravity under the assumption that there is instantaneous vertical separation of the phases. This makes it possible to estimate the effectiveness of flooding a stratum by solutions of surfactants and polymers in the cases when gravitational segregation of the phases cannot be ignored.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–92, January–February, 1984.     

Nonisothermal displacement of high-paraffin oils by water with allowance for solid-phase precipitation

A mathematical model of the nonisothermal displacement of oil by water with allowance for solid-phase precipitation is proposed. Self-similar solutions of the problem of nonisothermal displacement of oil from a homogeneous, thermally insulated formation are obtained. The inverse problems of determining the relative phase permeabilities and the temperature dependence of the paraffin saturation concentration from laboratory displacement data are solved. Exact solutions of the non-self-similar problems of the displacement of high-paraffin oil by a slug of hot water and of the thermal delay problem are obtained. The nonisothermal displacement of high-paraffin oils by water with allowance for heat transfer to the surrounding strata is subjected to qualitative analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–137, May–June, 1989.The authors are grateful to A. K. Kurbanov and Yu. V. Kapyrin for useful discussions and their interest in the work.     

Gas-gas displacement in a fractured porous reservoir

The results of an experimental investigation of the process of miscible displacement of a gas from a fractured porous reservoir by another gas are presented. It is established that the displacement process is influenced by convective and molecular diffusion. The displacement coefficient depends both on the reservoir properties of the formation and on the technological displacement parameters. The experiments revealed a decrease in the displacement coefficient with increase in the permeability ratio of the joints and the blocks and with decrease in formation pressure. The dependence of the displacement coefficient on the average gas velocity in the reservoir, i.e., the ratio of the gas flow rate to the product of the flow area and the total reservoir porosity coefficient (including the blocks and the joints), is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–79, May–June, 1991.     

Motion of the interface of two fluids with formation of a region of two-phase flow

A study is made of the problem of the displacement of one fluid by another with the formation of a region of combined flow in the case of an elastic flow regime in the region of the displaced fluid. A self-similar solution is constructed for the flow equations averaged with respect to the vertical coordinate. A numerical algorithm is developed for determining the saturation in the region of the mixture, the pressure, and also the position and shape of the interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 78–83, October–December, 1981.We thank A. A. Barmin for a helpful discussion of the work.     

Example of parametric resonance in a rotating flow

Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1–5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–177, March–April, 1987.     

Differential equation for a stratified fluid and its particular solutions

The plane steady motion of a stratified ideal incompressible fluid in a gravity field is examined. Considering that the parameter characterizing the fluid particles — their density ₀ — is constant along the streamline, it is convenient to take the stream function as one of the independent variables and, in view of the presence of the gravity force, the Cartesian coordinate as the other. In this study, on the basis of Lavrent'eva's equation [1, 2, 3], the differential equation is derived for a single unknown function — the vertical displacement of the streamline y(y₀, x), where y₀ is its initial position and x is the horizontal coordinate. The particular solutions corresponding to a wave guide, cnoidal and solitary waves and, moreover, waves of the type corresponding to a smooth ascent to a new level are presented. A similar coordinate system was used in [4], but there the problem was reduced to a system of partial differential equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 83–87, September–October, 1986.The authors are grateful to A. A. Barmin for discussing their results.     

Interaction between a vertical wall and a wave propagating in a channel of parabolic cross section

The reflection of a long wave from a vertical wall is studied on the assumption that the wave travels in a channel or river of parabolic cross section. According to [11], such cross sections are found in river beds formed in noncohesive soils. Expressions describing the evolution of the height of the wave at the vertical wall are obtained on the assumption that the exponent of the parabola takes the values k=2/(2n – 1). The conditions corresponding to the formation of a bore at the vertical wall are described.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 102–105, January–February, 1987.The author wishes to thank E. N. Pelinovskii for his interest in the problem.     

Interaction of an internal gravity current with a submerged circular cylinder

The problem of hydrodynamic loads due to the interaction of a gravity current propagating over a bottom channel with a submerged circular cylinder is studied experimentally. It was shown that in the examined range of parameters, the hydrodynamic loads are simulated after Froude. The hydrodynamic loads are maximal if the cylinder lies on the bottom, and they decrease rapidly with increase in the distance from the cylinder to the channel bottom. The effects of mixing and entrainment on the nature of the hydrodynamic loads are considered.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 81–90, March–April, 2005.     

