Polymer flooding of oil formations with bottom water

A quasi-one-dimensional model describing the process of polymer flooding of oil formations underlain by bottom water is proposed. The model is based on the assumption of instantaneous gravitational phase separation along the vertical and is a generalization of the hydrodynamic model previously considered in [1]. The self-similar solutions constructed show that in the case of polymer flooding of an oil formation the presence of bottom water leads to qualitative changes in the saturation and concentration distribution and has an important influence on both the running and the final oil output. The results obtained are consistent with the data of two-dimensional numerical modeling of the process [2] and indicate the possibility of more efficient exploitation of water-oil zones as a result of pumping thickened water into the formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–90, May–June, 1986.     

Hydrodynamic models of the residual oil distribution in water-flood reservoirs

Models of the residual oil saturation distribution are proposed for linear, axisymmetric, and general flows. The steady displacing fluid flow model makes it possible to find equilibrium residual oil saturation distributions corresponding to given flow regimes by treating the porous medium with capillary-trapped oil as a medium with permeability that depends on the displacement conditions. The dynamics of the mobilized globules of the residual oil are excluded from consideration. The simulation results indicate that the residual oil saturation distribution after stimulation of the wash-out zone by means of enhanced oil recovery techniques is generally essentially nonuniform. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–104, May–June, 2000.     

Hydrodynamic averaging of highly inhomogeneous porous media with linear flow

A method is proposed for constructing homogeneous anisotropic models of new classes of highly inhomogeneous nondeformable porous media consisting of arbitrarily oriented systems of layers representing fractures and impermeable barriers (screens) embedded in each other with an arbitrary depth of embedment. It is assumed that the permeability functions of the elementary cells of the media can be represented in some Cartesian coordinate system (proper to each cell) in the form of a product of three integrable functions that depend on the corresponding coordinates. As distinct from known methods of averaging differential operators, the method in question is based on porous media flow considerations and reduces to replacing the highly inhomogeneous soils with homogeneous anistropic soils, so that on the boundaries of the domain considered the basic flow parameters remain the same.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika, Zhidkosti i Gaza, No. 5, pp. 190–192, September–October, 1993.     

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 the interlayer connectivity of nonuniform reservoirs on the volume of the residual oil pillars

The limiting-equilibrium pillars of residual oil with an initial pressure gradient are calculated for reservoirs of the layer cake type whose nonuniformity conforms to a random (Pearson) distribution. It is assumed that hydrodynamically in the direction of stratification the layers are completeiy disconnected. A parametric investigation of the volume of the pillars is carried out for two problems (fivepoint area flooding scheme and a single well in a circular reservoir) and the results are compared with those for reservoirs with ideal interlayer connectivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5. pp. 184–186, September–October, 1989.     

The source-type solution in the problem of unsteady filtration in a medium with random nonuniformity

The fundamental problems of the theory of filtration in media with random nonuniformities were formulated in [1] and methods of solution were indicated. Primary attention was devoted to the steadystate filtration processes. In the following we solve one of the most important unsteady problems and indicate the connection of the result obtained with the widely used methods of determining strata parameters from the curves of the pressure variation in nonflowing wells. We note that the interpretation of the results of such measurements is usually carried out with the aid of the solution of the corresponding problem for a homogeneous stratum or for a stratum whose nonuniformity has a regular nature (for example, [2]), which definitely limits the possibilities of the method. At the same time it is obvious that the solution of these problems for irregular media and particularly the determination of their effective characteristics requires the use of statistical methods of computation.It is also not difficult to see that the results obtained below may be used for the solution of the corresponding problems of heat conduction, diffusion, etc.     

Effect of flows between formations and capillary forces on the process of oil displacement in a stratified inhomogeneous bed

The results of a numerical investigation of the process of oil displacement in a stratified inhomogeneous formation on the basis of the two-phase flow model with account for capillary forces are presented. It is shown that in many cases the vertical inhomogeneity of oil reservoirs may not be a cause of nonuniform displacement and the non-recovery of large oil reserves by the time of water breakthrough to the extraction surface. The action of the capillary forces is an additional factor leading to equalization of the water propagation front in the inhomogeneous formation, water breakthrough delay, and intensification of the mass transfer between the layers with different permeabilities. Analysis of the contribution of the interlayer flows to the water flooding of low-permeability formation intervals calls into question the practicability of blocking high-permeability inclusions in the neighborhood of pumping wells.     

