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.     

Flow processes with change of regime in fractured reservoirs

Experimental and industrial observations indicate a strong nonlinear dependence of the parameters of the flow processes in a fractured reservoir on its state of stress. Two problems with change of boundary condition at the well — pressure recovery and transition from constant flow to fixed bottom pressure — are analyzed for such a reservoir. The latter problem may be formulated, for example, so as not to permit closure of the fractures in the bottom zone. For comparison, the cases of linear [1] and nonlinear [2] fractured porous media and a fractured medium [3] are considered, and solutions are obtained in a unified manner using the integral method described in [1]. Nonlinear elastic flow regimes were previously considered in [3–6], where the pressure recovery process was investigated in the linearized formulation. Problems involving a change of well operating regime were examined for a porous reservoir in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–73, May–June, 1991.     

Exact solutions of problems of fluid inflow into a well with a vertical hydrofracture and their use in numerical models of flow through porous media

The plane steady flow of a homogeneous incompressible fluid in a reservoir containing a vertical elliptic hydrofracture is considered. The flow in the reservoir and fracture obeys Darcy's law. Exact solutions of the problem of inflow into a fracture of finite conductivity are obtained both in the case of a uniform reservoir and in the presence in the neighborhood of the fracture of a zone with permeability different from that of the rest of the reservoir. On the basis of the solutions obtained, the effect of the parameters of the polluted zone in the vicinity of the well on its production rate is estimated in the presence of a fracture of finite conductivity, the efficiency of hydraulic fracture of the producing and injection wells is analyzed for regular development systems, and a method of taking hydrofractures of arbitrary orientation and length into account is proposed for finite-difference models of flow through porous media in a system of wells.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–80, November–December, 1996.     

Problems of nonlinear flow through porous media in regions with curved boundaries

The investigation of two-dimensional problems of nonlinear flow through porous media in regions with given curved boundaries involves considerable mathematical difficulties due to the fact that neither the hodograph transformation nor transition to the plane of the complex potential leads to a simplification of the problem. Attention is drawn to a transformation which in the case of circular boundaries maps the flow region onto a canonical domain (half-plane), while the transformed system, which remains, in general, nonlinear, has a much simpler structure than the initial system. For a previously introduced model of the resistance law it is shown that it is possible to construct exact solutions of the problem of an eccentric well within a circular supply contour and the problem of a circular group of wells in an annular (circular) reservoir. The dependence of the dimensionless flow rate on the eccentricity is found and the boundaries of the stagnant zones are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 103–108, January–February, 1989.     

Contribution to the theory of nonisothermal flow through porous media with phase transitions

Nonisothermal three-velocity flow through porous media is investigated numerically with allowance for phase transitions. The modeling is based on the following common assumptions: it is possible to neglect the diffusive process of mixture component transport, longitudinal heat transfer due to heat conduction, and the transport of the liquid and gas phases as a result of the capillary pressure difference in the phases as compared with convective transport; the porous medium is in local thermodynamic equilibrium (equality of the temperatures, pressures and chemical potentials of the phases); and, moreover, the problems of heat transfer along and across the reservoir can be treated separately (Leverrier model).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 78–85, September–October, 1989.     

Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling

The paper presents a numerical analysis of the inelastic deformation process in porous rocks during different stages of its development and under non-equiaxial loading. Although numerous experimental studies have already investigated many aspects of plasticity in porous rocks, numerical modeling gives valuable insight into the dynamics of the process, since experimental methods cannot extract detailed information about the specimen structure during the test and have strong limitations on the number of tests. The numerical simulations have reproduced all different modes of deformation observed in experimental studies: dilatant and compactive shear, compaction without shear, uniform deformation, and deformation with localization. However, the main emphasis is on analysis of the compaction mode of plastic deformation and compaction localization, which is characteristic for many porous rocks and can be observed in other porous materials as well. The study is largely inspired by applications in petroleum industry, i.e. surface subsidence and reservoir compaction caused by extraction of hydrocarbons and decrease of reservoir pressure. Special attention is given to the conditions, evolution, and characteristic patterns of compaction localization, which is often manifested in the form of compaction bands. Results of the study include stress-strain curves, spatial configurations and characteristics of localized zones, analysis of bifurcation of stress paths inside and outside localized zones and analysis of the influence of porous rocks properties on compaction behavior. Among other results are examples of the interplay between compaction and shear modes of deformation.To model the evolution of plastic deformation in porous rocks, a new constitutive model is formulated and implemented, with the emphasis on selection of adequate functions defining evolution of yield surface with deformation. The set of control parameters of the model is kept as short as possible; the parameters are carefully selected to have simple and intuitive physical interpretation whenever possible. Results demonstrate that evolution of the yield surface with deformation has major influence on the resulting characteristics of deformation patterns, which is not sufficiently acknowledged in the literature.     

Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs

A numerical method as well as a theoretical study of non-Darcy fluid flow through porous and fractured reservoirs is described. The non-Darcy behavior is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The non-Darcy flow through a fractured reservoir is handled using a general dual-continuum approach. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in petroleum and geothermal reservoirs.     

Flow stress behavior of porous FVS0812 aluminum alloy during hot-compression

The hot deformation behavior of porous FVS0812 aluminum alloy prepared by spray deposition was studied by means of compression tests on a Gleeble 1500 machine. The samples were hot compressed at temperatures ranging from 573 K to 773 K under various true strain rates of 10⁻⁴–10⁰ s⁻¹. The deformation behaviors are characterized by a significant strain hardening during hot-compression due to the progressive compaction of the pores with increasing compressive strain. A revised formula describing the relationships of the flow stress, strain rate and temperature of the porous alloy at elevated temperatures is proposed by compensation of strain. The theoretical predictions are compared with experimental results, which show good agreement.     

On the connection between the principal components of the stress and permeability tensors of porous media

The dependence of the flow properties of rocks on the conditions under which they are loaded is one of the least studied questions in the general problem of the connection between the physical properties of porous systems and the loads acting on them. The experimental [l] and theoretical [2, 3] studies so far made have dealt primarily with the dependence of the permeability of oil and gas collector rocks on the hydrostatic compression to which they are subjected. In the present paper, a connection is established between the parameters of a nonuniform anisotropic load and the permeability tensor of rock.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 173–177, January–February, 1984.     

裂缝性低渗透油藏流-固耦合理论与数值模拟

根据裂缝性低渗油藏的储层特征,建立适合裂缝性砂岩油藏渗流的等效连续介质模型。将渗流力学与弹塑性力学相结合,建立裂缝性低渗透油藏的流-固耦合渗流数学模型,并给出其数值解.通过数值模拟对一实际井网开发过程中孔隙度、渗透率的变化以及开发指标进行计算,并和刚性模型以及双重介质模型的计算结果进行了分析比较.     

Gas-gas displacement in a fractured porous reservoir

The results of an experimental investigation of the process of miscible displacement of a gas from a fractured porous reservoir by another gas are presented. It is established that the displacement process is influenced by convective and molecular diffusion. The displacement coefficient depends both on the reservoir properties of the formation and on the technological displacement parameters. The experiments revealed a decrease in the displacement coefficient with increase in the permeability ratio of the joints and the blocks and with decrease in formation pressure. The dependence of the displacement coefficient on the average gas velocity in the reservoir, i.e., the ratio of the gas flow rate to the product of the flow area and the total reservoir porosity coefficient (including the blocks and the joints), is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–79, May–June, 1991.     

