Displacement of oil by a slug of an active additive forced by water through a stratum

The paper gives a solution to the problem of the displacement of oil by a slug for different forms of the sorption isotherm and the distribution function of the additive between the phases and for different values of the initial flooding of the stratum. The process is considered under conditions of reversible sorption and also under conditions of partial retention of the additive by the skeleton of the porous medium. The behavior of slugs in the case of cyclic pumping of a solution of an active additive is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp. 102–111, May–June, 1982.I thank M. V. Lur'e and M. V. Filinov for suggesting the problem and constant interest in the work, and also V. M. Entov for helpful discussions.     

Displacement of oil by water from clay bearing strata

The displacement of oil by water from collectors containing clay which swells has been investigated theoretically and experimentally. Swelling of clay due to a change in the ion composition of water filling a stratum can influence the displacement process not only by changing the permeability, as assumed in an earlier paper [1], but also directly by changing the pore space. A modification of the theoretical scheme of the displacement of oil by a solution of an active additive is constructed to take into account these effects; the structure of the displacement front is investigated and the experimental results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 59–65, July–August, 1981.     

Displacement of oil by a solution of an active and a passive additive

A study is made of the frontal displacement of oil from a homogeneous porous medium by a solution of an active additive in the presence in the flow a component (referred to as the passive additive) that does not directly influence the ratio of the mobilities of the water and the oil but does interact with the active additive, changing its adsorbability and (or) its distribution between the phases [1]. Such a situation arises when oil is displaced by solutions of surface-active substances and other reactants, whose effectiveness in application is significantly reduced by their adsorption by the porous medium (if the adsorbed matter itself does not reduce the mobility of the water, as in the case of the polymer in [2]). Under these conditions, it may be worth adding to the solution of the surface-active substance some cheap ballast substance that does not change the ratio of the mobilities of the phases but is capable of taking away from the surface-active substance some of the adsorption centers on the surface of the porous skeleton. Another example of a passive additive is provided by salts dissolved in water that influence the distribution of the active impurity between the water and the oil; this occurs in the case of displacement by carbonated water due to the dependence of the solubility of carbon dioxide gas in water on the mineralization of the water [3]. In the present paper, an investigation is made of the structure of the displacement front, and a technique is developed for constructing a self-similar solution in the case when the adsorbability of the passive additive and its distribution between the phases do not depend on the concentration of the active additive.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 74–83, November–December, 1982.     

Effect of the kinetics of sorption,solution and heat transfer processes on the displacement of oil by active solutions

Among the new methods of enhanced oil recovery the most important are the processes of oil displacement by solutions of active agents (chemical reagents) capable of modifying the hydrodynamic characteristics of the porous flow system. Self-similar processes of oil displacement by active solutions have previously been studied [1–4] for a thermodynamic-equilibrium distribution of the agent in the dissolved in both phases and sorbed states. However, for small-scale displacement processes the effect of the mass transfer kinetics is important. Here the problem of oil displacement by an active solution is solved with allowance for the thermodynamic nonequilibrium of the physicochemical heat and mass transfer processes. In the problem of oil displacement by a solution of water-soluble surfactant or polymer the sorption kinetics of the chemical reagent are taken into account, and in the problem of oil displacement by carbonated water the kinetics of the process of solution of the carbon dioxide in the displaced phase. Allowance for these effects is especially important in interpreting the results of laboratory displacement experiments. The problem of the displacement of oil by hot water is solved with allowance for heat exchange with the surrounding strata. As distinct from the previously investigated case of a stationary temperature distribution in a bounded neighborhood of the formation (supply of heat in accordance with Newton's law) [5, 6], here we analyze the case of nonstationary heating of surrounding rock strata of infinite thickness (Leverrier model).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 60–71, November–December, 1985.     

Nonisothermal displacement of oil by a solution of an active additive

In earlier work [1, 2] mathematical models have been constructed for processes of displacement of oil from a porous medium by a solution of an active additive, i.e., an additive capable of changing the hydro-dynamic characteristics of the fluid and the medium. An additive of this kind that was considered was a polymer that in the dissolved state influences the properties of the displacing fluid and in the adsorbed state the permeability of the porous medium. Self-similar solutions were obtained corresponding to the problem of frontal displacement from a homogeneous porous medium, and a number of numerical calculations were made. It is natural to generalize this treatment by introducing into the problem a second active factor, which is here taken to be the temperature of the injected fluid. The analysis of the nonisothermal displacement of oil by a solution of an active additive can be transferred without significant modifications to the general problem of displacement of oil by a solution carrying two active agents. The names additive and temperature are retained here only for convenience of exposition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 90–107, November–December, 1980.We thank A. A. Barmin, A. G. Kulikovskii, and L. A. Chudov for helpful discussions.     

