Determining equations of two-phase flows through anisotropic porous media

A new interpretation of the concept of relative phase permeability is given. Relative phase permeabilities are represented in the form of fourth-rank tensors. It is shown that in the case of anisotropic porous media functions depending not only on the saturation but also on the anisotropy parameters represented in the form of ratios of the principal values of the absolute permeability coefficient tensor correspond to the classical representation of the relative phase permeabilities. For a two-phase flow in anisotropic porous media with orthotropic and transversely-isotropic symmetry a generalized two-term Darcy’s law is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 87–94, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-00623).     

Averaged model with capillary nonequilibrium effects for two-phase flow through a highly heterogeneous porous medium

Two-phase flow through a medium with two porosities in which the absolute permeabilities and the capillary pressure functions of the components differ by an order of magnitude is investigated. A classification and diagram of the elementary flows are proposed at the single cell level. An averaged model is developed for a single class of systems in which source-type capillary-dispersion flow predominates in the blocks. This model contains a nonlinear kinetic relation between the average values of the capillary pressure functions. An expansion of the effective phase permeability tensor allowing it to be calculated efficiently is proposed. The capillary relaxation time is explicitly determined. Examples of calculations of the averaged phase permeability tensor and the capillary relaxation time are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 93–103, May–June, 1998. The work was carried out with the support from the Russian Foundation for Basic Research (project No. 95-01-01179a).     

Permeability anisotropy due to consolidation of compressible porous media

The characterisation of flow through porous media is important for all solid–liquid separation and fluid transport realms. The permeability of porous media can be anisotropic and furthermore, the extent of anisotropy can be increased as a result of an applied compressive force. However, the understanding of how anisotropy develops is incomplete. An overview of research on permeability anisotropy is given and an expression for predicting anisotropy as a function of void ratio is offered. The two underlying assumptions of the proposed model are: flow in different directions occurs within the same network of pores and deformation is primarily due to the compression of the particles in the direction of the applied force rather than due to particle rearrangement. The assumption of network connectivity allows permeability anisotropy to be described as a function of flow path tortuosity only. Results are presented for hydraulic anisotropy measured in lignite that has been upgraded by a compression dewatering method known as mechanical thermal expression. The lignite permeability is shown to be up to eight times greater in the direction perpendicular to compression, suggesting that the rate of dewatering could be significantly increased by choosing the drainage to also be perpendicular to the direction of the applied compressive force. It is illustrated that the proposed anisotropy model can be used to accurately predict the experimentally determined permeability anisotropy ratios for lignite, as well as for other materials including sand, clay and kaolin.     

Design of a thin airfoil in a channel with permeable walls

A general solution is obtained for the boundary value problem of designing a thin airfoil in a channel with permeable walls from the given pressure distribution. A suitable choice of permeability coefficients makes it possible to construct a thin airfoil in a channel with impermeable walls, in a jet, etc. The effect of the wall permeability on the shape of the airfoil is studied. Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–34, July–August, 1994.     

Suspended discontinuities in the field of two-dimensional internal waves

Using various shadow methods of visualization for a stratified flow near a horizontal cylinder towed with constant velocity, a new structural element of the flow, namely, the isolated high-gradient interlayers in the field of attached internal waves, is identified. In their basic characteristic features, these layers may be viewed as those belonging to the class of inner boundary layers which are the prevalent mechanism for formation of the fine structure of a continuously stratified medium. The data on optical visualization are confirmed by direct measurements of the electrical conductivity. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 40–50, September–October, 1999.     

Allowance for complex loading in transversely isotropic solids

A model of plasticity for a transversely isotropic material with allowance for complex loading is developed, based on results of experiments with homogeneous cylindrical specimens of isotropic materials. An empirical model of plasticity for isotropic metals is constructed with allowance for vector properties of the material. The model is extended to a particular case of anisotropy. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 128–133, January–February, 2009.     

Singular perturbation in bending problems for orthotropic plates

The paper deals with a number of singularly perturbed boundary-value problems and variational inequalities that arise in the theory of bending of orthotropic plates with strong anisotropy of elastic properties. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 195–201. September–October, 1999.     

Generalization of the poiseuille law based on the constitutive rheological relation for polymeric liquids

The method of perturbations of the small parameter determining the anisotropy of the properties of linear polymers is used to determine the velocity profile and rate for steady flow in a round tube. It is shown that for the four-parameter rheological model considered, the stress state of the Poiseuille flow along with the tangential shear stress is characterized by the first and second differences of normal stresses. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 158–163, September–October, 1999.     

Stress intensity factors and crack deviation conditions in a brittle anisotropic solid

For arbitrary anisotropy in the linear manifold of singular solutions generating square-root singularities of the crack tip stress, a special basis is introduced that possesses the same properties as in the isotropic case and provides simple integral representations for the attributes of the energy fracture criterion, in particular, the conditions of crack deviation from a straight path. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 98–107, May–June, 2005.     

On the nature of the organized structures in turbulent near-wall flows

A physical mechanism of onset of large-scale organized structures in turbulent flows along a plane wall which are the cause of intensification of turbulent fluctuations is formulated. The structures take the form of high-speed and low-speed streaks caused by streamwise vortices, i.e., motions in the plane of the transverse cross-section. The streamwise vortices are excited as a result of instability under the action of the anisotropy of the normal components of the Reynolds stress tensor. A model for describing these vortices that gives characteristics in qualitative and quantitative agreement with the experimental data is proposed. In particular, the most probable and mean distances between neighboring vortices are correctly reproduced. The theory makes it possible to explain certain methods of turbulent flow control for the purpose of drag reduction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–30, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00602).     

