Well production indicators in a deformable reservoir interacting with rocks

Steady-state flow towards a well through a thin porous deformable two-layer reservoir with allowance for deformation of the surrounding rocks is investigated. The permeability of the reservoir is considered to be a function of the displacements of its top and bottom. The effect of deformation on the well production indicators is studied. The results obtained agree qualitatively with the data of full-scale experiments. Earlier, in [1–5], in considering the self-consistent processes of flow through porous media and their deformation attention was concentrated on the analysis of the stress-strain state of the rocks and reservoir and on unsteady problems within the framework of the nonlocally elastic flow regime.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–93, January–February, 1995.     

Hydrodynamics of dispersive systems interacting with an electromagnetic field

A system of equations, which describes the behavior of magnetized or polarized dispersive media in electromagnetic fields in the diffusion approximation, is derived. It is assumed that the medium consists of several phases and components, each of which is generally magnetized or polarized according to its own law and has its own temperature. A formula for the force acting on such a medium due to the presence of the electromagnetic field is derived, which includes terms related to the nonequilibrium nature of the process (velocity derivatives, difference of pressure, chemical potentials, and temperatures of the different phases). The part of the force which is proportional to the differences of the pressures, chemical potentials, and the temperatures of the phases occurs in the equations of motion even in the case when the medium does not interact with the electromagnetic field or when there is no electromagnetic field. The terms associated with the magnetization or polarization occur in this part of the force through the difference of pressures and the chemical potentials of the different phases. The equations for the diffusion fluxes and heat flux, the equations for the rate change of the mass of the -phase (component) and entropy of the -phase (component), and also the equation for the rate of change of the volume concentration of the -phase (component) are written with the use of the methods of thermodynamics of irreversible processes. In the diffusion approximation these equations for the rate of change of entropy replace the more unwieldy energy equation usually used in the hydrodynamics of multiphase media. It should be particularly noted that the proposed method permits one to obtain equations for the change of volume concentration of the phases. Instead of these equations, usually a Rayleigh-type equation for the oscillations of the bubble is used for closing the complete system in liquid —gas bubble mixtures, which differs from the equation obtained in this work, and within the framework of the assumptions used here it does not follow from the general formalism of thermodynamics of irreversible processes. The obtained results and their corollaries are compared with the results of other authors. The basic premises discussed in [1, 2] are used in the derivation of the equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 59–70, May–June, 1977.     

Thermocapillary instability of a deformable liquid film

The instability of a plane liquid film with a uniform transverse temperature gradient under conditions of weightlessness is considered. The surface tension is assumed to depend linearly on the temperature. On the basis of an exact solution of the neutral perturbation problem for a layer with deformable boundaries, the instability domains, the dispersion curves, and the shape of the perturbations are determined. It is shown that on the interval of low Prandtl numbers both thermocapillary waves with predominantly longitudinal flow and capillary waves, supported by the thermocapillary effect, with intense transverse liquid flow can develop on the film.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–36, September–October, 1996.     

Hydrodynamics of a drying multicomponent liquid droplet

Using microscopy methods on light and dark fields, the flow patterns developing in drying droplets of pure transparent liquids, solutions, and suspensions of micro- and nanoparticles are investigated. The flow patterns inside drying droplets of real, colloid, and mixed solutions containing nanoand microparticles-markers are studied by means of video and photo registration of microscopic images. The analysis of particle displacements indicates the existence of a global convective flow which forms a toroidal circulation with an ascending jet at the droplet center. The typical types of the structures depending on the droplet composition are distinguished. It is shown that the intensity of the flow inside the droplet affects the surface convection. The effect of the hydrodynamic flow on the transport of a substance, forming the dry-deposit texture, is studied.     

Hydrodynamics of contact of a falling drop with a liquid free surface

A fine structure of the flows developing during primary contact of freely falling drops with a deep quiescent fluid is studied using the macrophotography and high-speed video filming methods. Water drops falling in water, alcohol, and oil, as well as drops of oil, petroleum, and aqueous solutions of salt or alcohol falling in water are investigated. The work is focused on the visualization of the finespray scattering from the primary contact area. The collisions of small droplets with the surface of the submerging drop are first recorded. The direction of the spray and streamer scattering is determined by the surface tension coefficients of the coalescing liquids. The conditions under which the spray droplets collide with the drop surface are determined.     

Unsteady-state flow induced by a well in a deformable stratum interacting with the adjacent rocks

Unsteady-state plane radial flow induced by a well in a thin deformable stratum is studied taking into account the stratum interaction with the adjacent rocks. The stratum permeability is assumed to depend on the lateral deformation. The behavior of the well productivity properties for harmonic reservoir pressure oscillations and after pressure drawdown in a bilayered stratum is analyzed. Steady-state well behavior under these conditions was studied in [1]. A qualitative estimate of the well productivity variation due to a stepwise pressure change in an adjacent stratum was previously derived in [2].Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 85–90, January–February, 1996.     

Time-dependent liquid metal flows with free convection and a deformable free surface

The finite element method is employed to investigate time-dependent liquid metal flows with free convection, free surfaces and Marangoni effects. The liquid circulates in a two-dimensional shallow trough with differentially heated vertical walls. The spatial formulation incorporates mixed Lagrangian approximations to the velocity, pressure, temperature and free surface position. The time integration is performed with the backward Euler and trapezoid rule methods with step size control. The Galerkin method is used to reduce the problem to a set of non-linear equations which are solved with the Newton–Raphson method. Calculations are performed for conditions relevant to the electron beam vaporization of refractory metals. The Prandtl number is 0·015 and Grashof number are in the transition range between laminar and turbulent flow. The results reveal the effects of flow intensity, surface tension gradients, mesh refinement and time integration strategy.     

FLOW OF A TRAIN OF DEFORMABLE FLUID PARTICLES IN A TUBE

I.IntroductionWangandSkalakll]studiedforsolidspheresintubes.HymanandSkalak12--31studiedthemovementofacompactfluidspheres(non-deformable)intubes.Theyonlystudiedcompactdropswhoseradiusesarenotbiggerthan0.7.Pozrikidisl4]studiedthenlotiollofdeformabletluidparticlesintubes.Inthispaper,westudiedtwo-phasenowregime,consistingofaperiodictrainofequallyspacedliquidslugsmovingaxisymmetricallyinacontinuousliquidphasewhichisimmisciblewiththeslugphase(Fig.l(a)).Wereportnumericalsolutionsforthehydrodynamic…     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

The added mass of a deformable cylinder moving in a liquid

Let an infinitely long cylinder move perpendicular to its length in an infinite mass of liquid which is at rest at infinity. If the cylinder is rigid, the whole effect of the presence of the liquid may be represented by adding to the inertia per unit length of the solid cylinder the mass per unit length of the displaced fluid. If, however, the cylinder is elastically deformable, the mass of the moving fluid depends on the change in shape of the, initially circular, cross-sections of the cylinder. Thus the added mass is no longer a constant, but a function of the pressure exerted by the fluid on the solid cylinder.     

The average stress tensor in systems with interacting particles

The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T ^I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.     

Dynamics of deformable flexible systems in liquid

The state-of-the-art in the investigation of nonlinear oscillations and evolution of deformable flexible systems in fluid is analyzed. Statements of problems and methods of solving them as well as results on the dynamics of flexible systems interacting with the ambient medium are briefly outlined. Important quantitative and qualitative results are presented, and conclusions of applied and fundamental importance are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 3–29, August 2007.