Dynamic model of liquid motion in a porous medium

A theory which takes account of the role of inertial effects in liquid motion in a porous medium is developed. For a compressible liquid, not only the hydrodynamic equations but also the thermodynamic transfer equation are formulated. The initiation, propagation, and dissipation characteristics of eddy motion are considered. Matching conditions at the interface between the media and boundary conditions are obtained. An approximate formulation of the problem is given, isolating in the porous medium a basic flow region in which the classical Darcy law is valid. As an illustration, weakly perturbed liquid flow in a plane channel with an insert of porous material is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 89–95, November–December, 1978.     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

Development of a high performance flexible porous burner(FPMB) with an adjustable cooling effect

A high performance flexible porous medium burner that can burn gaseous and liquid fuel with different type of flames(premixed and non-premixed) is proposed. The merit of the combustion within porous medium is that heat is recirculated from the combustion gas to porous medium at upstream wherein vaporization is taken place(in case of liquid fuel) or preheated(in case of gaseous fuel) before mixing with the combustion air followed by combustion within another porous medium at downstream. In a former version of the high performance flexible porous medium burner, the upstream porous medium is incorporated with a cooling system using the combustion air as a coolants to prevent thermal decomposition of fuels and thus the burner clogging caused by carbon deposit within the porous medium can be avoided. However, the cooling effect cannot be properly controlled such that the boiling point of the liquid fuel is maintained at suitable value irrespective of the volume flow rate of the combustion air,which is linearly varied with the firing rate of the burner. In particular at the lean burn condition, where high air flow rate is required with high cooling effect with porous medium. This can result in the porous medium temperature lower than the corresponding boiling point of the liquid fuel and thus evaporation of the fuel is failed and the combustion is ceased. Therefore, method of controlling the cooling air flow rate in the porous medium is proposed and studied in order to appropriately control the porous medium temperature and maintain it at above the boiling point irrespective of the combustion conditions. In this research, experimental and computation analysis are used to design the flexible porous burner(FPMB),with adjustable cooling effect. The result shows that, the new design of FPMB which has temperature in the upstream porous medium is higher than boiling point and lower than thermal decomposition temperature of fuel(kerosene) at all conditions and can be operated at a wide range of equivalence ratio without fuel decomposition and fuel non-vaporization problem.     

Transmission of waves in a liquid through absorbing layers and subsequent interaction of the waves with an obstacle

The propagation of waves in porous media is investigated both experimentally [1, 2] and by numerical simulation [3–5]. The influence of the relaxation properties of porous media on the propagation of waves has been investigated theoretically and compared with experiments [3, 4]. The interaction of a wave in air that passes through a layer of porous medium before interacting with an obstacle has been investigated with allowance for the relaxation properties [5]. In the present paper, in which the relaxation properties are also taken into account, a similar investigation is made into the interaction with an obstacle of a wave in a liquid that passes through a layer of a porous medium before encountering the obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–53, March–April, 1983.     

Motion of a multicomponent sorbed mixture in a porous medium when the medium is preliminarily saturated with certain components of the mixture

The numerical and invariant solutions of a system of quasilinear equations in partial derivatives, describing the motion of a multicomponent sorbed gas (or liquid) mixture through a porous medium previously saturated by certain sorbed components of the mixture, are analyzed; in the presence of Langmuir sorption isotherms, invariant solutions are obtained in the form of Riemann invariants.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 50–56, January–February, 1976.     

Nonstationary Gas Filtration Caused by an Intense Thermal Action on a Damp Porous Medium

A mathematical model and an algorithm are proposed for evaluating nonstationary heat and mass transfer in a porous medium that contains a mechanically absorbed liquid and a two–component gas (vapor—inert gas mixture). The case of an intense thermal action on a damp porous mixture caused by an external heat flux and convective heat transfer is considered. Typical flow regions and typical regions of the interaction between the phases are described.     

