Filtration of a three-component mixture in a nonhomogeneous porous medium

We shall consider the problem of injecting a mixture of two incompressible fluids having different viscosities into an infinite nonhomogeneous porous stratum which is initially filled with a third fluid. The filtration rate of each of the phases depends basically on its concentration and viscosity, and therefore in the displacement process in the general case their rates of movement will be different, and as a result of this, zones of three-, two-, and single-phase flow are formed. These zones will be separated from one another by moving interfaces (fronts) at which there are jumps of the corresponding concentration levels.We shall assume for simplicity that in the entire region where there is combined flow of several fluids they are incompressible and insoluble, and outside this region, in the external zone, a homogeneous elastic fluid moves.     

Motion of a nonisothermal multicomponent sorbable mixture in a porous medium

The numerical solutions of a system of quasilinear equations in partial derivatives, describing the motion of a nonisothermal multicomponent sorbable gas mixture (or mixture of liquids) through a porous saturated medium consisting of porous grains and incapable of undergoing deformation, are analyzed; the conditions for the convergence of the iteration process used in solving the difference scheme and for the stability of the numerical solutions are obtained; the necessary and sufficient conditions for the existence of solutions of the traveling-wave type, permitted by the system of equations of motion, are also analyzed.     

Convective stability of a binary mixture in a fractured porous medium

The effect of the gravity field and the concentration and thermal gradients on the convective stability of a mixture in a nonhomogeneous porous medium containing a system of thin highly permeable fractures separating relatively impermeable blocks is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 88–97, January–February, 1994.     

Analysis of the convective instability of a binary mixture in a porous medium

The problem of the stability of a binary mixture in a porous medium is investigated in the complete formulation with allowance for cross kinetic and gravitational effects. Boundary conditions of the first and second kinds for a plane horizontal layer of the porous medium are considered. The boundaries of the region of instability are determined. The region of the parameters corresponding to the stability paradox effect, i.e., the instability of a mixture that becomes heavier with depth, is described. It is established that the multicomponent nature of the mixture helps to stabilize the equilibrium state.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 110–119, January–February, 1993.     

Influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium

This work concerns an analysis of the influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium. The analysis is based on the continuum theory of a deformable porous medium in which the pore structure is described by two macroparameters. Considerations comprise two questions: the influence of the pore structure on wave-propagation velocity analysed for the quasilinear case and the role of structure in the reflection-refraction wave phenomenon in fluid at the contact surface of two porous media. It has been shown that the pore structure reduces the velocity of wave and together with the angle of incidence it defines the reflection-refraction wave phenomenon.     

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.     

Equilibrium of a crack in a porous medium with injection of the filtering liquid

In connection with the exploitation of petroleum deposits, the article discusses the equilibrium of a porous medium with a crack under conditions of plane deformation, with the steady-state filtration of a liquid injected into the porous medium through a crack. It is assumed that the crack, which has initial zero dimensions, can become wider and longer with a rise in the pressure. The displacement of the sides of the crack is determined on the basis of the theory of elasticity, taking account of the deformation properties of a saturated porous medium. The stress and the displacement are expressed in terms of two analytical Muskhelishvili functions and the complex filtration potential. A change in the volume of the porous medium leads to a discontinuity of the displacements at the feed contour, and to distortion in the filtration region. For a circular stratum, the dimensions of the crack and the mass flow rate of the liquid are determined in the first approximation. The region of values of the pressure in which there exists a stable equilibrium state of the open crack and a steady-state flow of the liquid is found.     

Barothermal effect in the displacement of oil from a porous medium

The formation of the temperature field due to the barothermal effect when oil is displaced from a porous medium by water is investigated in the piston displacement and two-phase flow approximations. The approach of the displacement front to the outlet from the porous medium leads to a sharp increase in temperature and the temperature anomalies are observed to depend on the saturation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 104–109, May–June, 1992.     

Motion of a gas mixture through a porous medium with sorption

Solutions are investigated of a system of linear partial differential equations describing the motion of a gaseous (liquid) mixture through an undeformable homogeneous porous medium with sorption at interfaces between gaseous (liquid) and solid phases, the kinetics of which are described by a linear equation. If the porous medium consists of spherical granules, the problem is solved in quadratures. For the case of symmetric granules with arbitrary symmetry parameter, various approximate solutions are obtained; first and central moments are used as criteria for the accuracy of the approximations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–100, September–October, 1970.     

