Steady filtration through foam

The process of filtration of a liquid through a deformable porous medium with the structure of a gas-liquid foam is considered. A basis is provided for a model of fluid flow through foam. Expressions are obtained for the differential law of steady filtration and the integral laws of filtration through a vertical column of foam under the influence of body and surface forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–103, May–June, 1986.     

Two-dimensional problems of displacement in the case of nonlinear filtration laws

A method is proposed for calculating the multidimensional displacement of oil possessing anomalous properties from productive strata by water. Numerical solutions are obtained on the basis of the most generally accepted models of non-Newtonian oil within the framework of the theory of two-phase filtration of immiscible liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–75, September–October, 1976.     

Problems of pressureless nonlinear filtration

The article discusses pressureless flows for filtration with a limiting pressure gradient. In the plane of the hodograph of the filtration rate, the search for the stream function reduces to the solution of a boundary-value problem for an elliptical equation in a region with curvilinear boundaries. A numerical solution of this problem is constructed by the method of finite elements, after which the whole picture of the flow is reconstructed by integration. An analysis is made of the effect of a limiting gradient on the integral characteristics of the flow. The fundamental special characteristics of problems of pressureless filtration in the presence of a limiting gradient are noted: the nonsingularity of the solution, the formation of stagnant zones adjacent to the free surface, etc.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–181, March–April, 1978.     

Investigation of filtration with a nonstationary free boundary

The article indicates an inverse method for constructing filtration flows in the presence of a free surface. It gives concrete series of varying free surfaces, equalizing-out elevations and depressions, and surfaces of a rise or fall of the ground waters as a result of the work of drainage or injection boreholes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–172, November–December, 1974.     

Effect of an impermeable inclusion in the underlying highly permeable pressurized horizon on the conditions of ground water in an irrigated layer of soil

The problem of plane, nonpressurized, steady-state filtration through a layer of soil into an underlying pressurized horizon, which contains an impermeable section at the top, with uniform infiltration on the free surface is solved in a hydro-dynamic formation. A constructive solution of the problem is given with the help of the method of P. Ya. Polubarinova-Kochina; representations are obtained for the characteristic dimensions of the flow scheme and the depression. The case of limiting flow — no head in the bottom, highly permeable layer — studied in [1] is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–5, May–June, 1986.The author thanks V. N. Emikh for useful remarks and discussions.     

Plane filtration in a laminar medium in the presence of imperfect reservoirs

Exact and approximate solutions were obtained describing filtration flow in a plane region in sectors corresponding to imperfect reservoirs and suction gaps. These equations make it possible to obtain an approximate solution to the three-dimensional problem of the filtration of ground waters by solution of the two-dimensional problem; imperfect reservoirs are permitted in the filtration region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–83, May–June, 1973.     

Viscous hypersonic flows for various aerophysical models

The results of mathematical simulation of hypersonic air flow past a sphere with allowance for chemical nonequilibrium and ionization are presented. The calculated data are obtained on the basis of a numerical solution of the Navier-Stokes equations and the hypersonic viscous shock layer equations. The equilibrium radiation temperature of the body surface, the pressure, and the shock wave detachment are compared for these models. The combined effect of molecular transport and the catalytic properties of the body surface on the aerodynamic heating is analyzed. The results of the effect of certain models of the thermochemical disequilibrium of the gas on the temperature of the body surface are also analyzed along a heat-stressed interval of the reentry trajectory of an aerospace vehicle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–161, July–August, 1996.     

Unsteady flows of an inhomogeneous incompressible viscous fluid

This paper deals with a theoretical analysis of the transfer of reactive impurities by open and filtration flows of an incompressible viscous fluid. The first section of the paper studies the model of an inhomogeneous incompressible viscous fluid, which is widely used in meteorology and oceanology, with additional allowance for the drag of the magnetic field or porous medium. Another object of research in this paper is the model of filtration of an inhomogeneous incompressible fluid in porous media proposed by V. N. Monakhov (1977) (Section 2). In both models, hydrodynamic flows determine the motion of the mixture as a whole and the temperature and concentration distributions of the components of an inhomogeneous fluid are described by a common nonlinear system of equations of diffusive heat and mass transfer.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 44–51, March–April, 2005.     

