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.     

Unsteady-state filtration of a liquid in a fractured-porous stratum to a well with a hemispherical end-face

A study is made of the motion of a liquid toward a well with a hemispherical end-face with unsteady-state spherical-radial filtration in a fractured-porous stratum consisting of hemispherical regions with different values of the permeability of the system of cracks, superposed one on another. A Laplace transform is used to find exact solutions to the problem of the lowering of the stratum pressure as a function of time and distance as well as of the output of a well working with a constant end-face pressure. The article discusses partial cases corresponding to the exploitation of closed and bounded open fractured-porous strata by a central well with a hemispherical end-face. On the basis of numerical calculations, the effect of the parameters of fractured-porous strata on the change in the indices of the process of their exploitation is established. It is established that, with the exploitation of fractured-porous strata, the process of the lowering of the end-face pressure of the well and its output become stabilized with sufficiently large values of the time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–123, November–December, 1973.     

Hydrodynamics of a liquid with deformable and interacting particles

Interest in the hydrodynamics of a liquid with particle rotations and microdeformations has recently intensified [1–9] in connection with the technical applications of different artificially synthesized structured media. A model of a liquid with deformable microstructure was first proposed in [4] and was thermodynamically analyzed in [6], in which a model of a liquid was constructed by means of methods from the thermodynamics of irreversible processes. A model of a macro- and microincompressible liquid with particle rotations and deformations has been proposed [7, 8] based on constitutive equations from [6]. Below we will solve the sphere rotation problem in an infinite liquid given different boundary conditions on the rates of particle rotation and microdeformation within the context of the system of equations presented in [7]. The solution of an analogous problem for a micropolar liquid simulating a suspension with solid particles has been obtained [9] and the solution for a viscous liquid was found by Stokes in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnieheskoi Fiziki, No. 1, pp. 79–87, January–February, 1976.     

Unsteady-state filtration of a liquid to a rectilinear gallery in a two-layer fractured porous stratum

In connection with investigations of the filtration of a liquid in oil-bearing strata with fractured and fractured-porous types of collectors, the article discusses the unsteady-state filtration of a homogeneous liquid in a two-layer stratum of great extension, with different values of the permeabilities of the system of fractures of the intercalations.     

Unsteady processes in the neighborhood of a well in the case of a nonlinear flow law and determination of stratum parameters

A study is made of the propagation of disturbances in the neighborhood of a well in the case of a linear elastic regime for a flow law with limiting gradient, and also for a nonlinear elastic regime for different forms of the flow law. The obtained results are used to investigate the difference between two forms of flow anomaly — nonlinearity of the flow law associated with non-Newtonian behavior of the fluid and a pressure dependence of the parameters of the nonlinear flow law due to nonlinear elastic deformations of strata [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–70, July–August, 1983.I thank V. M. Entov and L. A. Chudov for helpful advice and discussion.     

Plane viscoplastic flow in narrow channels with deformable walls

The equations of motion of a continuum in a thin layer are derived for a given functional dependence of the stress tensor on the strain rate tensor. The general problem of viscoplastic flow is considered in the thin-layer approximation for boundary surface material points travelling in the lateral direction in a predetermined fashion.The projections of the continuum point velocity, pressure, flow rate through a cross-section of the channel, and the power of external forces are expressed as functions of the boundary deformation law. The problem of determining the channel boundary deformation law is formulated for a given boundary pressure distribution. The expressions for the continuum flow rate and pressure and the power of external forces written as functionals of the channel width allow formulation of the problems of controlling viscoplastic flows in thin layers and optimizing the processes.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 23–31, March–April, 1996.     

Flow in a stratum in the case of pumping from an imperfect well near a basin

A study is made of the three-dimensional stationary problem of the flow of ground water to a well of the type of a point sink in a stratum of unbounded thickness in one direction. The stratum is bounded at the top by the bottom of the basin and a stratum of impermeable ground. The problem is investigated in the framework of potential flow theory based on Darcy's law [1, 2], and the solution is obtained in the form of quadratures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–164, September–October, 1980.     

Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow

The paper outlines a technique to analyze the nonstationary vibrations of cylindrical shells interacting with a fluid flow and subjected to external periodic pressure with slowly varying frequency. The dynamic processes occurring in the shell–fluid system as the resonance region is passed forth and back are analyzed     

Unsteady flow of anomalous fluids in a nonuniform layered stratum

A numerical investigation was made into unsteady flow in a nonuniform layered porous stratum with allowance for the nonlinearity of the flow law. The qualitative features of the flow resulting from the interaction of the flow anomalies with the nonuniformity of the stratum were established. The obtained results can be used in the planning of hydrodynamic methods of investigating strata and oil wells in the case of a nonlinear flow law.     

Analysis of fluctuations induced by a scale hierarchy of interacting particles

We investigate the two-point averaging over space of fluctuations arising from a multiscale hierarchy of interacting particles. We assume this will satisfy a condition of homogeneity with respect to scale. We consider the second-order correlation of fluctuations arising from particles of a single scale in the hierarchy; we then form an average over the set of such single-scale correlations. As the hierarchy is refined, a condition of scale continuum is approached. We use the limiting value of this procedure to define a two-point correlation function for the multiscale system as a whole, and identify this with the experimental measurement of correlation in such a multiscale context. In the energy spectrum which emerges in this limit, one term comes to dominate the spectrum for large k; this term has the form ‘k ⁻² ln k’. In fact, a variety of different shape functions (intended to represent correlation functions) leads to this energy spectrum, which bears a qualitative resemblance to a Kolmogorov power-law. In this sense a degree of universality is exhibited. The ideas are illustrated for two simple one-dimensional test cases before a more general treatment in one and three dimensions is developed.     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.