Mathematical simulation of micellar-polymer displacement of oil from flooded strata

The micellar-polymer method of increasing the oil recovery from strata [1] is currently regarded as promising. The method consists of injecting into an oil stratum, which has previously undergone ordinary flooding, a relatively small amount, a slug, of micellar solution (5–10% of of the pore volume), which is propelled through the stratum by slugs of a highly viscous buffer fluid (aqueous solution of a polymer). In turn, the system of slugs is propelled from the injection points to the extraction wells by the water used for ordinary flooding. The displacement of the oil that remains after flooding in the stratum is achieved by a decrease in the coefficient of surface tension at the boundaries of the micellar solution with the oil and the water to the value 10^–2-10^–3 dyn/cm, which leads to a decrease in the amount of fixed oil and also to a control of the mobility of the fluids, which is achieved by varying the concentrations of the components of the micellar solution and the buffer fluid. The main components of micellar solutions are: a hydrocarbon fluid (oil or its fractions), water, surface-active substances. The relationships between the main components, and also the addition of salts and alcohol to the water component have a strong influence on the interaction between the solution and the stratal oil and water [2]. The micellar solution considered in the present paper dissolves oil but does not mix with water; the relationships between the components in it are characteristic of the solutions used to increase oil recovery from strata.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 84–93, November–December, 1982.     

Unsteady displacement of an oil deposit in a flow of stratal water

Unsteady problems concerning the displacement of gas and oil deposits in a seepage flow of stratal water are of specific interest to oil and gas hydrogeology, and in the planning and analysis of the processes of reservoir exploitation. Firstly, a change of the hydrogeological environment in a region of already formed deposits involves their displacement. Secondly, when one of two adjacent deposits is developed, a displacement of the other occurs in the artificial flow of stratal water which is produced. Papers [1–3] investigate the steady configuration of gas—water or water—oil contacts in the presence of a seepage flow of stratal water under the deposit. The unsteady problem considered below is a generalization of the problem in paper [3]. Its characteristic property is the presence of mobile boundaries separating the regions with flow of different fluids in the horizontal plane.Translated from Izvestiya Akademii Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, pp. 177–179, March–April, 1985.     

Barothermal effect in three-phase flow through a porous medium with phase transitions

The formation of a temperature field in a porous medium due to the barothermal effect and phase transitions associated with oil, water, and gas flow is investigated. Degassing of the liquid has an important influence on the formation of the temperature field, the presence of stratal water tending to reduce the cooling anomaly.Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 113–117, November–December, 1994.     

Vertical displacement of immiscible fluids from heterogeneous formations

The modified phase permeability model [1, 2] is extended to the case of vertical displacement with allowance for the force of gravity. It is assumed that in connection with vertical displacement a thicker dometype formation may be regarded as a stream tube of variable cross section. An exact solution of the one-dimensional displacement problem is constructed. It is shown that in vertical displacement from heterogeneous formations the gravity forces stabilize the displacement, so that at low velocities it approaches displacement of the pure piston type. It is established that a decrease in the injection and extraction rates leads to an increase in hydrocarbon output, and an increase in formation pressure to a fall in output.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 91–97, March–April, 1991.The authors wish to thank K. S. Basniev and A. K. Kurbanov for formulating the problem and taking an interest in the work.     

Experimental investigation in filtration of hydrocarbons with mass transfer

The results are given of an experimental investigation into the process of extraction from a porous medium of a liquid hydrocarbon (precipitated condensate) filling part of the pore space by means of hydrocarbon solvents.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–170, September–October, 1979.     

Gas-dynamic calculation of pulsating flow in pipelines

A numerical solution is examined for a system of equations of one-dimensional isothermal flow of a perfect gas in a horizontal pipe with a periodically varying function of the flow rate at the boundary. The numerical solution is compared with the solution of the linearized problem. The results can be used to calculate the pulsating motion of gas in the pipeline systems of piston compressors [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 85–88, July–August, 1972.     

Onset of liquid-phase flow as a result of the accumulation of gaseous products

The flow of a gaseous mixture of hydrocarbons and carbon dioxide through a model reservoir with a stationary hydrocarbon liquid phase has been investigated theoretically and experimentally. The possibility of the onset of liquid-phase flow as a result of the accumulation of gaseous products is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 185–188, March–April, 1990.     

Flow and heat transfer of a viscous fluid when there is a phase transition

A study is made of the problem of the flow and heat transfer of a fluid formed by the phase transition (melting or sublimation) when the end of a rod touches a heated surface. Problems of this kind arise, in particular, when a heated surface is cooled by means of the heats of the phase transitions of materials with an energy content. A solution is obtained to a simplified system of heat and mass transfer equations obtained by estimating the order of magnitude of the various terms in the Navier-Stokes equations in a manner similar to that in [1–3]. The parameters that govern the process are identified, and an approximate analytic solution is found for the quasi-stationary case. The analytic solution is compared with a numerical solution obtained iteratively.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–131, May–June, 1931.     

Nonlinear steady-state motion of an elastic plate floating on the surface of a liquid of infinite depth

The nonlinear problem of steady-state waves in an ideal fluid of infinite depth with a thin elastic plate floating on its surface is considered. The solution is found by a perturbation method. Three approximations are obtained. A case of branching of the solution is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–123, March–April, 1987.     

