Theory of nonsteady nonequilibrium filtration of immiscible liquids

A modification to the model developed in [1] for the nonequilibrium filtration of an inhomogeneous liquid is proposed. The structure of the saturation discontinuity is investigated, taking into account the nonequilibrium conditions; it is shown to be stable in a linear approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–58, May–June, 1978.It remains to thank G. I. Berenblatt for his constant interest in the work.     

Fingering associated with immiscible displacement in a two-layer porous medium

The effect of capillary cross flows on the structure of the displacement front in a two-layer porous medium with different layer permeabilities is examined. It is shown that capillary cross flows along the curved displacement front may lead to stabilization of the displacement. Approximate expressions are obtained for the limiting finger length and the oil displacement coefficient at the moment of breakthrough of the water as functions of the displacement parameters and the form of the functional parameters of the two-phase flow in the porous medium; the results obtained are compared with the results of numerical calculations and the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–104, January–February, 1991.     

Multi-fluid model of suspension filtration in a porous medium

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.     

Micromechanics of residual saturation formation during immiscible displacement in a porous medium

The process of displacement of a nonwetting fluid has been studied experimentally on a transparent model of a porous medium for various percolation velocities in the stable front regime, when the viscosity of the displacing fluid is greater than that of the fluid displaced. The flow structures in the final displacement regime, when the nonwetting phase is distributed in the pore space in the form of individual drops or ganglia, have been visually investigated. Imbibition is numerically modeled on a two-dimensional network model with allowance for various microdisplacement mechanisms. The effect of the initial displacing phase saturation on the magnitude and structure of the residual displaced fluid saturation is demonstrated. The fractal dimensionality of the displacement boundary is measured.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 116–121, May–June, 1994.     

Numerical study of single-phase gas filtration in a porous medium

This paper describes a method for numerical solution of single-phase nonstationary gas filtration in a porous medium. Linearization of the classical Leibenzon equation is performed. To solve the resulting linear equation, an efficient numerical algorithm was constructed without saturation over spatial variables and time.     

Experimental investigation of microsuspension filtration in a highly-permeable porous medium

Filtration of a microsuspension of aluminosilicate particles in a highly-permeable porous medium formed by a glass-sphere filling is investigated. The particle-to-filling granule diameter ratio varied from 0.046 to 0.109 and the volumic particle concentration ratio from 0.001 to 0.02. The data on the specimen permeability dynamics and its dependence on the initial concentration of the suspension microparticles and the ratio of their diameter to that of the porous medium granules are obtained. The permeability is shown to considerably vary along the specimen. Two stages of the porous medium damage by the trapped microparticles are established. The critical parameter of the formation of an impermeable cake in the initial region of the specimen are determined.     

Three dimensional simulation of unstable immiscible displacement in the porous medium

I.IntroductionThedisplacementofimmisciblefluidsiswidelyutilizedinenhancedoilrecovery.ThestabilityoftheinterfaceisveryimportantandpeopIehavepaidmoreandmoreattentiontoit,becauseitrelatestotheefficiencyofoilrecovery.Manypapersreportedthecharacteristicsoftheu…     

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.     

“Hanging” discontinuities in the saturation with the filtration of immiscible liquids in inhomogenous media

The article discusses the flow of two incompressible immiscible liquids in a porous medium. A study is made of “hanging” discontinuities of the saturation arising at the points of the breakaway of the absolute permeability, taking account of capillary forces and of the force of gravity.     

Mathematical model of deep-bed filtration of a two-component suspension through a porous medium

A model of deep-bed filtration of a two-component suspension through a porous medium with formation of two types of the deposit which have different structures and properties is constructed. The influence of the parameters of fluid and particle flux densities which determine mass transfer between different components of the suspension and deposits on the filtration characteristics and properties of the resulting deposits is estimated on the basis of numerical experiments for the suspensions with contrast particle fractions.     

Conjugate free convection along a thin vertical plate with internal nonuniform heat generation in a porous medium

 The steady state heat transfer characteristics of a thin vertical strip with internal heat generation placed in a porous medium is studied in this work. The non-dimensional temperature distribution in the strip is obtained as a function of the intensity and distribution of the internal heat sources. Both the thermally thin as the thick wall approximations are considered in this paper. The mass flow rate of fluid induced by heating the strip decreases as the longitudinal heat conduction effects along the strip decreases. Received on 22 November 2000 / Published online: 29 November 2001