Hydrodynamic drag of the dolphin

An experimental study of the hydrodynamic drag of the dolphin is reported. The results are compared with calculations for the steady-state motion of a similar rigid model, and previously reported data on the hydrodynamic drag of the dolphin are refined. The drag turns out to be much less than the calculated drag, even when the initial laminar region is taken into account. Several conclusions can be drawn from the results: 1) The experimental results show quite reliably that hydrodynamically the dolphin is in fact a unique phenomenon. 2) The phenomenon is explained in terms of Gray's paradox for the dolphin. 3) The mechanism by which the dolphin's drag is reduced is apparently controllable. 4) Flow around the dolphin can be assumed to be laminar undetached flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 160–164, March–April, 1971.     

Flow behaviour of highly concentrated emulsions of supersaturated aqueous solution in oil

A set of highly concentrated water-in-oil emulsions with supersaturated dispersed phase were investigated in this work to verify and/or develop the models that have been presented both in the literature and in this work. The material used to form emulsions consisted of supersaturated oxidiser solution, hydrocarbon oil and PIBSA-based surfactants. The interfacial characteristics for different surfactant types were first examined. Then, the rheology of samples was studied, and different scaling methods and fitting of experimental data were studied. On the basis of flow curve measurements and observed $\tau _\emph{v} \sim \dot {\gamma }^{1/2}$ scaling, a modified version of Windhab model was suggested which showed excellent fitting of experimental results. The linear dependences of ?? _y0/?? versus 1/d ₃₂ for studied emulsions showed non-zero intercept which implies a non-linear dependence (resulting from interdroplet interaction) to fulfil the zero-intercept requirement. It was established that the zero intercept condition was fulfilled in the $\tau _{y0} \sim \sigma /d_{32}^2 $ scaling, although the experimental results for different surfactants were not superimposed.     

Numerical simulation of the nonuniform breakup of capillary jets

The problem of the evolution of the surface of a jet up to the stage at which it breaks up into droplets is solved numerically for two initial wave disturbances. The wave number of one of these coincides with the wave number of the disturbance that grows most strongly according to the linear theory, while the wave number of the other is varied. The effect of the wave numbers and the amplitude ratio of the initial disturbances on the breakup time and the appearance of nonuniformity is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 12–17, March–April, 1993.     

Generalization of the blunt-body problem in nonuniform supersonic flowfields

The properties of the steady-state gas flow in the shock layer associated with a blunt body immersed in a supersonic stream with an arbitrary shear-like nonuniformity are studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 164–170, March–April, 1996.     

Hydrodynamic theory of the spherical gas bearing

The problem of the spherical gas bearing has been considered in [1,2]. In the present study, following [3], to improve the convergence of the series for the pressures use is made of the method of separation of the singularity, which allows the solution to be used also for large eccentricities.     

Hydrodynamic Structure of the Augmented Born-Infeld Equations

The Born-Infeld system is a nonlinear version of Maxwells equations. We first show that, by using the energy density and the Poynting vector as additional unknown variables, the BI system can be augmented as a 10×10 system of hyperbolic conservation laws. The resulting augmented system has some similarity with magnetohydrodynamics (MHD) equations and enjoys remarkable properties (existence of a convex entropy, Galilean invariance, full linear degeneracy). In addition, the propagation speeds and the characteristic fields can be computed in a very easy way, in contrast with the original BI equations. Then, we investigate several limit regimes of the augmented BI equations, by using a relative-entropy method going back to Dafermos, and recover the Maxwell equations for low fields, some pressureless MHD equations for high fields, and pressureless gas equations for very high fields.     

Determination of the natural frequencies of vibration of nonuniform slabs

The natural frequencies of vibrations of laminated plates are determined in a three-dimensional formulation by analytical separation of the sought functions for plate thickness. The system of differential equations which describes the natural vibrations of the plates is solved analytically. The solution makes it possible to study plates with a large number of layers, including orthotropic plates with elastic characteristics that vary through the thickness. Numerical experiments show that a step approximation can be used to approximate the variable elastic modulus. Ukrainian Transportation University, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 47–53, February, 1999.