Diffusiophoresis of an aerosol particle in a binary gas mixture

The diffusion force and rate are calculated for the diffusiophoresis of a spherical particle in a binary gas mixture by solving the gas–kinetic equations. Two schemes of diffusiophoresis are considered: constant–pressure diffusion and diffusion of one mixture component through the other fixed component. The problem is solved by the integral–momentum method at arbitrary Knudsen numbers. Diffuse scattering of the gas molecules on the particle surface is assumed. The Lorentzian and Rayleigh models of a binary gas mixture are considered. The dependences of the force and rate of diffusiophoresis on the Knudsen number and the other determining parameters are analyzed. The results obtained are compared with well–known experimental data.     

Ground water regime in an irrigated soil layer with lower lying strongly permeable pressure level

A solution is found to the problem of planar pressureless steady filtration from a system of equidistance channels of the same thickness through a soil layer to a lower lying pressure level in the case of uniform infiltration (evaporation) to the free surface. The unique solvability of the system of equations for the two unknown transformation parameters is established. The filtration flow rate from a channel is investigated analytically as a function of the infiltration intensity and the magnitude of the backwater.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 168–174, March–April, 1979.I thank N. S. Kolodei for assistance in the calculations and the simulation.     

Exponential filtration of a liquid in the presence of sources

A study is made of the plane exponential filtration of an incompressible liquid under the action of two sources (sinks). The solution is based on an S. A. Chaplygin transformation, the possibility of whose use in the investigation of nonlinear filtration was first noted in [1]. In [2–5] this transformation was used in a consideration of filtration with a limiting gradient. In the present article, another nonlinear law of resistance, an exponential law, is used to construct an exact solution. The use of S. A. Chaplygin variables makes it possible to transform the starting system of equations to a Helmholtz equation, which then reduces to a functional relation which is solvable by the Wiener-Hopf method. The results obtained point to the possibility of using the proposed method to solve other problems of plane exponential filtration, generated by sources or sinks, particularly when they are arranged symmetrically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–96, September–October, 1973.     

Calculating reclamation drainage in a two-layer medium with infiltration

This article presents the solution of the filtration problem in application to reclamation drainage, a system of horizontal pipe drains, under conditions of a two-layer medium and infiltration feed (see figure), where, in contrast with [1], the solution is given in a more rigorous and compact form. We note that such a problem has been considered previously by several authors under conditions of a uniform medium.Similarly, as has been done by other authors, for example in [1, 2], the problem solution is carried out under two assumptions: a) the slightly curved surface of the underground water is replaced by an averaged straight line, b) in place of the known exact condition at the free surface we take Im( ₁)=–, i.e., the vertical component of the filtration velocity at the free surface is equal to the infiltration rate.As noted in [3], these assumptions will not introduce a significant error in the practical calculations.We first seek the problem solution for a single drain (sink), and then we use the superposition method for an infinite series of drains (sinks) located at the same distance from one another, which is then the final problem solution.     

Elasticoplastic conditions of the filtration of a liquid in porous media

The article discusses questions in the theory of filtration in porous media, taking account of elastic, elasticoplastic, and plastic deformations. Parameters are introduced to evaluate irreversible effects in petroleum- and water-bearing strata, i.e., coefficients of the change in the porosity and the permeability. Equations are derived for filtration under unsteady-state and steady-state working conditions of wells and galleries. Two limiting cases, which allow analytical solutions, are separated out. In the general case, the equations of elasticoplastic filtration conditions are solved on an electronic computer. The numerial calculations show that the predominating effect results from taking account of the irreversible change in the permeability, depending on the change of the pressure in the stratum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 84–90, September–October, 1973.The author is grateful to V. N. Nikolaevskii for his evaluation of the work.     

Modeling Floodplain Filtration for the Improvement of River Water Quality

A mathematical model was developed to describe a treatment method of floodplain filtration for the improvement of river water quality. The process consists of spraying poor quality river water onto the river floodplains and thus allowing soil filtration to treat water before it gets back again into the main river stream. This technique can be readily employed in Korea because it exploits the characteristics of the climate and rivers in the country, as described in an experimental study of Chung et al. The model was analyzed by numerical methods and validated by comparing the simulated values with experimental data. A scenario analysis of the model was also performed in order to have a better understanding of the floodplain filtration process. Our results show that the model was able to predict the reduction in organic matter and NO₃^– in river water through the floodplain filtration. Furthermore, it was found that only a few decimeters of top soil profile were enough to degrade most of the organic matter under wider operational conditions than those reported in the literature. Also, it was found that significant infiltration of atmospheric oxygen took place near the soil surface. The N₂O emission and the NO₃^– leaching increased with the increase in the influent NO₃^– concentration. However, the N₂O emission due to floodplain filtration was not expected to exceed 0.1 mL/m²-day.     