Propagation of nonlinear waves in a porous medium with two-phase saturation by a liquid and a gas

The propagation of nonlinear waves through a porous medium saturated with a viscous liquid and a gas is investigated with allowance for the capillary pressure. Numerical solutions of the traveling-wave type are constructed for the generalized Korteweg-de Vries-Burgers equation for the wave amplitudes. Three types of regimes of longitudinal wave propagation, including soliton-like regimes, are found.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 86–95, July–August, 1996.     

Mixed Convection Effect on Melting from a Vertical Plate in a Porous Medium

In the present work, the effect of mixed convection about vertical surfaces on the phenomenon of melting process in a fluid-saturated porous medium is analyzed on the basis of boundary layer approximations. Similarity solutions are obtained for aiding external flow. The final similarity equations are integrated numerically by use of the fourth-order Runge–Kutta method. Results are reported for the flow and thermal fields in the melt region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface.     

Experimental investigation in filtration of hydrocarbons with mass transfer

The results are given of an experimental investigation into the process of extraction from a porous medium of a liquid hydrocarbon (precipitated condensate) filling part of the pore space by means of hydrocarbon solvents.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–170, September–October, 1979.     

Surface porosity and permeability of porous media with a periodic microstructure

Various ways of determining the surface porosity, the relation between the porosity and the surface porosity and the representation of the permeability in terms of the characteristics of the microstructure of the porous medium are analyzed with reference to model porous media with a periodic microstructure. It is shown that it is necessary to distinguish between the geometric (scalar) and physical (tensor) suface porosities and that the geometric surface porosity, the physical surface porosity and the porosity are different characteristics of the porous medium.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 79–85, January–February, 1995.     

Mechanics of a porous two-phase strongly viscous medium and some geophysical applications

According to modern geophysical ideas [1], the oceanic crust is formed when the lithospheric plates move apart in the axial regions of the rift zones of the Earth due to the penetration of molten matter from the asthenosphere into cracks and pores of the lithosphere and the subsequent solidification of this matter (the lithosphere and asthenosphere are the upper layers of the Earth). In these regions, which have a width of the order of several tens of kilometers, the liquid magmatic material penetrates the crystalline skeleton of the crust, which means that one must regard this region as a saturated fissured and porous deformable medium that permits phase transitions between the skeleton and the liquid filler. Geophysical data indicate that there is a similar two-phase fissured and porous structure of the medium in the asthenosphere (at least in certain regions) and in regions of high tectonic and volcanic activity. Because geological processes take place slowly, it can be assumed that the skeleton of the two-phase medium is deformed as a strongly viscous incompressible Newtonian liquid with a viscosity much greater than the viscosity of the filler.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 53–63, November–December, 1979.We thank V. P. Myasnikov and V. N. Nikolaevskii for helpful discussion of the present work.     

The Use of Fick's Law for Modeling Trace Gas Diffusion in Porous Media

Two models for combined gas-phase diffusion and advection in porous media, the advective-diffusive model (ADM) and the dusty-gas model (DGM), are commonly used. The ADM is based on a simple linear addition of advection calculated by Darcy's law and ordinary diffusion using Fick's law with a porosity–tortuosity–gas saturation multiplier to account for the porous medium. The DGM applies the kinetic theory of gases to the gaseous components and the porous media (or dust) to develop an approach for combined transport due to diffusion and advection that includes porous medium effect. The ADM and Fick's law are considered to be generally inferior for gas diffusion in porous media, and the more mechanistic DGM is preferred. Under trace gas diffusion conditions, Fick's law overpredicts the gas diffusion flux compared to the DGM. The difference between the two models increases as the permeability decreases. In addition, the difference decreases as the pressure increases. At atmospheric pressure, the differences are minor (<10%) for permeabilities down to about 10^–13 m². However, for lower permeabilities, the differences are significant and can approach two orders of magnitude at a permeability of 10^–18 m². In contrast, at a pressure of 100 atm, the maximum difference for a permeability of 10^–18 m² is only about a factor of 2. A molecule–wall tortuosity coefficient based on the DGM is proposed for trace gas diffusion using Fick's law. Comparison of the Knudsen diffusion fluxes has also been conducted. For trace gases heavier than the bulk gas, the ADM mass flux is higher than the DGM. Conversely, for trace gases lighter than the bulk gas, the ADM mass flux is lower than the DGM. Similar to the ordinary diffusion variation, the differences increase as the permeability decreases, and get smaller as the pressure increases. At atmospheric pressure, the differences are small for higher permeabilities (>10^–13 m²) but may increase to about 2.7 for He at lower permeabilities of about 10^–18 m². A modified Klinkenberg factor is suggested to account for differences in the models.     