Coalescence of viscous drops translating through a capillary tube

An experimental study of the interaction and coalescence of viscous drops moving through a cylindrical capillary tube under low Reynolds number conditions is presented. The combined pressure- and buoyancy-driven motion of drops in a Newtonian continuous phase is examined. The interaction between two drops is quantified using image analysis, and measurements of the coalescence time are reported for various drop size ratios, Bond numbers, and viscosity ratios. The time scale for coalescence in the non-axisymmetric configuration is found to be substantially larger than that for coalescence in the axisymmetric configuration. Measurements of the radius of the liquid film formed between the two drops at the instant of apparent contact are used in conjunction with a planar film drainage model to predict the dependence of the coalescence time on drop size ratio for coalescence of low viscosity-ratio drops in the axisymmetric configuration.     

Investigation of the evolutionarity of discontinuities in binary mixture flows through a porous medium

The discontinuity surfaces (shock waves) that arise in nonisothermal carbon dioxide-water binary mixture flows through a porous medium are considered. In the plane of determining parameters the discontinuity adiabats are investigated and their evolutionarity diagrams are plotted. It is shown that one of the adiabat branches corresponds to the displacement fronts at which there are no temperature jumps and phase transitions and the other branch to temperature jumps and phase transition fronts. The adiabat branches may intersect at a point that corresponds to the Jouguet point for the parameters both ahead of and behind the finite-amplitude jump. It is shown that in the neighborhood of this double Jouguet point the adiabat behavior differs from the classical adiabat behavior at single Jouguet points.     

Coalescence and break-up of drops in two-phase flows

The systematic experimental study of physical phenomena taking place at collisions of drops of water, water-glycerine solutions and transformer oil moving with moderate and high relative velocities has been carried out. The cases of drops interaction of one fluid and various fluids are considered. The regularities of drops collisions both in the quiescent and the moving gaseous medium have been studied. It has been stated that interaction is almost always accompanied by breaking a large drop with forming a certain amount of polydisperse fragments. The generalizing formulae are obtained for the parameter of coalescence and break-up Φ_ji, as well as for the function of fragments distribution by their size and initial velocity.     

One-dimensional problem of water-oil displacement in a medium with fracture porosity

We consider the one-dimensional displacement of oil by water in a medium with fracture porosity. A special dependence of saturation on time is assumed, which approximates well the experimental curve. The position of the injected water front in the course of time is found for several flow rate variation laws.The author wishes to thank V. L. Danilov for his scientific guidance.     

Integration of the quasilinear equations of motion of a mixture through a porous nondeformable medium

Numerical methods are analyzed of solving the quasilinear system of partial differential equations describing the motion of a sorbed gas (liquid) mixture through a porous, saturated, nondeformable medium consisting of porous grains. Conditions are obtained for convergence of the iteration process of a difference scheme. Conditions are found under which the system attains invariant solutions of the running-wave type. Estimates are obtained of times and coordinates, during which and through whose passage the solutions of the boundary-value problem become invariant.     

Mathematical model of nonisothermal multiphase binary mixture flow through a porous medium

A model of nonisothermal binary mixture flow through a porous medium, applicable over a wide range of thermobaric conditions, including temperatures higher than the critical mixture temperature, is proposed. A nonclassical approach used for modeling the mixture properties makes it possible to uniformly describe its single-, two- and three-phase thermodynamic equilibria and the corresponding flows under sub- and supercritical thermodynamic conditions. The wide application of thermodynamic methods to determining the real mixture properties leads to a nonstandard mathematical model in which the conservation laws are closed with a conditional extremum problem, not finite or differential equations. A dispersion analysis of the model equations is performed and the characteristic velocities in zones of different mixture phase states are determined.     

Motion of a nonisothermal adsorbable mixture with enhanced values of the concentrations through a porous medium

The equations of motion of a nonisothermal adsorbable mixture with enhanced values of the concentrations of the components in the case of infinitely large coefficients of heat and mass transfer reduce to a hyperbolic quasilinear system of equations. The invariant solutions of this system are analyzed. Convexity conditions are obtained under which a traveling-wave regime is realized in the porous medium. A system of equations is found for determining the concentrations of the adsorbable components of the mixture when a self-similar regime of dispersing waves is realized. For the case of finite values of the coefficients of heat and mass transfer, expressions are given for the width of the stationary front in the traveling-wave regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 76–86, September–October, 1980.     

Steady temperature field associated with the flow of gassy oil in a porous medium

The steady thermal field associated with the flow of gassy oil through a porous medium is investigated with allowance for the Joule-Thomson and degassing effects. A formula is obtained for estimating the temperature anomalies at the well bottom on oil inflow intervals which correspond to a bottom pressure lower than the saturation pressure. Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 113–116, January–February, 1994.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.