Structure of the front of oil displacement by a solution of an active additive under nonisothermal conditions when the water saturation of the stratum is high

The structure of the front of oil displacement by a solution of an active additive under nonisothermal conditions in the large-scale approximation without allowance for heat losses has been studied in detail by Braginskaya and Entov [1, 2]. In the present paper, this study is augmented by an analysis of displacement problems when the initial water saturation of the stratum is high. These problems simulate the use of active additives and the pumping of hot water in the lat stage of extraction when an appreciable fraction of the oil has already been displaced from the stratum by ordinary flooding and the initial water saturation of the stratum is high. The exposition is based on the earlier studies [1, 2], whose content is assumed known.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–180, January–February, 1982.I thank V. M. Entov for suggesting the problem and helpful discussions.     

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.     

Two-phase three-component flow through a porous medium with variable total flow

In analyzing the processes of the displacement of oil, in which intensive interphase mass transfer takes place, it is normally assumed that the partial volumes of the components as they mix are additive (Amagat's Law) [1, 2]. Then the equations of motion have an integral, which is the total volume flow rate through the porous medium, and the basic problems of frontal displacement, if there are not too many components in the system, permit an exact analytical study to be made [3–5]. If this assumption is rejected, the total flow becomes variable [3, 6, 7]. It appears that the consequences of this as applied to the processes of the displacement of oil by high pressure gases have not previously been considered. The results of such a study, developing the approach outlined in [4], are given below. The initial multicomponent system is simulated by a three-component one which contains oil (the component being displaced), gas (the neutral or main displacing component), and intermediate hydrocarbon fractions or solvent (the active component). It is shown that instead of the triangular phase diagram (TPD) normally used where the partial volumes of the components are additive, in this case it is convenient to use a special spatial phase diagram (SPD) of the apparent volume concentrations of the components to construct the solutions and to interpret them graphically. The method of constructing the SPD and its main properties are explained. A corresponding graphoanalytical technique is developed for constructing the solutions of the basic problems of frontal displacement which correspond to motions with variable total flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–120, May–June, 1985.     

One-dimensional displacement of petroleum by aqueous solutions of sorption agents taking account of interlayer return flows

Experimental and theoretical investigations of the process of the displacement of petroleum by aqueous solutions of surface-active substances (surfactants), polymers, micelle solutions, and their combinations show that sorption phenomena can exert a considerable effect on the process of flooding [1, 2]. In some cases, they can lead to an appreciable lag of the front of the dissolved substance behind the carrier liquid and to the appearance of a second jump in the saturation of the displacing liquid [1, 3]. In [4] a mathematical model is proposed for the displacement of petroleum from a laminar stratum with isolated intercalculations of aqueous solutions of surfactants and polymers, taking account of sorption phenomena. In the present article, a study is made of the displacement of petroleum from a stratum by aqueous solutions of sorption agents, taking account of interlayer return flows of liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 38–45, March–April, 1977.     

On the mechanism of cyclic flooding for oil extraction

A two-dimensional model is considered for the displacement of oil by water from a stratum that is nonuniform over its thickness when a periodic elastic flow regime is employed.Translated from Izvestiya Akademii Nauk SSSR, Meknanika Zhidkosti i Gaza, No. 3, pp. 58–66, May–June, 1980.     

Calculation of limiting configuration of stagnant zones when viscoplastic oil is displaced by water

A study is made of the problem of determining the position of the limiting equilibrium portions of unrecovered viscoplastic oil displaced by water from a porous stratum in a many-well system. This problem was formulated by Bernadiner and Entov [1] and is of interest in connection with the obtaining of estimates of the volume of displaced oil. For two-dimensional isothermal flow in a homogeneous undeformed stratum and certain restrictions on the geometry of the flow region, the problem can be investigated by the methods of the theory of analytic functions [1–3]. An approximate solution of one problem with complicated flow geometry has been obtained [4] by means of potential theory. In the present paper the methods of the theory of jets are used to construct and analyze an exact analytic solution to the problem for three possible flow schemes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–81, March–April, 1991,We thank M. M. Alimov for discussing the work.     