Hydrodynamics in weak gravitational fields two-dimensional oscillations of an ideal fluid in a rectangular channel

The two-dimensional problem of determining the frequencies and modes of small natural osciliations of an ideal fluid in a rectangular channel under near-weightless conditions is considered. It is assumed that a weak gravitational field acts parallel to the vertical walls of the channel. The Ritz method is employed for the variational problem, which is equivalent to the problem of oscillations of a fluid under weightless conditions [1, 2].Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–13, September–October, 1972.     

Diffraction of regular waves by an arbitrarily oriented system of vertical circular cylinders

The linear theory of small-amplitude waves is used to construct a solution to the problem of the diffraction of surface gravity waves by a system of arbitrarily oriented vertical circular cylinders. Analytic expressions are obtained for the wave forces and overturning moments acting on each cylinder of the system. A system of two rows of cylinders with three cylinders in each row is considered as an example. It is shown that for certain relationships between the diameter of the cylinders, the distance between them, the angle of approach of the wave, and its wavelength, the maximal values of the hydrodynamic forces acting on the cylinders of the system with allowance for the interaction of the diffracted fields may be appreciably greater than when no allowance is made for it.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 177–181, January–February, 1984.     

Hydrodynamics in weak gravitational fields small oscillations of an ideal liquid in a cylindrical vessel

The problem of determining the frequencies and forms of small natural oscillations of an ideal liquid in a cylindrical vessel under conditions close to weightlessness is examined. It is assumed that a weak homogeneous gravitational field acts parallel to the vertical generatrix forming the cylinder. In contrast to [1], where only the first antisymmetric oscillation frequency is found for a semiinfinite cylindrical vessel, the frequencies of several axiosymmetric, antisymmetric, etc. oscillations are obtained as functions of the gravitational-field intensity and other parameters of the problem. The Ritz method is employed for two different variations of the problem, equivalent to that of oscillations of an ideal liquid under conditions of weightlessness [1–5].Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–13, March–April, 1973.     

Self-similar solutions of problems of two-phase flow through porous media with allowance for the compressibility of one of the phases

Self-similar problems of mutual displacement are solved with allowance for the compressibility of one of the phases. It is found that when an incompressible liquid is displaced by a gas the extent of displacement increases. The mutual displacement of gas-liquid mixtures results in the formation of not one but several saturation jumps, i.e., the structure of the displacement zone is much more complex.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 71–80, January–February, 1990.The authors are grateful to V. I. Maron for useful discussions.     

Miscible displacement from fractured porous media

A model of miscible displacement of incompressible fluids from a fractured porous medium is proposed. The model describes the process of displacement of oil by solvents, the cycling process of displacement of aliphatic hydrocarbon gas by dry gas at low repressions on the formation, and other processes of single-phase multicomponent displacement from fractured porous media. Problems relating to the pumping of a neutral admixture and admixture slugs through a fractured porous reservoir are solved.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–110, November–December, 1989.The authors are grateful to K. S. Basniev, A. K. Kurbanov, V. I. Maron, and M. I. Shvidler for useful discussions.     

Turbulent wake in a stratified medium

The problem of determining the form of the turbulent wake being formed behind a selfpropelled body in a medium with density varying in the direction of the effect of gravity is considered. The schematic picture of wake development behind a moving object is the following: Initially, diffusion is identical in all directions, and the wake broadens symmetrically; diffusion becomes strongly anisotropic with recession from the object, it diminishes in the vertical direction under the effect of gravity, and the wake becomes flattened; turbulent mixing within the wake results in the production of a more homogeneous density distribution within the volume occupied by the wake than in the surrounding medium; such a fluid volume turns out to be removed from the equilibrium state and tends to return to the equilibrium state under the effect of gravity; collapse of the wake occurs accompanied by its further expansion in the horizontal direction and the excitation of internal waves.Translated from ZhurnalPrikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 68–72, September–October, 1970.     

