Mechanics of a fluid-gas mixture in a porous medium

The compressibility behaiour of a fluid-gas mixture is determined from several physical aspects such as the gas compressibility, the fluid compressibility, the gas solubility in the fluid, the vapour pressure, the surface tension and geometrical effects.The highly compressible gas dominates the resultant compressibility of the mixture. The present paper gives and expression for the resultant compressibility including the stability behaviour of the gas bubbles on the basis of a mixture theory.     

A numerical model for immiscible two-phase fluid flow in a porous medium and its time domain solution

The governing equations for the interaction of two immiscible fluids within a deforming porous medium are formulated on the basis of generalized Biot theory. The displacement of the solid skeleton, the pressure and saturation of wetting fluid are taken as primary unknowns of the model. The finite element method is applied to discretize the governing eqations in space. The time domain numerical solution to the coupled problem is achieved by using an unconditionally stable direct integration procedure. Examples are presented to illustrate the performance and capability of the approach.     

The analysis of a two-phase zone with condensation in a porous medium

The one-dimensional steady-state heat and mass transfer in a two-phase zone of a water-saturated porous medium is studied. The system consists of a sand-water-vapour mixture in a tube that is heated from above and cooled from below. Under certain conditions, a two-phase zone of both vapour and water exists in the middle of the tube. A model problem for the temperature and the liquid saturation profiles within this two-phase zone is formulated by allowing for an explicit temperature dependence for the saturation vapour pressure together with an explicit saturation dependence for the capillary pressure. A boundary-layer analysis is performed on this model in the asymptotic limit of a large vapour-pressure gradient. This asymptotic limit is similar to the large-activation-energy limit commonly used in combustion problems. In this limit, and in the outer region away from any boundary layers, it is shown that the temperature profile is slowly varying and that the corresponding saturation profile agrees very well with that obtained in the previous model of Udell [J. Heat Transfer 105 (1983) p. 485] where strict isothermal conditions were assumed. The condensation and evaporation occurring within the boundary layers near the edges of the two-phase zone is examined. Finally, an iterative method is described that allows the temperature profile in the two-phase zone to be coupled to the temperature profiles in the two single-phase zones consisting of either water or vapour. This allows for the computation of the locations of the edges of the two-phase zone within the tube. Numerical computations are performed with realistic values of the parameters.     

Stability of a moving interface in porous medium for non-newtonian displacing fluids and its applications in oil displacement mechanism

Summary In this paper a theoretical analysis regarding the rheological effects of non-Newtonian behavior of the displacing fluid on the stability of a moving interface in a porous medium. separating two immiscible and incompressible fluids, is performed. Conditions under which a piston-like displacement could be maintained in oil displacement mechanism with a non-Newtonian displacing fluid of power law are shown and discussed, with regard to the possibility of improving oil recovery from polymer flooding projects used in oil reservoir engineering.Nomenclature h layer thickness - H consistency index - k permeability - n rheological parameter for power law fluids - p pressure distribution - V interface velocity - v velocity - porosity - ₀ threshold gradient - viscosity - _ef effective viscosity - _ap apparent viscosity - ₀ yield stress - angle to the upward vertical     

On the motion of two-phase systems in a porous medium taking account of heat- and mass-transport processes

The essential influence of the process of mass transport of the condensate on the filtration resistance is shown. It is explained that mass transport of residual water occurs in the isothermal filtration of gas-liquid systems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 6, pp. 1025–1031, June, 1970.     

Propagation of disturbances of pressure in a porous medium under conditions of filtration of a two-phase flow

The paper deals with the results of experimental investigation of unsteady-state processes in a channel with a porous medium under conditions of filtration of liquid-vapor flow and pressure disturbances initiated by injection of steam or noncondensing gases from an outside source. Singular features are studied of the propagation of pressure waves in a porous medium compared to dynamic processes occurring in an unfilled round pipe. The experimentally measured values of the propagation velocity of low-amplitude pressure waves in a channel with a pebble bed correspond to the calculated values of the equilibrium sound velocity of a liquid-vapor medium. It is for the first time that this result is obtained.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 947–953.Original Russian Text Copyright © 2004 by B. G. Pokusaev, E. G. Tairov, and M. Yu. Gritsenko.     

Wave effects in a two-phase medium

A wave equation derived in the article is used to obtain a relation for the propagation velocity of small perturbations in a two-phase medium. This relation is confirmed indirectly by a computer analysis of a wet-steam nozzle, as well as experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 92–99, July, 1971.     

Theory of two-phase porous cooling. I

In conformity with systems of two-phase porous cooling, a statistical model of boiling of a liquid in a porous body consisting of nonintersecting capillaries is set up.Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 6, pp. 1058–1064, June, 1976.     

Torsional sensor applications in two-phase fluids

A solid corrosion-resistant torsional waveguide of diamond cross section has been developed to sense, online and in real-time, the characteristics of the liquid in which it is submerged. The sensor can measure, among other things, the liquid content of a bubbly medium, the density of adjacent pure liquids, the equivalent density of liquid-vapor mixtures or particulate suspensions, a suspension's concentration, and the liquid level. The sensor exploits the phenomenon that the speed of propagation of a torsional stress wave in a submerged waveguide with a noncircular cross section is inversely proportional to the equivalent density of the liquid in which the waveguide is submerged. The sensor may be used to conduct measurements along distances ranging from 20 mm to 20 m and over a wide range of temperatures and pressures, e.g., from the cryogenic temperature of liquid nitrogen, -196 degrees C, up to hot pressurized water at 300 degrees C and 7 MPa. A self-calibrating three-zone sensor and associated electronics have also been developed to compensate for any sensor inaccuracies due to operation over a wide range of temperature.     

Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium

This article deals with the combined effects of heat and mass transfer on the peristaltic propulsion of two-phase fluid flow through a Darcy-Brinkman-Forchheimer porous medium with compliant walls. The Sisko fluid model together with small particles is considered in the presence of extrinsic magnetic field and chemical reaction. It is well-known that different biological fluids behave like a Newtonian or non-Newtonian fluid depending upon the shear rates. The non-Newtonian fluid models are more complicated than Newtonian fluid and difficult to express using the single constitutive relationship between stress and strain rate. These constitutive equations provide a complex mathematical formulation and become numerous challenges to find numerical and analytical solutions. Small magnetic particles are helpful to manipulate and control the two-phase flow by magnetic force. Moreover, it is also beneficial in drug targeting for the treatment of different diseases. Further, two-phase flow plays an important role to examine the muscular expansion and contraction during the propagation of various biological fluids. An appropriate approximation is considered such as long wavelength and creeping flow regime to model the governing equations. Analytical solutions are obtained using the perturbation method. Moreover, numerical computations are performed to determine the features of peristaltic pumping. The results of different rheological properties for particle and fluid phase are discussed mathematically as well as graphically for different sundry parameters. The current analysis has an extensive amount of applications in medical engineering and also significant importance of smart fluid pumping systems in various engineering processes.     

Development of a stable two-phase porous cooling system

The use of a two-layer porous wall instead of a one-layer wall is shown to create the necessary precondition for the practical realization of a two-phase porous cooling system.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 5, pp. 870–877, May, 1977.     

Limited-Angle inverse scattering problems and their applications for geophysical explorations

The effect of the limited-angle measurements on the nonlinear inverse scattering problem is investigated. Because of incomplete information obtained in the limited-angle inverse problem, the linearized system matrix in the inversion procedure becomes more ill-conditioned compared to that of the conventional inverse scattering problem where the receivers are placed in a circle that completely surrounds the object. Consequently, the quality of the reconstruction is considerably reduced, and sometimes it is almost impossible to reconstruct the profile because of the sparsity of the measurement data. To overcome the above difficulty, a boosting procedure, which will help us to obtain the maximum amount of information for an arbitrary predefined experimental setup, has been proposed based on a physical viewpoint. The results of the computer simulations for well-to-well tomography demonstrate that by applying the boosting procedure the quality of the reconstruction and the speed of the convergence are improved significantly. Furthermore, for subsurface detection where both the transmitters and receivers are confined to the ground, the reconstruction becomes possible after applying the boosting procedure.     

Mechanics of porous elastic materials containing multiphase fluid

A continuum theory of mixtures for a porous elastic solid saturated by immiscible viscous fluids is presented. The theory includes micro-inertial effects for the local fluctuation in volume fractions of the solid and fluid constituents. Gradients of volume fraction of both the elastic solid and fluid constituents are included in the constitutive variables. Equations governing the macroscopic motion are developed and show that the present theory contains both Biot's equations and multiphase Darcy flow through porous media as special cases.     

Computer model of a porous medium

A computer model has been set up to represent a porous medium. The basis for this model is a two-dimensional square network (100×100) of channels that have randomly assigned widths between the value of zero (closed) and the value of one (open, unrestricted flow). The channel width assignments have been made by a random selection from five different distributions:f(q)=q, f(q)=sinq, f(q)=erf(q),f(q)=1–sinq, andf(q)=1 –erf(q). Diffusion of particles in the network has been studied by a random-walk procedure for each realization of the channel width assignments. The diffusivity is quite sensitive to the distribution of channel widths. The percolation properties of the networks obtained from the three most restrictive distributions have been investigated and the independent, linked clusters within the network have been determined. For cluster sizes that are less than the full width of the network, the network does not percolate and either the flow is not diffusive or the diffusivity is severely reduced. An approximate value for the percolation threshold has been determined in each case and the fractal dimension has been calculated also.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

High-temperature processes in a porous medium

A study is made into a nonlinear filtration problem on the flow of gas in a porous weakly conducting medium, which simulates the process of superheating in a reactor. Explicit estimates are obtained of two critical values of the similarity parameter of the problem, which define the condition of existence of the steady-state mode of cooling a system open to the atmosphere and the condition of global superheating. The second one of these critical values is also the bifurcation point for the input set of equations. It is found that a thin layer forms at high temperatures corresponding to this point, in which the thermal energy is concentrated. A simultaneous radical variation of the physical process of heat transfer occurs, namely, convection is replaced by molecular heat conduction.     

Polar fluid through a porous medium

Summary An analysis of the steady flow of a polar fluid through a porous medium bounded by an infinite plate by using the generalized Forchheimer's model is considered. The velocity profiles are shown for different values of the permeability parameter.     

Effects of porous boundaries on peristaltic transport through a porous medium

Summary Peristaltic pumping by a sinusoidal traveling wave in the porous walls of a twodimensional channel filled with a viscous incompressible fluid through a porous medium is investigated theoretically and graphically. It has been considered that the fluid is entering the flow region through one plate at the same rate as it is leaving through the other plate. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. It has been noticed that the mean axial velocity and the reversal flow increase by increasing the permeability parameterW. The mean axial velocity and the reversal flow decrease by increasingV until at the upper quarter of the channel it increases by increasingW. Also, the fluid motion is nonsymmetric. Numerical results are reported for various values of the physical parameters of interest.     

Formation of a two-phase region during vaporization in porous media

A physically consistent model is constructed to describe vaporization in a water-saturated porous medium. Results are presented from a numerical analysis of a frontal model and a model with a two-phase region.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 59, No. 10, pp. 568–575, October, 1990.     

Sapropel drilling-mud infiltration into a porous medium

Sapropel drilling muds show a high rate of decrease in the infiltration, which have been tested to produce controlled blocking in productive strata.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 594–599, October, 1988.