Dispersion of a gas cloud with de-excitation. Self-similar solution

A solution of the problem of cloud dispersion in a vacuum with de-excitation is obtained by the method of separation of variables in a Lagrange coordinate system. The energy equation corresponds to the de-excitation of an optically thin volume with a power-law dependence of the radiativity on the density and temperature. The self-similar solution is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhani'ka Zhidkosti i Gaza, No. 6, pp. 128–131, November–December, 1971.     

Theory of slightly perturbed three-dimensional flows in nozzles

The theory of slightly perturbed flows in conical nozzles is used to determine the transverse force and moment generated in the presence of asymmetric perturbations. A system of ordinary differential equations is derived for finding the transverse force and moment. An approximate analytical solution of this system is constructed and its qualitative features are studied. A comparison is made with a numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1977.     

Application of potential theory to a problem of the limiting configuration of the stagnant zones in the displacement of viscoplastic oil by water

A solution of the problem of determining the limiting-equilibrium portions of residual viscoplastic oil in connection with the displacement of oil by water from a porous formation in a multiwell system is constructed by the methods of potential theory and analyzed. The results of a comparison with a standard exact solution are presented for certain asymptotic cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January–February, 1989.     

Transverse flow of a rarefield gas around a plate

A method of characteristics is developed for the numerical solution of kinetic equations in the case of fully developed plane-parallel motions of a gas. A solution is given to the problem of flow around a plate arranged normal to an oncoming supersonic flow. The results of the calculations are in satisfactory agreement with existing experimental data.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 107–113, November–December, 1972.     

Solution of the inverse problem of thermal conductivity for a melting slab with entrainment

This article proposes an approximate solution to the inverse problem of the Stefan type for a finite region with arbitrary boundary and initial conditions. A comparison with exact solutions is made.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 132–137, May–June, 1973.     

Analysis of the transition from constant output to fixed well-bottom pressure for elastic regime of oil extraction

The elastic flow regime of stratal fluids has been well studied in the literature [1, 2] and the results have been widely applied in practice in the development of oilfields [3, 4]. Consideration is given below to the new problem of the reduction in the output of a well at fixed well-bottom pressure after it has been operating for some time at constant output. There is a practical aspect to this sort of problem. For instance, the degassing of the reservoir in the region of the well is considered an undesirable feature in the exploitation process. If degassing begins, the resistance to flow grows sharply and the well outputs fall considerably. Once the well-bottom pressure has fallen to the saturation pressure, it must not be allowed to fall further, or gas will be given off in the well region of the reservoir. It is desirable to keep the well-bottom pressure higher than the saturation pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 82–87, March–April, 1985.     

Numerical investigation of convective heat transfer in liquid hydrocarbons stored in underground reservoirs

In planning for the underground storing of liquid hydrocarbons and calculating the technological parameters of underground reservoirs formed by leeching from a rock salt massif, it is necessary to understand the hydrodynamic and heat transfer processes produced by natural convection. The paper is devoted to numerical study of the initial stage of convective heat transfer in a vertical cylindrical cavity completely filled with a liquid hydrocarbon. It is assumed that at the initial time the temperature of the liquid, which is at rest, is homogeneous, Convective flow develops in part due to the initial temperature difference between the liquid and the massif and partly due to the geothermal temperature gradient in the latter. The problem is regarded as coupled, the convective process in the liquid being determined simultaneously with the solution of the heat-conduction problem in the surrounding rock. The Grashof numbers characterizing the intensity of the real process are very large: G lO¹²–lO¹⁵. A numerical solution was obtained for moderate Grashof numbers G lO⁷–lO¹¹. The asymptotic dependences for the integral characteristics of the unsteady process obtained in a series of calculations were extrapolated to the real values of the Grashof number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–148, March–April, 1981.     

Some problems of centrally symmetrical percolation of a gas

A solution is considered for the centrally symmetrical problem of unsteady inflow of gas to a stratum sampler on a logging cable in a thick stratum with constant pressure at the discharge and variable pressure when filling the closed cylinder of the sampler with gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 117–121, November–December, 1971.     

Investigation of the transitional process of the startup of a gas bearing

In this article we derive equations for transitional conditions of a gas lubricant under nonisothermal conditions. A numerical solution of the Reynolds equation is described for the problem of the pulsed startup of a radial bearing with a fixed geometry, and the results of this solution are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1977.     

Solution to problem of strong evaporation of a monatomic gas by the Monte Carlo method

The Monte Carlo method has been used to obtain a numerical solution to the problem of strong evaporation of a monatomic gas in which the molecules are modeled by pseudo-Maxwellian and hard spheres. A comparison with the results of other authors is made. The results agree well with the solution of the problem obtained on the basis of the model Bhatnagar—Gross—Krook kinetic equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 1984.I should like to thank M. N. Kogan for discussing the results.     

Below-surface irrigation

The wetting of soil from sources of infinitesimally small size is considered with allowance for the formation of two zones, i.e., a zone of complete saturation around the source and a surrounding zone of incomplete saturation. A self-similar solution to a definite problem is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–147, March–April, 1980.