Solution of some problems of flow through fractured porous media

Problems of fluid flow through a fractured porous medium consisting of fractures and blocks with different filter characteristics are solved. The mass exchange between fractures and blocks is assumed to be proportional to the pressure difference between them. The porosity in the fractures is assumed to be negligibly small. Under these assumptions the determination of the pressure fields reduces to the integration of a system of linear differential equations. The solution is found by the operational method using the Efros theorem. The cases of oil reservoir operation by means of both galleries and wells are considered. The solutions are obtained in an analytical form convenient for calculations.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 94–102, January–February, 1995.     

Induced anisotropy effect in the neighborhood of an operating well

The mathetical model of porous medium anisotropy induced by an intense flow is discussed. The model is based on the orientation and deformation of the particles of the elastic matrix. The governing law of flow with induced anisotropy is analyzed and the model is numerically investigated for plane-radial flow. Problems and boundary conditions are formulated. The results of the numerical solution explain the effects observed under field conditions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 67–72, November–December, 1993.     

Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

The results of solution of the self-similar problem of planar flow of gas through a porous medium in the case of a quadratic law of resistance [1] are generalized to the case of axisymmetric motion. The equation in similarity variables for the velocity of isothermal gas flow is reduced to an equation having cylindrical functions as solution. Analytic dependences of the pressure and the gas velocity on the coordinate and time are obtained for a given flow rate of the gas at the coordinate origin and for zero Initial gas pressure in the porous medium.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 168–171, July–August, 1982.     

Solution of problems of unsteady flow through porous media with an extended fracture (barrier)

A method of constructing the potentials describing the elastic regime of flow through porous media is proposed. The flow is induced by the initial conditions in media with an extended fracture-drainage or barrier-curtain used, in particular, for blocking off polluted zones. The fracture and barrier are simulated by infinitely thin strata with permeability which is infinitely large for the fracture and infinitesimal for the barrier. Similar problems for steady processes were considered in [1–3].Chita. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 95–98, November–December, 1995.     

Drag of porous cylinders in a viscous fluid at low reynolds numbers

The problem of flow past a permeable cylinder at low Reynolds numbers is of interest for the solution of a number of problems in chemical technology in, for example, the design of porous electrodes and porous catalysts and in the calculation of nonstationary filtration of aerosols by fibrous filters. In the present paper, we solve the problem of transverse flow of a viscous fluid past a continuous cylinder in a porous shell and, in particular, in the case of a porous cylinder under conditions of constrained flow (system of cylinders) and an isolated cylinder at arbitrary permeability. The analogous problem of Stokes flow past permeable spheres has been solved in a number of papers [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 122–124, November–December, 1979.     

Percolation model of equilibrium three-phase flow through porous media

Percolation models of one-phase and two-phase flow through porous media are extended to the three-phase case. The characteristic regions of realization of one-phase, two-phase and three-phase flow are determined, Relative phase permeability calculations are presented for a model capillary radial density function. The theory is compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 109–114, January–February, 1989.     

Laminar flow between porous disks for intense homogeneous asymmetric inflow and outflow

In [1–3], a class of self-similar solutions was considered for the flow of incompressible fluid in a plane channel with porous walls, through which there is homogeneous symmetric inflow or outflow. An analogous class of self-similar solutions for flow between porous disks with natural homogeneous conditions at the periphery was considered in [4], where the asymptotic behavior of these solutions at a small Reynolds number of the outflow R was investigated, and the limiting form of the solution for symmetric outflow with R= was noted. In the present paper, the boundary-function method is applied to the singular problem corresponding to the flow between porous disks for asymmetric inflow and outflow characterized by large R.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1976.     

Numerical study of the flow and heat transfer in a Reiner-Rivlin fluid on a rotating porous disk

An unsteady flow and heat transfer to an infinite porous disk rotating in a Reiner—Rivlin non-Newtonian fluid are considered. The effect of the non-Newtonian fluid characteristics and injection (suction) through the disk surface on velocity and temperature distributions and heat transfer is considered. Numerical solutions are obtained over the entire range of the governing parameters.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 85–95, January–February, 2005.