Multi–Front Phase Transitions During Nonisothermal Filtration of Live Paraffin–Base Crude

By numerical modeling of nonisothermal filtration of multicomponent oil with allowance for the Joule—Thomson effect, adiabatic effect, and heat of phase transitions that occur during oil degassing and paraffin crystallization, the formation of profiles of phase–saturation, concentrations of oil components, and temperature in oil beds is studied. It is shown that consideration of many components results in occurrence of phase–transition fronts during degassing of oil components and paraffin crystallization. In turn, paraffin crystallization gives rise to temperature oscillations. Depending on the initial paraffin concentration and on the ratio of phase–transition heats for oil degassing and paraffin crystallization in an oil bed, either decaying or steady–state temperature oscillations are observed.     

Steady-state filtration of gas-condensate mixtures

In the present article, in an analysis of the results of an investigation of gas-condensate wells by the method of steady-state samples, use is made of known solutions to the problem of the steady-state filtration of a stratified liquid (gas) with constant properties [1, 2]. However, the filtration of a gas-condensate mixture to a well with the reduction of the pressure below the pressure of the start of condensation p₊ is accompanied by considerable changes in the composition and properties of the gas and liquid phases which, in turn, have an effect on the filtration characteristics of a porous medium. Among the many communications devoted to this problem (see, for example, the reviews [3, 4]), there are investigations which take account of the effect of a change in the composition and properties of the phases on the characteristics of steady-state filtration [5–7]. Here, it is proposed to model real gas-condensate mixtures by pseudobinary or pseudoternary systems with experimentally determined phase ratios. However, there are still no sufficiently well-justified examples of the reduction of multicomponent mixtures to the above-mentioned model systems. The present article, within the framework of the theory of the filtration of multicomponent systems, discusses the problem of the steady-state filtration of a real gas-condensate mixture to a central well in a round stratum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 69–75, September–October, 1973.The authors thank V. N. Nikolaevskii for his invaluable evaluation of the work, and R. G. Zotov for his aid in making the calculations.     

Prediction of salt conditions in irrigated soils in the presence of drainage

The equations of convective diffusion are solved for two flat layers, using the method of finite integral transformations. Exact solutions are obtained to the problem in the presence of a descending or ascending filtration flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 113–117, November–December, 1972.     

Laminar boundary layer stability on membrane type deformable surfaces

In connection with the successful experiments of Kramer [l, 2] on models sheathed by flexible coverings, attempts have been made to explain theoretically the effect of boundary deformation on the position of the point of stability loss in the boundary layer. Korotkin [3] examined the stability of a plane laminar boundary layer on an elastic surface under the assumption of a linear connection between the pressure perturbation and the normal deformation of the surface. Benjamin [4] and Landahl [5] investigated the stability of the laminar boundary layer on a membrane type surface under the assumption that the physical characteristics of the surface depend on the perturbing flow wavelength. In the following we examine stability of Blasius flow on a membrane type surface whose physical characteristics are constant along the length.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, vol. 10, no. 6, pp. 52–56, November–December, 1969.     

Ablation under the combined erosive and thermal influence of a two-phase flow

A study is made of the combined effect of a high-velocity two-phase (gas—solid particles) flow to the surface of a body. Different ablation models are proposed for simultaneous thermal (or thermochemical) and impact influence of the flow on the material. A numerical investigation is made of the unsteady thermal state of a body on which solid particles impinge, and the ranges of the determining parameters in which the thermal effect is negligibly small compared with the erosive effect are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 120–126, January–February, 1984.     

Unsteady-state filtration from screened water reservoirs and from the storage elements of industrial drainage systems

This paper considers the axisymmetric problem of unsteady-state filtration from a water reservoir or from the storage element of industrial drainage systems, which are round in a plan view.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 165–170, November–December, 1971.