Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

One-Dimensional Steady Infiltration with Water Extraction

Exact solutions of the one-dimensional steady infiltration with water extraction are obtained for a particular but realistic form of the soil–water conductivity. The results are compared with numerical solutions for slightly different forms of the soil–water conductivity function, showing the sensitivity of the shape of the profiles on the exact representation of the soil–water conductivity. The exact solutions are an extension of Warrick's (1974) solution for the case where the soil can become saturated.     

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.     

Three-dimensional problem for entry of a disk into a compressible liquid

The unsteady problem for the oblique entry of a disk into water is solved. The water is assumed a perfect compressible liquid and the flow is assumed adiabatic. The flow and state parameters are determined during the numerical integration of the system of nonlinear equations which describe the given flow by means of a three-dimensional finite-difference scheme [1]. The variation in time of the drag coefficient as a function of the Mach number and the angles of entry and attack, the pressure distribution and the shape of the free surface formed behind the disk are investigated. The oblique entry of a disk into water and its subsequent motion have mainly been studied for velocities at which the compressibility of the water is negligible [2–4]. The influence of compressibility on the duration of the rise time and the impact load was investigated experimentally in the range of Mach numbers 0 < M0 <–0.3 [5]. Semiempirical dependences are obtained for the maximum of the drag coefficient and its rise time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–20, January–February, 1988.     

A Parametric Model for Predicting Relative Permeability-Saturation-Capillary Pressure Relationships of Oil–Water Systems in Porous Media with Mixed Wettability

A parametric two-phase, oil–water relative permeability/capillary pressure model for petroleum engineering and environmental applications is developed for porous media in which the smaller pores are strongly water-wet and the larger pores tend to be intermediate- or oil-wet. A saturation index, which can vary from 0 to 1, is used to distinguish those pores that are strongly water-wet from those that have intermediate- or oil-wet characteristics. The capillary pressure submodel is capable of describing main-drainage and hysteretic saturation-path saturations for positive and negative oil–water capillary pressures. At high oil–water capillary pressures, an asymptote is approached as the water saturation approaches the residual water saturation. At low oil–water capillary pressures (i.e. negative), another asymptote is approached as the oil saturation approaches the residual oil saturation. Hysteresis in capillary pressure relations, including water entrapment, is modeled. Relative permeabilities are predicted using parameters that describe main-drainage capillary pressure relations and accounting for how water and oil are distributed throughout the pore spaces of a porous medium with mixed wettability. The capillary pressure submodel is tested against published experimental data, and an example of how to use the relative permeability/capillary pressure model for a hypothetical saturation-path scenario involving several imbibition and drainage paths is given. Features of the model are also explained. Results suggest that the proposed model is capable of predicting relative permeability/capillary pressure characteristics of porous media mixed wettability.     

Penetration of a compressible liquid by a plate and a disk of finite mass

The incidence of a plate and a disk of finite mass on a free water surface and the subsequent inertial motion are investigated. The effect of the air medium above the liquid is neglected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 177–179, May–June, 1989.     

Propagation of a shock wave through a jet of water

The problem of the propagation of a shock wave emerging from a circular tube into a jet of water is solved numerically. The solution is carried out by the method in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. I, pp. 190–192, January–February, 1977.     

Stability of the displacement front and development of “fingering” in a porous medium

The effect of random disturbances at the fluid interface on the formation and development of fingering in the immiscible displacement of liquid hydrocarbons by water is experimentally investigated in a modified Hele-Shaw cell.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1989.     

Instability of convective flow of water near 4 °C

A study is made of the stability of the plane-parallel convective flow of water in a plane vertical layer bounded by planes heated to different temperatures in the region of anomalous thermal expansion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 189–192, March–April, 1979.     

Electromagnetic Sounding of Oil and Gas Formations

A mathematical model is proposed that describes electrical conductivity variation in the near-well zone during drilling formations containing three immiscible phases: oil, gas, and a small amount of native salt water. It is assumed that borehole drilling is performed using a clay–water solution, the mass-exchange process between the moving mud filtrate and immovable native water is infinitely fast, and displacement of the gas phase occurs by piston flow. The redistribution of the immiscible phases is described by the conventional Buckley–Leverett equations. The electromagnetic response of the medium is interpreted using the earlier proposed method of probabilistic convolutions.     

Onset and development of wind agitation

Within the framework of the two-dimensional inviscid model of Euler, the study considers the linear and nonlinear stability of a wind flow over a water surface. Account is taken of the nonzero velocity gradients in the surface layers of the air and the water. The problem is solved by the Bubnov-Galerkin method together with the method of Fourier and the generalized method of Rayleigh.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 163–169, May–June, 1988.     