Filtration of a three-phase liquid (Buckley-Leverett model)

Buckley and Leverett [1] formulated the problem of the displacement of immiscible liquids in a porous medium and obtained a very simple one-dimensional solution for a two-phase flow. Different generalizations of it are known [2]. In [3, 4], a method of characteristics is proposed for numerical solution of the problem of three-phase flow. Articles [5, 6] consider the problem of the injection (at a given pressure) of two incompressible liquids into a porous stratum previously saturated with a third, elastic liquid. The authors started from the assumption of the existence, for this problem, of zones of three-, two-, and single-phase flow, separated by unknown mobility gradients. The present work investigates the solution for a three-phase flow, analogous to the Buckley-Leverett solution for two phases. It is shown that the character of the degrees of saturation depends essentially on the initial saturation of the porous stratum and on the phase composition of the mixture being injected.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–44, January–February, 1972.     

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.     

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.     

Numerical simulation of flow of multicomponent mixtures in porous media

A study is made of the isothermal flow of multicomponent mixtures in a porous medium, accompanied by phase transitions, interphase mass exchange, and change in the physicochemical properties of the phases [1–3], It is assumed that at each point of the flow region, phase equilibrium is established instantaneously and the flow velocities of the separate phases conform to Darcy's law. Approximate solutions of problems of displacing oil by high-pressure gas were obtained in [1]. By generalizing the theory developed in [4], a study is made in [5] of the structure of the exact solutions of the problems of the flow of three-component systems which describe the displacement of oil by different reactants (gases, solvents, micellar solutions). The numerical solutions of the problems of multicomponent system flow are considered in [2, 3, 6, 7]. This paper presents a numerical method which is distinguished from the well-known ones [2, 3, 6, 7] by the following characteristics. The flow equations are approximated by a completely conservative finite-difference scheme of the implicit pressure-explicit saturation type, the calculation being carried out using Newton's method of iteraction with spect to both the pressure and the composition of the mixture. The minimum derivative principle [8] is used in the approximation of the divergence terms of the equations. The phase equilibrium is calculated using the equation of state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 101–110, July–August, 1985.     

Level kegulation of ground water in irrigation

Level regulation of ground water is important for preventing the irrigated ground from becoming bogged up or salinated; the evaporation and the existence of a weakly permeable horizontal waterproof stratum are taken into account. The solution is found in an explicit form. It is also shown that the solution tends asymptotically either to one of the two stationary solutions or to periodic solutions which are also obtained in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 125–133, September–October, 1973.     

Nonisothermal displacement of high-paraffin oils by water with allowance for solid-phase precipitation

A mathematical model of the nonisothermal displacement of oil by water with allowance for solid-phase precipitation is proposed. Self-similar solutions of the problem of nonisothermal displacement of oil from a homogeneous, thermally insulated formation are obtained. The inverse problems of determining the relative phase permeabilities and the temperature dependence of the paraffin saturation concentration from laboratory displacement data are solved. Exact solutions of the non-self-similar problems of the displacement of high-paraffin oil by a slug of hot water and of the thermal delay problem are obtained. The nonisothermal displacement of high-paraffin oils by water with allowance for heat transfer to the surrounding strata is subjected to qualitative analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–137, May–June, 1989.The authors are grateful to A. K. Kurbanov and Yu. V. Kapyrin for useful discussions and their interest in the work.     

Two-phase filtration to an imperfect borehole in an inhomogeneous producing stratum

A finite-difference method is proposed for solving the filtration equations of a two-phase liquid passing into a borehole partly revealing an oil stratum. The results of a finite-difference calculation of the dynamics of borehole flooding are compared with the solutions obtained by the zonallinearization method, as proposed by Abramov, Danilov, and Kats [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 64–69, May–June, 1976.In conclusion, the author wishes to thank R. M. Kats and M. I. Shvidler for interest in the work and useful comments.     

Exchange model of displacement in porous media

A displacement model constructed on the assumption of the exchange of components between the volumes of the pore space moving and not moving in the direction of displacement is considered. The theoretical solution is shown to be in good agreement with the actual results of the displacement of oil by water. Criterial equations for predicting the interphase exchange coefficient and the relation between the nonmoving and moving volumes of the pore space are constructed on the basis of a series of experiments in uncemented porous media.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97. January–February, 1991.     

Self-Similar Solutions of Problems of Physicochemical Subsurface Hydromechanics

Self-similar solutions of the equations of physicochemical subsurface hydromechanics corresponding to one-dimensional oil displacement by a solution of an active additive are considered. An approach in which a self-similar solution of a hyperbolic problem is obtained as the limit of the self-similar solution of a parabolic problem when the transport coefficients tend to zero is proposed and realized. Examples of regular and nonregular passage to the limit, when the limit is unique and when the limit depends on a ratio of small transport coefficients, respectively, are given. The physical meaning of nonregularity is discussed in the case of oil displacement by a solution of an ambivalent active additive.