The stokes problem for a porous particle with radially nonuniform porosity

The flow past a nonuniform porous spherical particle immersed in a uniform steady-state stream is studied in the Stokes approximation. For a power-law radial dependence of the particle permeability coefficient, an analytical solution for the velocity and pressure fields outside and inside the particle is obtained. Volgograd, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–184, January–February, 2000.     

Stress-strain state and durability of mechanically inhomogeneous welds under low-cycle loading

Relations are proposed for the determination of the stress-strain state, strength, and life of butt welds with mild and hard interlayers under cyclic elastoplastic tension-compression. The accumulation of cyclic and quasistatic damages is determined with allowance for the redistribution of the cyclic elastoplastic strains and hardness of the stress state due to changes in the cyclic properties of separate regions of welds. The theoretical distribution of cyclic strains and the durability of welds under cyclic elastoplastic loading are supported by experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 29–38, February 2008.     

Simulation of micellar-polymer flooding of a layered oil reservoir of nonuniform thickness

The dynamics of oil displacement from a layered reservoir of nonuniform thickness consisting of two hydrodynamically connected layers of different absolute permeability is studied. Results of numerical calculations are given. The influence of the main determining factors on the oil displacement dynamics is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 115–123, November–December, 2008.     

Effect of anisotropy of porous media on the onset of buoyancy-driven convection

A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law is used to explain characteristics of fluid motion and the anisotropy of permeability is considered. Under the Boussinesq approximation and the principle of exchange of stabilities, the stability equations are derived by using the linear stability theory and the energy method. The linear stability equations are analyzed numerically by using the frozen-time model and the linear amplification theory and the global stability limits are obtained numerically from the energy method. For the various anisotropic ratios, the critical times are predicted as a function of the Darcy–Rayleigh number and the critical Darcy–Rayleigh number is also obtained. The present predictions are compared each another and with existing theoretical ones.     

Steady flow of homogeneous fluid in an oil reservoir recovery element with a hydrofracture

The plane problem of steady flow of a homogeneous fluid in a five-point oil reservoir recovery element with a hydrofracture of finite conductivity is considered. It is assumed that the motion of the fluid in the reservoir and in the fracture obeys a linear resistance law and that the permeability of the reservoir and the effective permeability of the fracture are sharply different. Analytic solutions are obtained for the case of an ideal fracture (fracture of infinite conductivity). The flows are analyzed numerically with allowance for the finite conductivity of the fracture. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 104–112, January–February, 1994.     

Effective Permeabilities in a Porous Medium with Log-Stable Statistics

Equations for the effective coefficients of random permeability fields for fluid flow through a porous medium with log-stable distributions are derived using the Wilson renormalization group approach. Results of the theoretical modeling are compared with data of numerical modeling. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 146–158, November–December, 2005.     

Two-front mathematical model of water injection into a steam-saturated geothermal reservoir

A mathematical model of the process of water injection into a high-temperature steam-saturated geothermal reservoir is proposed. In the reservoir there is a zone of co-existence of steam and water which is separated from the steam and water zones by moving interfaces (phase transition fronts) whose location is determined in the process of solving the problem. Within the framework of the proposed model the thermodynamic contradiction that exists in the single-front case for low permeabilities, expressed as supercooling of the steam in the corresponding zone ahead of the interface [1, 2], is not observed. With increase in the permeability the two-front solution obtained goes smoothly over into a noncontradictory single-front solution. Neutral curves separating the domains of existence of the different types of solution in parameter space are constructed. Moscow. e-mail: barmin@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 105–112, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-01042).     

Flow in a Porous Matrix with Anisotropic Structure

The flow of a viscous fluid through a porous matrix undergoing only infinitesimal deformation is described in terms of intrinsic variables, namely, the density, velocity and stress occurring in coherent elements of each material. This formulation arises naturally when macroscopic interfaces are conceptually partitioned into area fractions of fluid–fluid, fluid–solid, and solid–solid contact. Such theory has been shown to yield consistent jump conditions of mass, momentum and energy across discontinuities, either internal or an external boundary, unlike the standard mixture theory jump conditions. In the previous formulation, the matrix structure has been considered isotropic; that is, the area fractions are independent of the interface orientation. Here, that is not assumed, so in particular, the cross-section area of a continuous fluid tube depends on its orientation, which influences the directional fluxes, and in turn the directional permeability, anisotropy of the structure. The simplifications for slow viscous flow are examined, and particularly for an isotropic linearly elastic matrix in which area partitioning induces anisotropic elastic response of the mixture. A final specialization to an incompressible fluid and stationary matrix leads to potential flow, and a simple plane flow solution is presented to illustrate the effects of anisotropic permeability.     

Study of crack resistance of plastically anisotropic metal materials

A version of the Hahn and Rosenfield model is used to develop a structural approach to crack-resistance anisotropy evaluation of dispersion-hardening alloys of semi-finished products with initial strength and plastic anisotropy formed by high-temperature deformation and age-hardening processes. Correlations are obtained which describe crack-resistance anisotropy exponents as functions of the deformation and yield point for uniaxial extension of crack-free specimens in the longitudinal, transverse, and vertical directions. The proposed approach is experimentally substantiated for a number of plastically anisotropic aluminum alloys. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 87–94, April, 1999.     

Long-term strength of metals under an equiaxial plane stress state

This paper reports test results suggesting a significant dependence of the long-term strength of metals on the form of the stress state and the method of short-term loading. The experimental data obtained are described using a modification of the kinetic theory of long-term strength containing a vector damage parameter and taking into account strength anisotropy and the damage due to short-term loading. It is shown that the experimental and theoretical values of the time to rupture are in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 150–157, July–August, 2009.