Numerical analysis of oscillations of a gaseous cavity in a compressible liquid

The radial oscillations of a gas-filled spherical cavity in an infinite compressible ideal liquid are investigated. The numerical solution of the equation of motion of a gaseous sphere is used for the comparison of acoustic and energy characteristics of underwater trotyl explosion and small-amplitude explosion sound sources (detonation of explosive gaseous mixture, expansion of a compressed inert gas).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–182, March–April, 1971.     

Stability of convective viscous fluid flow in porous and free vertical layers

The linear stability of convection in a system consisting of a vertical layer of fluid and an adjacent layer of porous medium saturated with that fluid is investigated. The fluid and the porous medium are bounded by isothermal surfaces heated to different temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–9, September–October, 1990.The author wishes to thank G. Z. Gershuni for supervising the work and D. V. Lyubimov for useful discussions.     

Filtration of two miscible liquids in a fractured porous medium in a gravity field

The article discusses the one-dimensional problem of the displacement of a liquid (petroleum), saturating a fractured porous medium, by another liquid miscible with it in all ratios, in a gravity field. A system of two nonlinear equations in partial derivatives, of the hyperbolic type, is obtained for the concentration of one of the liquids in fractures and blocks. The system is integrated numerically by the method of characteristics. On the basis of the results universal dependences are obtained for the distribution of the concentrations over the stratum and the yield of petroleum.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–168, March–April, 1973.The authors axe grateful to V. M. Entov for his evaluation of the work.     

Barothermal effect in three-phase flow through a porous medium with phase transitions

The formation of a temperature field in a porous medium due to the barothermal effect and phase transitions associated with oil, water, and gas flow is investigated. Degassing of the liquid has an important influence on the formation of the temperature field, the presence of stratal water tending to reduce the cooling anomaly.Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 113–117, November–December, 1994.     

Modeling of retrograde condensation in the process of steady radial flow through a porous medium

The problem of the steady axisymmetric two-phase flow of a multicomponent mixture through a porous medium with phase transitions is considered. It is shown that the system of equations for the two-phase multicomponent flow process, together with the equations of phase equilibrium, reduces to a system of two ordinary differential equations for the pressures in the gas and liquid phases. A family of numerical solutions is found under certain assumptions concerning the pressure dependence of the molar fraction of the liquid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 92–97, November–December, 1994.     

Exact solutions of the problem of adsorption-desorption dynamics with a nonlinear sorption isotherm

Analytic solutions of the problem of adsorption-desorption dynamics with a nonlinear Sorption isotherm are obtained for cases of practical importance in which the Danckwerts condition is satisfied at the inlet to the porous medium and the adsorbate concentration in the mobile phase at the surface of the porous medium is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 107–112, September–October, 1989.     

Rheological properties of solutions of gases in a liquid in the saturation pressure zone

The flow of single-phase gas-liquid systems through a porous medium near the saturation pressure is accompanied by nonequilibrium effects [1, 2]. A series of experimental investigations has been carried out with the object of making a detailed study of the rheological properties of solutions of gases in a liquid at pressures close to the gas release pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 172–175, January–February, 1988.