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.     

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 displacement of compressible fluids from stratified reservoirs

Mutual displacement equations are derived within the framework of the modified phase permeability model, taking the compressibility of one of the phases into account. A self-similar solution of one-dimensional displacement problems is obtained. The role of compressibility in displacement from nonuniform stratified reservoirs is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 74–83, March–April, 1993.     

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.     

Micromechanics of residual saturation formation during immiscible displacement in a porous medium

The process of displacement of a nonwetting fluid has been studied experimentally on a transparent model of a porous medium for various percolation velocities in the stable front regime, when the viscosity of the displacing fluid is greater than that of the fluid displaced. The flow structures in the final displacement regime, when the nonwetting phase is distributed in the pore space in the form of individual drops or ganglia, have been visually investigated. Imbibition is numerically modeled on a two-dimensional network model with allowance for various microdisplacement mechanisms. The effect of the initial displacing phase saturation on the magnitude and structure of the residual displaced fluid saturation is demonstrated. The fractal dimensionality of the displacement boundary is measured.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 116–121, May–June, 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.     

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.     

Stability of frontal displacement of fluids in a porous medium in the presence of interphase mass transfer and phase transitions

To preserve the stability of the front relative to small perturbations when one fluid is displaced by another the pressure gradient must decrease on crossing the front in the direction of displacement. Initially, this criterion was established for the piston displacement of fluids [1, 2], and later in the case of two-phase flow of immiscible fluids in porous media for the displacement front corresponding to the saturation jump in the Buckley—Leverett problem [3, 4]. Below it is shown that the same stability criterion remains valid for flows in porous media accompanied by interphase mass transfer and phase transitions [5, 6]. Processes of these kinds are encountered in displacing oil from beds using active physicochemical or thermal methods [7] and usually reduce to pumping into the bed a slug (finite quantity) of reagent after which a displacing agent (water or gas) is forced in. The slug volume may be fairly small, especially when expensive reagents are employed, and, accordingly, in these cases the question of the stability of displacement is one of primary importance. These active processes are characterized by the formation in the displacement zone of multiwave structures which, in the large-scale approximation (i.e., with capillary, diffusion and nonequilibrium effects neglected), correspond to discontinuous distributions of the phase saturations and component concentrations [5–10]. It is shown that the stability condition for a plane front, corresponding to a certain jump, does not depend on the type of jump [11, 12] and for a constant total flow is determined, as in simpler cases, by the relation between the total phase mobilities at the jump. An increase in total flow in the direction of displacement is destabilizing, while a decrease has a stabilizing influence on the stability of the front. Other trends in the investigation of the stability of flows in porous media are reviewed in [13].Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 98–103, March–April, 1986.     

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.     

Motion of a cylindrical cavity near a free boundary of a liquid

The dynamics of a cylindrical cavity in a liquid with no allowance for vertical displacement are considered in [1–3]. The present study investigates the pulsation motion of a cylindrical cavity near a free boundary of a liquid, allowing for displacement of the axis of the cavity in the vertical direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1988.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

Self-similar solutions of problems of two-phase flow through porous media with allowance for the compressibility of one of the phases

Self-similar problems of mutual displacement are solved with allowance for the compressibility of one of the phases. It is found that when an incompressible liquid is displaced by a gas the extent of displacement increases. The mutual displacement of gas-liquid mixtures results in the formation of not one but several saturation jumps, i.e., the structure of the displacement zone is much more complex.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 71–80, January–February, 1990.The authors are grateful to V. I. Maron for useful discussions.     

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.     

Friction in an elastohydrodynamic contact

The problem of the movement of a fluid in an elastohydrodynamic contact is examined in cases of high pressures, high displacement velocities, and low characteristic times, taking into account the nonlinear properties of the fluid — dependence of viscosity on pressure, temperature, and displacement velocity. Simple asymptotic formulas are obtained. The problem is solved numerically in the one-dimensional case. A comparison is made with an experiment on the measurement of the frictional force in an elastohydrodynamic contact.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 135–137, July–August, 1976.The authors wish to thank V. D. Danilova and A. I. Petrusevich for supplying the experimental data.     

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.     

Dispersion coefficient with the displacement of a gas from a porous medium by a gas

The article gives the dependence of the dispersion coefficient on the Péclet number, obtained with the analysis of experimental data on the displacement of a gas by a gas from a porous medium of varying permeability.Translated from Zhurnal Prikladkoi Mekhaniki i Teknicheskoi Fiziki, No. 4, pp. 142–145, July–August, 1975.The authors are grateful to N. P. Baturina and L. N. Demidova for their aid in carrying out and analyzing the experiments, and to V. M. Ryzhik for evaluating the results of the work.     

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.     

Nonstationary model of immiscible fluid flow through porous media

Unsteady two-phase flow through a microinhomogeneous porous medium is considered. A forest growth model — a percolation model that enables nonequilibrium effects to be taken into account — is proposed for describing the dynamics of the process. In the context of the plane problem expressions are obtained for determining the saturation and the characteristic dimensions of the stagnation zones of trapped phase behind the displacement front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 73–80, November–December, 1993.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

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.