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.     

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.     

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.     

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 solutions of an active additive from a uniform stratum with allowance for gravity

Self-similar solutions describing the displacement of oil by solutions of an adsorbed active additive have been obtained and investigated [1–3] in the framework of a one-dimensional flow model with neglect of diffusion, capillary, and gravity effects. In the present paper, a self-similar solution is constructed for the problem of oil displacement by an aqueous solution of an active additive from a thin horizontal stratum with allowance for gravity under the assumption that there is instantaneous vertical separation of the phases. This makes it possible to estimate the effectiveness of flooding a stratum by solutions of surfactants and polymers in the cases when gravitational segregation of the phases cannot be ignored.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–92, January–February, 1984.     

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.     

Barothermal effect in the displacement of oil from a porous medium

The formation of the temperature field due to the barothermal effect when oil is displaced from a porous medium by water is investigated in the piston displacement and two-phase flow approximations. The approach of the displacement front to the outlet from the porous medium leads to a sharp increase in temperature and the temperature anomalies are observed to depend on the saturation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 104–109, May–June, 1992.     

Fingering associated with immiscible displacement in a two-layer porous medium

The effect of capillary cross flows on the structure of the displacement front in a two-layer porous medium with different layer permeabilities is examined. It is shown that capillary cross flows along the curved displacement front may lead to stabilization of the displacement. Approximate expressions are obtained for the limiting finger length and the oil displacement coefficient at the moment of breakthrough of the water as functions of the displacement parameters and the form of the functional parameters of the two-phase flow in the porous medium; the results obtained are compared with the results of numerical calculations and the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–104, January–February, 1991.     

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.     

Two-dimensional problems of displacement in the case of nonlinear filtration laws

A method is proposed for calculating the multidimensional displacement of oil possessing anomalous properties from productive strata by water. Numerical solutions are obtained on the basis of the most generally accepted models of non-Newtonian oil within the framework of the theory of two-phase filtration of immiscible liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–75, September–October, 1976.     

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.     

Numerical investigation of the process of displacement of oil by steam

A calculation model of the process of displacement of oil by steam, based on the equations of three-phase nonisothermal flow with allowance for phase transitions in the water-steam system, is proposed. This model is used for the numerical investigation of the recovery of oil from wateroil zones by means of steam injection. The extraction of oil from wateroil zones is one of the difficult problems of the theory of exploitation of petroleum deposits. The presence of two zones with sharply different fluid resistances leads to considerable nonuniformity in production rates. It is shown that injecting steam significantly reduces this nonuniformity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 78–84, July–August, 1987.     

Numerical modeling of the process of oil displacement from reservoirs with zonal nonuniformity

In extracting oil from nonuniform reservoirs a considerable fraction remains unrecovered from the zones of lesser permeability. The mechanism of displacement of oil from reservoirs with zonal nonuniformity is investigated within the framework of the two-dimensional Muskat-Meres model of combined oil, water and gas flow [1]. A wholly conservative difference scheme implicit in the saturations and pressure is used for the calculations. Various reservoir exploitation regimes are considered with the object of seeking means of improving the characteristics of the process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1987.     

Miscible displacement from fractured porous media

A model of miscible displacement of incompressible fluids from a fractured porous medium is proposed. The model describes the process of displacement of oil by solvents, the cycling process of displacement of aliphatic hydrocarbon gas by dry gas at low repressions on the formation, and other processes of single-phase multicomponent displacement from fractured porous media. Problems relating to the pumping of a neutral admixture and admixture slugs through a fractured porous reservoir are solved.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–110, November–December, 1989.The authors are grateful to K. S. Basniev, A. K. Kurbanov, V. I. Maron, and M. I. Shvidler for useful discussions.     

Micromodel Observation of the Role of Oil Layers in Three-Phase Flow

We have studied the flow of a non-aqueous phase liquid (NAPL, or oil), water and air at the pore scale using a micromodel. The pore space pattern from a photomicrograph of a two-dimensional section through a Berea sandstone was etched onto a silicon wafer. The sizes of the pores in the micromodel are in the range 3–30,m and are the same as observed in the rock from which the image was taken. We conducted three-phase displacement experiments at low capillary numbers (in the order of 10^-7) to observe the presence of predicted displacement mechanisms at the pore scale. We observed stable oil layers between the wetting phase (water) and the non-wetting phase (gas) for the water–decane–air system, which has a negative equilibrium spreading coefficient, as well as four different types of double displacements where one fluid displaces another that displaces a third. Double imbibition and double drainage are readily observed, but the existence of an oil layer surrounding the gas phase makes the other double displacement combinations very unlikely.     

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.     

Experimental investigation of countercurrent capillary imbibition (CCI) in natural rock samples at various temperatures

CCI in natural oil-saturated core samples has been experimentally investigated. The oil displacement coefficient is determined by comparing the initial and final oil saturations of the sample. The effect of temperature and time on the intensity and rate of CCI is explored. The results of the investigation are scaled up to correspond to the conditions of a real oil deposit on the basis of a well-known similarity criterion. It is shown that the rate of CCI falls significantly with increase in the size of the blocks. In order to intensify CCI it is necessary to heat most of the reservoir with a high-temperature heat transfer agent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 62–67, May–June, 1990.     

Numerical simulation of the displacement of oil by water

If the mobility of a displacing fluid is greater than the mobility of the displaced fluid, the displacement is unstable (see, for example, [1–3]), and the originally plane displacement front is broken up into irregular tongues. It follows from the linear analysis of stability that initially the amplitude of the perturbation increases exponentially, and according to [1] the extended tongues that are formed move with constant velocity relative to the displaced fluid. The intermediate stages in the development of the instability, like questions relating to a more precise formulation of the problem (which involves giving up the piston displacement approximation) remain unstudied. A natural approach to their study is through numerical simulation, which was realized for the first time in [4, 5]. Some of the results of such an investigation are presented in the present paper. In contrast to [4], the main attention is devoted to the development of regular perturbations. It is shown that for the investigated mobility ratios the development of the perturbations follows the linear theory unexpectedly long, and then arrives at a stationary asymptotic regime. We also investigate the influence of the loss of displacement stability on waterless oil extraction in the case of displacement in homogeneous and inhomogeneous strata.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 58–63, September–October, 1979.We thank L. A. Chudov for advice and 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.     

Characterisation of non-linear viscoelastic foods by the indentation technique

A method to determine the non-linear viscoelastic constitutive constants from indentation force–displacement data corresponding to different indentation speeds has been developed. The method consists of two parts. In the first part, the force–displacement data is expressed as two functions which represent the strain and the time-dependent responses, respectively. From these functions, the time-dependent constants and the instantaneous force–displacement response are obtained. In the second part, the strain-dependent variables are determined from the instantaneous force–displacement response through an inverse analysis based on the Levenberg–Marquardt method. The method was verified by numerical experiments using the properties of cheese as examples.