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.     

A Numerical Study of Micro-Heterogeneity Effects on Upscaled Properties of Two-Phase Flow in Porous Media

Commonly, capillary pressure–saturation–relative permeability (P ^c–S–K _r) relationships are obtained by means of laboratory experiments carried out on soil samples that are up to 10–12 cm long. In obtaining these relationships, it is implicitly assumed that the soil sample is homogeneous. However, it is well known that even at such scales, some micro-heterogeneities may exist. These heterogeneous regions will have distinct multiphase flow properties and will affect saturation and distribution of wetting and non-wetting phases within the soil sample. This, in turn, may affect the measured two-phase flow relationships. In the present work, numerical simulations have been carried out to investigate how the variations in nature, amount, and distribution of sub-sample scale heterogeneities affect P ^c–S–K _r relationships for dense non-aqueous phase liquid (DNAPL) and water flow. Fourteen combinations of sand types and heterogeneous patterns have been defined. These include binary combinations of coarse sand imbedded in fine sand and vice versa. The domains size is chosen so that it represents typical laboratory samples used in the measurements of P ^c–S–K _r curves. Upscaled drainage and imbibition P ^c–S–K _r relationships for various heterogeneity patterns have been obtained and compared in order to determine the relative significance of the heterogeneity patterns. Our results show that for micro-heterogeneities of the type shown here, the upscaled P ^c–S curve mainly follows the corresponding curve for the background sand. Only irreducible water saturation (in drainage) and residual DNAPL saturation (in imbibition) are affected by the presence and intensity of heterogeneities.     

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.     

A variational problem in the hydrodynamics of open channels

A solution is found to the problem of the control of the unsteady motion of water in an open channel bounded by a pumping station. The law of variation of the discharge of the pumping station which ensures the least cost of pumping water from the channel is determined. The solution is found by the method of undetermined Lagrangian multipliers. Examples of calculations are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–163, July–August, 1980.     

The effect of water vapor on the distribution of the parameters of a turbulent wake

In the experimental study of phenomena occurring in the flow of air round models flying along a aeroballistic range with hypersonic velocities, the question arises of the effect of water vapor along the range on the measurements of the gas parameters, for example, on the electron concentration or on the intensity of the radiation. Water vapor is usually present in atmospheric air and, in the absence of special measures to remove it, it may have an influence on the results of measurements. In [1] a theoretical study has been made of the effect of chemical reactions involving the participation of water vapor in the air on the chemiluminescent radiation in the wake alone. In particular, there was no consideration of the effect of water vapor on the electron concentration. In the present study, the results are given of calculations of the distributions of the nonequilibrium parameters in the wake, with allowance for the occurrence of chemical reactions in the air and water vapor under conditions characteristic of aeroballistic experiments [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 138–142, January–February, 1985.     

Unsteady-state filtration from screened water reservoirs and from the storage elements of industrial drainage systems

This paper considers the axisymmetric problem of unsteady-state filtration from a water reservoir or from the storage element of industrial drainage systems, which are round in a plan view.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 165–170, November–December, 1971.     

Analysis of systematic drainage of irrigated land underlain by saline water

The efficiency of systematic horizontal drainage of irrigated land underlain by saline water is investigated analytically. Quantitative values which make it possible to estimate the influence of the geometric parameters of the drainage system on its efficiency are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 68–73, March–April, 1993.     

Evolution of a long wave in shallow water

Asymptotic expressions are obtained for the amplitude of a nonlinear long wave propagating in shallow water of variable (smoothly varying) depth.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 186–188, September–October, 1987.The authors are grateful to S. L. Lopatnikov for discussing their results.     

Unsteady air–water flow measurements in sudden open channel flows

Measurements of air–water flow properties are reasonably simple in steady flows, but not so in unsteady flows. Some studies investigated periodic flows in which instantaneous data were averaged over several cycles. During the present work, new unsteady air–water flow measurements were performed in sudden open channel flow surges. Unsteady air–water flow measurements were performed in the wave front with an array of resistivity probes. The results demonstrated quantitatively strong aeration of the leading edge in terms of void fractions, bubble count rates and specific interface areas. Experimental results highlighted that this strongly aerated region was relatively short: i.e. typically 0.3 to 0.5 m long. Measurements of air and water chord sizes highlighted a wide range of bubble and droplet sizes. Time-variations of air–water flow structure were observed.

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