Discontinuous solutions of an interacting three-dimensional hypersonic boundary layer

The paper is a mathematical study of the three-dimensional flow of viscous gas in a hypersonic boundary layer that develops along a flat wing whose leading edge has a step shape. The flow interacts with a flap on the wing set at a small angle. A linear solution to the problem is constructed under the assumption that the deflection angle of the flap is small and the difference between the length of the plates is of order unity. It is shown that an important part in the formation of the flow near and behind the flap may be played by the change in the pressure along the span of the wing due to the step shape of the leading edge. It is significant that although the pressure and displacement thickness are continuous functions of the transverse coordinate, the longitudinal and transverse components of the friction force have discontinuities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 19–26, March–April, 1991.I thank V. V. Sychev and A. I. Ruban for suggesting the problem, for valuable advice, and assistance.     

Circulation instability of steady falling of a flat layer of fine dispersed particles

A numerical investigation has been made of the linear instability of the steady falling under gravity of an infinite horizontal layer of fine dispersed particles in an incompressible atmosphere. The layer has an inhomogeneous vertical distribution of the dispersed phase and a small volume concentration of the particles, the hydrodynamic interaction between which occurs solely through the carrier phase. It is shown that steady falling is unstable and that the layer of particles breaks up into individual convective cells with a characteristic scale of the order of the thickness of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 78–83, January–February, 1991.     

Interaction of Internal Gravity Current with an Obstacle on the Channel Bottom

The problem of hydrodynamic loads arising from the interaction of gravity currents with an obstacle on the channel bottom was studied experimentally. The gravity-current structure was visualized at the stage of formation and at the stage of interaction with the obstacle. The dependence of the propagation velocity of the gravity-current front on the nondimensional current depth and the Archimedes number was studied. In the region of self-similarity in the Archimedes number, the behavior of hydrodynamic-load coefficients was studied as a function of the nondimensional gravity current depth.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 39–46, July–August, 2005.     

Motion of a cylindrical cavity near a free boundary of a liquid

The dynamics of a cylindrical cavity in a liquid with no allowance for vertical displacement are considered in [1–3]. The present study investigates the pulsation motion of a cylindrical cavity near a free boundary of a liquid, allowing for displacement of the axis of the cavity in the vertical direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1988.     

Polymer flooding of oil formations with bottom water

A quasi-one-dimensional model describing the process of polymer flooding of oil formations underlain by bottom water is proposed. The model is based on the assumption of instantaneous gravitational phase separation along the vertical and is a generalization of the hydrodynamic model previously considered in [1]. The self-similar solutions constructed show that in the case of polymer flooding of an oil formation the presence of bottom water leads to qualitative changes in the saturation and concentration distribution and has an important influence on both the running and the final oil output. The results obtained are consistent with the data of two-dimensional numerical modeling of the process [2] and indicate the possibility of more efficient exploitation of water-oil zones as a result of pumping thickened water into the formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–90, May–June, 1986.     

Stability of frontal displacement of fluids in a porous medium in the presence of interphase mass transfer and phase transitions

To preserve the stability of the front relative to small perturbations when one fluid is displaced by another the pressure gradient must decrease on crossing the front in the direction of displacement. Initially, this criterion was established for the piston displacement of fluids [1, 2], and later in the case of two-phase flow of immiscible fluids in porous media for the displacement front corresponding to the saturation jump in the Buckley—Leverett problem [3, 4]. Below it is shown that the same stability criterion remains valid for flows in porous media accompanied by interphase mass transfer and phase transitions [5, 6]. Processes of these kinds are encountered in displacing oil from beds using active physicochemical or thermal methods [7] and usually reduce to pumping into the bed a slug (finite quantity) of reagent after which a displacing agent (water or gas) is forced in. The slug volume may be fairly small, especially when expensive reagents are employed, and, accordingly, in these cases the question of the stability of displacement is one of primary importance. These active processes are characterized by the formation in the displacement zone of multiwave structures which, in the large-scale approximation (i.e., with capillary, diffusion and nonequilibrium effects neglected), correspond to discontinuous distributions of the phase saturations and component concentrations [5–10]. It is shown that the stability condition for a plane front, corresponding to a certain jump, does not depend on the type of jump [11, 12] and for a constant total flow is determined, as in simpler cases, by the relation between the total phase mobilities at the jump. An increase in total flow in the direction of displacement is destabilizing, while a decrease has a stabilizing influence on the stability of the front. Other trends in the investigation of the stability of flows in porous media are reviewed in [13].Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 98–103, March–April, 1986.